Learning Lumatone: Ep. 26 - "Just Intonation"
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- เผยแพร่เมื่อ 8 ธ.ค. 2022
- Ever wondered what they mean by "Just Intonation?" Dave walks through the basics of what this is and how it relates to the many tunings you can play on a Lumatone.
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This is not really about Just Intonation but how well certain just intervals are approximated in various EDOs. I hope you'll make a video of playing Lumatone in actual just intonation. There are excellent extended-JI tunings for the standard 31-, 41-and 53- Bosanquet layouts.
The problem with just intonation is that it requires multiple axes to represent; e.g. 7-limit requires 4 dimensions.
@@ValkyRiver That is not necessarily a problem, it's a property. As I said, there are excellent Lumatone mappings for JI that use the default Bosanquet layouts for 41 and 53. There's also a huge reservoire of JI mappings for isomporphic keyboards by Erv Wilson.
@@nylonius You can map the tonality diamond to a hexagonal grid. If the Lumatone allows freely mapping the keys. With eight keys in one direction, 15-limit is possible. Wouldn't the tonality diamond be best for just intonation?
The full keyboard with a 53- or 41-note mapping gives much more possibilities, but a tonality diamond is cool and I have tried that on the Lumatone.
Unequal tunings were probably neglected because breaking the isomorphism might make the lumatone look bad and less groundbreaking
You don't suck at math. You're doing fine so far - take it from your friendly music-loving math professor...!
7:45 -- Bingo, Dave! There's no ideal temperament, nor tuning in general; it just depends upon what sort of sensation you're trying to express at the time.
However, it's not _only_ about ratios in vertical, block harmony! We often forget that the choice of tuning also has big effects upon melody as well! As an example of a small difference, 22TET, 34TET, 53TET and others, have pseudo-commas: Using C-major as an example, the step from C to D is larger than that from D to E (or the pitch a M3 above the root). As a much-more-extreme example, 88CET tuning has no really convincing perfect fourths, so ever-famous melodies beginning with 5 up to 1 ("here comes the bride," and many other melodies) just don't really work!
Of course, the fact that it doesn't work is a *_good_* thing, not a bad thing, because it forces you be creative and come up with something even more melodically interesting!
Plus of course, any choice of tuning system has to also weighed against complexity: 53 absolutely nails the usual "5-limit" Just ratios, but you have to deal with a pretty complex system of 53 keys per octave, the comma adjustments (etc.). 12TET in contrast, is extremely simple and convenient, but its thirds and sixths are cartoon of what they really should sound! Sometimes that simple cartoon sound is exactly perfect, but sometimes it can be pretty nerve-grating.
Cool concept and intro for many. Sorry, but a few nitpicks from me, that I feel impact negatively on teaching and transmitting this information.
A couple of little things that are a shame they weren't picked out before uploading:
In 22-equal, you've stated the [5:6] minor third is 11.63c sharp of JI, but you've played the regular [sub]minor third, very close to 6:7.
With the minor sevens, it seems like sometimes you're comparing to the ratio 9:16, and sometimes to 5:9... both are great, as is 4:7, but you should perhaps specify *which* JI ratio you're talking about. 12-equal you compare with 9:16, 19-equal with 5:9, 22-equal with 5:9, but you actually play the wrong approximation, the flat one closer to both 9:16 and 4:7. Ditto with the nines. Sometimes you're comparing with 8:9, sometimes with 9:10.
For some reason the 19-equal minor nine is being played with a subminor third but a minor seven, so not so just at all, somewhat close to 32:37:48:58:73 or something wild.
The 5-6c thing is based on studies on melodic pitch only, without any harmonic reference, whereas the average person can probably hear a difference of 1-2c or less with sustained notes in rich harmonic timbres (and Amelia's proven she can hear less than 0.5c).
I do agree (with Juhani? nylonius, below) that perhaps this should have been called "JI and some ET approximations" or something similar, as we don't hear very much JI here at all, although there are a ton of great JI tunings that can be played using these layouts in 19, 22, 31, 41 and 53 tones per octave. One option is of course my 53-JI circulating tuning, but if you know what you're after, you can design your own and get exactly what you want in whichever keys you need,
I have used 53-TET as a micro temperament for 5-limit just intonation (the thing about just intonations is that they require multiple axes to represent)
53-TET is pretty good for 7-limit also, even though 41-TET is probably better for that, and 68-TET and 72-TET better still.
118-TET is almost perfect as 5-limit JI (better than both 53-TET and 65-TET), but 171-TET is even more perfect as 5-limit JI, and even as 7-limit JI.
For 11-limit JI we should go to 342-TET or 270-TET. 13-limit JI is almost accomplished in 270-TET, and even more so in 494-TET.
In the mere 3-limit 665-TET is for all purposes the same as 3-limit Just Intonation, and it is pretty good in higher limits as well, although 612-edo is a bit better.
It is true that each new prime of (tempered or untempered) Just Intonation gives you a new axis, but each new independent comma tempered to unison also reduces the axes by one.
There are many multi-dimensional temperaments between Just Intonation and Equal Temperaments, so e.g. Meantone as such lies between 5-limit JI and 31-TET (and others).
And Marvel lies between 7-limit JI and Miracle (and others), while Miracle lies between Marvel and 72-TET (and others).
Even when using temperaments, it is often clearer to use multiple axes in theory, even though they may be reduced in practice to just one or a few axes.
@@henrikljungstrand2036 Though TETs above 55 don’t fit on the Lumatone with the Bosanquet layout, so I only focus on those up to 55.
