I've been a piano tuner all my life. I had my piano tuned in an historic temperament by another tuner, and it really did sound fuller and more sonorous. I tried both methods, and decided that the equal temperament sounds constricted. It is easy to explain why. The historical temperaments all have more intervals without beats, so they are more effective in activating the upper strings through sympathetic resonance. The problem is that all these historical temperaments sacrifice a few keys (F sharp and C sharp, for instance). These keys have a lot of beats in certain fifths, which makes the keys quite dissonant. This was not a problem when people were playing harpsichords, because harpsichords go out of tune so fast that every performer had to know how to tune the instrument themselves. They could tune it in a way that fit the key of the piece they were going to play. People in earlier times knew about the equal temperament but hated how sharp the thirds sounded. We have just gotten used to the very sharp thirds in equal temperament. However, when a piano starts going out of tune, it is the thirds that are most unpleasant, when they go even sharper. I knew a tuner who worked in various historical temperaments. He had a piano in his shop that sounded terribly out of tune to me. I asked why he had it tuned that way, since no one would buy it. He put a piece by Palestrina in front of me and asked me to play it. He asked me how I liked it and I said It was very interesting. He asked, "How do you think that would sound in equal temperament?" I said, "Probably totally boring." He said, "It is, and that's why almost no one plays Palestrina any more." He gave a concert where three pieces were played on three different pianos tuned to the historical temperament they were composed on. It was very eye-opening. The Brahms, especially, had effects that would have been totally lost in equal temperament.
Then there is also the question of instrument. I've been enjoying the Beerhoven recordings of Ronald Brautigam that he's done on the pianoforte that has a very different sonority to modern grand pianos. The pianoforte has definitely more string-like sound that has somewhat less blending of sympathetic resonance (I believe) which makes particularly the bass register ring out with far more clarity than on a Steinway. I would probably rather pick a good pianoforte recording in equal temperament (not unhistorical by any means, actually) rather than on a contemporary grand in an unequal temperament.
@@Veepee92 The modern piano is a much better instrument on many levels. I played a late eighteenth century fortepiano once. It was pretty horrible. It had thin harpsichord-like strings with very little resonance. When Steinway put in the metal plate around 1850, it allowed the strings to be much heavier, and under much greater tension. These two things together made each note sustain way longer. And sustaining power is the single most important factor in "melodiousness." Before the metal plate, Beethoven would simply break the strings (and hammers) when he played, because they were so flimsy. As for Chopin's long "singing" melodies, they were largely imagined by the audience, not heard. Before the metal plate, the notes would die off very quickly. This is one reason that there were so many trills in classical music--it was a way of keeping the note going.
How long did it take you to learn how to tune a piano correctly? Is it possible to be done in one day? There is a guy I know and I informed him that piano tuning is a profession, and it is a very delicate and risky process. Later on, the same guy proceeds to let his social media know that he learned how to tune a piano in a day. I do not know if he was trying to prove a point or something.
@@salomongreen It's ridiculous to say you can learn to tune a piano in a day. The basic Idea of tuning can be taught in a day. Then you have to train yourself to tune in to and count the beats of various harmonics. You have to memorize beat rates. After that, you have to actually learn how to manipulate the hammer (or wrench) so that you can produce those beat rates in a way that is stable. And that is just the rank beginning of it. Every piano tuner I have ever known has apprenticed to another piano tuner in order to learn the trade. There's a lot to it, and most people have neither the patience nor the concentration to do it.
With electric instruments there should really be an option to quickly switch tuning. Or even an option for automatically switching the tuning to give the best harmony for what is currently being played, so you can play music with key changes without having to think about it.
I'm not much of a musician, but I also feel like this is something that should be optional in software. If modern music workstations can generate appropriate accompaniments, then surely there should be an option to adjust to just intonation if needed.
The issue is that it's impossible to preserve just intonation even within a single key. Easy example is that 6/9 chords are impossible with just intonation as they're basically just stacks of perfect fifths, and you can't do that without ruining the intonation of the major third. Anyway, details aside, I can't help feeling that the differences between tuning systems are a little overblown, and it tends to only be widely discussed when somebody famous mentions it or it's being sold as a product. Equal temperament is really just incredibly practical as a baseline, and musicians can and do make small changes to their intonation on the fly when their instrument allows for it and it's appropriate.
That's pretty easy to do, to be honest. All you need to do-at least in the case of an analog synth-is have an incoming CV that has the same mathematical function as the tuning system you want to play on
I agree that equal temperament is "not that bad", it's a practical concession but not necessarily a creative one. Tuning is such a misunderstood concept that I'm not sure people fully realise how out of tune almost all music is, often far more than the difference between just and 12TET. Another way to think of just intonation or other tuning systems is that they are not out of tune as such, but that each key sounds different (and I mean actually different, not "D Minor is the saddest key" different) and that functionally they are harder to work around than equal temperament is, but can yield far more interesting results, and that's not even taking into account fixed vs moveable 12 just intonation. It is interesting that while the vast majority of instruments are capable of swapping between equal temperament and just intonation on the fly, albeit with a substantial learning curve on the part of the performer, we have somehow moved further and further away from any differential tuning systems to the point where they feel set in stone. Perhaps with the advent of more and more electronic music on the horizon we will start to see tuning in different ways become more mainstream, much like non instrumental MIDI interfaces have. tldr Good video
MIDI isn't really made for anything other than 12-TET sadly, and it takes so many hacks to make it work (like using pitch bend, which only works per channel). Does anyone know any better alternatives for alternative tuning?
@@ItsaDigitalHamster actually yes, "Sforzando" by Plogue does a great job of this, especially for its age, it uses scala files (.scl) to map the notes of a midi instrument to whatever division of the octave desired. It's free, but obviously has its limitations, it works best with supported sounds within Sfz (it comes with basic midi instruments) or with samples which you can drop in etc, obviously it will stretch and twist samples of something like a violin or something of a more intimate nature and make them sound... suspicious to a trained ear, but for electronic or art music it is still fantastic and widely used, even listed in an article written this year. VVVVVVVVVV producelikeapro.com/blog/getting-started-making-microtonal-music/ You do need to find an archive of Scala files to download, I can't recall where I got mine but the files themselves date back to 1996 from the metadata, so obviously there are a trove of different custom systems out there
I’ve seen so many you tubers crash on equal temperament just because it’s not in tune but completely ignore the fact that it’s the exact point. If every song I heard was in the key of C and never modulated just to keep recording sessions quick and cheap, music would be sooo different and way more limiting.
@@MostLikelyMortal That's what a lot people claim. There are Jazz musicians exploring JI and other tuning systems at the moment. How is it that people think they can predict what would have/could have happened in the past? Western temperament was very close to 31 tone equal temperament because of its almost exact approximations to Meantone. Who's to say how Jazz would have developed had it been 31 et or extended JI? What other music would have happened had western music not been entirely dominated by one tuning system for the last 200 years? One tuning system that the vast majority of musicians accept without question. It's also unfortunate because the Halberstadt keyboard layout isn't even very good for 12 ET compared to Isomorphic layouts but that's a whole other kettle of fish (similar to how the qwerty keyboard is actually not a great design either...but we're stuck with it because that's what we're used to.) However, 12 et as good at certain things, and other tuning systems are good at other things. Whether I'm listening to Harry Partch, LaMonte Young, Debussy, Miles, or Soundgarden, I'm loving the music either way and am thankful that tuning alternatives are being explored but there are statements in the video I have issues with.
We never used just intonation on fixed pitch instrument? There was the time of pythagorean temperament, then meantone, then well and now regrettably equal temperament. Also, tuning a whole scale just is nonsense. We only use just intonation in the context of intervals
I totally see what you mean, it's a small difference, and when one is used to 12tet it sounds more right most of the time. Using just intonation at higher volumes for music that draws attention to melody, harmony and tone is a special experience though. I reccomend trying it on a good sound system rather than headset, as the way the waves interact in the air is a big part of it. An artist called Zhenna Erose does a lot of microtonal stuff where she works with variant tuning, like just intonation, good place to start. If you really just don't get it though, that's fine, music is so much more than pitches, and 12tet is pretty good at most things.
the minor third, tritone, and half-step are some of the most expressive intervals in JI, because of how variable they can be while maintaining (fairly) simple proportions. In fact, I think jazz music in the 21st century might be entirely understood and contextualised by the relationship of the 5th and 7th harmonics
@Vinnie EVH Thank you for asking! If you look up and down the overtone series intervalically, you'll find more examples of major/minor thirds than you would say, fourths or fifths. I should have included major seconds and thirds in my first comment but here's the reasoning: 5:6 and 6:7 are both minor thirds, but a 6:7 is smaller because the seventh partial is 31¢ flat. Because of that, if you're in the key of D and you sing an F natural a 6:7 above the root, you will have a "buesy" sounding F. If instead you sing a 5:6 minor third above D, your F will sound "triadic" and more stable. In more plain terms if your D is at concert pitch, a minor triad tuned from it might include F+16¢. Alternatively, a minor seventh chord might sound twangier and more evocative with F-33¢, especially if the C of that D minor seventh is tuned 31¢ flat, like a seventh partial 7:1 is. After that you can play around with other JI intervals and imagine how they might work as members of a chord, resolve or not resolve, etc. 4:5 7:9 and 9:11 are all examples of major thirds. 5:7 7:10 8:11 and 12:17 are all unique tritones. 7:8 8:9 and 9:10 are all major seconds. 14:15 15:16 and 16:17 are all good examples of minor seconds (most of them wider than the standard minor second). On the other hand, 3:5 is the only major sixth, and 5:8 is the only minor sixth. 2:3 is the only perfect fifth and 3:4 is the only perfect fourth until you get to 21:16. So I call those intervals less expressive because they can not be adjusted easily without in my opinion jumping the shark (21st partials are strange and icky).
@@ChrisChapin_chapes Ahh I see what you were trying to say. Indeed… some of these intervals are extremely flexible. The major/minor third in particular is a perfect example because of how malleable it is in the blues and especially blues-based guitar music!
So for a complete beginner: Is the idea that the way you tune a piano affects the mathematical ratios between notes, so you can make some groups of notes sound really good together at the cost of other groups of notes? And therefore 12 tone equal temperment is kind of a compromise to make a lot of groups of notes sound fine at the cost of some of them no-longer sounding great?
Yes, but it's to keep octaves (& only octaves) sounding great w/ small sacrifices made to *all* other intervals (or groups of notes). They all sound good enough, w/ none sticking out as really bad. Earlier systems tried to make more intervals sound better w/ one or more sounding noticeably worse.
Yes. If you pick a note and tune "mathematically" to that, then it sounds hella wonky if you play in certain other keys. The compromises are so that you can play in any key on the piano
Basically. Pithagoras established the harmonic series by shortening a string and calculating ratios (2/3, 1/2, etc) which defined the common intervals. But if you calculate them this way (and because the ratios have very different denominators), they won't add up consistently (you won't get exactly an octave (2/1) by adding all the intervals in between). That's why the equal temperament establishes an irrational ratio (¹²√2), the same for all the semitone intervals, which will give you an octave after 12 steps That is because a superior octave is two times the frequency of the previous note. So an A (440Hz) has an octave below of 220Hz, one above of 880Hz and so on. For example, a third (of one note) for Pithagoras, was found when playing a string 2/3rds the length of the one that played the original tone, that is 3/2 of the original frequency. In equal temperament it's found at (¹²√2)(¹²√2)(¹²√2)(¹²√2)(¹²√2)=(¹²√2⁵) of the original note (in hertzs); that is, 5 times the ratio equivalent to one semitone. I don't properly remember the proof, but with Pithagorean ratios there's a mathematical deviation when putting all the intervals together. And the harmonic series follows the same principle, but uses overtones instead (so whole intervals, a third is taken into account in the next octave, 3 times the original frequency -instead of 3/2).
12 tone equal makes many notes a bit out of tune, while just intonation is in tune in its key, and can sound like a dog with a tepped-on tail when leaving the tune. I prefer werkmeister 2 as a tuning system. It was really eye-opening when I found out about the different systems. Before, i thought my hearing was bad, music sounded out of tune to me all the time. Now I know that it really IS out of tune very often.
I've always found it fascinating that we had to tweak the natural harmonic series in order to play jazz and music that generally moves from one key center to another. Like nature doesn't want jazz to exist..lol
Isn't it more the case that equal temperament encourages the mobility of jazz? There's nothing more or less natural about one set of mathematical ratios over another, they all just have different potentials in music.
@@wiegraf9009 my understanding is that the use of upper extensions (7 9 13) for dissonance and color would not work with just intonation, since the relationships of those more extreme overtones are drastically altered
@@wiegraf9009 it is the case of course, which is his point... and no, there is nothing really natural about ET, unless you consider human-made lakes to be natural?? Just Intonation already exists in nature. ET was created by humans... Also, ET is not ratio based. It's based on the 12th root of 2 and it wasn't even possible until we could apply decimal numbers like 1.059463 to instrument construction or tone analysis.
Surprisingly, my ear picked up this difference over the years before I knew the terms. Luckily, I'm a violinist so I can take cues from my ear on what sounds good and what doesn't and adjust on the fly. Because of that, every performance has a combination of just tuning and equal-temperment 😅
Music education is designed to give you a perfection complex...which eventually leads you to put down your instrument for good. Seen it happen to all my peers after music school.
@@PhoenixSplash On the flip side, I would love nothing more than to get college-level music education. There are so many skills that I want that are basically unavailable to me.
@FreedomIII my piano teacher treated me like a winde up toy and showed me off for 2 years. Learned more about piano on my own. Method books. Musescore, Guitar Pro. You will always be your best teacher in music no matter how much money you throw at them. Or find a private teacher that hasn't put down their instrument. No one really cares how flashy you become. Might be a neat party trick if you learn a fast section, but once it's done. It's done.
When a good singer sings, he/she will intuitively change the intonation (dynamic intonation) as he/she goes. That's part of what makes each singer unique, and why it's great to use singing to compose, rather then say a piano.
My first instrument was piano, and it was not for many years that I ever heard of just intonation. During college, I noticed a strange thing occasionally happening while playing trombone in a local semi-pro orchestra. I sometimes would hold the same note through various chords, and suddenly, that note would sound out of tune! I wrongly assumed that I was just drifting out of tune, and would just adjust best I could to what I thought I should be doing. Later, during a master class taught by a trombonist from the LA Phil, I really got some in-depth specific training on just intonation, which took much of the guesswork out of properly tuning. If I am not mistaken, one of the big reasons why just intonation is superior (in my opinion) to all other tunings, is that such tuning of a chord triggers what I call "phantom" harmonics that would not be there using things like equal temperament. On trombone in high school before I understood just intonation, I was shown a neat trick, where I would play a F just below middle C, hum a D (apparently in just intonation), and suddenly, you can hear a "phantom" Bb above middle C be created! Bottom line, just intonation creates a wonderfully extra set of higher harmonics (and lower?) that you just don't get anywhere else.
First of all: great video! I just find fun in nitpicking, as some misunderstanding might arise, but I know what you're aiming for, and it's great that you did :) For those interested, I wanted to add that 12TET is by far not the only 'well-tempered' (allows-every-key) tuning system we have nowadays, and my understanding that's where the 'equal temperament ruined harmony' comes from. It would be pretty easy to simply equally tune a concert grand piano, but that's why good piano tuners are so rare and are paid a fair amount of money. They don't tune them in 12TET, but they still do work in every key. For example, in general the middle octaves seem to be more in tune while upper and lower octaves are more permissive. And from tuner to tuner they have different preferences for thirds, fifths, etc. So a concert piano is very differently tuned from a Casio keyboard in 12TET. *That* is usually the equal temperament people pick on (at least among the people I know), not just any temperament that allows playing and modulating to all keys vs. just intonation. There's tons of other nuances in between. Also 'Why Equal Temperament ruined Harmony (and why you should care)', doesn't focus too much on keyboard instruments, but discussed also string and wind instrument practice, how sharps and flats have been handled in different periods and other very interesting stuff, so don't let yourself get discouraged from picking up said book ;) Have a great day everyone!
I’ve been a piano tuner for forty years, and I want to tell you that you are correct. Equal temperament is where I start, but I’ll tweak things away from that in order to get the sound I’m looking for. And it’s different with every piano; the piano tells me what I need to do.
