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- เผยแพร่เมื่อ 10 มิ.ย. 2021
- Want to play better in tune on the violin? Here is a brief overview of the pythagorean and just intonation tuning systems. In addition to having a good sense of relative pitch and left hand fundamentals, string players also need to have a basic understanding of both vertical and horizontal intonation, and through experience learn how to adjust in real time to stay in tune with an ensemble. Just intonation is built on the harmonic series, and pythagorean system is based on perfect fifths. One helps tune harmonies; the other, melodic lines. String players typically use a combination of the two, and sometimes compromises are necessary - this is especially apparent in chamber music and solo repertoire that has many double stops (ie - Solo Bach, Ysaye Sonatas, etc)
📘To learn about the history of different tuning systems, and explore this topic in greater detail, I strongly recommend Ross Duffin's book "How Equal Temperament Ruined Harmony (and why you should care." Check it out here: ➡ amzn.to/3gsflXk
▶️🎶PART 2, with musical examples: • Pythagorean Tuning vs ...
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That chart at 0:52 deserves its own video!!!
Haha! It's a rabbit hole of a chart!
A very nice short introduction to this rather complex issue. I would just add, that the conflict between Pythagorean and Just Intonation is not really a paradox; it's a simple consequence of the math. No power of two is also a power of three: thus no "circle" of perfect fifths can close on an octave. Also, no power of three is also a power of five, making it impossible to combine perfect fifths and just thirds in a circle.
Cheers from a tuning and temperament freak in Vienna, Scott
Perfectly explained! Thank you! =)
True!
@@LatchezarDimitrov Hey, Latchezar, how are you doing? I remember chatting with you about intonation a while back. Nice to hear from you.
While not exact, it does get absurdly close after 53 fifths, making extended Pythagorean functionally equivalent to 53 edo.
@@Dayanto Yes, 53EDO is quite an interesting tuning. But it's a lot of notes, so it's a bit unwieldy for acoustic instruments.
THIS SHOULD HAVE A MILLION VIEWS
Best video on youtube about intonation. Thank you, also for the book recommendation.
So glad you enjoyed the video! Thank you! The book is truly excellent!
pythagorean is a type of just intonation btw
Bravo, Inna!! 👏🏻👏🏻 Very clear explanation of the two systems! I can’t wait to see their application to some repertoire in the next videos 🎶🎶
Thanks so much, Laura!❤️
So awesome! Great coverage of a fundamental concept of tuning but also important to understanding microtonal as well as non-western music! You rule.
Thanks for watching :)
Great treatment to this fascinating topic!!!
Many thanks for watching & commenting!
Thanks Inna. Very helpful to understand this a bit better.
You're very welcome - Glad it was helpful! =)
This is such a great video with amazing insights!
Thank Kaya!
Thanks Inna! That was a great explanation!
Glad it was helpful!
Great video!! Thank you for comparing these two systems. Really interesting comparison!
Thanks Darlene! ☺️
Great video, informative and very well done!!!
Thanks so much, Jason!
Brava. This is great information on this subject.
Thank you! =)
This is such a great topic! Very interesting and useful!
Thank you, April!
I m so glad i found you
So beautiful and wonderful talent
Everything you explain is so amazing! I wish I understood anything you say! :D
😉
Another AmaZing video!
Thanks Carol!
Inna, very good discussion.
Thank you!
Streaming your channel now!!!
So interesting again!
Thanks Bico!
This needs more views!!
Thanks for watching and comment =)
Wonderful video!
Thank you so much!
BRAVISSSSIMOOOOO, I LOVE IT!!!
Thank you very much, Sam!
super great vid
Thank you very much!
Thank for sharing,,,, 😍
My pleasure!
@@Violinna th-cam.com/video/yirMaINPTy4/w-d-xo.html
A Pythagorean major third is 81/64. A just major third is 5/4, or 80/64. The third scale tone is Ground Zero for tuning, because it can either be a Pythagorean note in a melodic line, or a just part of a sustained tonic triad.
I bought that book. Thanks
Enjoy
Bravissima!
Grazie!
Quick sub
A solution that i have never heard is to have more then one tuning for certain notes and as you move from a note in one context the pitch could change to match another context.
For example lets say you play Dm7 and then CM9 now both chords share the C note and the D note.
So we have three choices. Either the chords will not be just tuned or the C note will change it's tuning or the D note will change it's tuning.
Let's say you are playing C major key so it would make sense to keep the C note the same tune so then when play CM9 you would play 9/8 for the D note but when you are playing Dm7 you would play 10/9. So as the D note from the Dm7 goes to the CM9 it would change 20 cents.
Has anyone tried such a solution? And does it sound good?
If it sounds good then there is no paradox at all. Well at least to those people who think it sounds good.
Yes, actually your solution is exactly what I discuss in part 2 of this, in rep examples. When I mentioned the word "paradox" in my title it was more along the lines of "there is no one single way to tune a note" and "there is no such thing as perfect intonation"
The concept is sound.
