@@ev4836 equal temperament didn’t mean what it means today. Electronic tuners give you the equal temperament as of today, but the equal temperament back in the day wasn’t the same. To solve the confusion, people sometimes call the old equal temperament the “well temperament”.
Workoutfanatic787, That was the best comment I have heard yet. Things seem to taste, feel, smell, look, and sound correct because of our conditioning (think about what you liked as a child and what you have learned to like as years and experiences added up). That's a big reason why we "cuss" and "discuss" our preferences daily. But the other issue of natural born senses should not be ignored as well. Maybe even used as a measuring tool to see how far-out our life-conditioning experiences can take us before we begin to reject.
It is? How can it be? If the pitches are a certain value (such as A4 = 440 Hz), why is there a band for each note? What do those "blocks" mean? To me, the chart causes confusion to some people because it is implying that anything within that block is that note but that is not true. There are 1/4 tones in between our 1/2 steps (C, C#, D...)
Nice video but, when you are talking about equal temperament, you mention Vicenzo Galilei in 1584 while you are missing the spanish composer and theorist Bartolomé Ramos de Pareja (c. 1440- 1521/22) the first one who talked about equal temperament in "De musica practica" (1482) and the one who introduced this idea in Italy during his residency in Bologna and Rome. Here you can find the treatise imslp.org/wiki/Musica_practica_(Ramos_de_Pareja,_Bartolomeo) Although it is written in latin you can see the ilustrations which exemplify his theories. Anyway, great work with the maths and ratios.
What if I tolf you that Equal Temperament was invented first in China by Zhu Zaiyu (also romanized as Chu-Tsaiyu. Chinese: 朱載堉) in 1584. en.m.wikipedia.org/wiki/Equal_temperament So calling Equal Temperament as Western tuning is misleading
@A W I dont care that you dont care lmao, fact is fact. China invented the tuning earlier than Europe so it is misleading to call it western tuning, end of story
Absolutely EXCELLENT ! Thank you. Well, indeed very well, presented, too. I would like to hear you lecture on this topic using a keyboard to give us examples.
If the fifths are out of tune on the modern piano, and a string player tunes their A to the piano, would the string player’s open strings be out of tune to the piano?
The point is that without a system that allows for comprehensive modulation then we could never have had the history of Western art music. None of your favourite composers from Bach to Schoenberg could have functioned ( get it?) Anyway no altered harmonies no interesting notes outside the key from Bach to present. Everything from Jazz to Copland from Beethoven to Bartok from mature Mozart to Debussy. You arent exactly conveying what's exciting and fundamental about this subject.
The two figures frequently credited with the achievement of exact calculation of equal temperament are Zhu Zaiyu (also romanized as Chu-Tsaiyu. Chinese: 朱載堉) in 1584 and Simon Stevin in 1585. According to Fritz A. Kuttner, a critic of the theory, it is known that "Chu-Tsaiyu presented a highly precise, simple and ingenious method for arithmetic calculation of equal temperament mono-chords in 1584" and that "Simon Stevin offered a mathematical definition of equal temperament plus a somewhat less precise computation of the corresponding numerical values in 1585 or later." The developments occurred independently. Kenneth Robinson attributes the invention of equal temperament to Zhu Zaiyu[6] and provides textual quotations as evidence. Zhu Zaiyu is quoted as saying that, in a text dating from 1584, "I have founded a new system. I establish one foot as the number from which the others are to be extracted, and using proportions I extract them. Altogether one has to find the exact figures for the pitch-pipers in twelve operations."Kuttner disagrees and remarks that his claim "cannot be considered correct without major qualifications." Kuttner proposes that neither Zhu Zaiyu or Simon Stevin achieved equal temperament and that neither of the two should be treated as inventors. i'm Just telling the fact. China invented the tuning earlier than Europe so it is misleading to call it western tuning.
Yes it was first discovered (i wouldn't' say invented) in china. But it isn't misleading to say that it became the prominent western tuning. After all this video details changes in tuning in western systems, and China didn't see any major adaptation of the system. The global spread of equal temperament is sometimes viewed as a form of western imperialism.
@@NathanNokes exactly -- western music put it to use to create extremely complex harmony; while perhaps found a few years earlier in China it didn't change the course of Chinese music the same way.
Without a system that allows for comprehensive modulation then we couldn't have Bach as we know him (as the fellow who set the stage for the entire subsequent history of Western Art Music till today including Jazz.) That history could accurately be discribed as a composer driven high speed power dive into higher and higher levels of chromaticism expressed both virtically and horizontally through modulation and chromatically altered harmonies and other methods of allowing more and more of those wonderfully subversive notes outside the key in thereby increasing the expressivity or ambiguity of the music untill a point a actual saturation was reached in the early 20th century. Bernstein famously calls this the 20th century crisis. In order for composers to continue to increase chromatic density after this point then the conventions of diatonic containment had to be more or less done away with; enter modernism. So without keyboard technology then no Bill Evans or Igor Stravinsky or Arnold Schoenberg or Bartok or Samule Barber or Charlie Parker or Gill Evans or or.
Nice work! Well narrated, well-illustrated, well-produced. This is a complicated subject for non-musicians like me, and this is one of the best expositions of it that I've seen.
Nicely explained for sure...I now just need a reason for ET and I don't find a valid one anywhere on the Internet. The professional musicians I have spoke with also don't know of any valid reason to use equal temperament on pianos, organs, lyres...(instruments with 12 tone octaves that have fixed pitch).