You are talking about stretching, right? I'm not a piano tuner, I was a classical piano student (now I play only in my free time) and despite studying engineering I have made a few projects on music and piano in particular for university. Recently I was synthesizing a piano sound for a project and one of the things I did was include octave stretching. It's those little things like the stretching and the inharmonicity that really added to the overall quality of the sound. It was a really fun project.
In just intonation, if you play a C major triad, it sounds like one note: the low C whose overtone series the chord perfectly matches. In 12-tet each of those notes sounds like its own voice, ready to move around.
Heck, there are even multiple "just" ratios you can choose from. A 19:16 ratio minor third sounds almost like it does in 12-TET, but a 6:5 minor third is uncomfortably bright -- you'd never get the "sad" connotations we typically associate with minor keys nowadays.
What is "in tune" then? When you tune an interval or a chord, you naturally listen to beating and try to get rid of it. And when there's no beating, it is in just intonation. How else would you determine whether something sounds in or out of tune (without using a tuner)? It is true, though, that piano sounds weird in just intonation, because a part of what makes piano sound like piano is equal temperament (similarly as certain imperfections in tuning are a part of what makes guitar sound like guitar).
Very worthwhile video! Thank you. I think it absolutely a must that non-fixed pitch instruments learn to play in tune . . . perfect 5ths as a drone. It make a huge difference if students try to play with equal tempered 5ths. The accoustic stringed instruments come alive with vibration (color, projection, sympathetic vibrations) when "perfect" or Pythagarian tuning is employed. There are times when compromising with open string tuning is called for (e.g., after the orchestra has tuned to an A=440 for example and the cellos and violas have to play open C strings is playing a C-major or Ab-major chord). So much of the beauty of Baroque music rests on perfect 5ths and other intervals that adjust to the fundamental of any chord.
The best short description of the advantages and disadvantages of 12TET I've heard so far. Kudos. I should add that I haven't played in 12TET for many years now, because I tend to keep to at most eight tones per octave. I satisfy my desire for complexity in polyrhythms and polymeters. _Suum cuique._ cheers from sunny Vienna, Scott
I've been fooling around with just intonation and I fell in love with a nice compromise. Two 6-Tet separated by a just 5th, which means that the 4th and 5th are always in tune, while other notes are as expected. It sounds better than the 12-Tet, is more practical than just intonation, and doesn't require more than 12 notes.
I'm so thankful that my ears are NOT good enough to find these issues more than trivial! I'd hate to miss whole worlds of music because I could not get past 'perfection!'
The secret of Eddie Van Halen's beautiful rock guitar sound was detuning the B-string down a tad to get perfect thirds out of his raunchy chords! That was a major part of his "brown sound".
All my life I've had "good ear", like I was the one who detected an instrument out of key if we, as hobbyists, were to play in my garage. I'm no musician, just a hobbyist as said. Hard hit to reality when watching this video with headsets I have not been able to tell those subtle differences, that all sound just equal to me... Kudos to those who notice differences. EDIT: I DO hear that 'out of tune' demo by Jacob Collier, but for some reason I do not notice that in my digital keyboard...
I really do think conditioning plays a huge part in how we experience tuning systems. If you grew up in the West, well, then equal temperament is probably gonna sound best to your ears. I know that is the case for me, I can still enjoy other tuning systems, but it'll sound slightly off, always, though, not in a bad way necessarily.
I dunno, I'm not much of a musician and grew up in the West, but the just intonation sounds much better to me in the samples given here, not "off." I think cultural differences in habituation to rhythms may be more significant. Edit: Someone elsewhere in the comments mentioned a study showing that most trained musicians are more habituated to TET, so JI sounds more off to them than to average schlubs like me. Makes sense since making music requires more active listening than just hearing it passively.
Grew up on western music and particularly classical (and classical violin). A skilled choir sounds best to me, and I don't even know how a really good choir handles "temperament", if you could even make the concept relevant for an " instrument" that can re tune each time a new note is sounded. String instruments do the same... :-)
I used to hang out with a holistic new age crowd who villainized JS Bach for inventing equal temperament and ruining "true" harmony. First of all, Bach didn't invent equal temperament, and secondly, he didn't use it, at least not exclusively. He was a champion of "well" temperament, as in "The Well Tempered Clavier." Well Temperament was equal temperament tweaked here and there to tone down some of the stinkiest intervals in some keys without causing worse problems in other keys, like whack-a-mole. The Well Tempered Clavier, Books I & II demonstrated Well Temperament with pieces written in all twelve major keys and all twelve minor keys. The idea was to be able to play in all 24 keys without totally sucking in any of them. Piano tuners still use "tweaked" tunings to make pianos sound better with strings or with horns or whatever. Strings can play correct intervals if you want or any others; horns tend to play sharp no matter how hard you try. Tweaked tuning can make everyone play a little more nicely with others.
The actual scholarly consensus regarding Bach's tuning seems to be "we don't know". It's not that he certainly tuned in 12-tone equal temperament, or that he certainly tuned in meantone or a variant thereof; we simply don't have enough historical evidence to give definite proof of either.
new age folk are attached to words like "resonance" and "frequency" while having no respect whatsoever for the actual expressions of these terms, it's purely posturing same for most thinking tunings need to be ranked lmfao, ridiculous
Cannot believe that such a great composer like Bach, or any other recognized composer, would have ever used a tuning with such an amount of inharmonicities! Every harmony, except for octaves, is out of tune if a keyboard instrument is tuned with a uniform distribution of the twice the frequency divided between 12 notes. You guys called it equal temperament tuning, but I would called if No Temperament Tuning. The feelings that music evoque depend on harmonies, octaves are the simplest harmonies, in 1 to 2 frequency ratios, but other harmonies must ge present also. Fifths are the next more important, in 2 to 3 ratios. Next are 3 to 4, 4 to 5, 5 to 6 ratios and so on. In order to be able to listen to harmonies other than octaves, a tuning using some kind of temperament, like the ones invented by Vallotti or Kirnberger, is a must.
I love the way the less in-tune, brighter keys like C# tend to be faster in the Well Tempered Clavier. It's definitely nicer in Werkmeister III or Young's temperament than equal tempered. It's nice having the pleasant thirds even at the price of worse thirds in other keys. On the other hand, I've heard that Bach would play in Ab whenever the organ tuner arrived because this has the wolf notes in 1/4 comma mean tone. This was the most common tuning for organs even into the 19th century.
It is very noticeable to me. But then again I have perfect pitch. I actually love equal temperament cuz that is the best way to navigate especially in a piece that is "changing keys" but if we were doing acapella especially barbershop we use just intonation cuz in barbershop we want to "ring them chords" lol. The point is I like both.
@@Talaxianer honestly as much as I am grateful to have perfect pitch any great musician doesn't have to have perfect pitch to do what they love. Relative pitch has its uses
My digital piano has settings for some non-equal temperaments like Werckmeister 3 and Kirnberger 2. The first thing I noticed is how perfect fifths really stand out, often in places where they shouldn't. No wonder Bach wanted to avoid them in counterpoint. The only positive aspect I noticed is that some five-note chords in Beethoven's music sound less dissonant. I think it's because some pairs of notes like E+F, D+Eb and G+Ab are further apart from one another in those temperaments. I also experimented with playing Romantic era music in these temperaments, but shifting the base note so that the "best-sounding" scale is not C. I kept hopping from one base note to another, until I had a weird realization that base note C sounds best for G flat major, because that results in the fewest in-tune perfect fifths.
@@epichdsheep You seem to care too much about just intonation. I mean all I can say is music would sound off if not tuned equally, plus it would just inconvenience most modern music as a whole
It seems like a digital piano could analyze the chords and intervals being played and adjust the temperament on the fly. If you're playing a C6 chord, A would be 435 Hz, but playing a D chord will play A at 439 Hz. Kinda like what violin players do naturally.
@@abillionjivebars9888 Kinda sorta? While you can't tune a piano on the fly, most otherinstruments that aren't similarly tied to unchangeable tuning (anything with a mouthpiece or anything without frets) can be tuned note-to-note. As a violinist, I realised I was doing that instinctively and instinctively leaning towards making each harmony sound as if it was in just tuning in the correct key a decade starting more than a decade before I learned different tuning systems 😂
When tuning a harp, using fifth based just intonation, it "sings" much better, more resonance from other strings. The problem: the last fifth is completely out of tune. This can be fixed: start with C, and tune the following fifths based on the 3rd harmonic: cgdaeb, the next would be F#, but don't use the 3rd harmonic, in stead use the 5th harmonic to tune D# to the fifth harmonic from b. Now tune the rest of the notes from D# based on 3rd harmonic again. You will get a just intonation where the last fifth fc is closer to 3rd harmonic tuning than equal temperament. It works really great for harp.
The harmonic series is a thing also in mathematics. I never realized it came from this. I understand why now, and I have to say it makes a lot of sense. The harmonic series goes as such: 1, 1+1/2, 1+1/2+1/3, 1+1/2+1/3+1/4, etc. etc. The thing is that tone is calculated in a logarithmic scale (don't worry if it sounds too complicated), while functions are evaluated linearly. Put simply, to go an octave higher you must double the pitch, so, when you count 1,2,3,4 in music you count 1,2,4,8. And using this logic, every new step of the tonal values of the harmonic series adds 1/2, then 1/3, 1/4 etc.
I like the sound of equal temperament. It creates movement and sounds richer to my ears. Just intonation is too sterile. Like a synth sound with no modulation.
Agreed. Just Intonation for steel string acoustic guitar is especially bad imo, it's that twang and dissonance that gives a particular flavor that I and many others love!
try Bach's well temperament. And, also think about all those composers (Bach, Händel, Mozart, Beethoven) who didn't use equal temperament: you are listening to their music not as they wrote it but as it has been modified by music culture dating from the 20th century.
Studies show that when violin players are permitted to tune their instruments according to hearing, the intervals are NOT those of just intonation. I would refer you to the study of Paul C. Greene published in the J.A.S.A. in 1937. I would also refer you to the musical experiment performed by Houtsma, Rossing, and Wagenaars: "Demonstration 31: Tones and Tuning with stretched partials.," which shows that harmony is unrelated to the beat theory of Helmholtz. This can be found online at the Correlograms Project at Stanford University.
this is why computers are the most powerful and fantastic musical instrument ever created. i just finished writing a tune that changes tunings multiple times, from 12tet, to 15tet, to 53tet. and every instrument is automatically retuned via automation so it all remains harmonically sound.
Though I agree that computers are wonderful for this purpose, instrumentalists, especially those playing something like a violin (hi, that's me) can adjust tuning on the fly by listening to our ears because we aren't bound by frets or keys 😊
There are lots of temperaments besides just intonation and 12T equal. Also singers and violists approached tuning a lot like Jacob Collier does before the XIX century. Equal temperament is ok for fretted instruments and keyboards, but there's life beyond them.
YES. As someone who has been singing for years, I have always wondered why a major triad on a piano just doesn't sound right. I'm so used to just intonation from choirs that I could tell it was off without knowing it!
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I would say, for the example piece tuned in C major, there's a reason Orchestral pieces tune the bass/tonic of a chord/key to equal temperament, and then tune the thirds and fifths of that to the bass. It's a shifting system to make it sound the best.
Thank you so much for showing the actual math, so interesting! Also want to add being a string player in contemporary music settings is actually really difficult, it's hard to fight the just intonation impulse, especially when it's really difficult to hear keys to adjust so all you can go by is the root. I've had to just memorize the difference, and yes, those thirds and 7ths are incredibly out of tune, gets even worse when the arranger is breaking low interval limits. I wish people understood this more
I've tried so many time to prove the 'Third in G Major is 14 cents flat' thing like Jacob Collier does, but I end up just going 'ooooo' in 12 Tet. Subsequently I make a total fool out of myself.
I think of it like this: In a broad sense it's the question of specialization vs generalization. What is "better" is totally subjective and based on individual needs. It's not really just that way in music, but in all things.
This is why playing violin or similar string instruments is way harder than it sounds, learning perfect 3rds as alternate notes from playing them in a scale is not easy.
In Western Classical Music (before mid 18th century) There were many more temperaments than 12 tone equal temperament and just intonation. A temperament rearranges the distances between the notes of the scale, so you can have all the intervals that are the same distance from pure (12 tone equal temperament), or you can have some intervals that are closer to pure while sacrificing others to be less pure, like other renaissance and baroque temperaments. Quarter comma meantone temperament is probable one of the most well-known. However, when speaking about temperaments, music theorists from the baroque would distinguish between well-tempered temperaments and non-well tempered temperaments. Quarter-comma meantone temperament is not well-tempered, because while in many keys, the major thirds are pure or close to pure, there are certain keys that are to be avoided, because some intervals sound too much out of tune. A well-tempered temperament (in baroque times) was a temperament in which all usual intervals in all keys sound acceptably in tune, meaning that you can play in all keys without retuning the instrument. 12 tone equal temperament is obviously well-tempered, but it's not the only one: Werckmeister and Kimberger temperaments are also well-tempered, but they are not equal: there's variation in the intervals, but it is arranged in such a way that all keys are playable. I think using temperaments other than 12 tone equal gives more variety of sounds, each key has its own identity.
12-TET is a miracle. It is a miracle from mathematics, that we can acquire notes so close to the major third, major fourth, and major fifth by dividing the scale by 12. Why should 2^(5/12) be so close to 4/3? You have to go all the way to 29-TET to get a better 5th.
Fifths can take a lot more "damage" than other intervals before sounding sour. That was the whole idea behind meantone temperament: sacrifice the purity of fifths in exchange for better thirds/sixths. And people were fine with fifths being ~6 cents flat for centuries. People are less okay with 12-TET's ~14 cent sharp major third (case in point, videos like this one). 31-TET is arguably the "ideal" system for Western tonal music. It's just too many damn notes.
@@karawethan But then it's not the ideal one, because there are too many notes for it to be practical, and there are bound to be many notes in there that approximate integer rarios very badly. (It's not just about whether the scale contains good approximations of rational intervals.) I suppose I should add to my original comment that it's a miracle that we have such a relatively small number - 12 - having these properties.
@@diabl2master That's why I put "ideal" in quotes. If it was practical, then we would be using it instead of 12tet. "and there are bound to be many notes in there that approximate integer ratios very badly." This I do not agree with. Or at least when it comes to the intervals that we care about. Major thirds are essentially just. Minor thirds are close to just. #4 and b5 (31tet differentiates between the two) are near-just approximations of 7:5 and 10:7. #6 is near-just. b2 and #7 are closer to just than in 12tet. The only important interval further from just are the perfect 4th/5th, and they are still very tolerable.
@@karawethan I have to disagree that 31edo is too many tones, I've built an instrument for 53edo (with optional third steps for 159edo) and it's surprisingly manageable ;)
"In tune" doesn't really exist, it's all a question of different compromises. I would say all music is out of tune, regardless of instrument or temperament choices, it's just a question of how badly out of tune it sounds and how you prefer to distribute the "out-of-tuneness" amongst the notes and keys (largely personal preference). Also: the harmonic series, when realised on actual instruments, doesn't have frequencies that are exact integer multiples of the fundamental. The physical limitations of strings, reeds, pipes etc mean that the harmonics may well start to drift sharp or flat wrt the ideal integer multiple relationship. So the fact that just intonation (whichever of the many flavours of integer ratio patterns you choose) is based on these exact integer multiples is itself an approximation of reality. Finally, we should recognise that many parts of the world do not use 12 tone equal temperament in their instruments, so the line about virtually all instruments being tuned this way since the 18th century overlooks so many musical traditions. There are almost certainly many more places in the world that don't typically use 12TET for their instruments than do (e.g. Greece, Turkey, most countries in the middle east, south america, far east, many countries in Africa).
And idiophones (bells, bars, pitched membranes, etc.) never have harmonic timbres, and musical traditions based around idiophones (many in SE Asia and Africa) therefore tend to use tunings that do not resemble 12TET. In fact, idiophones in the Western tradition (like orchestral marimba) need to be carefully shaped to sound acceptable in 12TET.
