with really simple harmony this might work, but equal temperament allows for lots of jazz harmony that wouldn't be possible with just intonation, like 6-9 chords
@@benknightguitar Well, it has to do with the orientation of the tensions vs the root of the chord. Say you've got a C6-9 chord. You've got a C on the left hand and on the right hand you've got, in ascending order, E-A-D-G. For the sake of the E being more consonant with the C, the E is a just a touch flatter than usual. This sounds good against the C, but then the E sounds like utter dog ass next to the A, which is now no-longer a perfect fourth away. Then you have the G and the D which are also a fourth away, but then you have an issue with how the G and D are adjusted to be more consonant with the C as well. The fourth intervals sound awful when isolated. If you adjust those intervals, then the rest of the notes don't line up with the chord well. It's just dog ass all the way down. You could try to tune all of the intervals in the chord to absolute perfect fourths, but then you'll find that over a couple octaves the notes on the upper and lower end suddenly no longer resemble the notes they're supposed to be. They can end up a semi tone off entirely, which ruins the chord and your sanity. Equal temperament is the only way to avoid ripping your hair out, at the cost of all those tasty consonant overtones.
@@pirojfmifhghek566 That's so true. The only thing I'd like to add is that we must bear in mind that here he is using a very simple sound, quite similar to a sine wave. When using more complex sounds, like a piano, guitar, strings, etc., this vibration due to equal temperament being slightly out-of-tune is much less noticeable, if at all.
I have played piano and guitar for years and these "beats" have always annoyed me but until today I did not understand what was happening or how to describe it. I will never be able to unhear this.
It probably plays a huge role in what they call "expression" and all that abstract jazz - dynamics, volume, interval, etc. etc. all play a role in those "beats" which most likely influence "emotion" in at least a subtle way.
@@Pakkens_Backyard Dynamics and volume is the same thing and that doesn't have anything to do with temperament. This effect causes dissonance which is usually undesirable unless you're writing for a horror theme and trying to convey fear/uneasiness. Even then the beating effect from equal temperament is too subtle to use in that way. Of course the choice of temperament does change slightly how a song will sound, however most people are using equal temperament for practical reasons. "Just temperament" would be the most technically correct, however all musicians with fixed pitch instruments would have to retune their instruments each time they play in a different key.
In college I was always confused when playing strings or singing especially with a piano because the pitch always sounded off. I especially hated piano accompaniment when in choir, and singing along with the radio I would also notice the pitch issues. Rarely my sense of pitch would closely line up with the singer's but I can't remember which songs those were. I didn't realize until recently that I'm probably sensitive to the inherent out of tune-ness of equal temperment.
When 2 tones are "out of tune" they vibrate, the more out of tune the more vibration. You'll also notice the ET version was a bit louder, because like the guy above me said, phase cancellation. You could argue the 12tet tuning is superior not just because of its broad possibilities within the music, but also a richer fuller sound created by a slight dissonance of 2 tones not perfectly matching up. The chorus effect utilises this detuning to create rich full bodied sound, and producers know about the benefits of detuning a synth to make it sound bigger.
I use that vibrating to tune my guitars once I have a good reference point. I strum E string 5th fret and open A string one after another and level out the waves until it's even.
I feel like the extra frequencies from equal temperament makes it sound oddly more complete where as just intonation sounds like a wall of perfect and soulless frequencies hitting me. I think thats probably just because I'm used to equal temperament.
slightly imperfect harmonies create a more complex waveform, which is satisfying for our brains. Just like why mix engineers always make music sound better by distorting it through imperfect amplifiers such as Neve desks.
@@Lee-xs4dj reminds me of a recording session story where the producer asked the singer to sing flat for part of the song. Had a very hard time trying to do it but he finally achieved it and was rewarded with a big hit.
@@Lee-xs4dj It's also why playing, say, 2 clarinets or saxophones or whatever other instrument together sounds drastically fuller and bigger than just playing 1.
You are a total detective, I couldn't notice that the major third was flat. Well, it's mostly because people get the emotion plaing just major 3rd chords, just wait until someone plays the just subminor 3rd chord, and then tell me if it's flat, mr. Ears.
@@nathanmcmath yes, that's because in just tuning you have perfect match between multiples of a base wave frequency (C for example), and when you compare it with equal temperment you get that wobbly sound. That wobbly thing is interference between the waves that are not perfectly multiples of each other
a 5/4 major third is fairly flat from a 12edo major third. This is one of the reasons why guitars are so hard to tune :) Historically, the process of reconciling these differences was called "tempering", but since 12edo (and the keyboard) took over the world of music theory, these subtle distinctions have been lost from the general awareness
Also so much harder at live jam sessions. Everyone is tuning, riffing, making noise. Lol. I once played a couple of minutes before I realized I made a mistake. Oh that string is loose. Lol downtuned to match another interval of a different string
This area of music is so interesting to me because I spent most of my life totally unaware of it. I assumed the notes were equally spaced by nature. Nerds and spergs in Germany figured out equal temperament and made it standard, African legends in America used that system to invent the blues, and then that American blues sound reached the docks of Liverpool and we got the Beatles. Equal temperament leads to instant key modulation and endless modality. You can jump from major to minor modes very fluidly, and that style of melody writing is the backbone of western music. When instruments became more popular, high-level composers meticulous worked with and around pure intonation and could stay within the western style, but if equal temperament was never standardized, average people would have more difficulty playing all the music of composers, and would probably develop their own kind of folk music that sounded eastern. Maybe it would be more interesting if it happened like that, but the equal temperament nerds made it possible for the public to write and play music like composers without learning the deeper physics of harmony and tuning. Anyone can get started immediately. It's like the way Apple and Microsoft standardized the computer interface and software so you don't have to learn how to code.