@@ValkyRiver What if you use layouts not based in the five whole-steps and two half-steps of the diatonic scale, like it is in standard Bosanquet? I.e. let's try e.g. the Miracle layout of ten secors and one quomma of the Miracle basic scale.
Six secors give us a perfect fifth, ten secors plus one quomma gives us a perfect octave, other 11-limit consonant intervals are pretty easy to reach.
This layout should work for Miracle in 72-TET, probably on the Lumatone as well.
@@henrikljungstrand2036 That would work also.
Discussion of big edos: 😀
Music in big edos:🫥
Couldn't you bypass all these EDO issues by having the keys on the Lumitone tuned to different Just Scales? That way, when you wanted to have a key change in a song, you'd just switch to a different pair of rows. It looks to me like you have enough buttons for four Keys at a time - maybe five? You might lose the isomorphic property by doing that, but you'd gain a new solution with a unique, ultra-harmonious sound.
Hey fellas excellent job as usual!! So when are you going to release the video featuring Amalia?
13-prime-limit Just Intonation, and microtemperings of that, is good enough for most musical purposes. It's important that the music actually is composed to be beautiful and emotionally moving, it's not just a mental mathematics thing.
First post this time! 😂
Just kidding, but i really like both the Lumatone and (almost) Just Intonation tunings, where only VERY small important commas are tempered to Unison. 🥰
I am also somewhat versed in Xenharmonic music theory. 🤓
And i LOVE mathematics!!! 😍
The minor third that you played in the 22EDO minor example doesn't correspond with the interval written above. The one you played is the subminor third (272.7 cents, which is an approximation of 7/6). The minor third that is 11.63 cents sharp is the standard minor third in 22EDO and approximates 6/5 (it should sound sharper than the 19EDO minor third). The subminor third sounds great, but just thought I'd give you a heads up in case you can still change it in the video 🙂
I'm a bit confused by some of the other information you've given too. For example, the 7/4 minor seventh in 19edo is 21.45 cents flat. The interval you have used is an approximation of 9/5, as are the ones you used for 31 and 53EDO, but not 22EDO, where you added a perfect fifth onto the subminor third, making it a 7/4 minor seventh... I understand that you wanted to build on the minor 3rds from the previous example and maintain the perfect fifth relationship between the thirds and sevenths, but it may have been better to give examples of dominant 7ths with 5/4 thirds and the 7/4 sevenths, since you're talking about just intonation. Then you could have gone all the way up to the eleventh harmonic in each EDO. Because with different ratios all muddled up and lumped into the same general intervallic categories it's very confusing.
Are you programming the keyboard to these intervals or was there a vat you were playing that did it?
What books does Figure 1 come from? I don't recognize it by date and author.
Wish the sounds of the harmonics were also played on the video and not just represented on staff.. i was internally yelling 'okay let's hear them'
my favourite temperaments are 12
I like your human suit
I thought just itonation had to do with doing something to the fifths to accomadate the thirds.
No, that's what twelve tone equal temperament does, along with a number of meantone temperaments. Just intonation makes no accomodations, just pure integral ratios.
You should go beyond 5-limit into 7-limit! Please demonstrate the augmented sixth 7/4! ☺
In different tunings, like 12edo, 19edo, 22edo, 31edo, 53edo. 💚
I'm quite upset you did not play the just intonated versions of the chords as well.
nice....piano?
lumatone
Pianoteq
I hate math in theory because its the underpinning of reality but it comes in handy in many real-world situations. This is the dilemma. I wrote this comment without needing any commas. Universe the ball is in your court now. Dont let us down.
Mina are a better unit of logarithmic frequency difference than Cents.
A cent is 1/1200 * log(2), while a mina is 1/2460 * log(2).
Mina are far more accurate w.r.t. Just Intonation.
We believe cents are good enough for most musical purposes. :) We wholeheartedly agree with your comment above, about focusing on the musical side of these concepts, vs. the focusing too much on the math. Even though I know the math is super interesting too! But for us, Lumatone is about enabling the musical exploration of these concepts. -Matt
@@lumatone Would you like to explore other linear temperaments than Meantone, Superpyth and Helmholtz/Garibaldi (Pythagorean based temperaments), with their pentatonic, diatonic/heptatonic and "chromatic"/dodecatonic scales Matt?
Like the Pajara, Porcupine, Magic, Octacot or Miracle scales?
Or the ancient Greek genera (variations of diatonic, chromatic and enharmonic), or Arabic maqamat?
Also, would you like to try layouts based on these temperaments and scales, like e.g. the heptatonic (or octatonic) Porcupine scale, the decatonic Pajara scale or the Blackjack 21-tone Miracle scale (undecatonic Miracle is easier of course)?
17-tone Superpyth scales and 19-tone Meantone scales are also of interests for layouts of course.
True just intonation is Pythagorean tuning, not this 5 limit stuff. People for the last few hundred years have been repeating this thing about 5 limit ji being ji. Pythagorean tuning is the right tuning for music. It gives you something similar to the fifth harmonic, but just flat of it, it being derived from the undertone series. But the true default major third, even for chords is the 81/64. The diminished fourth is not a third, but can give a similar harmonic sound, being a chromatically altered fourth derived from 8 fifths down the spiral of fifths.
53 equal still doesn't cut it either. It has got to be 53 Pythagorean. The diminished fourth which can sound similar to a third, a subharmonic major sound, it functions diatonically as a fourth, most commonly pulling down to the minor third..
Rather than learning the lumatone, why not just use a regular keyboard and have AI software actively adjust temperament.