I really don't think anything your saying works all that well. A phrase like 'nothing is really in tune' is a big dramatic phrase that sounds very bold, but it's just not true. A justly tuned C Major chord will be in tune. The rest of your scale won't be worth much, but you can't take deny the C Major chord that. Not saying this to hate on equal temperament, as I think it's a very good system. A system of compromises, but necessary ones for our modern musical environment. As for saying that so many cultures are overlooked in his phrase; completely correct. However, in contemporary high art and pop music, 12TET has been in consistent use. I can understand not feeling the word 'virtually' give enough credit to these other cultures, but I'm personally kind of willing to give it a pass for the sake of oversimplicity. And if you really want some fun music, Bulgarian folk is some very good stuff. :D
@@GamingKindling Maybe I could have phrased some of what I said more clearly, but in terms of saying this is "in tune" or "out of tune" my point is that it's misleading (at best) to use these kind of binary choices. There are no absolutes: tuning is always about compromise. Even given anybody's personal preferences, I don't think it's helpful to think of any particular combination of notes as being "perfectly in tune", because the context of what could come before or after those notes, or what other notes might play at the same time, will change the perception of good tuning vs bad tuning. In terms of a justly tuned C major chord: what system of integer ratios is being used to define the intervals? There are different schemes, so are all just intonation schemes as "in tune" as each other? Or are they just different compromises being made? In any case, judging how good 3 notes sound together is one thing, but in a musical context - where that chord is supporting a melody, or comes between many other chords - then the perception of what tuning/temperament is worse or better could well change, even with a simple diatonic harmony. And yes, I'm a huge fan of Bulgarian folk music, especially their fantastic (mostly female) vocal music!
I wrote a paper on this in college. My thesis was basically that atonal harmony was the inevitable result of equal-temperament, and I used Fetis' Traité complet to show the evolution of harmony over history and showed how Equal Temperament enabled this evolution because it's basically just the tuning equivalent of atonality
Another problem with just intonation is if you have a piece or song with a lot of chord changes and you want every single note perfect, it might result in the key being shifted by a quarter-tone or half-tone or more even though it’s meant to stay in the same key the whole time. I saw video on this one time but I can’t remember what it was called lol
“Equal temperament is a compromise which allows full compositional freedom, at the expense of perfection.” That statement gets to the very heart of what perfection is. What makes “great art” great? It certainly isn’t precision, so what is it? Perfection is an attribute that is often mistaken for accuracy or precision. But how do precision and accuracy relate to perfection? What do the Mona Lisa, the Parthenon and Michelangelo’s David have in common? A precise inaccuracy is the magic key to their perfection. If the Mona Lisa were a precise image, it would lack the very attributes that make it famous. The Parthenon is Intentionally warped in order to correct for our perspective. Similarly David is proportionally “out of tune”, in a manner of speaking, for the same reason. In short, I believe it is our subconscious awareness of these subtle discrepancies and irregularities that draw our attention to and ultimately compels us to contemplate the beauty in things.
It'd be fun to have a keyboard that analyzes your harmonies in real time and slightly detunes from 12T·ET to some sort of midpoint between the blend of the likeliest chord centers in your playing. I'm gonna mull this over a bit, but I might be able to make a MIDI interpreter that does this.
So the idea that Equal Temperament was in used since the 18th Century is a common misconception. What was used during that time was "Good" or "Well" Temperament. These historical tunings (such as the Werckmeister III, the Kimberger, or Young's) were what composers from Bach to Chopin had in mind when they very purposely chose specific keys and were the reason why each of these keys were often described as having their own individual characters. There are recordings out which showcase these tunings and indeed Bach's WTC (named the Well-Tempered Clavier, not the Equally-Tempered Clavier) or any set of Sonatas etc take on a new character when heard within these more "perfect" or "imperfect" (wolfy) keys. This dimension was lost around the beginning the 20th Century, which is when Equal Temperament was adopted at large.
To add to this point, all or most of the 12 keys worked under these tunings. The point is that the relative imperfections gave each key its own "flavor." Think of them as a "bridge" between just intonation and Equal Temperament.
I’ve always wondered, with so much music being produced largely electronically, it should be possible to produce a temperament almost on a per track basis, for whatever the harmonic needs of the piece might be. I wonder if anyone has been doing that at all.
Yes, it is possible to change the temperament on the fly. Personally, I wouldn't want to do this on a per-track basis. No matter which level of "granularity" we consider, I don't know if it's been done in practice but wouldn't be surprised if that's the case.
Tho other day i farted, stopped moving instantly, was captured by the silent echoes in my head and the fact that some thing had escaped what wasnt ment to be free at first. While beeing fascinated by these impressions i noticed how my state of consciousness was shifting towards a deeper level of awareness, deep like the cause of the phenomenon i just got to witness. A true feeling of gratitude and joy for having this kind of sensation. So I guess it was perfectly normal having all of it resonate with the flow wich I was in, and was in me, pushing some thing, forcing it to come alive. And then... I farted again! Great video btw. Undoubtedly only a certain sort of human beings is going to watch and/or enjoy it. So I had to make this post in order to keep things in balance. Just in case you wandered about my sanity. I suggest you better be concerned about yourselves.
I'm so messed up by various indigenous musical traditions (among instruments I use are for example Chinese flutes which you obviously can't retune without a file and a carving knife) and modern microtonal experiments that I don't even know which interval version sounds right. Also my main instrument is classical guitar so that might explain it (especially the major third problem)
Had a piano prof in my undergrad have one of her pianos tuned in just intonation. Hearing Chopin and Debussy was so beautiful not to mention the piece was played at high proficiency
I dislike the phase "Equal Temperament is out of tune" because it is the tuning. It can't be out of tune. It doesn't match up with the harmonic series, that's fair. But that's different than "out of tune". Fixed Just Intonation doesn't sound good to me on any piece. Any interval or chord other than root is incorrect, and more out of tune than TET. So we lose the main purpose. TET is way more practical for instruments with fixed tuning. Dynamic Just Intonation could be interesting, since many instruments can adjust each note of each chord, and with tools like PianoTeq we could adjust even piano tunings dynamically. But most instruments will likely be a couple of cents out, and have some vibrato. Unless every instrument is perfectly on pitch, it's likely it wouldn't feel different.
love you lad :D such a creative and joyful energy.. also thanks for that last quote xD probably not the best, but i have accumulated quite a lot of hobbys (2D animation, drawing, making music, 3D stuff etc.) and sometime its hard to prioritize on what i should focus the most
I prefer a little harmonic stretch, i wouldn't make too much attempt to temper out an instrument but i like to intonate my guitars by ear with the 19th fret harmonic instead of the octave and i make the b and e strings a little sharp by comparing them to the low E and the A string. Ive heard that pianos are tuned with the fifth above the octave so i tried it, i like it.
Honestly the out-of-tune-ness of equal temperament is cool, the guitar is one of the most popular instruments and that thing isn’t even in tune with equal temperament. Everything being perfectly mathed out isn’t cool because humans aren’t perfect math machines, we play a beat to fast, we sing a note to sharp, that’s just what we do
6:22 - I’m a long-time Microtonalist, but I largely agree with your statement here: 12-tone-per-octave equal-temperament - AKA “12TET” - is a very practical tuning, but not ideal. I recently have been working with 31TET on my Lumatone keyboard (ua-cam.com/video/cpYBnzaWZqU/v-deo.html), and two things have become ever-more apparent (although neither surprised me much): - On the Lumatone, 31TET is _not much more complicated_ to perform than 12TET. - Every well-conceived tuning has its own distinctive sound, or “mood” as Ivor Darreg termed it. 12TET’s mood is comparatively unsettled, because its thirds are a bit … ratty. Sometimes an unsettled feeling is exactly what you want to portray in music, though! It’s great for ragtime or bluegrass, for example. 31TET is much calmer, almost to the point of sounding a little bland - _only a little, though_ ! That, despite its minor thirds, perfect fourths and fifths being a tiny bit “off” (about 2 to 2 1/2 times more accurate than 12TET’s thirds). Much more importantly though, 31TET gives you a lot more very-interesting-sounding melodic and harmonic possibilities - not just major and minor thirds, but also subminor, neutral, and supermajor. 12TET abstracts such distinctions away, like a cartoon! So, choosing 12TET is not entirely a matter of convenience, but it just has the right kind of mood for some kinds of music.
I think this discussion misses several important points. The first is that there are many non-equal-temperament tuning systems other than just intonation, so justifying ET by presenting it as a binary choice with JI is disingenuous. Although since the author declares that virtually all Western music has used ET since the 17th century, then it's also quite possible that he just doesn't know about all of these other tuning systems and presumes that they're just all ET. It's a common mistake. Like I was taught in college that Bach's Well-Tempered Clavier was written to demonstrate the virtues of ET, when it was really quite the opposite. My understanding is that ET didn't even become significantly used until the late 18th century, and didn't dominate until the early 20th. The whole point of all "temperaments" is how to distribute the out-of-tuneness, and there are several viable strategies. Most of them allow for doing all of the things that ET can do, like playing in different keys or using chords other than the root. But I think the biggest deficiency in the discussion is that dissonance is an extremely useful artistic tool. Most music alternates the building of tension with the release of the tension, and dissonance can be a good way of creating tension. With the traditional temperaments, some keys were more consonant than others, and different intervals and chords were more consonant than others in each of them. This gave the composer a much wider palette, and choosing the key to play in was an important decision. I kind of suspect that this is why so much of Western classical music tells us the key that it is in. That was important information about what the piece would sound like. A serene piece could use a more in-tune key, while a more emotional one might choose a less in-tune one. You could modulate to dissonant key to create tension and then modulate to consonant one to release it. This is musical tool that has completely disappeared from our vocabulary. Bach Well-Tempered Clavier is perhaps the most easily grokable demonstration of the artistic use of out-of-tuneness. The point of this collection of pieces was to demonstrate the virtues of what was known as "well-tempering," hence the name. This was a system in which all keys were "usable" (enough in tune), but with some more in tune than others. As with most tunings, the keys with more accidentals in the signature are less in-tune than those with fewer. In the WTC, Bach demonstrates the type of composition that is best suited for each of the keys. The problem with ET is not that it is out of tune, but rather that it is boring. What's the point of having twelve keys if they all sound alike? But yes, ET does also deprive us of more consonant music. One of the beauties of choral music is that it is perfectly in tune. Listening to it can be tremendously rewarding spiritually, and even the non-spiritually-attuned people can sense the relaxation that it brings.
Incredible video! :) I knew all of this, but it's even better explained than I ever could have! Next time instead of leaving a comment to teach the basics of this myself I can just link this video
I think it's beyond current technology: our perception of key centre is so grounded in trend/tradition/context that no machine would be able to be programed to understand. As an example, you'd need it to pick apart the melodic line from the rest of the texture before it could even differentiate properly between relative major/minor keys. Maybe one day someone will hire enough people to distinguish the melodic line(s) in enough hours of every single style of melodic music to be fed to an AI for machine learning to be able to finally distinguish... and that's just to tell the difference between C Major or A minor haha
not to mention picking apart the whole texture to understand which notes actually play a significant contribution to the chord, and which ones are just passing notes or textural embellishment. We do so much intuitively when we engage with music, it's so easy to take for granted how much of what we interpret is purely from a 'cultural' context, and how much this is an art and not a science
Agreed. Wouldn’t be totally automsgic or work for some things. Wouldn’t have to be perfect.for all situations, could require some programming per tune. Or could have like an organ stop for manuslly indicating a change.
Since we live in the age of MIDI recorded and rendered digital music, how about creating a system where the tuning system is changed to fit whatever chord or passage is currently being played? This way you could get a performance with "perfect" just intonation even across changing keys, and therefore it would be even better compromise compared to using just intonation on one key or equal temperament. I wonder if you could notice the dynamic changes in the tuning, or if things would simply sound cleaner overall.
it was a better world when most people tuned “by ear”, guitarists would slightly turn the tuning pegs intuitively between songs to achieve better balance depending on the key. Digital tuning is dangerous. Beethoven apparently identified that keys had “characters” for him. I think we forgive slight fluctuations in pitch while listening to music. It rarely becomes “painful” to listen to. Personally Ive played a piano which was tuned in the old way, and it undoubtedly sounded better overall in some keys. Very technically and intellectually orientated musicians (jazz in particular) prefer even-toned, it’s to do with their ‘removed’ perception of music.
Tuning a piano or other keyboard was, and is, a very deliberate procedure. The keyboard tuning Beethoven was familiar with was not simply "by ear," but was a careful and calculated compromise. Modern piano technicians do not rely on digital tuners, yet they are able to reasonably approximate equal temperament. De-tuning the strings of a guitar or other fretted string instrument has a very limited application, unless you are playing music that doesn't modulate. The frets are placed according to equal temperament, so de-tuning a string effectively de-tunes all the fretted notes available on that string. Re: jazz, It's essential that keyboardists and guitarists are in equal temperament because the music modulates freely. But there is plenty of intonational subtlety for horns/winds.
Whenever listening to piano music, live or recorded, there are always a few pitches that pop out as being out of tune. I decided that this is due to equal temperament and that I should stick to jazz where dissonance is part of the creative tension, even in a harmonious major 7 #11 chord.
Now I have a question: what temperament does a violinist use if she/he has to play melodies comprised of a single-note? what if the melody is double-note or triple-note?
Depends if they can infer a tonality, if they have a reference pitch that they want to maintain, what their priorities are on a note-by-note and phrase-by-phrase level, etc etc. They might want to priorities hitting just intonations relative to some reference, move the centre of just intonation as the music modulates between tonal centres, choose particular justly-tuned intervals depending on the harmonic context as well as tonal context (e.g. the minor seventh between the root and the seventh is much flatter in a harmonic 7th chord compared to a minor seventh chord on the same root), choose to deviate from one particular just system into another to highlight particular moments or sections, or choose to return to equal temperament if they start to serve another purpose or if that would suit their needs better.
It wouldn't specifically have to just be string instruments too! Any brass or reed (idk much about flute but probably them too) player can bend their pitches by quite a large degree.
@@antimon40 the larger an ensemble gets the easier and harder it gets to tune. One violin sounds in tune, forty violins sound in tune, two violins sounds like death without some serious practice. The benefit of having a massive orchestra wrt tuning is that they can all be tiny tiny tiny bits off and it'll all work out. Solo players won't want to miss their note by more than maybe 3-5 cents, but a massive group of players have way more wiggle room to play with. So much so that the difference between intonation systems are, I think, statistically indistinguishable. There's a reason they call barbershop the "black belt of a capella", and that's because they're being assholes, but they're also kinda not wrong - it's incredibly impressive and really difficult to get a chorus of 100 amateurs to sing with pitch accuracy within 2 cents of equal temperament. They get the advantage of ring and resonance indicating where the correct pitch is with great accuracy, but still
Have you heard of the Belgian quarter-tone pianist Seppe Gebruers? I recently came across his videos (on a youtube channel from Troika vzw). He improvises with two pianos tuned a quarter-tone apart, and plays very unconventional versions of jazz standards like 'In a Sentimental Mood' and 'You and the Night and the Music.' I had never heard anything like it in that context-so surreal. That’s how I ended up here looking for more information. Thanks for the video. Ciao, John.
Thanks for the video. Although I agree with the common complaints of equal temperament, including those presented in the book you mentioned, workable alternatives are never mentioned. Before pitch and temperament were standardized, for a recorder and an oboe to play together, they practically had to come out of the same shop. Just intonation? Sure, if you’re Data from Star Trek. Baroque flutist think they can do it because they find pure intervals against a drone, but in real time, in a Bach sonata? Differentiating between d sharp and e flat? Even if you could, no one would notice.
Equal temperament is a 20th-century thing. Even during the majority of the 19th century, most keyboards were not tuned in equal temperament. If you look at Erard's tuning instructions for tuning their pianos in the 1890s it is NOT for equal temperament. The majority of keyboards in the 18th century were NOT tuned in equal temperament. Just intonation is hardly the ONLY alternative to equal temperament, there are hundreds of other historical temperaments that allow for other keys. Just intonation is not, in fact, a single thing you can use for a keyboard at all but requires shifting of pitches to constantly maintain perfect intervals. BTW, the title of Ross Duffin's book was meant to be provocative and interest readers. He was not of the belief that equal temperament is bad for everything, just that historical temperaments are better for historical music.
Give me a good Well-Temperament, like Young's or Kirnberger III over 12-EDO any day. It allows all keys to still be playable, but retains some unique "character" of each key, making modulations more interesting and piquant.