@@vitulus_ A good thing to note for sure - this is possible on non-fixed-pitch instruments, like fretless stringed instruments, voices, etc, where you can make very fine adjustments to pitch - you can have dynamically just-intoned performances that modulate keys while still maintaining simple harmonious relationships
wow, so much to unpack. where did you get that africans used just intonation? isnt their biggest thing was rhythm and syncopation? also, how about the fact that first ppl to equalize the intervals were ancient greeks.
@@Timbyte I think anyone with experience would avoid the beats when there is free control of frequency, in fret-less instruments and human voice. The problem is fixed tuning and mostly in harmonies that last a while. Have you seen this? ua-cam.com/video/7GhAuZH6phs/v-deo.html
Actually equal temperament always existed, but other temperaments where more popular depending on the place and year, lots of composers created their own tempdrament. In the 19th equal temperament became the standar but allways existed.
How interesting! We learned about this in school. The concept of the "saddest" minor key holds more water when you have just intonation, as the intervals sounded different than they would in equal temperament, so individual keys would - well - sound different. What do you think about the concept of microtones?
Have you ever seen the true temperament guitar? ua-cam.com/video/-penQWPHJzI/v-deo.html The fun things that money can buy! C'mon UA-cam, where's my paycheque :P
I would like to mention Arabic music, Chinese scales... I found this on a website "The most pleasing sounds to the ear are usually combinations of notes related by ratios of small integers, such as the fifth (3/2) or third (5/4). The Just scale is constructed based on the octave and an attempt to have as many of these "nice" intervals as possible. In contrast, one can create scales in other ways, such as a scale based on the fifth only" Well. Usually. For western music🎶😉🎸
Plus, a nice test. Sing the notes of a simple children's song and leave out the last note. Western people will immediately know what the last note should be, even if they don't know the song. Most eastern / Asian people, being used to different musical ladders and notes, often do not. It's a culture thing.
I couldn't hear it until you held the C major triad and pressed the pure major button, then it was obvious. Good choice of voice to explain this as well. Thanks
In "Equal Temperament" the intervals are actually in a geometric series. All the ratios are exactly the same, and that is why any piece can be played in any key, without sounding out of tune.
I couldn’t put my finger on why the just intonation sounded out of tune when actually playing music versus just playing a chord in which it’s MORE in tune, you explained it perfectly and made me realize that you have to actually tune the justonic root to fix it! My question now becomes, is there a microtonal version of the justonic temperament which eliminates the need for tuning to adjust for off-ness in different chords???
you work completely differently when you work with JI. For example, I am aware of at least 3 significantly different sounding "minor" triads. You choose different ones depending on the context required by the rest of the music. If you want to get a feel for it start listening to barbershop quartet and black gospel choir music. Both of those genres use a lot of just harmonies which arise from the practice of singing together: they are rarely notated accurately (e.g. the 7/4 version of the Dom7 chord), but they sound amazing.
I have no idea what I'm talking about here, crazy how you can just lose knowledge like that, like reading something written by someone else. Humans are so interesting.
@@PranavJoshi6687 Indian classical ragas don't change chord, much less change key The issues of changing keys in JI simply never occur and never need to be solved
I kind of like the creepy, unsettling sound that just intonation gives when you play in a different key than its tuned to. I wouldn't write a whole piece in it but maybe for one chord. The part at 1:35 especially reminds me of a creepy recording I can't remember. It also kind of reminds me of that hidden track Ambient/Secret off of the Hybrid Theory EP, maybe they used just intonation tuned to the key a semitone lower to get that sound
That's actually how temperaments are used. I.e. the Well-Tempered Clavier by Bach was written for a particular tuning scheme called Well-Temperament, though I think people debate about what that exactly meant for his time and place. So, every piece of the Well-Tempered Clavier was written to have chords land in the optimal place for the maximal effect. So, the C-major prelude that everyone knows in Well-Temperament is very harmonic with a lot of resonance because it is made up of chords that are more harmonic with one another: ua-cam.com/video/US8NHFgKxoE/v-deo.html&ab_channel=PeterWatchorn-Topic www.ethanhein.com/wp/2020/what-does-the-well-tempered-clavier-sound-like-in-actual-well-temperament/
Great demonstration. Only small thing is that this is not the only just intonation tuning (although it is definitely one of the most common ones historically). For example, instead of the flat major third with a 5:4 just ratio (which I believe was used in this video), you could use the very sharp and bright major third with a 9:7 just ratio, or a Pythagorean major third with a 81:64 ratio, etc.
I think different keys has incorporated this imperfection into their character in the history of composition. Personally I have a distinctive feel on E minor mode.
Just intonation to me sounds "cold" on a piano by comparison to equal temperment. You would have to switch to just intonation with every chord change for a song to sound okay - a lot of extra button pressing. I wonder how just intonation would sound in a song with some minor chord changes. I do love the way accapella singers sound using it becasue in that format it really shines.
Great video comparison! In my opinion, a traditional piano sound would display the beauty of just/pure intonation better though. It's fun to think about all the possibilities an instrument like this has too offer with different intonations.