thank you for the explanation i has been a struggle with my music assignments you have me some understanding about the tuning and temperaments please keep explaining and give a few examples please
Hello Nathan, Nice try. I think it helps novices (as you can see by earlier comments) but watch out next time for inaccuracies that confuse those who may have previously understood the issues from a more exacting source. 1) Just Tuning is NOT a temperament: Pythagorean Tuning is NOT a temperament and True Tuning is NOT a temperament due to the fact that all intervals sound genuine. YES. Mean Tone and ET are indeed temperaments. So be careful with your nomenclature! You are right that it is not possible to use Just Tuning in a 12 tone system (which is NOT our modern system - but only that which is used on limited keyed or fretted fixed pitch instruments). Choirs and acoustical ensembles in western music do not limit themselves to a 12 tone system. They actually do adjust for the differences between G# and Ab (as well as other #s and flats) who's differences you explained well. 2) In Pythagorean Tuning the octave is NOT preserved but the "perfect consonant" lesser intervals are (fourths and fifths): This is a problem and the reason we have the "Pythagorean Comma" or discrepancy. 3) In Equal Temperament the octave (in theory) is preserved. On tightly wound string instruments like the piano (Klavier) the harmonics are out-of-tune and therefore the octave is generally stretched to sound in-tune. The tritone IS in-tune by the way and the minor thirds (major sixths) do sound in-tune. The other intervals are indeed out-ot-tune as up say. 4) Pythagoras did define the major third as the ratio of 1.25:1 not 81:64. You will get that ratio of 81:64 if you tune a 12 tone system to a circle of Pythagorean fifths, yet Pythagoras determined that the 1.25: 1 ration was the major third and that it sounded genuine to the trained and untrained ear. We find different ensembles actually prefer different sized thirds depending on the energy that is required from both harmonic and melodic movement in a particular situation. So major thirds smaller and slightly larger are often interchanged in actual performance (even when an equally tempered instrument is used with voice or instruments that can adjust "on-the-fly".
Thank you for taking the time to comment. Oops I did let temperament slip out for just intonation.(writing making graphics shooting and editing is time consuming) I'll add a square text correction. As for choir tuning to just intervals I'm very well aware of this. It is actually a relatively complex phenomenon and some American ensembles do better then others (I've heard some fairly sharp 3rds in many performances.) That said the video is intended as an introduction. Sometimes pedagogy must simplify and approximate structures. Just like we typically don't introduce Einstein before we introduce the Newton(even though the later was slightly wrong and Einstein fixed it. People need to know about equal temperament being off just intonation before they learn how not fixed pitched instruments adjust between them. I didn't even have enough time to discuss Partch and Young or breakout calculus. :-)
_-WIKIPEDIA GUY_-_ do not listen! do not listen! We have more than 2 temperaments here. for example 1/4 middle tone temperament. This is just compromis between other tonal systems... We know pytharogean tonal system and also didymic tonal system. Didymic tonal system was created for minor/major need for playing music but didymic has a lot of problems and if you play in didymic tonal system you need to re-tune your instrument for each one key... We hear wolf tone on the cello, especially on the G string on the e tone, specially in the fourth position of play. You totally mixed it up and your video is a total garbage! Do not listen this overwhelmed guy. sorry!
Ha ha.. we would have done jazz or other modern music?? .Here says a guy in who does not even play a key to show. You can do better. Adiós forever buddy..
Great video, buds. You understand the importance of explaining any/every term/concept you introduce into your topic, which is so important...and appreciated. Also, I loved that sick reference to the ever famous Mach piece: Lick My Love Pump
Great video. Thank you! I have a question: "in Pythagorean tuning the Major 3rd was out of tune"... compared to what? What is a Major 3rd in tune and how did Pythagoras know that his system yielded an out of tune Major 3rd?
an "out of tune" major third would be out of tune in reference to the frequency ratio 5/4, which is the just intonation major third: pages.mtu.edu/~suits/scales.html If you compare that ratio to others you can hear the difference (major thirds on piano for example are a little sharp compared to 5/4), and too my ear sound a bit more dissonant (while being totally acceptable)
Thanks for this vid - I found it informative... I only have one issue with the commentary, and that is when you said that Just Intonation is NOT a good way of tuning. You need to be careful here because yes JUST INT. is not good if you want to shift into different keys, but you are totally forgetting (or perhaps were never aware) that there are many types of music which simply remain in ONE KEY. Indian Classical music for example. So you need to quality what you are saying, and do not mislead people into automatically writing off Just Inton.. Just Intonation is GREAT, and we should try to return to it. On the other hand I agree that Equal Temp. resulted in some great music... Jazz, Rock, etc etc...
There are a bunch of amazing works in different forms of just intonation written over the last 50 years. Have a go before you label something as "useless". The problem is usually when people only want to deal with 12 tones, whereas just intonation tends to lead to far more pitches per octave. This can be a pro, not just a con. Also, many non-fixed pitched musicsare performed in or informed by just intonation - barbershop, choral singing,string quartets, dronal music, overtone singing, folk musics from around the world. Hardly something I would call useless. Thousands of years of music in the making.
+edwardpowellmusic Sorry to say that, but your conception of good intonation is so poor and personal...If you play any music in you head must be clear where to play ALL notes, not only for a specific tonality! It is crazy to think that in each tonalyty we must use different places for the same notes! This way is not universal and it mislead people!
+Cam Taylor You forget that the progress exist and this Just intonation is too old to be progresive...But it is not true about the 12 tones in an octave! Absolutely not! It is like you change the 12 hours in a day...please stay logic!
Neither time nor music is as set as you think. There are plenty of adherents of decimal time and should it ever catch on it would be no more annoying than when we switched from lbs and oz to kgs. (Also there are 24 hours in the day not 12) anyway there are 60 minutes in a hour so it's perfectly valid to say a day is made up of 48 1/2 hours. X-D As to music that's even less set in stone. Arabic music has 24 tones in an octave. Thai classical music uses just seven roughly evenly spaced tones. Indian classical music uses 12 tones but those tones vary slightly depending on the Key. In the West we settled on 12-TET because it's a good enough solution. Music is compromise. A system where nothing except the octave is quite right versus a system requiring multiple fingerings or rapid re-tuning.
Nathan, You may have learned some history behind the use of equal temperament, but you are definitely not teaching it clearly here. You are overlooking the difference between melodic and harmonic use of intervals in historical context, for starters. Then you confuse things more with use of terms such as "out of tune", and by not explaining whether you are referring to a specific interval (or which of the two notes of the relation is "out" to the other), or an entire tuning system, and it gets worse from there. I went to your demo video for sound examples and found myself not able to follow your "lessons", because you are playing two different "e"s from different tuning systems at the same time, instead of letting us hear the different interval sizes between a major third in just vs. pythag. intonation systems, for example. Please give yourself time to get more clarity into your explanation, as well more basic details on the size of intervals that people can really measure with their own ears, and don't need to be told are "out of tune".