Are you talking of Sebastien Erard? He was far dead in 1890s, so you must mean 1790s. However, him residing in French during that time is the reason why he did not recommend equal temperament, because at that time it was still a Germanic-only tuning solution - although a widespread one. Neidhardt, Sorge, and Marpurg had all advocated for equal temperament in Germany already in the early 18th century, and less than ten years after Erard's death, Claude Montal's influental 1834 tuning guide would standardize equal temperament as the de facto tuning in France.
@@edthewave Like Mr. Duffin, I prefer regular meantone temperaments like 6th comma especially for baroque music and 1/4 comma for Renaissance. To me, Young sounds not very good in any key and since it's so irrecular it's difficult for other musicians to match it, like Valotti.
thank you omg, im so sick of people who have literally no way of knowing the difference claiming that just intonation is SOOO much better, equal temperament has so much more possibility
Yeah, it's true. Equal temprament has a lot more possibility, but it is sad that Just Intonation has fallen out of style and I'm really glad that it's making a bit of a comeback. Take this *gorgeous* piano piece written in JI in 2018 ( ua-cam.com/video/i6rDR5s3B8Q/v-deo.html ). It's so damn pretty and it explores the perfectly in tune chords along with the weird out of tune chords you get as an artefact of the system. I think that music which explores this relationship should be further looked into and cherished. I will agree with you that JI is a rather specialised tool which should be used only sometimes because JI has it's extreme limitations. I like how the video doesn't say that JI is bad but rather that equal temprament is important and shouldn't be ignored.
@@minerscale yeah i didn't mean JI is bad it's just unless you're jacob collier its going to be really hard to tell the difference (most of the time) and im just sick of JI purists walking around acting like they're so much better because they only listen to music thats iN tUnE or whatever when they can't even really tell
@@user-km9bx3gf3z Oh yeah in that case the JI purists are totally dumb. But as a composer myself the possibilities that various JI tuning schemes offer (particularly dynamic JI) is fascinating
Just intonation on an instrument with fixed pitches (like piano) is very limiting. But on fretless string instruments (or in a choir) it's quite easy and natural to listen to and adjust the intonation of each individual note (the same also applies to wind instruments). Equal temperament is only necessary because of instruments like piano and guitar that can't really adjust the tuning of each individual note.
Different tools for different situations. I really want to start experimenting more with microtonality, but it will not be at the expense of 12-TET. Both are extremely useful and sound great when used right
@@GeorgeCollier incorrect. Foremost, In the video, you say ga-melan like ga as in gas and melan as in melon, as someone prior has said. Gamelan with the emphasis on lan as in land is Americanized and doesn’t pay homage to the correct pronunciation that the Indonesian peoples use. Gamelan with the ɑː/ə does so. A quick google search past that of the google pronunciation guide will prove well. Further study on the topic will prove fruitful as well. I love the video, but it immediately jumped out that the pronunciation was less than apt. To then refute others who point it out as well is not the best look.
This kind of video is very useful for people who wan't to play music but cannot or will not. For everyday musicians this is esoteric fluff made for clicks. If Mr. Collier's goal is to inspire people to play, this in not how you do it. If it's for clicks, I'm not sure that's paying the bills.
For digital synth and vocalists, there should be a 'floating temperament' where it "bends" non-diatonic notes to 'justify' harmonies to mesh with a pre-set key in real time according to an algorithm. There are probably many singers experienced with vocal harmonies who already do this instinctively. Perhaps it's something AI could be used to feel-out the rules for.
One of the best instruments to hear all the "overtones" is the flute. Just by adjusting the embushure and pressure. You can get 3 octaves of overtones from 1 fingering. Aka, C ,C octave, G fifth, C forth, E third, G fifth and Bb seventh. All from the middle C fingering. Also as a side note, Church bells in the UK, are not generally tuned to Equal Temperament.
Historically speaking, it's wrong to say "from the 18th century virtually all" were tuned equal temperament. There are many historical temperaments used and even today modern pianos sometimes are tuned using slightly uneven temperaments to add character to the different tonalities. Great video, but be careful with this subtleties. ;)
3:15 let the notes ring out long enough to hear the harmonic beats please. Interesting video. If I ever produces music I'd tune every song for intonation or my OCD would spike
As you nicely explained, equal temperament is a compromise where every interval between non-equivalent tones is out of tune. This allows free transposition and modulation, as it sounds just as good (or bad) in one key as in any other key. What you might not (yet) know is this: Equal temperament is NOT the best compromise. It’s just the one which was historically found centuries ago and used ever since. But this has just changed! The book MUSICAL TONALITY by Hans-Peter Deutsch (DOI: 10.2139/ssrn.4452394, also published on ResearchGate) determines the one, unique intonation which, in a strict mathematical sense, best adheres to the physics of overtones while allowing full transpositional freedom. So, after centuries of enduring either the inconsistencies of historical just intonations or the irrationality of equal temperament, the truly optimal intonation for the western tone structure has finally been found. In this optimal tone system, which is called CLEANTONE TEMPERAMENT, all thirds, fifths, sevenths, etc., and therefore all chords (which are stacks of thirds) sound clean above each and every tone, in every key. For example, a major third is always exactly 5/4, a minor third always 6/5, a perfect fifth always 3/2, a minor seventh always 9/5, a major ninth is 9/4, etc., over each and every base tone, in each and every key! In fact, half of all diatonic intervals have their justest possible frequency ratios - and the intonation is still consistent allowing full transpositional freedom. The book also develops detailed designs for new instruments, called CLEANTONE KEYBOARDS, which make full use of the new tone system. Just like any musical entity (an interval, a chord, or a melody) has the same sound above any tone in cleantone temperament, it also has the same form above any key on a cleantone keyboard: The keyboard is ISOMORPHIC. And since cleantone keyboards, just like cleantone temperament, are mathematical consequences of the physics of euphony, the geometric arrangements of keys on these keyboard directly correspond to harmonic relationships: The closer keys are on the keyboard, the closer their tones are harmonically. This not only makes playing but also understanding music very intuitive. To summarize: Not only does music in cleantone temperament sound just and pure in every key, it is also easier to understand and perform when using the corresponding cleantone keyboards. All this while allowing full compositional and transpositional freedom. To anyone with experience in musical tuning systems, this might sound almost too good to be true. But it is all real in cleantone temperament, mathematically proven in the publication. You might want to check it out. It might change your life.
I’m a piano technician. And a musician. First thought is who cares? We’ve been listening to music all our lives. And guitar players have been playing out of tune forever. When they bend strings etc. sounds good to me. BTW I passed the test. I’m an RPT. Took the test by ear. With a tuning fork.
It plays nicely if you only use a smattering of keys, don't use borrowed chords, don't do chromatic movement, don't use chromatic mediants, and the tritone movement. In other words, it works well for music written before 1900 and is hit or miss for everything else. And don't get me started on how a choir might want to change the key to better match the vocal range of the soloist or lead singer. "I Wanna Dance With Somebody" is a very popular song, a great display of vocal performance, and would be near impossible to do in just intonation.. unless you wanna sound like crap. Go ahead and play it out on your piano. It will sound like crap. Autumn Leaves? Sounds like crap too. Paradise City by Guns and Roses? Total crap in just intonation.
@@krisspkriss Nobody said just intonation works for everything. That is why I said it even works for some of the more diatonic jazz songs. Songs based on I, IV, V, vi, iv chords will work pretty well even if there are diatonic passing chords. As for choirs, beatless major thirds are a thing, and that is why we use just harmony keyboards.
@@nathanmcmath Songs in C or G sound good if they stick to I IV V vi iv. B... not so much. E flat? Again, not so much. Tell you what, try playing the top 100 in their original keys on your piana and tell me how it sounds. Beatless thirds are a trivial obsession that isn't limited to choir, but is probably least noticeable in an assembly of singers all out of phase and slightly off by a cent or so from each other... Oh and the reverb and echo in every concert hall. Nope not really that noticeable. But a solo singer in a sound room? Sure, you can hear the beats. A barbershop quartet? Definitely but your piano wont do them much good. They tune every chord to be beatless. Oh, those seventh chords they drop are divine. Unheard of outside of a vocal quartet. But a choir in a concert hall? Pft. Who are you kidding. Not going to hear a beat. You and the other teachers are doing those kids no favors by pushing a relic of a tuning system that doesn't fit modern music at all. Just about all paying gigs now are in even temperament. Commercials, live events, theater, movies... All of it is in even temperament. Everything except where there is a conservation effort to retain the past like a living museum. Not sure how many gigs like that are out there when compared to the number of students you train each year. Pretty low though. Anywho, it's pointless. You think you are doing the right thing and yet it conflicts with almost all modern music. And you make little mini me's every year. You won before I even said anything.
@@krisspkriss Pure tuning works in any key. you need to set the fundamental tone (the tonic of the key of the song to be played). So if the song is in Eb then set the keyboard to pure major tuning with Eb as the root. The better Yamaha and Casio keyboards allow this.
Thanks for this video. I would go a tiny step further and say that western music pretty much from the late 19th century forward was in fact an art form emergent from the palette of equal temperament . Everything from extended diatonicism to jazz to - and you know - "12 tone row" (chromaticism in its most literal form). To address the question "is modern music out of tune" the answer is no. People who say it is have a math fetish. Yes there's a consonance you get as a result of the physics of combining frequencies as low integer ratios... And yeah thirds are sharp from this frame of reference. And yeah "modern music" is largely tertiary. But music speaks to the heart and soul, and the heart and soul doesn't want to discuss the physics of combining frequencies as low integer ratios, or examining thirds under a microscope in a classroom... Tuning is about your frame of reference. Pick up your instrument, find how it speaks to you, tune it as you see fit. Compose, play, put it out there. Is it good music? Maybe, maybe not - but no one will care how you tuned it, unless that's what your music is somehow about.
The natural harmonies are more noticeable in certain rooms. I’ve heard these referred to as “standing waves” for years and becomes very noticeable trying to tune a instrument by ear in rooms that reverberate those harmonies.
There’s one old and even amongst professionals wide spread misconception about "just" intonation, which also this video doesn’t get quite clear, implying "just" intonation might be fully realized on all intervals, chords etc., as long as we only stay within a pure diatonic context (in the sense of a traditional seven tone scale, e.g. just c major). It can’t! It is mathematically impossible to tune a diatonic scale in such a way that ALL intervals amongst each other are "clean" or "in tune" in the sense of simple frequency ratios as found in the overtone scale (especially 1:2 for octave, 2:3 fifths, 3:4 fourth, 4:5 major third, 5:6 minor third). Especially, there is always the unsolvable conflict between just fifths and just thirds - no key change and no chromatics involved! "Just intonation" chooses "clean" major thirds (ratio 5:4) e.g. for the interval c-e; in consequence, in the chain of fifths c-g-d-a-e (all diatonic!) some or all of these fifths have to be tempered (!) quite drastically away from "clean" fifths (ratio 2:3) to match the e of our "clean" major third from a common c. The difference, the so called synthonic comma, makes over a fifths of a half tone step in equal temperament after all.
Just intonation has absolutely no limit. Want to play all the harmonics of A, Bb and C up to the 22th?, play them! The limitations you give them to it, most commonly by restricting JI to only 12 notes(of 12TET). Now a days we've got high-end digital computers and isomorphic keyboards. We've got and will have more programs to help us play JI, and change the note a key produces in real time! The music composed in well made JI sounds incredible. But better music is more expensive and worse music (12TET) is cheaper. We've taken the cheap path, but I, if i take a path, will take the expensive but rewarding path, with infinite possibilities! What do you decide? 12tet? meantone? JI? a mix of all?
It's interesting to consider that the compromise we describe is one of "perfection." All tuning systems have decisions to make - the Western ones are satisfied with taking intra-relationships between overtones to describe intervals, but there's no clear reason to me that explains "why" one should do that. You can make music using octaves and fifths. People have for millenia. There are several different types of "thirds" in the harmonic series. Someone had to decide which one was the right one. And now we call that "perfection"...
We have True Temperment which is an in tune version of that 12 Tone Equal Temperment & what about the Kite Guitar at 41-Tet? 41 TET combines the intune sound of Just Intonation w/ the freedom of Equal Temperament all in one.
Both are now compromises. Computers can let us tune each note on the fly based on the key, or implied key based on other notes being played and the new note value.
For any interested in digging deep into this topic, the Bible (in my belief) is Hermann Helmholtz’ “On the Sensation of Tone.” I first read it as a student 50 years ago and still occasionally go back to it for reference.
Honnestly, if what you seek is perfection, become a mathematician, not a musician. Music is all about imperfection, modulation, it's an art before it is a science. (I'm obviously a guitar player, so yes, imperfection is kinda my thing, most of the notes I play are out of tune ^^)
its a matter of personal preference. I personally find equal temperament more "in tune" than historical fractional ratio tuning probably due to exposure since birth
I've been a piano tuner all my life. I had my piano tuned in an historic temperament by another tuner, and it really did sound fuller and more sonorous. I tried both methods, and decided that the equal temperament sounds constricted. It is easy to explain why. The historical temperaments all have more intervals without beats, so they are more effective in activating the upper strings through sympathetic resonance. The problem is that all these historical temperaments sacrifice a few keys (F sharp and C sharp, for instance). These keys have a lot of beats in certain fifths, which makes the keys quite dissonant. This was not a problem when people were playing harpsichords, because harpsichords go out of tune so fast that every performer had to know how to tune the instrument themselves. They could tune it in a way that fit the key of the piece they were going to play. People in earlier times knew about the equal temperament but hated how sharp the thirds sounded. We have just gotten used to the very sharp thirds in equal temperament. However, when a piano starts going out of tune, it is the thirds that are most unpleasant, when they go even sharper. I knew a tuner who worked in various historical temperaments. He had a piano in his shop that sounded terribly out of tune to me. I asked why he had it tuned that way, since no one would buy it. He put a piece by Palestrina in front of me and asked me to play it. He asked me how I liked it and I said It was very interesting. He asked, "How do you think that would sound in equal temperament?" I said, "Probably totally boring." He said, "It is, and that's why almost no one plays Palestrina any more." He gave a concert where three pieces were played on three different pianos tuned to the historical temperament they were composed on. It was very eye-opening. The Brahms, especially, had effects that would have been totally lost in equal temperament.
Then there is also the question of instrument. I've been enjoying the Beerhoven recordings of Ronald Brautigam that he's done on the pianoforte that has a very different sonority to modern grand pianos. The pianoforte has definitely more string-like sound that has somewhat less blending of sympathetic resonance (I believe) which makes particularly the bass register ring out with far more clarity than on a Steinway.
I would probably rather pick a good pianoforte recording in equal temperament (not unhistorical by any means, actually) rather than on a contemporary grand in an unequal temperament.
@@Veepee92 The modern piano is a much better instrument on many levels. I played a late eighteenth century fortepiano once. It was pretty horrible. It had thin harpsichord-like strings with very little resonance. When Steinway put in the metal plate around 1850, it allowed the strings to be much heavier, and under much greater tension. These two things together made each note sustain way longer. And sustaining power is the single most important factor in "melodiousness." Before the metal plate, Beethoven would simply break the strings (and hammers) when he played, because they were so flimsy. As for Chopin's long "singing" melodies, they were largely imagined by the audience, not heard. Before the metal plate, the notes would die off very quickly. This is one reason that there were so many trills in classical music--it was a way of keeping the note going.
How long did it take you to learn how to tune a piano correctly? Is it possible to be done in one day? There is a guy I know and I informed him that piano tuning is a profession, and it is a very delicate and risky process. Later on, the same guy proceeds to let his social media know that he learned how to tune a piano in a day. I do not know if he was trying to prove a point or something.
@@salomongreen It's ridiculous to say you can learn to tune a piano in a day. The basic Idea of tuning can be taught in a day. Then you have to train yourself to tune in to and count the beats of various harmonics. You have to memorize beat rates. After that, you have to actually learn how to manipulate the hammer (or wrench) so that you can produce those beat rates in a way that is stable. And that is just the rank beginning of it. Every piano tuner I have ever known has apprenticed to another piano tuner in order to learn the trade. There's a lot to it, and most people have neither the patience nor the concentration to do it.
@@steveneardley7541 I figured, I knew I had done my research correctly. Thank you very much.