It's quite the opposite when you are playing an instrument with good timbre in a good acoustic environment that brings out the overtones. ET sounds flat where JI sounds full.
So this means that in "PURE" C, all songs will sound in tune as long as there are no sharps or flats (except for the dominant B flat)? If so, I'm really beginning to catch on.
None of the notes or combinations of notes over C will have beats. That doesn't mean that all the chords in C will sound in tune - but all the notes in the scale will sound in tune with the note C (which is usually the bass note).
the "dominant" Bb is a pretty difficult note to define in JI. The ratio you want is 7/4, but that is actually about 1/3 of a tone flat from the usual definition of the flat seventh scale tone in 5-limit JI.
Alternate temperaments can be really interesting, but none of them sound as pleasing as equal temperament to me. i often wonder if its because of how i was raised
For those guys who are creating theories from other worlds to illustrate this: this is simpler than it seems. You choose a democratic tuning method, with slightly out of tune everything (equal), or a pure method, which "rounds" some chords (not necessarily C major) and pulls even more out of tune other scales. It’s so easy to understand, no need of formulas here and there. Just understand that with 12 semitones its IMPOSSIBLE to create round octaves.
@@foteinimanou5516 that's because the comment you answered is actually confusing. Octaves are generally defined by the 2:1 frequency ratio - and "round" octaves aren't a thing. What @Michael Oliveira is getting at is the mathematical fact that the way we perceive frequencies can't divide an octave into equal parts with rational numbers. Of course, you can approximate irrational numbers as accurately as you like with rationals, so some music theorists work with "microtones" to try and approximate JI with a more math-friendly framework.
with 12 equal "tempered" semitones, what was wanted was precisely to have "pure octaves" ; it is the 3rd, 4th and fifths that are not pure in the current system. (thirds are a bit "longer" (sharp) than pure, and 4ths, 5ths are a bit "shorter" (flat)) Keyboard instruments were tuned either by pure 3rds or 5ths, (C to G, then G to D, D to A, etc) this resulted in the fact that, as you progressed adjusting the intonation of each key, the resulting upper or lower octave was no longer a pure 8th (in addition, very dissonant intervals were introduced (wolf notes) in keys farthest from C natural)
This is very interesting to me, I play the piano, guitar and bagpipes. Bagpipe tuning is a subject all of its own but it is essentially tuned by ear and it has always annoyed me how even a “perfectly tuned” piano or guitar sounds slightly off to my ear vs playing the same notes on the bagpipes.
This is fascinating. Aren't we lucky that it's even possible to produce an equal temperament where the errors are small enough so as not to be very noticeable in normal music?
Amazing demonstration! I do wish you would have played other major chords while in pure C major to get the affect of how far off those chords would be too. Or are they all equally as off as the C# major chord, in terms of frequency ratios?
I wish I did too. Maybe one day when I can borrow it again :) C# and B are definitely the most offensive. The annoying beats comes and goes after that.
This is the clearest demonstration I've ever seen of this, thank you. So this need to switch that you demonstrated is why we need Hermode tuning, which is supposed to do the adjustment automatically?
I don’t hear it on the first one 😓. I thought at first that the vibration underneath the notes at disappeared, but then you played the, side by side again and it seems I was wrong
Does all the diatonic chords in a justly tuned major scale ring "perfectly" or does the reference pitch somehow change even between keys in the same scale? What I'm actually wondering is how "easy" it is to write a diatonic chord sequence using just intonation - do all chords share the same tuning?
This is a genuinely hard question to answer because the notion of a scale becomes problematic in JI. If you listen to barbershop quartet music, you might begin to see what I mean. The voice parts are clearly staying in a particular set of related tones, but they also migrate around quite a lot - and then they use an intentional "key change" to bring everything back together again. So with that said, if you use the fractions {1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8} as your "major" scale, then you will have perfect 4:5:6 major chords for I, IV, & V, but you will get a much more complex 135:160:192 sound for the ii chord than the "perfect" 10:12:15, and your iii chord will be 15:18:20 which is much simpler and more "open" sounding than the ii chord. The vi chord falls somewhere in between with a 20:24:27. The diminished triad is particularly problematic with the 45:54:64 harmonic ratio - the problem is that defining the diminished fifth in JI is not very straightforward, and the 7-limit diminished fifths sound a lot better than the available pair of 5-limit candidates. So TL;DR - the major chords are pretty OK, the minor chords are a bit all over the shop. But if you're ready to take a more flexible view of what a "scale" means, you can have a lot of fun
Excellent. I'm still foggy on why we have them. Why aren't all Cs, Es and G's (well all notes really) just Cs, Es and G's instead of this tune or that tune only if it's a Tuesday with a full moon type of scenario? 😟
@Boodysaspie Ya, no surprise there, in fact I often try and talk my professional musician friends to tune in 432 which is mathematically correct, not 440, 444 etc. because some paradigm in some day wanted a change. Apparently/purportedly 440Hz was chosen by some King as it allowed more control over people. People would act too authentic listening to music at 432 vs 440 which just sours the milk enough so we enjoy the music but are still controllable. Just like fluoride in the water. It makes people more docile and was a good way to get rid of industrial waste. Hmm, even Crisco. Designed for submarine engine lubricant but an unnamed company ended up with it and figured using it in cooking would get rid of the supply. Ooops a ramble rant.