I so wish you had played musical examples. You provide a good explanation, but it's abstract.
Hi! There is a Part 2, with musical examples. Link is in the description.
@@Violinna Thanks!
How about 53TET ? Nearly perfect Pythagorean fifth (31/53TET = 701.89 < 701.96 = JI 3:2) and fourth (JI 4:3 = 498.04 < 498.11 = 22/53TET ) and an excellent meantone third (17/53TET = 384.9 < 386.3 = JI 5:4). Pythagoran Db and C# and Meantone C# and Db (4/53 and 5/53).
41edo is also a viable alternative Pythagorean tuning system. Its fifth is at the interval 24\41, about 702.44 cents, only 0.5 cents sharper than pure 3:2 (although, 53edo does better than 41 in its fifth). Its fourth is at the interval 17\41, about 497.56 cents, 0.5 cents flatter than the pure 4:3 fourth. Its 5:4 approximation is slightly worse than 53edo's at 380.49 cents instead of the ideal 386.31 cents. Although 53edo does better than 41 in the 5-limit, 41 does better than 53 in the 7-limit and higher, so this could be an alternative tuning system to both Pythagorean tuning and 53edo tuning (it's also fewer notes).
I have a question, if I play a major 3rd with C and the open E string, would that 3rd be in just intonation or in equal temp?
Because the same 3rd played an octave lower (the one of the Bach Andante), you say it must be a pure major 3rd to be harmonically in tune, but wouldn't that E be a little lower compared to the open E string?
For example if I have to play a scale of 3rds (C major), which of the two 3rds would be most appropriate? Sorry if I’m confused
You are correct! I actually talk about this exact problem in Bach Andante in part 2 of this topic, with repertoire examples (should be linked in description box somewhere). It's not possible to play this Bach opening "100% in tune" and different players interpret what sounds best, where there is more than one compromise that's possible - this is where intonation actually becomes subjective!
Thanks for the answer! I think I’m going to stick with equal temp :)
I have a question, when playing thirds in violin solo repertoire, which voice is the one that remains in the pytagorian system?, example, when i practice 3rds i always keep the lower note in pytagorian and the higher note is the one that i move aroun to tune the third, but i dont know if i am doing it wrong, should i keep the higher note in pytagorian and move around de lower one?
By default, I'll keep the main melody (which is most often in the top voice) pythagorean, and have the other voice adjust.
What system should I use when tunning open strings?
By default, most violinists tune to pure 5ths (i.e. Pythagorean). However in a string quartet it's common to very slightly brighten up G. And in baroque ensembles it might be completely different tuning (e.g. tuning each string individually to the harpsichord).
I would think that a string quartet that adds a piano would necessarily have to play in Equal Temperament and not Pythagorean or Just Intonation. As you put it it seems like it only has to do some adjustments. Would those adjustments entail playing in just intonation in some passages and Pythagorean in others and on Equal Temperament in others ? If I made some sense, would that mean that all 3 tunings can coexist in the same piece ?
Correct - depending on the context of the notes in relation to harmony, the tuning systems can all live within the same piece. For example, an F# as a passing tone in a melodic G major scale would likely be Pythagorean. But the same F# would be in Just Intonation for a held D major chord. Any part that doubles one of the hands in the piano would have to opt for the equal temperament (or whatever the piano is tuned to).
How is it that the octaves aren't in tune? Is that in relation to equal fitting tuning?
The piano is not tuned to an exact equal temperament. It would sound out of tune with itself. As notes go lower, they are not tuned exactly to the note an octave above. Instead, the slightly sharp octave overtone is tuned to that note. The result is that piano notes get flatter and flatter as you go down the keyboard. This is called “stretch” tuning. Wasn’t it Casals who told his students not to play in tune to a piano? Choirs singing a cappella get flatter and flatter over the course of a piece if they sing in tune vertically. You can blame math for that one, too. BTW, I heartily agree with her book recommendation. I read it a few years back and found it entertaining as well as informative.
Casals was a genius! I just read the book about him called "Art of Interpretation".. it's incredible.
ugh my head is spinning. so basically I have to play out of tune to play in tune, in equal temperament and in tune is out of tune in Just intonation and vice versa depending on the tuning?? ughhhhh what about playing so that it sounds in tune, whenever I play anything? and make adjustments(cello) sharp or flat as needed?
Don't overthink it!! Just follow and trust your ear! :)
The exact opposite, you have to play in tune, but being in tune depends on the context. The notes of the 12-T system change based on what context you play in. Basically just use your ears to tune,
I don't think this video is true for music as a whole because whether or not to use Pythagorean tuning for the melody depends on the music and taste of the individual.
For example it could be the reason why we prefer Pythagorean tuning for the melody is because we are used to the Equal temperament tuning which is much closer to Pythagorean tuning than to just intonation. But when it comes ti harmony the pleasent sounds of just intonation are too strong for cultural influence to have an effect. Also by focusing on leading tones we may be skewing our view. It might say sound like a stronger resolution to have a sharper fifth but there may be other benefits in having it a bit flatter.