With electric instruments there should really be an option to quickly switch tuning. Or even an option for automatically switching the tuning to give the best harmony for what is currently being played, so you can play music with key changes without having to think about it.
I'm not much of a musician, but I also feel like this is something that should be optional in software. If modern music workstations can generate appropriate accompaniments, then surely there should be an option to adjust to just intonation if needed.
The issue is that it's impossible to preserve just intonation even within a single key. Easy example is that 6/9 chords are impossible with just intonation as they're basically just stacks of perfect fifths, and you can't do that without ruining the intonation of the major third.
Anyway, details aside, I can't help feeling that the differences between tuning systems are a little overblown, and it tends to only be widely discussed when somebody famous mentions it or it's being sold as a product. Equal temperament is really just incredibly practical as a baseline, and musicians can and do make small changes to their intonation on the fly when their instrument allows for it and it's appropriate.
That's pretty easy to do, to be honest. All you need to do-at least in the case of an analog synth-is have an incoming CV that has the same mathematical function as the tuning system you want to play on
thats called choir my friends. its why they are so beautiful to listen to
Working on it.
Try 600-tone equal temperament. It gets every interval correct within a cent!
Ugh. How can't you hear how out of tune that is?? 1200-tone equal temperament is where it's at.
@@ruebene2223 You noob... you must train your ear to reach beyond into the 2400-TET realm... that's where everything is definitely at. 😆
@@rumar4u pretty sure 4800-TET is better than any of this nonsense.
If you start building that 4,200-key piano today, you might finish it before you expire.
@@cedarfall "No one will ever need more than 5 notes." - Bill Gatesieri
I agree that equal temperament is "not that bad", it's a practical concession but not necessarily a creative one. Tuning is such a misunderstood concept that I'm not sure people fully realise how out of tune almost all music is, often far more than the difference between just and 12TET.
Another way to think of just intonation or other tuning systems is that they are not out of tune as such, but that each key sounds different (and I mean actually different, not "D Minor is the saddest key" different) and that functionally they are harder to work around than equal temperament is, but can yield far more interesting results, and that's not even taking into account fixed vs moveable 12 just intonation.
It is interesting that while the vast majority of instruments are capable of swapping between equal temperament and just intonation on the fly, albeit with a substantial learning curve on the part of the performer, we have somehow moved further and further away from any differential tuning systems to the point where they feel set in stone. Perhaps with the advent of more and more electronic music on the horizon we will start to see tuning in different ways become more mainstream, much like non instrumental MIDI interfaces have.
tldr Good video
you should look up Sevish, does a LOT of cool electronic music with different tuning systems. Just intonation, 22edo, 7edo, etc.
ok
MIDI isn't really made for anything other than 12-TET sadly, and it takes so many hacks to make it work (like using pitch bend, which only works per channel). Does anyone know any better alternatives for alternative tuning?
@@ItsaDigitalHamster actually yes, "Sforzando" by Plogue does a great job of this, especially for its age, it uses scala files (.scl) to map the notes of a midi instrument to whatever division of the octave desired. It's free, but obviously has its limitations, it works best with supported sounds within Sfz (it comes with basic midi instruments) or with samples which you can drop in etc, obviously it will stretch and twist samples of something like a violin or something of a more intimate nature and make them sound... suspicious to a trained ear, but for electronic or art music it is still fantastic and widely used, even listed in an article written this year. VVVVVVVVVV
producelikeapro.com/blog/getting-started-making-microtonal-music/
You do need to find an archive of Scala files to download, I can't recall where I got mine but the files themselves date back to 1996 from the metadata, so obviously there are a trove of different custom systems out there
I wonder if we can use technology similar to autotune to dynamically adjust tuning in various creative ways.
I half expected the last bit to go "Only 2.6% of you can tell the difference."
97.4% of Americans will fail this test...
I’ve seen so many you tubers crash on equal temperament just because it’s not in tune but completely ignore the fact that it’s the exact point. If every song I heard was in the key of C and never modulated just to keep recording sessions quick and cheap, music would be sooo different and way more limiting.
You can still modulate without equal temperament. Stringed instruments for example do this all the time.
A lot of it comes down to the unfortunate fact that the west settled on the modern keyboard layout.
@@killboybands1 I mean, we did, but just like the video said, we couldn’t have jazz without it so it’s not that unfortunate
@@MostLikelyMortal That's what a lot people claim. There are Jazz musicians exploring JI and other tuning systems at the moment. How is it that people think they can predict what would have/could have happened in the past? Western temperament was very close to 31 tone equal temperament because of its almost exact approximations to Meantone. Who's to say how Jazz would have developed had it been 31 et or extended JI? What other music would have happened had western music not been entirely dominated by one tuning system for the last 200 years? One tuning system that the vast majority of musicians accept without question. It's also unfortunate because the Halberstadt keyboard layout isn't even very good for 12 ET compared to Isomorphic layouts but that's a whole other kettle of fish (similar to how the qwerty keyboard is actually not a great design either...but we're stuck with it because that's what we're used to.) However, 12 et as good at certain things, and other tuning systems are good at other things. Whether I'm listening to Harry Partch, LaMonte Young, Debussy, Miles, or Soundgarden, I'm loving the music either way and am thankful that tuning alternatives are being explored but there are statements in the video I have issues with.
We never used just intonation on fixed pitch instrument? There was the time of pythagorean temperament, then meantone, then well and now regrettably equal temperament. Also, tuning a whole scale just is nonsense. We only use just intonation in the context of intervals
I feel like I’m not the getting the other worldly experience of just intervals. For that reason alone… I’d much prefer equal temperament.
I totally see what you mean, it's a small difference, and when one is used to 12tet it sounds more right most of the time.
Using just intonation at higher volumes for music that draws attention to melody, harmony and tone is a special experience though. I reccomend trying it on a good sound system rather than headset, as the way the waves interact in the air is a big part of it. An artist called Zhenna Erose does a lot of microtonal stuff where she works with variant tuning, like just intonation, good place to start.
If you really just don't get it though, that's fine, music is so much more than pitches, and 12tet is pretty good at most things.
As Lydia said, it's a small difference. However, at least for me, justly intonated jazz chords sound simply divine.
Me too. Music played in equal temperament just sounds off to me.
@@Astronometric Wait, everything that is played on the radio from the 40's to 2021 sound off to you?
@@vetlerradio I wanted to write just intonation. Lol. I wrote that line after a very tiring day, I mixed up things 😂.
the minor third, tritone, and half-step are some of the most expressive intervals in JI, because of how variable they can be while maintaining (fairly) simple proportions. In fact, I think jazz music in the 21st century might be entirely understood and contextualised by the relationship of the 5th and 7th harmonics
I’m not really sure I know what you mean- why are these intervals variable based on their simple proportions?
@Vinnie EVH Thank you for asking! If you look up and down the overtone series intervalically, you'll find more examples of major/minor thirds than you would say, fourths or fifths. I should have included major seconds and thirds in my first comment but here's the reasoning:
5:6 and 6:7 are both minor thirds, but a 6:7 is smaller because the seventh partial is 31¢ flat. Because of that, if you're in the key of D and you sing an F natural a 6:7 above the root, you will have a "buesy" sounding F. If instead you sing a 5:6 minor third above D, your F will sound "triadic" and more stable.
In more plain terms if your D is at concert pitch, a minor triad tuned from it might include F+16¢. Alternatively, a minor seventh chord might sound twangier and more evocative with F-33¢, especially if the C of that D minor seventh is tuned 31¢ flat, like a seventh partial 7:1 is.
After that you can play around with other JI intervals and imagine how they might work as members of a chord, resolve or not resolve, etc.
4:5 7:9 and 9:11 are all examples of major thirds. 5:7 7:10 8:11 and 12:17 are all unique tritones. 7:8 8:9 and 9:10 are all major seconds. 14:15 15:16 and 16:17 are all good examples of minor seconds (most of them wider than the standard minor second). On the other hand, 3:5 is the only major sixth, and 5:8 is the only minor sixth. 2:3 is the only perfect fifth and 3:4 is the only perfect fourth until you get to 21:16. So I call those intervals less expressive because they can not be adjusted easily without in my opinion jumping the shark (21st partials are strange and icky).
@@ChrisChapin_chapes Ahh I see what you were trying to say. Indeed… some of these intervals are extremely flexible. The major/minor third in particular is a perfect example because of how malleable it is in the blues and especially blues-based guitar music!
@@ChrisChapin_chapes Amazing and insightful comment, I get what you mean with the bending and warping you can do with some intervals.
I didn’t understand a single thing, but sounds about right.
Keep making these kinds of videos ! I highly enjoy them !
So for a complete beginner:
Is the idea that the way you tune a piano affects the mathematical ratios between notes, so you can make some groups of notes sound really good together at the cost of other groups of notes? And therefore 12 tone equal temperment is kind of a compromise to make a lot of groups of notes sound fine at the cost of some of them no-longer sounding great?
the general idea, yes
Yes, but it's to keep octaves (& only octaves) sounding great w/ small sacrifices made to *all* other intervals (or groups of notes). They all sound good enough, w/ none sticking out as really bad. Earlier systems tried to make more intervals sound better w/ one or more sounding noticeably worse.
Yes. If you pick a note and tune "mathematically" to that, then it sounds hella wonky if you play in certain other keys. The compromises are so that you can play in any key on the piano
Basically.
Pithagoras established the harmonic series by shortening a string and calculating ratios (2/3, 1/2, etc) which defined the common intervals. But if you calculate them this way (and because the ratios have very different denominators), they won't add up consistently (you won't get exactly an octave (2/1) by adding all the intervals in between). That's why the equal temperament establishes an irrational ratio (¹²√2), the same for all the semitone intervals, which will give you an octave after 12 steps
That is because a superior octave is two times the frequency of the previous note. So an A (440Hz) has an octave below of 220Hz, one above of 880Hz and so on. For example, a third (of one note) for Pithagoras, was found when playing a string 2/3rds the length of the one that played the original tone, that is 3/2 of the original frequency. In equal temperament it's found at (¹²√2)(¹²√2)(¹²√2)(¹²√2)(¹²√2)=(¹²√2⁵) of the original note (in hertzs); that is, 5 times the ratio equivalent to one semitone.
I don't properly remember the proof, but with Pithagorean ratios there's a mathematical deviation when putting all the intervals together. And the harmonic series follows the same principle, but uses overtones instead (so whole intervals, a third is taken into account in the next octave, 3 times the original frequency -instead of 3/2).
12 tone equal makes many notes a bit out of tune, while just intonation is in tune in its key, and can sound like a dog with a tepped-on tail when leaving the tune.
I prefer werkmeister 2 as a tuning system.
It was really eye-opening when I found out about the different systems. Before, i thought my hearing was bad, music sounded out of tune to me all the time. Now I know that it really IS out of tune very often.
I've always found it fascinating that we had to tweak the natural harmonic series in order to play jazz and music that generally moves from one key center to another. Like nature doesn't want jazz to exist..lol
Isn't it more the case that equal temperament encourages the mobility of jazz? There's nothing more or less natural about one set of mathematical ratios over another, they all just have different potentials in music.
@@wiegraf9009 my understanding is that the use of upper extensions (7 9 13) for dissonance and color would not work with just intonation, since the relationships of those more extreme overtones are drastically altered
@@Lmjacks they do work JUST fine.... he's talking about key changes.
@@wiegraf9009 it is the case of course, which is his point... and no, there is nothing really natural about ET, unless you consider human-made lakes to be natural?? Just Intonation already exists in nature. ET was created by humans... Also, ET is not ratio based. It's based on the 12th root of 2 and it wasn't even possible until we could apply decimal numbers like 1.059463 to instrument construction or tone analysis.
Some days I wish I had been like my friends and studied music seriously in school. But, on days like today, I'm glad I studied biochemistry instead.
god i wish i had money
Surprisingly, my ear picked up this difference over the years before I knew the terms. Luckily, I'm a violinist so I can take cues from my ear on what sounds good and what doesn't and adjust on the fly. Because of that, every performance has a combination of just tuning and equal-temperment 😅
Music education is designed to give you a perfection complex...which eventually leads you to put down your instrument for good.
Seen it happen to all my peers after music school.
@@PhoenixSplash On the flip side, I would love nothing more than to get college-level music education. There are so many skills that I want that are basically unavailable to me.
@FreedomIII my piano teacher treated me like a winde up toy and showed me off for 2 years. Learned more about piano on my own.
Method books. Musescore, Guitar Pro. You will always be your best teacher in music no matter how much money you throw at them.
Or find a private teacher that hasn't put down their instrument.
No one really cares how flashy you become. Might be a neat party trick if you learn a fast section, but once it's done. It's done.
When a good singer sings, he/she will intuitively change the intonation (dynamic intonation) as he/she goes. That's part of what makes each singer unique, and why it's great to use singing to compose, rather then say a piano.
My first instrument was piano, and it was not for many years that I ever heard of just intonation. During college, I noticed a strange thing occasionally happening while playing trombone in a local semi-pro orchestra. I sometimes would hold the same note through various chords, and suddenly, that note would sound out of tune! I wrongly assumed that I was just drifting out of tune, and would just adjust best I could to what I thought I should be doing. Later, during a master class taught by a trombonist from the LA Phil, I really got some in-depth specific training on just intonation, which took much of the guesswork out of properly tuning.
If I am not mistaken, one of the big reasons why just intonation is superior (in my opinion) to all other tunings, is that such tuning of a chord triggers what I call "phantom" harmonics that would not be there using things like equal temperament. On trombone in high school before I understood just intonation, I was shown a neat trick, where I would play a F just below middle C, hum a D (apparently in just intonation), and suddenly, you can hear a "phantom" Bb above middle C be created! Bottom line, just intonation creates a wonderfully extra set of higher harmonics (and lower?) that you just don't get anywhere else.
Nice touch at 6:13 where the chord Jacob plays (and sings ig) fits right over rhapsody in blue in the background
Woah, indeed. I hope it’s intentional, and otherwise, it’s a welcome coincidence.
First of all: great video! I just find fun in nitpicking, as some misunderstanding might arise, but I know what you're aiming for, and it's great that you did :)
For those interested, I wanted to add that 12TET is by far not the only 'well-tempered' (allows-every-key) tuning system we have nowadays, and my understanding that's where the 'equal temperament ruined harmony' comes from. It would be pretty easy to simply equally tune a concert grand piano, but that's why good piano tuners are so rare and are paid a fair amount of money. They don't tune them in 12TET, but they still do work in every key. For example, in general the middle octaves seem to be more in tune while upper and lower octaves are more permissive. And from tuner to tuner they have different preferences for thirds, fifths, etc.
So a concert piano is very differently tuned from a Casio keyboard in 12TET. *That* is usually the equal temperament people pick on (at least among the people I know), not just any temperament that allows playing and modulating to all keys vs. just intonation. There's tons of other nuances in between.
Also 'Why Equal Temperament ruined Harmony (and why you should care)', doesn't focus too much on keyboard instruments, but discussed also string and wind instrument practice, how sharps and flats have been handled in different periods and other very interesting stuff, so don't let yourself get discouraged from picking up said book ;)
Have a great day everyone!
I’ve been a piano tuner for forty years, and I want to tell you that you are correct. Equal temperament is where I start, but I’ll tweak things away from that in order to get the sound I’m looking for. And it’s different with every piano; the piano tells me what I need to do.
You are talking about stretching, right? I'm not a piano tuner, I was a classical piano student (now I play only in my free time) and despite studying engineering I have made a few projects on music and piano in particular for university. Recently I was synthesizing a piano sound for a project and one of the things I did was include octave stretching. It's those little things like the stretching and the inharmonicity that really added to the overall quality of the sound. It was a really fun project.
In just intonation, if you play a C major triad, it sounds like one note: the low C whose overtone series the chord perfectly matches. In 12-tet each of those notes sounds like its own voice, ready to move around.
I love this way of looking at it!
Personally I like detuned sounds and used detuned synths all the time in my music.
just ratio ≠ in tune, it's just one of many potential sounds to aim for
Heck, there are even multiple "just" ratios you can choose from. A 19:16 ratio minor third sounds almost like it does in 12-TET, but a 6:5 minor third is uncomfortably bright -- you'd never get the "sad" connotations we typically associate with minor keys nowadays.