Ever since I learned of equal temperament, it has kind of frustrated me. I heard perfect harmonies once, and suddenly it nags at me whenever something is just slightly out of tune. But I do not know enough about music theory, and cannot afford lessons or tuition, thus I cannot navigate the world of pure intonation alone. I must begrudgingly rely on equal temperament just to get by. This reliance haunts me every time I try to play music.
The patch you're using is almost a sine wave so the pure tuning isn't as obvious, although the C# major does sound bad. A richer sound would be more obvious.
Great video! I just (heehee) wanna mention, Just Temperament isn’t really a thing; it’s Just Intonation. Tempering means altering. In Just Intonation, none of the notes are tempered. They’re all just.
I always tune my guitars by ear to get best result over the complete neck and you can easily play on the 12th fret, Barre chords, as well as at the neck or nut. Sometimes if tune with device, only the strings, this won't always work out well. I tune by ear, on the 5th fret, the flageolets after and then finally couple of strums to test result Of course sometimes the guitar could use a little recalibration of the neck 🎸😏.
Yeah, I do that too with 5th and 7th harmonics of the adjacent string. I think that generates the pythagorean tuning (?). It makes open string E sound heavenly :)
Recently ran into a person who tunes their guitar by ear using chords and he was wondering why after he was done, the chords sounded in tune but the tuner was registering his open strings as out of tune. I told him about just vs equal temperament and I think it blew his mind. It's something that most people never even entertain as a possibility ... there's an assumption that the 12-tone system is somehow perfect and when it's so clearly demonstrated to be flawed it's pretty eye-opening (ear-opening?).
Sorry to nitpick, but the phrase “Just temperament” or “pure temperament,” is an oxymoron: A tuning is either Just or tempered. You could say it’s “just intoned.” Nevertheless good work!
As you nicely demonstrated, just intonations sound well only in the one key an instrument was tuned, but prevent transposition and modulation as their inherent inconsistencies make them sound awful in other keys. Equal temperament, on the other hand, 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 bad in one key as in any other key. But what you might not 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. And it's NOT equal temperament. 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 nineth 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. 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.
For me, certain notes in unharmonised melodies often sound wrong in equal temperament. I generally tend to prefer chords in just intonation, (or compromise intonation).
Just imagine a dynamic pure tuner that follow the harmonic structure of the piece. Every modulation would get it's optimal tuning ratio.
with really simple harmony this might work, but equal temperament allows for lots of jazz harmony that wouldn't be possible with just intonation, like 6-9 chords
@@jimbrandom2820 can you explain why a 6-9 chord is impossible?
@@benknightguitar I am also interested, have you found an answer?
@@benknightguitar Well, it has to do with the orientation of the tensions vs the root of the chord. Say you've got a C6-9 chord. You've got a C on the left hand and on the right hand you've got, in ascending order, E-A-D-G. For the sake of the E being more consonant with the C, the E is a just a touch flatter than usual. This sounds good against the C, but then the E sounds like utter dog ass next to the A, which is now no-longer a perfect fourth away. Then you have the G and the D which are also a fourth away, but then you have an issue with how the G and D are adjusted to be more consonant with the C as well. The fourth intervals sound awful when isolated. If you adjust those intervals, then the rest of the notes don't line up with the chord well. It's just dog ass all the way down.
You could try to tune all of the intervals in the chord to absolute perfect fourths, but then you'll find that over a couple octaves the notes on the upper and lower end suddenly no longer resemble the notes they're supposed to be. They can end up a semi tone off entirely, which ruins the chord and your sanity. Equal temperament is the only way to avoid ripping your hair out, at the cost of all those tasty consonant overtones.
@@pirojfmifhghek566 That's so true. The only thing I'd like to add is that we must bear in mind that here he is using a very simple sound, quite similar to a sine wave. When using more complex sounds, like a piano, guitar, strings, etc., this vibration due to equal temperament being slightly out-of-tune is much less noticeable, if at all.
Impressed. Such a clear demonstration. 1000 thanks.
Same here!! Very helpful 🎉
I have played piano and guitar for years and these "beats" have always annoyed me but until today I did not understand what was happening or how to describe it. I will never be able to unhear this.
It probably plays a huge role in what they call "expression" and all that abstract jazz - dynamics, volume, interval, etc. etc. all play a role in those "beats" which most likely influence "emotion" in at least a subtle way.
@@Pakkens_Backyard Dynamics and volume is the same thing and that doesn't have anything to do with temperament. This effect causes dissonance which is usually undesirable unless you're writing for a horror theme and trying to convey fear/uneasiness. Even then the beating effect from equal temperament is too subtle to use in that way. Of course the choice of temperament does change slightly how a song will sound, however most people are using equal temperament for practical reasons. "Just temperament" would be the most technically correct, however all musicians with fixed pitch instruments would have to retune their instruments each time they play in a different key.
In college I was always confused when playing strings or singing especially with a piano because the pitch always sounded off. I especially hated piano accompaniment when in choir, and singing along with the radio I would also notice the pitch issues. Rarely my sense of pitch would closely line up with the singer's but I can't remember which songs those were. I didn't realize until recently that I'm probably sensitive to the inherent out of tune-ness of equal temperment.
Thanks. At last I can really hear the difference.
dingoswamphead yes can't find anyone on UA-cam only math dorks
to my ear the ET major chord sounds like its "vibrating", while the JI major chord doesn't
That's what he meant by "beat frequency".
yes that's literally what he's talking about. adding tones together creates phase cancellation.