The notion out of tune is not possible to avoid! All people knows that it is impossible to use all intervals just in the same time. We do a compromises all the time. The true questions is how much to be out from the just intonation. But also we must know that the just intonation is good only in theory! Human ear don't apreciate the just octave nor the so narrow major third...Officialy only the classic equal temperament permits to stay nearly possible to Just intonation but it is possible to do better! I have a solution wich nobody want to listen or approuve, no problem for me! My new equal temperament works very well on my violin and it is enought for my satisfaction...
Very Nice Video A lot of these videos do not address the limitations of the keyboard design and I'm glad to see that you mentioned split keyboards It's a great shame that we settled on the 12 note Halberstadt keyboard. Also, lute players were not all were using equal temperament. John Dowland had a temperament of his own that he championed. Pythagorean tuning is why 3rds were considered dissonances and usually resolved quickly if they were used at all. While it's impossible to say whether or not 12 tone equal temperament "ruined" tonality it certainly limited it. One could only speculate how music would have developed had we settled on 31 tone equal temperament (which is a very close approximation of meantone). The 5ths are squeezed and the 3rd and 7th harmonics are almost indistinguishable to pure.
A "perfect" interval would be one where the frequencies of the two notes are related by some simple ratio. For instance if one note's frequency is exactly 3/2 the frequency of the other note's frequency (a "perfect" fifth interval). This is important because the two notes then have a natural relationship between them, both tones are natural harmonics of another note, one octave down from the lower note. If something were vibrating at this lower note, you'd naturally expect it to also produce these harmonics, which in principle means the two tones together should sound pretty natural and comfortable due to the close, fundamental physical relation between the two frequencies. The challenge is that if you try to build the whole scale across multiple octaves out of "perfect" intervals, you wind up with some intervals that are far from "perfect". Going up an octave should always be doubling the frequency. If you try to build the scale according to simple ratios (for instance in Pythagorean, where a fifth is 3/2 and a major second is 9/8) you can't continue those same intervals and reach a perfect octave (you can multiply by 3 and divide by 2 as many times as you like and will never reach something that exactly equals 2). Also, using the same interval at different points on the scale might not produce the same effect either, depending on the tuning system being used. Equal temperment is a trade-off: The benefit is that a certain interval played at different positions on the scale will generally produce the same effect - a major 5th will be a major 5th regardless of where in the scale you start it. But *none* of the intervals, apart from octaves, have that integer-ratio relationship. The half-step interval is the 12th root of 2 - a transcendental number. A major fifth wouldn't be exactly 3/2 times the frequency of the lower note, it'd be around 1.498 times. A major third wouldn't be 5/4 (1.25) times the frequency of the lower note, or even 81/64 (1.266) times the frequency as in Pythagorean tuning, but the cube root of 2, around 1.26 times the frequency of the lower note. So in equal-temperment tuning none of the intervals other than octaves will have that super-pure, clean-sounding natural relationship between the tones. But the trade-off is that you can move freely up and down the scale, modulate to different keys, etc. and still produce the same effect. And when you're used to hearing one particular tuning system, you expect it and it tends to sound natural to you. Or maybe you just don't know what you're missing...
Great topic and video! 2:09 - “just temperament”: Careful! Just Intonation is a *tuning* , yes, but *not* a temperament. Temperaments are tunings that systematically compromise pitches *away from Just Intonation* mostly to allow you to play in a variety of keys. As Ivor Darreg amusingly put it, saying “Just Temperament” is like saying “dehydrated water”! 🤪
There used to be a text notice correcting the misspeak. But UA-cam disabled that feature. So that's fun. It still isn't as bad as an error as I have seen in a few textbooks or academic journals, but is still embarrassing none the less.
Couple of small points it's not called just temperament is called just intonation because none of the notes are tempered, I.e altered, these are the natural notes from the harmonic series and the book is called *How equal temperament ruined Harmony* not tonality
this isn't an issue for fretless instruments, correct? eg violin, cello, human voice Unless they're being played in concert with fretted instruments like keyboards, yes?
Not an issue for those instruments. But it is a factor in Brass instruments. Since natural horns will play the harmonic series. French horn players use a combination of valves embouchure and their hand in the bell to adjust their tuning to match other players
Nice presentation. I would dispute a couple of things however. 1. That pythagorean intonation was the dominant system for thousands of years. Pure Pythagorean tuning is quite an unnatural system and I think most early music focused around voice and non fixed pitch instruments. The tonic was also generally fixed for the performance so there wasnt a need for a compromise to natural intonation. Indian Classical and Georgian choir music would be extant examples.
12-tone equal temperament works because 12 is a very easy number to work with and is the smallest number of equal divisions of the octave that is able to adequately approximate all of the frequency ratios in just intonation.
I agree with comment about the brave stroke of genius in adopting a visual display approximating through the difficulties of explaining 12 tones really ?.... expressing an Art form and Life with mathematics as the queen of science!?! Congratulations. You have crossed thousands of years of thinking and 'aural problem solving in tuning '. through this attempt in giving some clarity to this simplification to explain to non-professionals.
You started out talking about "equal temperament" and then suddenly in the same breath you started using the term "just temperament" without explanation. Do these terms mean exactly the same thing or are they two different things? This made your explanation difficult to follow after that point.
Marian Kotúč Thank you very much Marian for that explanation. It took six months to get an answer but I think I understand now. When you use the term just intonation instead of just temperament it makes more sense and I see the difference now.
66 years old, playing since 14, I only understood very little, as to what I just learned from Nathan EXCELLENT Explanation.specially the visual display at 8:07 Thank You so much Nathan.
This is a good presentation. True Tuning (which is not tempered) was used by the classical Greeks in their modes. By taking the seven tones produced by the True Dorian octachord and the True Tone C Major scale and obtaining the five remaining tones formed from the "geometric mean tones" of those produced already (referenced to prime [C-128Hz]) we get a 12 tone scale that is aurally genuine in all 24 major and minor keys. Now, a reasonably good piano can be "in tune" in all keys. Very few masters can actually do this. They are not technicians but tuning specialists and are also hard to find and well paid! ET is about 40yrs out-of-date with modern advancements. It looks like we have to wait for the current generation of lazy tuners to die out before we can move forward in this area and hear less percussive and more expressive pianos.