He meant in tune in respect to the harmonic series.
What is "in tune" then? When you tune an interval or a chord, you naturally listen to beating and try to get rid of it. And when there's no beating, it is in just intonation. How else would you determine whether something sounds in or out of tune (without using a tuner)?
It is true, though, that piano sounds weird in just intonation, because a part of what makes piano sound like piano is equal temperament (similarly as certain imperfections in tuning are a part of what makes guitar sound like guitar).
@@MaggaraMarine why isn't a tuner allowed?
@@MaggaraMarine "In tune" is when something sounds the way you want/expect it to. That includes intervals that beat.
Very worthwhile video! Thank you.
I think it absolutely a must that non-fixed pitch instruments learn to play in tune . . . perfect 5ths as a drone. It make a huge difference if students try to play with equal tempered 5ths. The accoustic stringed instruments come alive with vibration (color, projection, sympathetic vibrations) when "perfect" or Pythagarian tuning is employed. There are times when compromising with open string tuning is called for (e.g., after the orchestra has tuned to an A=440 for example and the cellos and violas have to play open C strings is playing a C-major or Ab-major chord).
So much of the beauty of Baroque music rests on perfect 5ths and other intervals that adjust to the fundamental of any chord.
The best short description of the advantages and disadvantages of 12TET I've heard so far. Kudos.
I should add that I haven't played in 12TET for many years now, because I tend to keep to at most eight tones per octave. I satisfy my desire for complexity in polyrhythms and polymeters. _Suum cuique._
cheers from sunny Vienna, Scott
Great explanation! I love the mix of memes and music knowledge I'm getting in my feed from you. Keep em coming please!
I've been fooling around with just intonation and I fell in love with a nice compromise. Two 6-Tet separated by a just 5th, which means that the 4th and 5th are always in tune, while other notes are as expected. It sounds better than the 12-Tet, is more practical than just intonation, and doesn't require more than 12 notes.
Wait but…wouldn’t it be a 7tet followed by a 5tet? Because the fifth and fourth?
I'm so thankful that my ears are NOT good enough to find these issues more than trivial! I'd hate to miss whole worlds of music because I could not get past 'perfection!'
good for you?
@@deegrawnzyes the answer is it is good for him!
The secret of Eddie Van Halen's beautiful rock guitar sound was detuning the B-string down a tad to get perfect thirds out of his raunchy chords! That was a major part of his "brown sound".
All my life I've had "good ear", like I was the one who detected an instrument out of key if we, as hobbyists, were to play in my garage. I'm no musician, just a hobbyist as said.
Hard hit to reality when watching this video with headsets I have not been able to tell those subtle differences, that all sound just equal to me... Kudos to those who notice differences.
EDIT: I DO hear that 'out of tune' demo by Jacob Collier, but for some reason I do not notice that in my digital keyboard...
Same. Didn't hear any difference
Yes! 'Perfection' is SO constricting!
Look into precise temperament. A genius mathematician figured it out and it seems perfect.
I really do think conditioning plays a huge part in how we experience tuning systems. If you grew up in the West, well, then equal temperament is probably gonna sound best to your ears.
I know that is the case for me, I can still enjoy other tuning systems, but it'll sound slightly off, always, though, not in a bad way necessarily.
Yes, conditioning is the biggest factor, especially since music is a solely cultural endeavour.
Agreed. All of the just intonation examples sounded just a bit wrong to me.
I dunno, I'm not much of a musician and grew up in the West, but the just intonation sounds much better to me in the samples given here, not "off."
I think cultural differences in habituation to rhythms may be more significant.
Edit: Someone elsewhere in the comments mentioned a study showing that most trained musicians are more habituated to TET, so JI sounds more off to them than to average schlubs like me. Makes sense since making music requires more active listening than just hearing it passively.
I had this experience as well. JI doesn’t really sound better to me so far
Grew up on western music and particularly classical (and classical violin). A skilled choir sounds best to me, and I don't even know how a really good choir handles "temperament", if you could even make the concept relevant for an " instrument" that can re tune each time a new note is sounded. String instruments do the same... :-)
I used to hang out with a holistic new age crowd who villainized JS Bach for inventing equal temperament and ruining "true" harmony. First of all, Bach didn't invent equal temperament, and secondly, he didn't use it, at least not exclusively. He was a champion of "well" temperament, as in "The Well Tempered Clavier." Well Temperament was equal temperament tweaked here and there to tone down some of the stinkiest intervals in some keys without causing worse problems in other keys, like whack-a-mole. The Well Tempered Clavier, Books I & II demonstrated Well Temperament with pieces written in all twelve major keys and all twelve minor keys. The idea was to be able to play in all 24 keys without totally sucking in any of them.
Piano tuners still use "tweaked" tunings to make pianos sound better with strings or with horns or whatever. Strings can play correct intervals if you want or any others; horns tend to play sharp no matter how hard you try. Tweaked tuning can make everyone play a little more nicely with others.
The actual scholarly consensus regarding Bach's tuning seems to be "we don't know". It's not that he certainly tuned in 12-tone equal temperament, or that he certainly tuned in meantone or a variant thereof; we simply don't have enough historical evidence to give definite proof of either.
new age folk are attached to words like "resonance" and "frequency" while having no respect whatsoever for the actual expressions of these terms, it's purely posturing
same for most thinking tunings need to be ranked lmfao, ridiculous
Cannot believe that such a great composer like Bach, or any other recognized composer, would have ever used a tuning with such an amount of inharmonicities!
Every harmony, except for octaves, is out of tune if a keyboard instrument is tuned with a uniform distribution of the twice the frequency divided between 12 notes. You guys called it equal temperament tuning, but I would called if No Temperament Tuning.
The feelings that music evoque depend on harmonies, octaves are the simplest harmonies, in 1 to 2 frequency ratios, but other harmonies must ge present also. Fifths are the next more important, in 2 to 3 ratios. Next are 3 to 4, 4 to 5, 5 to 6 ratios and so on.
In order to be able to listen to harmonies other than octaves, a tuning using some kind of temperament, like the ones invented by Vallotti or Kirnberger, is a must.
I love the way the less in-tune, brighter keys like C# tend to be faster in the Well Tempered Clavier. It's definitely nicer in Werkmeister III or Young's temperament than equal tempered. It's nice having the pleasant thirds even at the price of worse thirds in other keys. On the other hand, I've heard that Bach would play in Ab whenever the organ tuner arrived because this has the wolf notes in 1/4 comma mean tone. This was the most common tuning for organs even into the 19th century.
I would claim 90% can't hear the difference between natural and equal fourths or fifths, including me.
i can't
It is very noticeable to me. But then again I have perfect pitch. I actually love equal temperament cuz that is the best way to navigate especially in a piece that is "changing keys" but if we were doing acapella especially barbershop we use just intonation cuz in barbershop we want to "ring them chords" lol. The point is I like both.
@@Jakeroo767 I'm jealous!
@@Talaxianer honestly as much as I am grateful to have perfect pitch any great musician doesn't have to have perfect pitch to do what they love. Relative pitch has its uses
But anyone can hear the difference between other intervals in JI vs 12et. IT also Depends on which JI intervals and which ET is approximating them.
My digital piano has settings for some non-equal temperaments like Werckmeister 3 and Kirnberger 2. The first thing I noticed is how perfect fifths really stand out, often in places where they shouldn't. No wonder Bach wanted to avoid them in counterpoint.
The only positive aspect I noticed is that some five-note chords in Beethoven's music sound less dissonant. I think it's because some pairs of notes like E+F, D+Eb and G+Ab are further apart from one another in those temperaments.
I also experimented with playing Romantic era music in these temperaments, but shifting the base note so that the "best-sounding" scale is not C. I kept hopping from one base note to another, until I had a weird realization that base note C sounds best for G flat major, because that results in the fewest in-tune perfect fifths.
The problem with equal temperament is that nothing stands out. And how can you claim that Bach wanted to avoid perfect fifths?
Bach did not compose in equal temperament. Wercknmeister and Kirnberger are not Just Intonation.
@@epichdsheep You seem to care too much about just intonation. I mean all I can say is music would sound off if not tuned equally, plus it would just inconvenience most modern music as a whole
It seems like a digital piano could analyze the chords and intervals being played and adjust the temperament on the fly. If you're playing a C6 chord, A would be 435 Hz, but playing a D chord will play A at 439 Hz. Kinda like what violin players do naturally.
@@abillionjivebars9888 Kinda sorta? While you can't tune a piano on the fly, most otherinstruments that aren't similarly tied to unchangeable tuning (anything with a mouthpiece or anything without frets) can be tuned note-to-note. As a violinist, I realised I was doing that instinctively and instinctively leaning towards making each harmony sound as if it was in just tuning in the correct key a decade starting more than a decade before I learned different tuning systems 😂
When tuning a harp, using fifth based just intonation, it "sings" much better, more resonance from other strings. The problem: the last fifth is completely out of tune. This can be fixed: start with C, and tune the following fifths based on the 3rd harmonic: cgdaeb, the next would be F#, but don't use the 3rd harmonic, in stead use the 5th harmonic to tune D# to the fifth harmonic from b. Now tune the rest of the notes from D# based on 3rd harmonic again. You will get a just intonation where the last fifth fc is closer to 3rd harmonic tuning than equal temperament. It works really great for harp.
This is a great explanation of tuning. I wish YT were still pushing longer form content like this...
Seven minutes is long form?
If anything there's *too much* long form nowadays. Other UA-camrs would've made this into a bloated 30 min video
The harmonic series is a thing also in mathematics. I never realized it came from this. I understand why now, and I have to say it makes a lot of sense. The harmonic series goes as such: 1, 1+1/2, 1+1/2+1/3, 1+1/2+1/3+1/4, etc. etc.
The thing is that tone is calculated in a logarithmic scale (don't worry if it sounds too complicated), while functions are evaluated linearly. Put simply, to go an octave higher you must double the pitch, so, when you count 1,2,3,4 in music you count 1,2,4,8. And using this logic, every new step of the tonal values of the harmonic series adds 1/2, then 1/3, 1/4 etc.
I like the sound of equal temperament. It creates movement and sounds richer to my ears. Just intonation is too sterile. Like a synth sound with no modulation.
Agreed. Just Intonation for steel string acoustic guitar is especially bad imo, it's that twang and dissonance that gives a particular flavor that I and many others love!
you could always add the modulation afterward.
i'd much rather have pure tones if that was possible.
Then you discover choral music specifically designed to be sung that way - it just resonates soooo much more, being the exact opposite of sterile
i feel like it's the opposite: 12-TET feels like all the life has been sucked out of it
try Bach's well temperament. And, also think about all those composers (Bach, Händel, Mozart, Beethoven) who didn't use equal temperament: you are listening to their music not as they wrote it but as it has been modified by music culture dating from the 20th century.
Studies show that when violin players are permitted to tune their instruments according to hearing, the intervals are NOT those of just intonation. I would refer you to the study of Paul C. Greene published in the J.A.S.A. in 1937. I would also refer you to the musical experiment performed by Houtsma, Rossing, and Wagenaars: "Demonstration 31: Tones and Tuning with stretched partials.," which shows that harmony is unrelated to the beat theory of Helmholtz. This can be found online at the Correlograms Project at Stanford University.
this is why computers are the most powerful and fantastic musical instrument ever created. i just finished writing a tune that changes tunings multiple times, from 12tet, to 15tet, to 53tet. and every instrument is automatically retuned via automation so it all remains harmonically sound.
Though I agree that computers are wonderful for this purpose, instrumentalists, especially those playing something like a violin (hi, that's me) can adjust tuning on the fly by listening to our ears because we aren't bound by frets or keys 😊
I like well temperaments the best. I tuned my fender rhodes to Kirnberger III and I am really happy with it.
There are lots of temperaments besides just intonation and 12T equal. Also singers and violists approached tuning a lot like Jacob Collier does before the XIX century. Equal temperament is ok for fretted instruments and keyboards, but there's life beyond them.
YES. As someone who has been singing for years, I have always wondered why a major triad on a piano just doesn't sound right. I'm so used to just intonation from choirs that I could tell it was off without knowing it!
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I would say, for the example piece tuned in C major, there's a reason Orchestral pieces tune the bass/tonic of a chord/key to equal temperament, and then tune the thirds and fifths of that to the bass. It's a shifting system to make it sound the best.
The Pachelbel’s Canon portion was eye-opening. I have always HATED that piece - but I found it to be pleasant in just intonation… very interesting.
I found just the opposite. It's all subjective in the end.
Thank you so much for showing the actual math, so interesting! Also want to add being a string player in contemporary music settings is actually really difficult, it's hard to fight the just intonation impulse, especially when it's really difficult to hear keys to adjust so all you can go by is the root. I've had to just memorize the difference, and yes, those thirds and 7ths are incredibly out of tune, gets even worse when the arranger is breaking low interval limits. I wish people understood this more
I've tried so many time to prove the 'Third in G Major is 14 cents flat' thing like Jacob Collier does, but I end up just going 'ooooo' in 12 Tet. Subsequently I make a total fool out of myself.
I think of it like this: In a broad sense it's the question of specialization vs generalization. What is "better" is totally subjective and based on individual needs. It's not really just that way in music, but in all things.
This is why playing violin or similar string instruments is way harder than it sounds, learning perfect 3rds as alternate notes from playing them in a scale is not easy.
In Western Classical Music (before mid 18th century) There were many more temperaments than 12 tone equal temperament and just intonation. A temperament rearranges the distances between the notes of the scale, so you can have all the intervals that are the same distance from pure (12 tone equal temperament), or you can have some intervals that are closer to pure while sacrificing others to be less pure, like other renaissance and baroque temperaments. Quarter comma meantone temperament is probable one of the most well-known. However, when speaking about temperaments, music theorists from the baroque would distinguish between well-tempered temperaments and non-well tempered temperaments. Quarter-comma meantone temperament is not well-tempered, because while in many keys, the major thirds are pure or close to pure, there are certain keys that are to be avoided, because some intervals sound too much out of tune. A well-tempered temperament (in baroque times) was a temperament in which all usual intervals in all keys sound acceptably in tune, meaning that you can play in all keys without retuning the instrument. 12 tone equal temperament is obviously well-tempered, but it's not the only one: Werckmeister and Kimberger temperaments are also well-tempered, but they are not equal: there's variation in the intervals, but it is arranged in such a way that all keys are playable. I think using temperaments other than 12 tone equal gives more variety of sounds, each key has its own identity.
12-TET is a miracle. It is a miracle from mathematics, that we can acquire notes so close to the major third, major fourth, and major fifth by dividing the scale by 12. Why should 2^(5/12) be so close to 4/3?
You have to go all the way to 29-TET to get a better 5th.
Fifths can take a lot more "damage" than other intervals before sounding sour. That was the whole idea behind meantone temperament: sacrifice the purity of fifths in exchange for better thirds/sixths. And people were fine with fifths being ~6 cents flat for centuries. People are less okay with 12-TET's ~14 cent sharp major third (case in point, videos like this one).
31-TET is arguably the "ideal" system for Western tonal music. It's just too many damn notes.
12 is such a beautiful number
@@karawethan But then it's not the ideal one, because there are too many notes for it to be practical, and there are bound to be many notes in there that approximate integer rarios very badly. (It's not just about whether the scale contains good approximations of rational intervals.) I suppose I should add to my original comment that it's a miracle that we have such a relatively small number - 12 - having these properties.
@@diabl2master That's why I put "ideal" in quotes. If it was practical, then we would be using it instead of 12tet.
"and there are bound to be many notes in there that approximate integer ratios very badly." This I do not agree with. Or at least when it comes to the intervals that we care about. Major thirds are essentially just. Minor thirds are close to just. #4 and b5 (31tet differentiates between the two) are near-just approximations of 7:5 and 10:7. #6 is near-just. b2 and #7 are closer to just than in 12tet. The only important interval further from just are the perfect 4th/5th, and they are still very tolerable.
@@karawethan I have to disagree that 31edo is too many tones, I've built an instrument for 53edo (with optional third steps for 159edo) and it's surprisingly manageable ;)
This explains so well why major thirds always sound too wide to me even when I’m perfectly “correct” according to my digital tuner.