When 2 tones are "out of tune" they vibrate, the more out of tune the more vibration. You'll also notice the ET version was a bit louder, because like the guy above me said, phase cancellation. You could argue the 12tet tuning is superior not just because of its broad possibilities within the music, but also a richer fuller sound created by a slight dissonance of 2 tones not perfectly matching up. The chorus effect utilises this detuning to create rich full bodied sound, and producers know about the benefits of detuning a synth to make it sound bigger.
I use that vibrating to tune my guitars once I have a good reference point. I strum E string 5th fret and open A string one after another and level out the waves until it's even.
I feel like the extra frequencies from equal temperament makes it sound oddly more complete where as just intonation sounds like a wall of perfect and soulless frequencies hitting me. I think thats probably just because I'm used to equal temperament.
slightly imperfect harmonies create a more complex waveform, which is satisfying for our brains. Just like why mix engineers always make music sound better by distorting it through imperfect amplifiers such as Neve desks.
@@Lee-xs4dj reminds me of a recording session story where the producer asked the singer to sing flat for part of the song. Had a very hard time trying to do it but he finally achieved it and was rewarded with a big hit.
It's like a singer's vibrato
@@foteinimanou5516 Not a video. All I can remember was that it was a male singer - it may have been a Motown hit.
@@Lee-xs4dj It's also why playing, say, 2 clarinets or saxophones or whatever other instrument together sounds drastically fuller and bigger than just playing 1.
My ears are so used to equal temperament, I find just intonation "sharp".
no shit, that's the point. Overtones are different.
The third is lower in just intonation, so it is actually flat...but to me just tuning also sounds more clear/transparent/thin
You are a total detective, I couldn't notice that the major third was flat.
Well, it's mostly because people get the emotion plaing just major 3rd chords, just wait until someone plays the just subminor 3rd chord, and then tell me if it's flat, mr. Ears.
then you ears are mesmerized into something wrong
@@nathanmcmath yes, that's because in just tuning you have perfect match between multiples of a base wave frequency (C for example), and when you compare it with equal temperment you get that wobbly sound. That wobbly thing is interference between the waves that are not perfectly multiples of each other
It's weird how the third sounds slightly flat on a pure tempered scale, yet the frequency ratios line up better.
a 5/4 major third is fairly flat from a 12edo major third. This is one of the reasons why guitars are so hard to tune :) Historically, the process of reconciling these differences was called "tempering", but since 12edo (and the keyboard) took over the world of music theory, these subtle distinctions have been lost from the general awareness
@@kumoyuki that's what I mean, I see your comment only now, lol but that's so true. That's why I tune by ear. You need good ears of course.
Also so much harder at live jam sessions. Everyone is tuning, riffing, making noise. Lol. I once played a couple of minutes before I realized I made a mistake. Oh that string is loose. Lol downtuned to match another interval of a different string
@@WhisperingWempe and if you have a keyboardist in the band, watch out! They're definitely going to tell you that you're the one who's wrong ;)
thats because it literally is. the third of any major chord should be about 13-14 cents flat to be perfectly in tune
This area of music is so interesting to me because I spent most of my life totally unaware of it. I assumed the notes were equally spaced by nature. Nerds and spergs in Germany figured out equal temperament and made it standard, African legends in America used that system to invent the blues, and then that American blues sound reached the docks of Liverpool and we got the Beatles.
Equal temperament leads to instant key modulation and endless modality. You can jump from major to minor modes very fluidly, and that style of melody writing is the backbone of western music. When instruments became more popular, high-level composers meticulous worked with and around pure intonation and could stay within the western style, but if equal temperament was never standardized, average people would have more difficulty playing all the music of composers, and would probably develop their own kind of folk music that sounded eastern.
Maybe it would be more interesting if it happened like that, but the equal temperament nerds made it possible for the public to write and play music like composers without learning the deeper physics of harmony and tuning. Anyone can get started immediately. It's like the way Apple and Microsoft standardized the computer interface and software so you don't have to learn how to code.
In case you're interested, classical stringed music uses just intonation, which still has key modulations, etc.
@@vitulus_ A good thing to note for sure - this is possible on non-fixed-pitch instruments, like fretless stringed instruments, voices, etc, where you can make very fine adjustments to pitch - you can have dynamically just-intoned performances that modulate keys while still maintaining simple harmonious relationships
wow, so much to unpack. where did you get that africans used just intonation? isnt their biggest thing was rhythm and syncopation? also, how about the fact that first ppl to equalize the intervals were ancient greeks.
@@Timbyte I think anyone with experience would avoid the beats when there is free control of frequency, in fret-less instruments and human voice. The problem is fixed tuning and mostly in harmonies that last a while. Have you seen this?
ua-cam.com/video/7GhAuZH6phs/v-deo.html
Actually equal temperament always existed, but other temperaments where more popular depending on the place and year, lots of composers created their own tempdrament. In the 19th equal temperament became the standar but allways existed.
This is a great demonstration of pure versus equal temperament. Thank you !
I just realized for the first time in my life that the dial tone for landline phones was just intonated.
How interesting! We learned about this in school. The concept of the "saddest" minor key holds more water when you have just intonation, as the intervals sounded different than they would in equal temperament, so individual keys would - well - sound different. What do you think about the concept of microtones?
Have you ever seen the true temperament guitar? ua-cam.com/video/-penQWPHJzI/v-deo.html
The fun things that money can buy! C'mon UA-cam, where's my paycheque :P
I would like to mention Arabic music, Chinese scales...