What are you talking about? European music HAS to be tuned in successive fifths due to the heavy usage of chords. For a fifth to sound in tune, it has to be in about the 694~702 cents range. The ONLY way to make this work with the circle of fifths is either Pythagorean tuning, Well temperament, Equal temperament or Meantone temperament. Anything else forces you to put an out-of-tune wolf fifth in a wildly popular chord. Example: if you tune C-E to the just 5/4 ratio, you cannot also have a just 3/2 ratio between C-G (used in the C major chord), G-D (G major), D-A (D minor) and A-E (A minor). Having perfect fifths between C-G-D-A-E forces you to tune C-E to 81/64, not 5/4. So something has to give, and any compromise such as distributing the wolf fifth gap evenly results in a temperament.
Thank you. Not an easy subject to explain. But by the way, it`s "fundamental", "actual", and "temperament", not "fundemental", "actuall", and "temprament", (though I see you have the correct spelling in the title, though not the video). Once a teacher, I suppose....
I have a question that I hope somebody knowledgeable can shed some light on. How did they manage to measure the ratios? Did they have tools? Because our modern digital tuners didm't exist back then, so how did they know the difference in frequencies? If it was all done by ear, then that is simply astounding.
You can use divisions of a string with a ruler, like a monochord, and you will have precision ratios. Also the harmonic series naturally follows the mathematical ratios so overtones make it super easy. For equal temperament there were mathematical models that were translated into practice.
What about woodwinds? I’ve been editing and spot tuning individual clarinet, oboe and bassoon parts for a client and I’m noticing that when I go to tune/correct individual blatantly out of tune notes, equal temperament tuning sometimes sounds out of tune with the pro template track. Your thoughts, please? 💭
Woodwind groups often adjust over the root of the chord. If they were individually recorded that's less likaly. Not sure what pitch correction software you are using, but I've had them be blatantly wrong before. As always for correction go with your ears. Any particular instrument throwing you off?
@@NathanNokes, Yeah, pretty much almost all of the woodwinds, and one brass instrument. The track I’m working with has adults from a community college playing individual parts from home. The instruments consist of: clarinets, a bass clarinet, oboe , bassoon, flute and what sounds like either a French horn, or baritone. I’m using Nutone (Pitch correction) inside of FL Studio. It’s very similar to Melodyne 5. FL also now comes with a tuner. But like you said, I’ve been also using my ears . I’ve just been really surprised at the results of the pitch correction plug-in and tuner as compared to what I’m hearing.
@@JeffoftheShout Can you set your FFT BIN size and windowing in Nutone? FFT's have to measure the change of the wave over time in samples, so longer is more accurate in pitch fidelity, but slower in response time. They normally window them to get around some of these issues. Good luck!!!
Equal Temperament (aka Pythagorean) didn't catch on until recently because it only took a few seconds to find out that equal temperament (all notes w/ the needle in the center of the tuner) is actually outta tune. Pythagorean & Equal Temperament are the same
Wow that ending bit about "ruining tonality" really struck a chord with me. I can definately see how the "leveling out" of tonal accuracy would be viewed as a loss of perfect tonal purity. Very resonating. I think, however, I've heard that there was an age where church organs would be built upon command of surreal complexity and painstaking intricacy, so to "naturally" blast out every single hundreds of the notes with near perfect tonal accuracy, so it isnt impossible to achieve
Even advanced pianos a long time ago understood the expressive strangle ET would have on the music and tone of the piano and tried a 17 pitch octave. The black keys were tuned to truer sharps and flats by splitting those keys 1/2 way back so that the top would be a sharp and the bottom a flat (i.e. D# and E-falt). A technician would understand how long it would take to tune one of theses and each treble tone would not have room inside the instrument for the three unison strings per pitch like we have today. Try playing highly technical music on one of these also.
The visual display at 8:07 is amazing! I've never seen it illustrated that way. Thank you!
I agree
Great long-lasting video, hope it stays here forever.
So........, there were some really, really smart people with really, really good ears before the invention of the electronic tuner.......
the electronic tuner does not give you equal temperament
Major Tom how so?
@@ev4836 equal temperament didn’t mean what it means today. Electronic tuners give you the equal temperament as of today, but the equal temperament back in the day wasn’t the same. To solve the confusion, people sometimes call the old equal temperament the “well temperament”.
Idk but they still have a tolerance.
a lot of them just say “440” and whatever with no decimal places
@@briansun6336That statement doesn’t mean anything unless you explain the difference .
7:05 - Galilei, not Galileo.
His dad's name was Vicenzo Galilei. A lutenist.
cool video; music theory is just that, a descriptive (not prescriptive) theory. alot of what we think sound good happened thru conditioning.
Workoutfanatic787, That was the best comment I have heard yet. Things seem to taste, feel, smell, look, and sound correct because of our conditioning (think about what you liked as a child and what you have learned to like as years and experiences added up). That's a big reason why we "cuss" and "discuss" our preferences daily.
But the other issue of natural born senses should not be ignored as well. Maybe even used as a measuring tool to see how far-out our life-conditioning experiences can take us before we begin to reject.
Thank you so much for this explanation.
That diagram at 7:59 is perfect.
It is? How can it be? If the pitches are a certain value (such as A4 = 440 Hz), why is there a band for each note? What do those "blocks" mean? To me, the chart causes confusion to some people because it is implying that anything within that block is that note but that is not true. There are 1/4 tones in between our 1/2 steps (C, C#, D...)
The kind of video one must watch 10 times to fully understand. Thanks though.
Nice video but, when you are talking about equal temperament, you mention Vicenzo Galilei in 1584 while you are missing the spanish composer and theorist Bartolomé Ramos de Pareja (c. 1440- 1521/22) the first one who talked about equal temperament in "De musica practica" (1482) and the one who introduced this idea in Italy during his residency in Bologna and Rome.
Here you can find the treatise imslp.org/wiki/Musica_practica_(Ramos_de_Pareja,_Bartolomeo) Although it is written in latin you can see the ilustrations which exemplify his theories.
Anyway, great work with the maths and ratios.
Great video. Knowing that equal temperament provides the ease of being able to transition into other keys makes me grateful.
What if I tolf you that Equal Temperament was invented first in China by Zhu Zaiyu (also romanized as Chu-Tsaiyu. Chinese: 朱載堉) in 1584.
en.m.wikipedia.org/wiki/Equal_temperament
So calling Equal Temperament as Western tuning is misleading
@A W
I dont care that you dont care lmao, fact is fact. China invented the tuning earlier than Europe so it is misleading to call it western tuning, end of story
@A W you're so pathetic, definitely a loser in real life.