"In tune" doesn't really exist, it's all a question of different compromises. I would say all music is out of tune, regardless of instrument or temperament choices, it's just a question of how badly out of tune it sounds and how you prefer to distribute the "out-of-tuneness" amongst the notes and keys (largely personal preference). Also: the harmonic series, when realised on actual instruments, doesn't have frequencies that are exact integer multiples of the fundamental. The physical limitations of strings, reeds, pipes etc mean that the harmonics may well start to drift sharp or flat wrt the ideal integer multiple relationship. So the fact that just intonation (whichever of the many flavours of integer ratio patterns you choose) is based on these exact integer multiples is itself an approximation of reality. Finally, we should recognise that many parts of the world do not use 12 tone equal temperament in their instruments, so the line about virtually all instruments being tuned this way since the 18th century overlooks so many musical traditions. There are almost certainly many more places in the world that don't typically use 12TET for their instruments than do (e.g. Greece, Turkey, most countries in the middle east, south america, far east, many countries in Africa).
And idiophones (bells, bars, pitched membranes, etc.) never have harmonic timbres, and musical traditions based around idiophones (many in SE Asia and Africa) therefore tend to use tunings that do not resemble 12TET. In fact, idiophones in the Western tradition (like orchestral marimba) need to be carefully shaped to sound acceptable in 12TET.
I really don't think anything your saying works all that well. A phrase like 'nothing is really in tune' is a big dramatic phrase that sounds very bold, but it's just not true. A justly tuned C Major chord will be in tune. The rest of your scale won't be worth much, but you can't take deny the C Major chord that. Not saying this to hate on equal temperament, as I think it's a very good system. A system of compromises, but necessary ones for our modern musical environment.
As for saying that so many cultures are overlooked in his phrase; completely correct. However, in contemporary high art and pop music, 12TET has been in consistent use. I can understand not feeling the word 'virtually' give enough credit to these other cultures, but I'm personally kind of willing to give it a pass for the sake of oversimplicity. And if you really want some fun music, Bulgarian folk is some very good stuff. :D
@@GamingKindling Maybe I could have phrased some of what I said more clearly, but in terms of saying this is "in tune" or "out of tune" my point is that it's misleading (at best) to use these kind of binary choices. There are no absolutes: tuning is always about compromise. Even given anybody's personal preferences, I don't think it's helpful to think of any particular combination of notes as being "perfectly in tune", because the context of what could come before or after those notes, or what other notes might play at the same time, will change the perception of good tuning vs bad tuning.
In terms of a justly tuned C major chord: what system of integer ratios is being used to define the intervals? There are different schemes, so are all just intonation schemes as "in tune" as each other? Or are they just different compromises being made? In any case, judging how good 3 notes sound together is one thing, but in a musical context - where that chord is supporting a melody, or comes between many other chords - then the perception of what tuning/temperament is worse or better could well change, even with a simple diatonic harmony.
And yes, I'm a huge fan of Bulgarian folk music, especially their fantastic (mostly female) vocal music!
I wrote a paper on this in college. My thesis was basically that atonal harmony was the inevitable result of equal-temperament, and I used Fetis' Traité complet to show the evolution of harmony over history and showed how Equal Temperament enabled this evolution because it's basically just the tuning equivalent of atonality
Another problem with just intonation is if you have a piece or song with a lot of chord changes and you want every single note perfect, it might result in the key being shifted by a quarter-tone or half-tone or more even though it’s meant to stay in the same key the whole time.
I saw video on this one time but I can’t remember what it was called lol
Dosen't matter that much in practice. It''s literally all about the reletave distance between notes during a timeframe.
“Equal temperament is a compromise which allows full compositional freedom, at the expense of perfection.”
That statement gets to the very heart of what perfection is. What makes “great art” great? It certainly isn’t precision, so what is it?
Perfection is an attribute that is often mistaken for accuracy or precision. But how do precision and accuracy relate to perfection?
What do the Mona Lisa, the Parthenon and Michelangelo’s David have in common? A precise inaccuracy is the magic key to their perfection.
If the Mona Lisa were a precise image, it would lack the very attributes that make it famous. The Parthenon is Intentionally warped in order to correct for our perspective. Similarly David is proportionally “out of tune”, in a manner of speaking, for the same reason.
In short, I believe it is our subconscious awareness of these subtle discrepancies and irregularities that draw our attention to and ultimately compels us to contemplate the beauty in things.
Couldn't agree more!
It'd be fun to have a keyboard that analyzes your harmonies in real time and slightly detunes from 12T·ET to some sort of midpoint between the blend of the likeliest chord centers in your playing. I'm gonna mull this over a bit, but I might be able to make a MIDI interpreter that does this.
Hey, Howd it go?
@@gutshoplilium3139 I got something working but it sucked, I need better training and validation data and more time to work on it lol.
So the idea that Equal Temperament was in used since the 18th Century is a common misconception. What was used during that time was "Good" or "Well" Temperament. These historical tunings (such as the Werckmeister III, the Kimberger, or Young's) were what composers from Bach to Chopin had in mind when they very purposely chose specific keys and were the reason why each of these keys were often described as having their own individual characters. There are recordings out which showcase these tunings and indeed Bach's WTC (named the Well-Tempered Clavier, not the Equally-Tempered Clavier) or any set of Sonatas etc take on a new character when heard within these more "perfect" or "imperfect" (wolfy) keys. This dimension was lost around the beginning the 20th Century, which is when Equal Temperament was adopted at large.
To add to this point, all or most of the 12 keys worked under these tunings. The point is that the relative imperfections gave each key its own "flavor." Think of them as a "bridge" between just intonation and Equal Temperament.
I’ve always wondered, with so much music being produced largely electronically, it should be possible to produce a temperament almost on a per track basis, for whatever the harmonic needs of the piece might be. I wonder if anyone has been doing that at all.
Yes, it is possible to change the temperament on the fly. Personally, I wouldn't want to do this on a per-track basis.
No matter which level of "granularity" we consider, I don't know if it's been done in practice but wouldn't be surprised if that's the case.
Tho other day i farted, stopped moving instantly, was captured by the silent echoes in my head and the fact that some thing had escaped what wasnt ment to be free at first.
While beeing fascinated by these impressions i noticed how my state of consciousness was shifting towards a deeper level of awareness, deep like the cause of the phenomenon i just got to witness. A true feeling of gratitude and joy for having this kind of sensation.
So I guess it was perfectly normal having all of it resonate with the flow wich I was in, and was in me, pushing some thing, forcing it to come alive. And then...
I farted again!
Great video btw. Undoubtedly only a certain sort of human beings is going to watch and/or enjoy it. So I had to make this post in order to keep things in balance. Just in case you wandered about my sanity. I suggest you better be concerned about yourselves.
I'm so messed up by various indigenous musical traditions (among instruments I use are for example Chinese flutes which you obviously can't retune without a file and a carving knife) and modern microtonal experiments that I don't even know which interval version sounds right.
Also my main instrument is classical guitar so that might explain it (especially the major third problem)
Had a piano prof in my undergrad have one of her pianos tuned in just intonation. Hearing Chopin and Debussy was so beautiful not to mention the piece was played at high proficiency
I dislike the phase "Equal Temperament is out of tune" because it is the tuning. It can't be out of tune. It doesn't match up with the harmonic series, that's fair. But that's different than "out of tune". Fixed Just Intonation doesn't sound good to me on any piece. Any interval or chord other than root is incorrect, and more out of tune than TET. So we lose the main purpose. TET is way more practical for instruments with fixed tuning.
Dynamic Just Intonation could be interesting, since many instruments can adjust each note of each chord, and with tools like PianoTeq we could adjust even piano tunings dynamically. But most instruments will likely be a couple of cents out, and have some vibrato. Unless every instrument is perfectly on pitch, it's likely it wouldn't feel different.
true.
love you lad :D such a creative and joyful energy.. also thanks for that last quote xD probably not the best, but i have accumulated quite a lot of hobbys (2D animation, drawing, making music, 3D stuff etc.) and sometime its hard to prioritize on what i should focus the most
Is modern English is out of grammar?
Gyaaat this is so skibidi
I prefer a little harmonic stretch, i wouldn't make too much attempt to temper out an instrument but i like to intonate my guitars by ear with the 19th fret harmonic instead of the octave and i make the b and e strings a little sharp by comparing them to the low E and the A string. Ive heard that pianos are tuned with the fifth above the octave so i tried it, i like it.
Honestly the out-of-tune-ness of equal temperament is cool, the guitar is one of the most popular instruments and that thing isn’t even in tune with equal temperament. Everything being perfectly mathed out isn’t cool because humans aren’t perfect math machines, we play a beat to fast, we sing a note to sharp, that’s just what we do
6:22 - I’m a long-time Microtonalist, but I largely agree with your statement here: 12-tone-per-octave equal-temperament - AKA “12TET” - is a very practical tuning, but not ideal.
I recently have been working with 31TET on my Lumatone keyboard (ua-cam.com/video/cpYBnzaWZqU/v-deo.html), and two things have become ever-more apparent (although neither surprised me much):
- On the Lumatone, 31TET is _not much more complicated_ to perform than 12TET.
- Every well-conceived tuning has its own distinctive sound, or “mood” as Ivor Darreg termed it.
12TET’s mood is comparatively unsettled, because its thirds are a bit … ratty. Sometimes an unsettled feeling is exactly what you want to portray in music, though! It’s great for ragtime or bluegrass, for example.
31TET is much calmer, almost to the point of sounding a little bland - _only a little, though_ ! That, despite its minor thirds, perfect fourths and fifths being a tiny bit “off” (about 2 to 2 1/2 times more accurate than 12TET’s thirds).
Much more importantly though, 31TET gives you a lot more very-interesting-sounding melodic and harmonic possibilities - not just major and minor thirds, but also subminor, neutral, and supermajor. 12TET abstracts such distinctions away, like a cartoon!
So, choosing 12TET is not entirely a matter of convenience, but it just has the right kind of mood for some kinds of music.
I think this discussion misses several important points. The first is that there are many non-equal-temperament tuning systems other than just intonation, so justifying ET by presenting it as a binary choice with JI is disingenuous. Although since the author declares that virtually all Western music has used ET since the 17th century, then it's also quite possible that he just doesn't know about all of these other tuning systems and presumes that they're just all ET. It's a common mistake. Like I was taught in college that Bach's Well-Tempered Clavier was written to demonstrate the virtues of ET, when it was really quite the opposite. My understanding is that ET didn't even become significantly used until the late 18th century, and didn't dominate until the early 20th. The whole point of all "temperaments" is how to distribute the out-of-tuneness, and there are several viable strategies. Most of them allow for doing all of the things that ET can do, like playing in different keys or using chords other than the root.
But I think the biggest deficiency in the discussion is that dissonance is an extremely useful artistic tool. Most music alternates the building of tension with the release of the tension, and dissonance can be a good way of creating tension. With the traditional temperaments, some keys were more consonant than others, and different intervals and chords were more consonant than others in each of them. This gave the composer a much wider palette, and choosing the key to play in was an important decision. I kind of suspect that this is why so much of Western classical music tells us the key that it is in. That was important information about what the piece would sound like. A serene piece could use a more in-tune key, while a more emotional one might choose a less in-tune one. You could modulate to dissonant key to create tension and then modulate to consonant one to release it. This is musical tool that has completely disappeared from our vocabulary.
Bach Well-Tempered Clavier is perhaps the most easily grokable demonstration of the artistic use of out-of-tuneness. The point of this collection of pieces was to demonstrate the virtues of what was known as "well-tempering," hence the name. This was a system in which all keys were "usable" (enough in tune), but with some more in tune than others. As with most tunings, the keys with more accidentals in the signature are less in-tune than those with fewer. In the WTC, Bach demonstrates the type of composition that is best suited for each of the keys.
The problem with ET is not that it is out of tune, but rather that it is boring. What's the point of having twelve keys if they all sound alike? But yes, ET does also deprive us of more consonant music. One of the beauties of choral music is that it is perfectly in tune. Listening to it can be tremendously rewarding spiritually, and even the non-spiritually-attuned people can sense the relaxation that it brings.
Incredible video! :) I knew all of this, but it's even better explained than I ever could have! Next time instead of leaving a comment to teach the basics of this myself I can just link this video
Has anyone made an intelligent keyboard capable of changing temperament as you modulate? Seems doable, but maybe I'm missing something.
I think it's beyond current technology: our perception of key centre is so grounded in trend/tradition/context that no machine would be able to be programed to understand. As an example, you'd need it to pick apart the melodic line from the rest of the texture before it could even differentiate properly between relative major/minor keys. Maybe one day someone will hire enough people to distinguish the melodic line(s) in enough hours of every single style of melodic music to be fed to an AI for machine learning to be able to finally distinguish... and that's just to tell the difference between C Major or A minor haha
not to mention picking apart the whole texture to understand which notes actually play a significant contribution to the chord, and which ones are just passing notes or textural embellishment. We do so much intuitively when we engage with music, it's so easy to take for granted how much of what we interpret is purely from a 'cultural' context, and how much this is an art and not a science
Agreed. Wouldn’t be totally automsgic or work for some things. Wouldn’t have to be perfect.for all situations, could require some programming per tune. Or could have like an organ stop for manuslly indicating a change.
Since we live in the age of MIDI recorded and rendered digital music, how about creating a system where the tuning system is changed to fit whatever chord or passage is currently being played? This way you could get a performance with "perfect" just intonation even across changing keys, and therefore it would be even better compromise compared to using just intonation on one key or equal temperament. I wonder if you could notice the dynamic changes in the tuning, or if things would simply sound cleaner overall.
it was a better world when most people tuned “by ear”, guitarists would slightly turn the tuning pegs intuitively between songs to achieve better balance depending on the key. Digital tuning is dangerous. Beethoven apparently identified that keys had “characters” for him.
I think we forgive slight fluctuations in pitch while listening to music. It rarely becomes “painful” to listen to. Personally Ive played a piano which was tuned in the old way, and it undoubtedly sounded better overall in some keys. Very technically and intellectually orientated musicians (jazz in particular) prefer even-toned, it’s to do with their ‘removed’ perception of music.
Tuning a piano or other keyboard was, and is, a very deliberate procedure. The keyboard tuning Beethoven was familiar with was not simply "by ear," but was a careful and calculated compromise. Modern piano technicians do not rely on digital tuners, yet they are able to reasonably approximate equal temperament.
De-tuning the strings of a guitar or other fretted string instrument has a very limited application, unless you are playing music that doesn't modulate. The frets are placed according to equal temperament, so de-tuning a string effectively de-tunes all the fretted notes available on that string.
Re: jazz, It's essential that keyboardists and guitarists are in equal temperament because the music modulates freely. But there is plenty of intonational subtlety for horns/winds.
Whenever listening to piano music, live or recorded, there are always a few pitches that pop out as being out of tune. I decided that this is due to equal temperament and that I should stick to jazz where dissonance is part of the creative tension, even in a harmonious major 7 #11 chord.
Based
Now I have a question: what temperament does a violinist use if she/he has to play melodies comprised of a single-note? what if the melody is double-note or triple-note?
Depends if they can infer a tonality, if they have a reference pitch that they want to maintain, what their priorities are on a note-by-note and phrase-by-phrase level, etc etc. They might want to priorities hitting just intonations relative to some reference, move the centre of just intonation as the music modulates between tonal centres, choose particular justly-tuned intervals depending on the harmonic context as well as tonal context (e.g. the minor seventh between the root and the seventh is much flatter in a harmonic 7th chord compared to a minor seventh chord on the same root), choose to deviate from one particular just system into another to highlight particular moments or sections, or choose to return to equal temperament if they start to serve another purpose or if that would suit their needs better.
@@TAP7a Thank you for the complicated answer xD
It wouldn't specifically have to just be string instruments too! Any brass or reed (idk much about flute but probably them too) player can bend their pitches by quite a large degree.
@@juliaf_ Now in a large ensemble like an orchestra, do they agree to play in a certain temperament? How do they harmonize?