I found this on a website "The most pleasing sounds to the ear are usually combinations of notes related by ratios of small integers, such as the fifth (3/2) or third (5/4). The Just scale is constructed based on the octave and an attempt to have as many of these "nice" intervals as possible. In contrast, one can create scales in other ways, such as a scale based on the fifth only"
Well. Usually. For western music🎶😉🎸
Plus, a nice test. Sing the notes of a simple children's song and leave out the last note.
Western people will immediately know what the last note should be, even if they don't know the song.
Most eastern / Asian people, being used to different musical ladders and notes, often do not.
It's a culture thing.
I couldn't hear it until you held the C major triad and pressed the pure major button, then it was obvious. Good choice of voice to explain this as well. Thanks
In "Equal Temperament" the intervals are actually in a geometric series. All the ratios are exactly the same, and that is why any piece can be played in any key, without sounding out of tune.
I couldn’t put my finger on why the just intonation sounded out of tune when actually playing music versus just playing a chord in which it’s MORE in tune, you explained it perfectly and made me realize that you have to actually tune the justonic root to fix it! My question now becomes, is there a microtonal version of the justonic temperament which eliminates the need for tuning to adjust for off-ness in different chords???
Indian classical music uses microtones, and just intonation. Maybe you'd like to listen to some. Try instrumental, not vocal, or you'd be put off.
you work completely differently when you work with JI. For example, I am aware of at least 3 significantly different sounding "minor" triads. You choose different ones depending on the context required by the rest of the music. If you want to get a feel for it start listening to barbershop quartet and black gospel choir music. Both of those genres use a lot of just harmonies which arise from the practice of singing together: they are rarely notated accurately (e.g. the 7/4 version of the Dom7 chord), but they sound amazing.
I have no idea what I'm talking about here, crazy how you can just lose knowledge like that, like reading something written by someone else. Humans are so interesting.
@@PranavJoshi6687 Indian classical ragas don't change chord, much less change key
The issues of changing keys in JI simply never occur and never need to be solved
Great video! Nice demonstration!
This is one reason I love performing with a chamber choir or ensemble without keyboards or fretted instruments!
Very well done. Perfect comparisons and contrasts. Thank you for taking the time to make this video.
I appreciate that this doesn't try to say one is better than the other. It lets the listener make their own decision.
Well you don't have much choices more than 99% of modern music is in Equal Temperament
Equal temperament is necessary for changing keys or using certain chords, just intonation falls out of tune very often.
@@ye_boimodern western music, sure!
I kind of like the creepy, unsettling sound that just intonation gives when you play in a different key than its tuned to. I wouldn't write a whole piece in it but maybe for one chord. The part at 1:35 especially reminds me of a creepy recording I can't remember. It also kind of reminds me of that hidden track Ambient/Secret off of the Hybrid Theory EP, maybe they used just intonation tuned to the key a semitone lower to get that sound
That's actually how temperaments are used.
I.e. the Well-Tempered Clavier by Bach was written for a particular tuning scheme called Well-Temperament, though I think people debate about what that exactly meant for his time and place.
So, every piece of the Well-Tempered Clavier was written to have chords land in the optimal place for the maximal effect.
So, the C-major prelude that everyone knows in Well-Temperament is very harmonic with a lot of resonance because it is made up of chords that are more harmonic with one another:
ua-cam.com/video/US8NHFgKxoE/v-deo.html&ab_channel=PeterWatchorn-Topic
www.ethanhein.com/wp/2020/what-does-the-well-tempered-clavier-sound-like-in-actual-well-temperament/
well explained, what keaboard are you using??
Yamaha Harmony Director HD-200
Great demonstration. Only small thing is that this is not the only just intonation tuning (although it is definitely one of the most common ones historically). For example, instead of the flat major third with a 5:4 just ratio (which I believe was used in this video), you could use the very sharp and bright major third with a 9:7 just ratio, or a Pythagorean major third with a 81:64 ratio, etc.
My mind was blown when I learned about this. That's so cool XD
I like the wobble of equal tempered.
I'd like to see this again but play F and G major when tuned to C just intonation.
I think different keys has incorporated this imperfection into their character in the history of composition. Personally I have a distinctive feel on E minor mode.
Thanks for the great demo, I was searching for this
Just intonation to me sounds "cold" on a piano by comparison to equal temperment. You would have to switch to just intonation with every chord change for a song to sound okay - a lot of extra button pressing.
I wonder how just intonation would sound in a song with some minor chord changes.
I do love the way accapella singers sound using it becasue in that format it really shines.
Great video comparison! In my opinion, a traditional piano sound would display the beauty of just/pure intonation better though. It's fun to think about all the possibilities an instrument like this has too offer with different intonations.
Its like a tremolo on a certain harmonic, wooow
Clear and concise demonstration. Thank you!!
Sir, can you please play a song in Just?
Are there any other models of Keyboard that have this feature?
I just found the price of this one (Yamaha Harmony Director HD-200).
What an awesome demonstration
The just intonation almost sounds "too pure" like it is thin because it lacks the beating
It's quite the opposite when you are playing an instrument with good timbre in a good acoustic environment that brings out the overtones. ET sounds flat where JI sounds full.
So this means that in "PURE" C, all songs will sound in tune as long as there are no sharps or flats (except for the dominant B flat)? If so, I'm really beginning to catch on.