Absolutely EXCELLENT ! Thank you. Well, indeed very well, presented, too. I would like to hear you lecture on this topic using a keyboard to give us examples.
thanks. I just wish you would've added musical examples as you went along
When did all instruments get re-tuned to Equal Temperament, in other words when did equal temperment start to be used
being able to play and modulate to any key is more important than technical perfection.
Very interesting!
Thank you, that was very helpful! :)
Did I use too many myltisylabic words?
8:00 saved my life!
If the fifths are out of tune on the modern piano, and a string player tunes their A to the piano, would the string player’s open strings be out of tune to the piano?
The point is that without a system that allows for comprehensive modulation then we could never have had the history of Western art music. None of your favourite composers from Bach to Schoenberg could have functioned ( get it?) Anyway no altered harmonies no interesting notes outside the key from Bach to present. Everything from Jazz to Copland from Beethoven to Bartok from mature Mozart to Debussy. You arent exactly conveying what's exciting and fundamental about this subject.
The two figures frequently credited with the achievement of exact calculation of equal temperament are Zhu Zaiyu (also romanized as Chu-Tsaiyu. Chinese: 朱載堉) in 1584 and Simon Stevin in 1585. According to Fritz A. Kuttner, a critic of the theory, it is known that "Chu-Tsaiyu presented a highly precise, simple and ingenious method for arithmetic calculation of equal temperament mono-chords in 1584" and that "Simon Stevin offered a mathematical definition of equal temperament plus a somewhat less precise computation of the corresponding numerical values in 1585 or later." The developments occurred independently.
Kenneth Robinson attributes the invention of equal temperament to Zhu Zaiyu[6] and provides textual quotations as evidence. Zhu Zaiyu is quoted as saying that, in a text dating from 1584, "I have founded a new system. I establish one foot as the number from which the others are to be extracted, and using proportions I extract them. Altogether one has to find the exact figures for the pitch-pipers in twelve operations."Kuttner disagrees and remarks that his claim "cannot be considered correct without major qualifications." Kuttner proposes that neither Zhu Zaiyu or Simon Stevin achieved equal temperament and that neither of the two should be treated as inventors.
i'm Just telling the fact. China invented the tuning earlier than Europe so it is misleading to call it western tuning.
Yes it was first discovered (i wouldn't' say invented) in china. But it isn't misleading to say that it became the prominent western tuning. After all this video details changes in tuning in western systems, and China didn't see any major adaptation of the system.
The global spread of equal temperament is sometimes viewed as a form of western imperialism.
@@NathanNokes exactly -- western music put it to use to create extremely complex harmony; while perhaps found a few years earlier in China it didn't change the course of Chinese music the same way.
Quite fashionable to say white man neither invented nor discovered anything.
awesome videos man. Also nice tap reference.
Without a system that allows for comprehensive modulation then we couldn't have Bach as we know him (as the fellow who set the stage for the entire subsequent history of Western Art Music till today including Jazz.) That history could accurately be discribed as a composer driven high speed power dive into higher and higher levels of chromaticism expressed both virtically and horizontally through modulation and chromatically altered harmonies and other methods of allowing more and more of those wonderfully subversive notes outside the key in thereby increasing the expressivity or ambiguity of the music untill a point a actual saturation was reached in the early 20th century. Bernstein famously calls this the 20th century crisis. In order for composers to continue to increase chromatic density after this point then the conventions of diatonic containment had to be more or less done away with; enter modernism. So without keyboard technology then no Bill Evans or Igor Stravinsky or Arnold Schoenberg or Bartok or Samule Barber or Charlie Parker or Gill Evans or or.
You are perfect, very useful video. Many thanks for sharing>
The lute players are called lutenists, not lutists.
This is the most pivotal sailent characteristic of Western music.
Nice work! Well narrated, well-illustrated, well-produced. This is a complicated subject for non-musicians like me, and this is one of the best expositions of it that I've seen.
Thank you.
Nicely explained for sure...I now just need a reason for ET and I don't find a valid one anywhere on the Internet. The professional musicians I have spoke with also don't know of any valid reason to use equal temperament on pianos, organs, lyres...(instruments with 12 tone octaves that have fixed pitch).
thank you for the explanation i has been a struggle with my music assignments you have me some understanding about the tuning and temperaments please keep explaining and give a few examples please
Hello Nathan, Nice try. I think it helps novices (as you can see by earlier comments) but watch out next time for inaccuracies that confuse those who may have previously understood the issues from a more exacting source. 1) Just Tuning is NOT a temperament: Pythagorean Tuning is NOT a temperament and True Tuning is NOT a temperament due to the fact that all intervals sound genuine. YES. Mean Tone and ET are indeed temperaments. So be careful with your nomenclature! You are right that it is not possible to use Just Tuning in a 12 tone system (which is NOT our modern system - but only that which is used on limited keyed or fretted fixed pitch instruments). Choirs and acoustical ensembles in western music do not limit themselves to a 12 tone system. They actually do adjust for the differences between G# and Ab (as well as other #s and flats) who's differences you explained well.
2) In Pythagorean Tuning the octave is NOT preserved but the "perfect consonant" lesser intervals are (fourths and fifths): This is a problem and the reason we have the "Pythagorean Comma" or discrepancy.
3) In Equal Temperament the octave (in theory) is preserved. On tightly wound string instruments like the piano (Klavier) the harmonics are out-of-tune and therefore the octave is generally stretched to sound in-tune. The tritone IS in-tune by the way and the minor thirds (major sixths) do sound in-tune. The other intervals are indeed out-ot-tune as up say.
4) Pythagoras did define the major third as the ratio of 1.25:1 not 81:64. You will get that ratio of 81:64 if you tune a 12 tone system to a circle of Pythagorean fifths, yet Pythagoras determined that the 1.25: 1 ration was the major third and that it sounded genuine to the trained and untrained ear. We find different ensembles actually prefer different sized thirds depending on the energy that is required from both harmonic and melodic movement in a particular situation. So major thirds smaller and slightly larger are often interchanged in actual performance (even when an equally tempered instrument is used with voice or instruments that can adjust "on-the-fly".