Yes, it definitely depends on the situation! And different cultures are accustomed to hearing intonation differently. This video is a basic overview/introduction of the two types of tuning system and the general definition, if that makes sense.
5-limit JI is not out of tune melodically. That's a very curious statement. A 9/8 whole step is just as in tune as a minor 10/9 whole step, and a 16/15 half-step is just as in tune as a 256/243 half-step. Maybe Western musicians and audiences aren't as accustomed to the sound of the 5-limit JI melodic intervals (10/9, 16/15) as much as they are to the 3-limit JI/Pythagorean ones (9/8, 256/243), which are better approximated by 12-TET, but this in no way makes these intervals "horizontally out of tune". Being in tune is, after all, a function of musical intention, and there is no established intention of emulating exclusively Pythagorean intervals in Western music as far as I am aware. In addition, the example of Arabic classical music goes to show that even the very wide 88/81 (3/4 of a whole step in 24-TET) interval can be successfully conceived of and used as a leading tone.
Since the syntonic comma of 81/80 is tempered out in 12edo, most musicians (even those who have to check their intonation) think in terms of one whole tone and one half-step and not as two separate whole tones and half-steps separated by 81/80.
@@YoVariable It's true that 12-TET splits the difference. However, it doesn't do so evenly, like meantone. The 12-TET whole tone is negligibly lower than the Pythagorean one, while the half-step is indeed somewhere in the middle, but still a tiny bit closer to 256/243. This talk about JI being melodically out of tune just goes to show how the acoustic identity of the individual notes in the scale is tied to the Pythagorean system.
It's all wrong! Only historical facts... All the notes must to have constant place like the A440Hz. Only the unisson must be perfect. All others intervals we must avoid to be in just intonation. Yes, the octave also! 12ET is the best way, but only without a just octave! We need a true reference how to stay in tune, an universal temperament! Nobody today ne propose different mesures for time or distance, stop please to lead people in wrong way!
I know no one else will tell you this, but it is not a paradox. Pythagorean tuning is always right. All the notes on the page are Pythagorean notes and should be tuned as such. A chord of C, E and G should have the E 81/64 and G 3/2 above the C. E should never be 5/4 ratio EVEN IN CHORDS, even in double stops. The 5/4 is a note of timbral distinction, NOT a note of the scale, not a note of pitch class, it is an overtone of timbral distinction.
Does the 81/64 major third beat, yes, more or less depending on the timbres of the instruments sounding, but it is always in tune. Even it's beats are whole number ratios to the fundamental. The 81/64 gives a difference tone of the 17th harmonic a few octaves down. This type of beating is totally different to the irrational nonharmonic beating of equal temperament.
5 Limit just intonation is out of tune melodically, while giving a nice buzz harmonically, BUT both the vertical listening and horizontal listening must be used to determine tuning, and while simultaneously taking in both directions, Pythagorean is the true intonation in all instances.
When you think about it, it is the only thing that makes sense. Our entire music notation system and conception is Pythagorean tuning. There are no other accidentals than sharps, flats, naturals, and their compounds. Pythagorean tuning gives you every note with a name. 5 limit tuning gives you detuned versions of all those same notes.
This confusion and lie about 5 limit tuning being the standard for harmony is what has lead to equal temperament and the destruction of all harmony. 5 limit tuning has a comma in the diatonic scale, and the two sizes of whole tones makes the music out of tune, unless you condition yourself only to listen to harmony and not melody. If you listen in both dimensions, it is clear 5 limit is out of tune.
If you want to play in tune you must use true intonation, what the world calls Pythagorean tuning (even though Pythagoras did not discover this tuning). I just call it what it is True Intonation.
Contrary to popular teachings of today, an orchestra can end on a major chord tuned with true intonation, and it will sound completely at rest and in tune, and MUCH BETTER, than if they used 5 limit. The going back and forth between 5 limit and 3 limit in classical music creates a disjointed spirit in the music.
When I say Pythagorean or true intonation, I am not talking about 12 tone Pythagorean, but Extended Pythagorean tuning, even with 53 notes per octave, from Ebbbb to Cxx on a chain of fifths.
So they make clickbait books too nowadays? Cool.
Last I checked, clickbait book titles existed before the internet ;) Keep an open mind
This is good. But if you haven't already, watch some other music instruction channels on what they do to make their videos more watchable for repeated subscribers. You talk really fast and almost look uncomfortable.
Thank you for watching. You're welcome to change playback speed in youtube settings to slow it down =)
LOL what a stupid comment. Maybe you cant process what she says like normal intelligent people and maybe you are projecting your insecurities on her
this isn't fast
Please stop talking about it and demonstrate what it sounds like. Sounds not speech.
Most certainly! In fact, here is Part 2, with a few examples: th-cam.com/video/R07c1Dfx0RA/w-d-xo.html