None of the notes or combinations of notes over C will have beats. That doesn't mean that all the chords in C will sound in tune - but all the notes in the scale will sound in tune with the note C (which is usually the bass note).
the "dominant" Bb is a pretty difficult note to define in JI. The ratio you want is 7/4, but that is actually about 1/3 of a tone flat from the usual definition of the flat seventh scale tone in 5-limit JI.
When you start with Jacob Collier's music, you need that :)
Alternate temperaments can be really interesting, but none of them sound as pleasing as equal temperament to me. i often wonder if its because of how i was raised
Are there any 88-key boards that do this? I need one. Pure temperament feels like "home".
For those guys who are creating theories from other worlds to illustrate this: this is simpler than it seems. You choose a democratic tuning method, with slightly out of tune everything (equal), or a pure method, which "rounds" some chords (not necessarily C major) and pulls even more out of tune other scales. It’s so easy to understand, no need of formulas here and there. Just understand that with 12 semitones its IMPOSSIBLE to create round octaves.
what do you mean by round octaves
what do you mean by round octaves
@@zneiko Our ears do not perceive octaves as 2:1 ratios, rather some irrational number.
@@foteinimanou5516 that's because the comment you answered is actually confusing. Octaves are generally defined by the 2:1 frequency ratio - and "round" octaves aren't a thing. What @Michael Oliveira is getting at is the mathematical fact that the way we perceive frequencies can't divide an octave into equal parts with rational numbers. Of course, you can approximate irrational numbers as accurately as you like with rationals, so some music theorists work with "microtones" to try and approximate JI with a more math-friendly framework.
with 12 equal "tempered" semitones, what was wanted was precisely to have "pure octaves" ; it is the 3rd, 4th and fifths that are not pure in the current system. (thirds are a bit "longer" (sharp) than pure, and 4ths, 5ths are a bit "shorter" (flat))
Keyboard instruments were tuned either by pure 3rds or 5ths, (C to G, then G to D, D to A, etc) this resulted in the fact that, as you progressed adjusting the intonation of each key, the resulting upper or lower octave was no longer a pure 8th (in addition, very dissonant intervals were introduced (wolf notes) in keys farthest from C natural)
Nice demo, love that pure 3rd !
This is very interesting to me, I play the piano, guitar and bagpipes. Bagpipe tuning is a subject all of its own but it is essentially tuned by ear and it has always annoyed me how even a “perfectly tuned” piano or guitar sounds slightly off to my ear vs playing the same notes on the bagpipes.
The pulse doesn't stop, it's just faster
This is fascinating. Aren't we lucky that it's even possible to produce an equal temperament where the errors are small enough so as not to be very noticeable in normal music?
Thanks for this it makes sense and its easy to hear. I definitely noticed the 'beat frequency'
How expensive is that keyboard?
About 2000 USD or so.
Ricardo Wiggett Oh wow. I wish money grew on trees, then I would buy one.
nice video, i can actually hear the difference and not just look at the numbers
This explains the sound of choirs and quartets etc.
Very subtle, but discernible difference. If this could be demonstrated with pure tones, it may be more apparent to many.
Amazing demonstration! I do wish you would have played other major chords while in pure C major to get the affect of how far off those chords would be too. Or are they all equally as off as the C# major chord, in terms of frequency ratios?
I wish I did too. Maybe one day when I can borrow it again :)
C# and B are definitely the most offensive. The annoying beats comes and goes after that.
This is the clearest demonstration I've ever seen of this, thank you. So this need to switch that you demonstrated is why we need Hermode tuning, which is supposed to do the adjustment automatically?
Whoah that is crazy! Yes I absolutely can!
So cool! Well done.
Good demonstration. This is why everything always sounds out of tune to me. There really is no solution.
Hello, many thanks for this video. where can I find this keyboard? Im searching for a pure intonation keyboard to buy. Thank you! Nena
Can you tell me what the namw and brand of the keyboard are?
Awesome piano wow
I don’t hear it on the first one 😓. I thought at first that the vibration underneath the notes at disappeared, but then you played the, side by side again and it seems I was wrong
Wtf, i love this keyboard😍😍
Does all the diatonic chords in a justly tuned major scale ring "perfectly" or does the reference pitch somehow change even between keys in the same scale? What I'm actually wondering is how "easy" it is to write a diatonic chord sequence using just intonation - do all chords share the same tuning?
This is a genuinely hard question to answer because the notion of a scale becomes problematic in JI. If you listen to barbershop quartet music, you might begin to see what I mean. The voice parts are clearly staying in a particular set of related tones, but they also migrate around quite a lot - and then they use an intentional "key change" to bring everything back together again.
So with that said, if you use the fractions {1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8} as your "major" scale, then you will have perfect 4:5:6 major chords for I, IV, & V, but you will get a much more complex 135:160:192 sound for the ii chord than the "perfect" 10:12:15, and your iii chord will be 15:18:20 which is much simpler and more "open" sounding than the ii chord. The vi chord falls somewhere in between with a 20:24:27. The diminished triad is particularly problematic with the 45:54:64 harmonic ratio - the problem is that defining the diminished fifth in JI is not very straightforward, and the 7-limit diminished fifths sound a lot better than the available pair of 5-limit candidates.
So TL;DR - the major chords are pretty OK, the minor chords are a bit all over the shop. But if you're ready to take a more flexible view of what a "scale" means, you can have a lot of fun
where can I get this keyboaaaarrrd???