Thank you for taking the time to comment.
Oops I did let temperament slip out for just intonation.(writing making graphics shooting and editing is time consuming) I'll add a square text correction.
As for choir tuning to just intervals I'm very well aware of this. It is actually a relatively complex phenomenon and some American ensembles do better then others (I've heard some fairly sharp 3rds in many performances.)
That said the video is intended as an introduction. Sometimes pedagogy must simplify and approximate structures. Just like we typically don't introduce Einstein before we introduce the Newton(even though the later was slightly wrong and Einstein fixed it. People need to know about equal temperament being off just intonation before they learn how not fixed pitched instruments adjust between them.
I didn't even have enough time to discuss Partch and Young or breakout calculus. :-)
Play an electronic keyboard -- which is pre-tuned perfectly to A-440. thoughout. And to me, the higher register sounds flat. Because it is.
_-WIKIPEDIA GUY_-_ do not listen!
do not listen! We have more than 2 temperaments here. for example 1/4 middle tone temperament. This is just compromis between other tonal systems... We know pytharogean tonal system and also didymic tonal system. Didymic tonal system was created for minor/major need for playing music but didymic has a lot of problems and if you play in didymic tonal system you need to re-tune your instrument for each one key... We hear wolf tone on the cello, especially on the G string on the e tone, specially in the fourth position of play. You totally mixed it up and your video is a total garbage! Do not listen this overwhelmed guy. sorry!
Thank you I learned a lot
Ha ha.. we would have done jazz or other modern music?? .Here says a guy in who does not even play a key to show. You can do better. Adiós forever buddy..
Nathan Nokes There's a true temperament Guitar which is an in tune version of an equal temperament Guitar.
Great video, buds. You understand the importance of explaining any/every term/concept you introduce into your topic, which is so important...and appreciated.
Also, I loved that sick reference to the ever famous Mach piece: Lick My Love Pump
Great video. Thank you!
I have a question: "in Pythagorean tuning the Major 3rd was out of tune"... compared to what? What is a Major 3rd in tune and how did Pythagoras know that his system yielded an out of tune Major 3rd?
an "out of tune" major third would be out of tune in reference to the frequency ratio 5/4, which is the just intonation major third:
pages.mtu.edu/~suits/scales.html
If you compare that ratio to others you can hear the difference (major thirds on piano for example are a little sharp compared to 5/4), and too my ear sound a bit more dissonant (while being totally acceptable)
Thanks for this vid - I found it informative... I only have one issue with the commentary, and that is when you said that Just Intonation is NOT a good way of tuning. You need to be careful here because yes JUST INT. is not good if you want to shift into different keys, but you are totally forgetting (or perhaps were never aware) that there are many types of music which simply remain in ONE KEY. Indian Classical music for example. So you need to quality what you are saying, and do not mislead people into automatically writing off Just Inton.. Just Intonation is GREAT, and we should try to return to it. On the other hand I agree that Equal Temp. resulted in some great music... Jazz, Rock, etc etc...
Great but ...useless!
There are a bunch of amazing works in different forms of just intonation written over the last 50 years. Have a go before you label something as "useless". The problem is usually when people only want to deal with 12 tones, whereas just intonation tends to lead to far more pitches per octave. This can be a pro, not just a con. Also, many non-fixed pitched musicsare performed in or informed by just intonation - barbershop, choral singing,string quartets, dronal music, overtone singing, folk musics from around the world. Hardly something I would call useless. Thousands of years of music in the making.
+edwardpowellmusic Sorry to say that, but your conception of good intonation is so poor and personal...If you play any music in you head must be clear where to play ALL notes, not only for a specific tonality! It is crazy to think that in each tonalyty we must use different places for the same notes! This way is not universal and it mislead people!
+Cam Taylor You forget that the progress exist and this Just intonation is too old to be progresive...But it is not true about the 12 tones in an octave! Absolutely not! It is like you change the 12 hours in a day...please stay logic!
Neither time nor music is as set as you think. There are plenty of adherents of decimal time and should it ever catch on it would be no more annoying than when we switched from lbs and oz to kgs. (Also there are 24 hours in the day not 12) anyway there are 60 minutes in a hour so it's perfectly valid to say a day is made up of 48 1/2 hours. X-D
As to music that's even less set in stone.
Arabic music has 24 tones in an octave. Thai classical music uses just seven roughly evenly spaced tones. Indian classical music uses 12 tones but those tones vary slightly depending on the Key.
In the West we settled on 12-TET because it's a good enough solution.
Music is compromise. A system where nothing except the octave is quite right versus a system requiring multiple fingerings or rapid re-tuning.
Tunning systems? Did you mean tuning systems?
Nathan, You may have learned some history behind the use of equal temperament, but you are definitely not teaching it clearly here. You are overlooking the difference between melodic and harmonic use of intervals in historical context, for starters. Then you confuse things more with use of terms such as "out of tune", and by not explaining whether you are referring to a specific interval (or which of the two notes of the relation is "out" to the other), or an entire tuning system, and it gets worse from there. I went to your demo video for sound examples and found myself not able to follow your "lessons", because you are playing two different "e"s from different tuning systems at the same time, instead of letting us hear the different interval sizes between a major third in just vs. pythag. intonation systems, for example. Please give yourself time to get more clarity into your explanation, as well more basic details on the size of intervals that people can really measure with their own ears, and don't need to be told are "out of tune".
The notion out of tune is not possible to avoid! All people knows that it is impossible to use all intervals just in the same time. We do a compromises all the time. The true questions is how much to be out from the just intonation.
But also we must know that the just intonation is good only in theory! Human ear don't apreciate the just octave nor the so narrow major third...Officialy only the classic equal temperament permits to stay nearly possible to Just intonation but it is possible to do better! I have a solution wich nobody want to listen or approuve, no problem for me! My new equal temperament works very well on my violin and it is enought for my satisfaction...
thank you Nathan, wish you could've known my genius late husband renown Master Piano Restorer Gary Sage of Carmel, CA
Thank you.
"Without equal temperament we wouldn't have modern music"
So, nothing of value would have been lost
Very Nice Video
A lot of these videos do not address the limitations of the keyboard design and I'm glad to see that you mentioned split keyboards
It's a great shame that we settled on the 12 note Halberstadt keyboard.