@@antimon40 the larger an ensemble gets the easier and harder it gets to tune. One violin sounds in tune, forty violins sound in tune, two violins sounds like death without some serious practice. The benefit of having a massive orchestra wrt tuning is that they can all be tiny tiny tiny bits off and it'll all work out. Solo players won't want to miss their note by more than maybe 3-5 cents, but a massive group of players have way more wiggle room to play with. So much so that the difference between intonation systems are, I think, statistically indistinguishable. There's a reason they call barbershop the "black belt of a capella", and that's because they're being assholes, but they're also kinda not wrong - it's incredibly impressive and really difficult to get a chorus of 100 amateurs to sing with pitch accuracy within 2 cents of equal temperament. They get the advantage of ring and resonance indicating where the correct pitch is with great accuracy, but still
Have you heard of the Belgian quarter-tone pianist Seppe Gebruers? I recently came across his videos (on a youtube channel from Troika vzw). He improvises with two pianos tuned a quarter-tone apart, and plays very unconventional versions of jazz standards like 'In a Sentimental Mood' and 'You and the Night and the Music.' I had never heard anything like it in that context-so surreal. That’s how I ended up here looking for more information. Thanks for the video. Ciao, John.
as someone who developed my perfect pitch based on equal temperament, just intonation very rarely sounds in-tune to me >.
Thanks for the video. Although I agree with the common complaints of equal temperament, including those presented in the book you mentioned, workable alternatives are never mentioned. Before pitch and temperament were standardized, for a recorder and an oboe to play together, they practically had to come out of the same shop. Just intonation? Sure, if you’re Data from Star Trek. Baroque flutist think they can do it because they find pure intervals against a drone, but in real time, in a Bach sonata? Differentiating between d sharp and e flat? Even if you could, no one would notice.
Equal temperament is a 20th-century thing. Even during the majority of the 19th century, most keyboards were not tuned in equal temperament. If you look at Erard's tuning instructions for tuning their pianos in the 1890s it is NOT for equal temperament. The majority of keyboards in the 18th century were NOT tuned in equal temperament. Just intonation is hardly the ONLY alternative to equal temperament, there are hundreds of other historical temperaments that allow for other keys. Just intonation is not, in fact, a single thing you can use for a keyboard at all but requires shifting of pitches to constantly maintain perfect intervals.
BTW, the title of Ross Duffin's book was meant to be provocative and interest readers. He was not of the belief that equal temperament is bad for everything, just that historical temperaments are better for historical music.
This ^
Give me a good Well-Temperament, like Young's or Kirnberger III over 12-EDO any day. It allows all keys to still be playable, but retains some unique "character" of each key, making modulations more interesting and piquant.
Are you talking of Sebastien Erard? He was far dead in 1890s, so you must mean 1790s. However, him residing in French during that time is the reason why he did not recommend equal temperament, because at that time it was still a Germanic-only tuning solution - although a widespread one. Neidhardt, Sorge, and Marpurg had all advocated for equal temperament in Germany already in the early 18th century, and less than ten years after Erard's death, Claude Montal's influental 1834 tuning guide would standardize equal temperament as the de facto tuning in France.
@@edthewave Like Mr. Duffin, I prefer regular meantone temperaments like 6th comma especially for baroque music and 1/4 comma for Renaissance. To me, Young sounds not very good in any key and since it's so irrecular it's difficult for other musicians to match it, like Valotti.
@@Veepee92 Sebastien Erard started a piano-making dynasty that lasted 150 years, well into the 20th century.
Shout out for including the Peterson trio c jam blues. My favorite video on UA-cam.
thank you omg, im so sick of people who have literally no way of knowing the difference claiming that just intonation is SOOO much better, equal temperament has so much more possibility
Yeah, it's true. Equal temprament has a lot more possibility, but it is sad that Just Intonation has fallen out of style and I'm really glad that it's making a bit of a comeback. Take this *gorgeous* piano piece written in JI in 2018 ( ua-cam.com/video/i6rDR5s3B8Q/v-deo.html ). It's so damn pretty and it explores the perfectly in tune chords along with the weird out of tune chords you get as an artefact of the system. I think that music which explores this relationship should be further looked into and cherished. I will agree with you that JI is a rather specialised tool which should be used only sometimes because JI has it's extreme limitations. I like how the video doesn't say that JI is bad but rather that equal temprament is important and shouldn't be ignored.
For reals, bruh!
@@minerscale yeah i didn't mean JI is bad it's just unless you're jacob collier its going to be really hard to tell the difference (most of the time) and im just sick of JI purists walking around acting like they're so much better because they only listen to music thats iN tUnE or whatever when they can't even really tell
@@user-km9bx3gf3z Oh yeah in that case the JI purists are totally dumb. But as a composer myself the possibilities that various JI tuning schemes offer (particularly dynamic JI) is fascinating
Just intonation on an instrument with fixed pitches (like piano) is very limiting. But on fretless string instruments (or in a choir) it's quite easy and natural to listen to and adjust the intonation of each individual note (the same also applies to wind instruments). Equal temperament is only necessary because of instruments like piano and guitar that can't really adjust the tuning of each individual note.
Different tools for different situations. I really want to start experimenting more with microtonality, but it will not be at the expense of 12-TET. Both are extremely useful and sound great when used right
4:08 It's /gaməlan/ not /gəmelən/.
a as in "arm",
ə as in "away".
it's gam-eh-lan with lan as in land and the emphasis on lan
@@GeorgeCollier You said it more like the fruit ga-melon? I am a native Indonesian speaker. However, it might be different in other language(s).
@@GeorgeCollier incorrect. Foremost, In the video, you say ga-melan like ga as in gas and melan as in melon, as someone prior has said. Gamelan with the emphasis on lan as in land is Americanized and doesn’t pay homage to the correct pronunciation that the Indonesian peoples use. Gamelan with the ɑː/ə does so. A quick google search past that of the google pronunciation guide will prove well. Further study on the topic will prove fruitful as well. I love the video, but it immediately jumped out that the pronunciation was less than apt. To then refute others who point it out as well is not the best look.
@@GeorgeCollier bro said gay melon trying to correct the native indonesian speaker, use google
@@liamneels8197 I didn’t record the voiceover.
The google pronunciation is correct, it’s just a small error :)
This kind of video is very useful for people who wan't to play music but cannot or will not. For everyday musicians this is esoteric fluff made for clicks. If Mr. Collier's goal is to inspire people to play, this in not how you do it. If it's for clicks, I'm not sure that's paying the bills.
For digital synth and vocalists, there should be a 'floating temperament' where it "bends" non-diatonic notes to 'justify' harmonies to mesh with a pre-set key in real time according to an algorithm. There are probably many singers experienced with vocal harmonies who already do this instinctively. Perhaps it's something AI could be used to feel-out the rules for.
One of the best instruments to hear all the "overtones" is the flute. Just by adjusting the embushure and pressure. You can get 3 octaves of overtones from 1 fingering. Aka, C ,C octave, G fifth, C forth, E third, G fifth and Bb seventh. All from the middle C fingering.
Also as a side note, Church bells in the UK, are not generally tuned to Equal Temperament.
Historically speaking, it's wrong to say "from the 18th century virtually all" were tuned equal temperament. There are many historical temperaments used and even today modern pianos sometimes are tuned using slightly uneven temperaments to add character to the different tonalities. Great video, but be careful with this subtleties. ;)
3:15 let the notes ring out long enough to hear the harmonic beats please. Interesting video. If I ever produces music I'd tune every song for intonation or my OCD would spike
Can we stop calling everything that uses equal temperament "out of tune" for clickbait?
As you nicely explained, equal temperament is a compromise where every interval between non-equivalent tones is out of tune. This allows free transposition and modulation, as it sounds just as good (or bad) in one key as in any other key. What you might not (yet) know is this: Equal temperament is NOT the best compromise. It’s just the one which was historically found centuries ago and used ever since. But this has just changed!
The book MUSICAL TONALITY by Hans-Peter Deutsch (DOI: 10.2139/ssrn.4452394, also published on ResearchGate) determines the one, unique intonation which, in a strict mathematical sense, best adheres to the physics of overtones while allowing full transpositional freedom. So, after centuries of enduring either the inconsistencies of historical just intonations or the irrationality of equal temperament, the truly optimal intonation for the western tone structure has finally been found.
In this optimal tone system, which is called CLEANTONE TEMPERAMENT, all thirds, fifths, sevenths, etc., and therefore all chords (which are stacks of thirds) sound clean above each and every tone, in every key. For example, a major third is always exactly 5/4, a minor third always 6/5, a perfect fifth always 3/2, a minor seventh always 9/5, a major ninth is 9/4, etc., over each and every base tone, in each and every key! In fact, half of all diatonic intervals have their justest possible frequency ratios - and the intonation is still consistent allowing full transpositional freedom.
The book also develops detailed designs for new instruments, called CLEANTONE KEYBOARDS, which make full use of the new tone system. Just like any musical entity (an interval, a chord, or a melody) has the same sound above any tone in cleantone temperament, it also has the same form above any key on a cleantone keyboard: The keyboard is ISOMORPHIC. And since cleantone keyboards, just like cleantone temperament, are mathematical consequences of the physics of euphony, the geometric arrangements of keys on these keyboard directly correspond to harmonic relationships: The closer keys are on the keyboard, the closer their tones are harmonically. This not only makes playing but also understanding music very intuitive.
To summarize: Not only does music in cleantone temperament sound just and pure in every key, it is also easier to understand and perform when using the corresponding cleantone keyboards. All this while allowing full compositional and transpositional freedom. To anyone with experience in musical tuning systems, this might sound almost too good to be true. But it is all real in cleantone temperament, mathematically proven in the publication. You might want to check it out. It might change your life.
I’m a piano technician. And a musician.
First thought is who cares? We’ve been listening to music all our lives.
And guitar players have been playing out of tune forever. When they bend strings etc.
sounds good to me.
BTW I passed the test. I’m an RPT. Took the test by ear. With a tuning fork.
I am a music teacher. I use just tuning all day long when working with choirs and singers. It even works with some of the more diatonic jazz songs.
It plays nicely if you only use a smattering of keys, don't use borrowed chords, don't do chromatic movement, don't use chromatic mediants, and the tritone movement. In other words, it works well for music written before 1900 and is hit or miss for everything else. And don't get me started on how a choir might want to change the key to better match the vocal range of the soloist or lead singer.
"I Wanna Dance With Somebody" is a very popular song, a great display of vocal performance, and would be near impossible to do in just intonation.. unless you wanna sound like crap. Go ahead and play it out on your piano. It will sound like crap. Autumn Leaves? Sounds like crap too. Paradise City by Guns and Roses? Total crap in just intonation.
@@krisspkriss Nobody said just intonation works for everything. That is why I said it even works for some of the more diatonic jazz songs. Songs based on I, IV, V, vi, iv chords will work pretty well even if there are diatonic passing chords. As for choirs, beatless major thirds are a thing, and that is why we use just harmony keyboards.
@@nathanmcmath Songs in C or G sound good if they stick to I IV V vi iv. B... not so much. E flat? Again, not so much. Tell you what, try playing the top 100 in their original keys on your piana and tell me how it sounds.
Beatless thirds are a trivial obsession that isn't limited to choir, but is probably least noticeable in an assembly of singers all out of phase and slightly off by a cent or so from each other... Oh and the reverb and echo in every concert hall. Nope not really that noticeable. But a solo singer in a sound room? Sure, you can hear the beats. A barbershop quartet? Definitely but your piano wont do them much good. They tune every chord to be beatless. Oh, those seventh chords they drop are divine. Unheard of outside of a vocal quartet. But a choir in a concert hall? Pft. Who are you kidding. Not going to hear a beat.
You and the other teachers are doing those kids no favors by pushing a relic of a tuning system that doesn't fit modern music at all. Just about all paying gigs now are in even temperament. Commercials, live events, theater, movies... All of it is in even temperament. Everything except where there is a conservation effort to retain the past like a living museum. Not sure how many gigs like that are out there when compared to the number of students you train each year. Pretty low though.
Anywho, it's pointless. You think you are doing the right thing and yet it conflicts with almost all modern music. And you make little mini me's every year. You won before I even said anything.
@@krisspkriss Pure tuning works in any key. you need to set the fundamental tone (the tonic of the key of the song to be played). So if the song is in Eb then set the keyboard to pure major tuning with Eb as the root. The better Yamaha and Casio keyboards allow this.
@@krisspkriss Here is how pure tuning is used in Japanese bands. Yamaha makes a special keyboard for this. ua-cam.com/video/yaDP2V2auN8/v-deo.html
There is no magic in tuning, there is magic in music. So do what serves your music, and you will find magic.
Thanks for this video. I would go a tiny step further and say that western music pretty much from the late 19th century forward was in fact an art form emergent from the palette of equal temperament . Everything from extended diatonicism to jazz to - and you know - "12 tone row" (chromaticism in its most literal form). To address the question "is modern music out of tune" the answer is no. People who say it is have a math fetish. Yes there's a consonance you get as a result of the physics of combining frequencies as low integer ratios... And yeah thirds are sharp from this frame of reference. And yeah "modern music" is largely tertiary. But music speaks to the heart and soul, and the heart and soul doesn't want to discuss the physics of combining frequencies as low integer ratios, or examining thirds under a microscope in a classroom... Tuning is about your frame of reference. Pick up your instrument, find how it speaks to you, tune it as you see fit. Compose, play, put it out there. Is it good music? Maybe, maybe not - but no one will care how you tuned it, unless that's what your music is somehow about.
The natural harmonies are more noticeable in certain rooms. I’ve heard these referred to as “standing waves” for years and becomes very noticeable trying to tune a instrument by ear in rooms that reverberate those harmonies.
There’s one old and even amongst professionals wide spread misconception about "just" intonation, which also this video doesn’t get quite clear, implying "just" intonation might be fully realized on all intervals, chords etc., as long as we only stay within a pure diatonic context (in the sense of a traditional seven tone scale, e.g. just c major). It can’t! It is mathematically impossible to tune a diatonic scale in such a way that ALL intervals amongst each other are "clean" or "in tune" in the sense of simple frequency ratios as found in the overtone scale (especially 1:2 for octave, 2:3 fifths, 3:4 fourth, 4:5 major third, 5:6 minor third). Especially, there is always the unsolvable conflict between just fifths and just thirds - no key change and no chromatics involved! "Just intonation" chooses "clean" major thirds (ratio 5:4) e.g. for the interval c-e; in consequence, in the chain of fifths c-g-d-a-e (all diatonic!) some or all of these fifths have to be tempered (!) quite drastically away from "clean" fifths (ratio 2:3) to match the e of our "clean" major third from a common c. The difference, the so called synthonic comma, makes over a fifths of a half tone step in equal temperament after all.
Great video, been following your channel for a while and great to see you upload an educational video like this, thanks and more of these vids pls
Just intonation has absolutely no limit. Want to play all the harmonics of A, Bb and C up to the 22th?, play them!
The limitations you give them to it, most commonly by restricting JI to only 12 notes(of 12TET).
Now a days we've got high-end digital computers and isomorphic keyboards. We've got and will have more programs to help us play JI, and change the note a key produces in real time!
The music composed in well made JI sounds incredible. But better music is more expensive and worse music (12TET) is cheaper.
We've taken the cheap path, but I, if i take a path, will take the expensive but rewarding path, with infinite possibilities!
What do you decide? 12tet? meantone? JI? a mix of all?
It's interesting to consider that the compromise we describe is one of "perfection." All tuning systems have decisions to make - the Western ones are satisfied with taking intra-relationships between overtones to describe intervals, but there's no clear reason to me that explains "why" one should do that. You can make music using octaves and fifths. People have for millenia. There are several different types of "thirds" in the harmonic series. Someone had to decide which one was the right one. And now we call that "perfection"...
We have True Temperment which is an in tune version of that 12 Tone Equal Temperment & what about the Kite Guitar at 41-Tet? 41 TET combines the intune sound of Just Intonation w/ the freedom of Equal Temperament all in one.
Both are now compromises. Computers can let us tune each note on the fly based on the key, or implied key based on other notes being played and the new note value.
For any interested in digging deep into this topic, the Bible (in my belief) is Hermann Helmholtz’ “On the Sensation of Tone.” I first read it as a student 50 years ago and still occasionally go back to it for reference.
Honnestly, if what you seek is perfection, become a mathematician, not a musician. Music is all about imperfection, modulation, it's an art before it is a science.
(I'm obviously a guitar player, so yes, imperfection is kinda my thing, most of the notes I play are out of tune ^^)
its a matter of personal preference. I personally find equal temperament more "in tune" than historical fractional ratio tuning probably due to exposure since birth