Excellent. I'm still foggy on why we have them. Why aren't all Cs, Es and G's (well all notes really) just Cs, Es and G's instead of this tune or that tune only if it's a Tuesday with a full moon type of scenario? 😟
@Boodysaspie Thanks for the comprehensive response!! That's the best succinct explanation I've heard yet. Put that in a one page book. 😀
Cheers!!
@Boodysaspie Are "pure" and "just" temperament the same??
My tuner (TE TUNER) only shows just or equal
@Boodysaspie Appreciate your response and knowledge on the subject. I found Chemistry easier than some of the music theory.
@Boodysaspie Ya, no surprise there, in fact I often try and talk my professional musician friends to tune in 432 which is mathematically correct, not 440, 444 etc. because some paradigm in some day wanted a change. Apparently/purportedly 440Hz was chosen by some King as it allowed more control over people. People would act too authentic listening to music at 432 vs 440 which just sours the milk enough so we enjoy the music but are still controllable. Just like fluoride in the water. It makes people more docile and was a good way to get rid of industrial waste. Hmm, even Crisco. Designed for submarine engine lubricant but an unnamed company ended up with it and figured using it in cooking would get rid of the supply. Ooops a ramble rant.
Wha keyboard is that you’re using?
is just intonation and pure temperate one and the same thing??
The real purpose of unequal temperament is to give each key a different character.
It’s all in the head.
Simply because we have gotten used to hearing it that way and not the other
Nice; I always wanted a digital piano that could do this, just to try :-)
Yeah there is a difference, but does it really matter? It actually gives a cool slight tremolo feel.
Ever since I learned of equal temperament, it has kind of frustrated me. I heard perfect harmonies once, and suddenly it nags at me whenever something is just slightly out of tune. But I do not know enough about music theory, and cannot afford lessons or tuition, thus I cannot navigate the world of pure intonation alone. I must begrudgingly rely on equal temperament just to get by. This reliance haunts me every time I try to play music.
start listening to barbershop quartets and gospel choirs :)
wow. the difference is huge. it is obvious even to such untrained ear as mine.
*OH MY GOD!*
*SCREAMS*
The patch you're using is almost a sine wave so the pure tuning isn't as obvious, although the C# major does sound bad. A richer sound would be more obvious.
It's so clear, if you use wave editor will clearer, thanks
This is so cool and mostly I'm glad you ended it on a nice sounding note rather than one in the wrong key 😂
What kind of keyboard is he using?
The quality is really poor on mobile.
Now, do the same experiment with 53-tone equal temperament and just intonation.
What does "so" as the first word of the video add?
A perfect fifth in a just intonation scale :)
(A 3:2 frequency ratio)
Do you know which just intonation is being used?
Using middle-C as the root note (261.6 Hz) E would be 1.25xC and G would be 1.5xC
I feel like a better recording device would have made it easier to hear the beats, but great demonstration
Oh god the pure tone in the wrong scale sounds so damned bad haha. I only found out about this today, and I'm playing 15 years lol. Really interesting
Great video! I just (heehee) wanna mention, Just Temperament isn’t really a thing; it’s Just Intonation. Tempering means altering. In Just Intonation, none of the notes are tempered. They’re all just.
Thank you!!
Great! Thank you!
I always tune my guitars by ear to get best result over the complete neck and you can easily play on the 12th fret, Barre chords, as well as at the neck or nut. Sometimes if tune with device, only the strings, this won't always work out well.
I tune by ear, on the 5th fret, the flageolets after and then finally couple of strums to test result
Of course sometimes the guitar could use a little recalibration of the neck 🎸😏.
Yeah, I do that too with 5th and 7th harmonics of the adjacent string. I think that generates the pythagorean tuning (?). It makes open string E sound heavenly :)
Recently ran into a person who tunes their guitar by ear using chords and he was wondering why after he was done, the chords sounded in tune but the tuner was registering his open strings as out of tune. I told him about just vs equal temperament and I think it blew his mind. It's something that most people never even entertain as a possibility ... there's an assumption that the 12-tone system is somehow perfect and when it's so clearly demonstrated to be flawed it's pretty eye-opening (ear-opening?).
So much thanks
I'd love to own one of those but I have neither the room nor the money for another keyboard
I don't understand why the pure temperature tuning makes playing other chords sound out of tune?
A little late, but because they are
Somebody should make a comprehensive video on the details of this topic. Tobias, you up for that? :P
all my frustrations with digital production stem from this concept.
Very good
Sorry to nitpick, but the phrase “Just temperament” or “pure temperament,” is an oxymoron: A tuning is either Just or tempered. You could say it’s “just intoned.”
Nevertheless good work!
well done!
In the pure temperment, I can hear the over and under tones. Dude that's so fucking cool!
Are you by any chance the organic chemistry teacher?
As you nicely demonstrated, just intonations sound well only in the one key an instrument was tuned, but prevent transposition and modulation as their inherent inconsistencies make them sound awful in other keys. Equal temperament, on the other hand, 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 bad in one key as in any other key. But what you might not 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. And it's NOT equal temperament. 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 nineth 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.
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.
Volume is so low that it's impossible to hear the nuances I'm listening for, even with the speaker in my ear!
No I feel they are same
Subtle, but discernible difference to my ear. If it could be demonstrated with pure tones, it may be even more apparent.
For me, certain notes in unharmonised melodies often sound wrong in equal temperament. I generally tend to prefer chords in just intonation, (or compromise intonation).
Yes!!! Thank you!!!! 1Nation4Life