Also, lute players were not all were using equal temperament. John Dowland had a temperament of his own that he championed.
Pythagorean tuning is why 3rds were considered dissonances and usually resolved quickly if they were used at all.
While it's impossible to say whether or not 12 tone equal temperament "ruined" tonality it certainly limited it. One could only speculate how music would have developed had we settled on 31 tone equal temperament (which is a very close approximation of meantone). The 5ths are squeezed and the 3rd and 7th harmonics are almost indistinguishable to pure.
Someone explain to me.
What's the problem? Some intervals work but others don't?
A "perfect" interval would be one where the frequencies of the two notes are related by some simple ratio. For instance if one note's frequency is exactly 3/2 the frequency of the other note's frequency (a "perfect" fifth interval). This is important because the two notes then have a natural relationship between them, both tones are natural harmonics of another note, one octave down from the lower note. If something were vibrating at this lower note, you'd naturally expect it to also produce these harmonics, which in principle means the two tones together should sound pretty natural and comfortable due to the close, fundamental physical relation between the two frequencies.
The challenge is that if you try to build the whole scale across multiple octaves out of "perfect" intervals, you wind up with some intervals that are far from "perfect". Going up an octave should always be doubling the frequency. If you try to build the scale according to simple ratios (for instance in Pythagorean, where a fifth is 3/2 and a major second is 9/8) you can't continue those same intervals and reach a perfect octave (you can multiply by 3 and divide by 2 as many times as you like and will never reach something that exactly equals 2). Also, using the same interval at different points on the scale might not produce the same effect either, depending on the tuning system being used.
Equal temperment is a trade-off: The benefit is that a certain interval played at different positions on the scale will generally produce the same effect - a major 5th will be a major 5th regardless of where in the scale you start it. But *none* of the intervals, apart from octaves, have that integer-ratio relationship. The half-step interval is the 12th root of 2 - a transcendental number. A major fifth wouldn't be exactly 3/2 times the frequency of the lower note, it'd be around 1.498 times. A major third wouldn't be 5/4 (1.25) times the frequency of the lower note, or even 81/64 (1.266) times the frequency as in Pythagorean tuning, but the cube root of 2, around 1.26 times the frequency of the lower note.
So in equal-temperment tuning none of the intervals other than octaves will have that super-pure, clean-sounding natural relationship between the tones. But the trade-off is that you can move freely up and down the scale, modulate to different keys, etc. and still produce the same effect. And when you're used to hearing one particular tuning system, you expect it and it tends to sound natural to you. Or maybe you just don't know what you're missing...
Great topic and video!
2:09 - “just temperament”: Careful! Just Intonation is a *tuning* , yes, but *not* a temperament. Temperaments are tunings that systematically compromise pitches *away from Just Intonation* mostly to allow you to play in a variety of keys.
As Ivor Darreg amusingly put it, saying “Just Temperament” is like saying “dehydrated water”! 🤪
There used to be a text notice correcting the misspeak. But UA-cam disabled that feature. So that's fun. It still isn't as bad as an error as I have seen in a few textbooks or academic journals, but is still embarrassing none the less.
What in the world is TUNNING ? (see the violin picture @42 seconds ).
A basic tip for filming: don`t have the speaker straight in line with a window .
Think about my open G on the electric guitar
Its tuning not tunning ;)
Neat presentation man, really appreciate your effort!!! :) THANKS!
Keep up, mate!
"coda"??? good move...I like so much you video....hugs from Ecuador
Hey PaVelMan: Hugs back to Ecuador!
Why is it called diatonic? Heptatonic is also a more obvious, but lesser known, name for these scales.
Couple of small points it's not called just temperament is called just intonation because none of the notes are tempered, I.e altered, these are the natural notes from the harmonic series
and the book is called *How equal temperament ruined Harmony* not tonality
Ah yes temperament vs intonation. There used to be a text notice correcting the misspeaking. But UA-cam however disabled that feature.
Thank you so much. I Feel less stupid now
I feel more stupid. :)
0:41 - “Tunning” Systems? OK, never mind.
this isn't an issue for fretless instruments, correct? eg violin, cello, human voice
Unless they're being played in concert with fretted instruments like keyboards, yes?
Not an issue for those instruments. But it is a factor in Brass instruments. Since natural horns will play the harmonic series. French horn players use a combination of valves embouchure and their hand in the bell to adjust their tuning to match other players
@@NathanNokes thank you for your reply! This topic is endlessly fascinating to me, and I'm just at the front end of learning...
Nice presentation. I would dispute a couple of things however. 1. That pythagorean intonation was the dominant system for thousands of years. Pure Pythagorean tuning is quite an unnatural system and I think most early music focused around voice and non fixed pitch instruments. The tonic was also generally fixed for the performance so there wasnt a need for a compromise to natural intonation. Indian Classical and Georgian choir music would be extant examples.
12-tone equal temperament works because 12 is a very easy number to work with and is the smallest number of equal divisions of the octave that is able to adequately approximate all of the frequency ratios in just intonation.
Very informative, thanks!
I agree with comment about the brave stroke of genius in adopting a visual display approximating through the difficulties of explaining 12 tones really ?.... expressing an Art form and Life with mathematics as the queen of science!?! Congratulations. You have crossed thousands of years of thinking and 'aural problem solving in tuning '. through this attempt in giving some clarity to this simplification to explain to non-professionals.
You started out talking about "equal temperament" and then suddenly in the same breath you started using the term "just temperament" without explanation. Do these terms mean exactly the same thing or are they two different things? This made your explanation difficult to follow after that point.
I'm not sure, but I think just temperament is when it's tuned so just one key is in perfect harmony.
Marian Kotúč Thank you very much Marian for that explanation. It took six months to get an answer but I think I understand now. When you use the term just intonation instead of just temperament it makes more sense and I see the difference now.
Great video! Shared it with my students!
Musicians can be so temperamental.
The rubber band explanation of overtones was enlightening! I paused the video, leaned back in my chair, and said "WOOOOAAAAAHHH....."
After 5 minutes I was totally lost
Love the Spinal Tap reference
These videos are phenomenal. I'm surprised they don't have more views. Keep it up
It´s not Galileo, it`s Galilei, Vicenzo Galilei. I think you also confused the pithagorean comma with the sintonic comma.
Excellent
66 years old, playing since 14, I only understood very little, as to what I just learned from Nathan EXCELLENT Explanation.specially the visual display at 8:07 Thank You so much Nathan.
what a brilliant video
Up until late 19th century, Well Temperament is still used, they are not equal temperament.
Yes, but the 19th C. is very not modern.
@@NathanNokes I said LATE 19th century. Well into 1910-20s the aural method of equal temperament still wasn’t wide spread.
With those heavy constructed "modern" pianos, it is very much nonsence to use other than equal temperament....
appreciated
I lost you.
Maybe its just me. Idk.
Good video though. Might need to watch it a second time.
Yes, the historic tunings can sound great in some keys, but very bad in more distant keys. The beauty of ET is that is sounds equally bad in all keys!
wonderful. thank you for all this great information!!!
3:28
Octaves are not perfect in Pythagorean tuning.
Octaves are perfect in Pythagorean tuning. Sethares, William A. (2005). Tuning, Timbre, Spectrum, Scale, p.163
Octaves are perfect; it's that you get 11 of 12 perfect fifths justly tuned but then you have a "wolf" fifth that is severely out of tune.
This is a good presentation. True Tuning (which is not tempered) was used by the classical Greeks in their modes. By taking the seven tones produced by the True Dorian octachord and the True Tone C Major scale and obtaining the five remaining tones formed from the "geometric mean tones" of those produced already (referenced to prime [C-128Hz]) we get a 12 tone scale that is aurally genuine in all 24 major and minor keys. Now, a reasonably good piano can be "in tune" in all keys. Very few masters can actually do this. They are not technicians but tuning specialists and are also hard to find and well paid! ET is about 40yrs out-of-date with modern advancements. It looks like we have to wait for the current generation of lazy tuners to die out before we can move forward in this area and hear less percussive and more expressive pianos.
What are you talking about? European music HAS to be tuned in successive fifths due to the heavy usage of chords. For a fifth to sound in tune, it has to be in about the 694~702 cents range. The ONLY way to make this work with the circle of fifths is either Pythagorean tuning, Well temperament, Equal temperament or Meantone temperament.
Anything else forces you to put an out-of-tune wolf fifth in a wildly popular chord. Example: if you tune C-E to the just 5/4 ratio, you cannot also have a just 3/2 ratio between C-G (used in the C major chord), G-D (G major), D-A (D minor) and A-E (A minor). Having perfect fifths between C-G-D-A-E forces you to tune C-E to 81/64, not 5/4. So something has to give, and any compromise such as distributing the wolf fifth gap evenly results in a temperament.
TUNNING
"How Equal Temperament Ruined HARMONY (and why you should care)". Not Tonality, Harmony. ;) Awesome video!
very nice just a little note ;) you wrote tunnings instead of tuning...
Thomas Young > ET
Awesome video and explanation Nathan. Just learning to tune my piano and I love having this foundation!
Is there notation for G# and Ab when using meantones?
Nice!
Dang.
Thank you. Not an easy subject to explain. But by the way, it`s "fundamental", "actual", and "temperament", not "fundemental", "actuall", and "temprament", (though I see you have the correct spelling in the title, though not the video). Once a teacher, I suppose....
Long live Vicentino and his 31 note per octave meantone!
I have a question that I hope somebody knowledgeable can shed some light on. How did they manage to measure the ratios? Did they have tools? Because our modern digital tuners didm't exist back then, so how did they know the difference in frequencies? If it was all done by ear, then that is simply astounding.
You can use divisions of a string with a ruler, like a monochord, and you will have precision ratios. Also the harmonic series naturally follows the mathematical ratios so overtones make it super easy. For equal temperament there were mathematical models that were translated into practice.
@@NathanNokes gosh that is fascinating. Thank you for answering my question! ^-^
there could still be jazz, it would just sound different
Very clear explanation thanks.
What about woodwinds? I’ve been editing and spot tuning individual clarinet, oboe and bassoon parts for a client and I’m noticing that when I go to tune/correct individual blatantly out of tune notes, equal temperament tuning sometimes sounds out of tune with the pro template track. Your thoughts, please? 💭
Woodwind groups often adjust over the root of the chord. If they were individually recorded that's less likaly. Not sure what pitch correction software you are using, but I've had them be blatantly wrong before. As always for correction go with your ears. Any particular instrument throwing you off?
@@NathanNokes, Yeah, pretty much almost all of the woodwinds, and one brass instrument.
The track I’m working with has adults from a community college playing individual parts from home. The instruments consist of: clarinets, a bass clarinet, oboe , bassoon, flute and what sounds like either a French horn, or baritone.
I’m using Nutone (Pitch correction) inside of FL Studio. It’s very similar to Melodyne 5. FL also now comes with a tuner. But like you said, I’ve been also using my ears . I’ve just been really surprised at the results of the pitch correction plug-in and tuner as compared to what I’m hearing.
@@JeffoftheShout Can you set your FFT BIN size and windowing in Nutone? FFT's have to measure the change of the wave over time in samples, so longer is more accurate in pitch fidelity, but slower in response time. They normally window them to get around some of these issues. Good luck!!!
Equal Temperament (aka Pythagorean) didn't catch on until recently because it only took a few seconds to find out that equal temperament (all notes w/ the needle in the center of the tuner) is actually outta tune. Pythagorean & Equal Temperament are the same
0:40 it says tunning instead of tuning :p
Your laptop screen exposed you a little bit... otherwise great video
Wow that ending bit about "ruining tonality" really struck a chord with me. I can definately see how the "leveling out" of tonal accuracy would be viewed as a loss of perfect tonal purity. Very resonating. I think, however, I've heard that there was an age where church organs would be built upon command of surreal complexity and painstaking intricacy, so to "naturally" blast out every single hundreds of the notes with near perfect tonal accuracy, so it isnt impossible to achieve
Even advanced pianos a long time ago understood the expressive strangle ET would have on the music and tone of the piano and tried a 17 pitch octave. The black keys were tuned to truer sharps and flats by splitting those keys 1/2 way back so that the top would be a sharp and the bottom a flat (i.e. D# and E-falt). A technician would understand how long it would take to tune one of theses and each treble tone would not have room inside the instrument for the three unison strings per pitch like we have today. Try playing highly technical music on one of these also.
struck which chord lol?
I hate equal temperament