has anyone tried writing music with 24 notes in the scale? so for each of the usual 12 notes an extra note is inserted between it and the next one 1 semitone above. I don't understand why people stop at 12, why not 24, 48 96 etc? one can take the limit 12*2^n with n->infinity, obtaining a continuous scale (technical won't be continuous as the notes only occupy a countable dense subset of the frequency spectrum, but you get my idea).

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    Why stick to multiples of 12? Go decimal and divide the scale into 10 deci-octaves? Or scrap the usual geometric progression between notes for an arithmetic progression. Or, just scrap intervals altogether and allow any frequency to be used. There is a chance that you will stumble onto something nice but, whatever you do, you will be fighting against what we have learned to consider normal. – badjohn Dec 31 '19 at 11:33
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    @badjohn You have lots of ideas! Why just comment here when you could try out your ideas? All the tools to do it are out there, easily available for free. – piiperi Reinstate Monica Dec 31 '19 at 12:43
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    I experiment a little with alternative tunings that have been used historically but I don't have much interest in trying new ones. – badjohn Dec 31 '19 at 12:48
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    Maybe you haven't heard any avant-garde music? There are lots of examples where pitch is continuous/indefinite. Stuff like this youtube.com/watch?v=etHtCVeU4-I – Michael Curtis Dec 31 '19 at 16:49
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    or this youtube.com/watch?v=SZazYFchLRI – ibonyun Dec 31 '19 at 17:58

Two composers who have worked with 24-tone equal temperament are Charles Ives (Three Quarter-Tone Pieces) and Ivan Wyschnegradsky (24 Preludes for Two Quarter-Tone Pianos). Wyschnegradsky has also apparently written Manual of Quarter Tone Harmony. He also used other divisions of the octave.

If you want to learn about non-12 divisions of the octave in general, and other tunings, search up microtonality and xenharmony. There's a whole wiki devoted to the topic.

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Look into Arabic pop music (ie: Najwa Karam, Amr Diab, Fairouz, Nancy Ajram) and classical music (Umm Kulthum). I would not bother with "modern composer" explorations into 24tone; because that stuff is almost completely academic music that nobody actually listens to in the real world.

But, Arab music (Maqam) is exactly what you describe; and there is a huge wealth of it. Bayati scales in particular. It's not exactly 24 equidistant notes, but it is clearly noted that way. This is almost entirely because they frequently cut minor thirds "in half". ie: (D E-quarterflat F).

For the most part, the notes in the scale flex around (by ear) to get "just" harmonies (ie: beat-free standing waves). In general: minor thirds need to be a little sharper, major thirds need to be a little flatter. Whole tone needs to be widened or narrowed depending on the situation. And in this, there is a "very wide" semitone such that the minor third is nearly bisected.

If you are insisting on an exact equidistant note setup, then something like 53-et most closely approximates common tunings. That comes as a consequence of tuning string instruments to harmonics at fifths, fourths, and octaves - by ear.

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  • Haven't the tunings in Arabic and other non-Western pop music already been practically ruined by adopting Western-based 12TET instruments and their default settings? Can you point to Arabic TOP20 electronic pop songs which use non-equal-tempered tunings in all of the instruments? I'm not an expert, but from what (little) I have heard, it seems to be approximated or dumbed down to equal temperament. Maybe a singer or soloist tries something but the backing track is equal tempered anyway. – piiperi Reinstate Monica Jan 1 at 15:06
  • @piiperiReinstateMonica I'm not an expert either, but pretty sure they do use scales outside of 12edo. Even popular music of the Middle East often features instruments like setar, and there are also keyboards available that have microtonal settings specifically for those scales. I've even heard heavily-autotuned vocals that seemed to use quarter-tones, though not sure... to me, anything noticeably autotuned always sounds horrible, regardless of what it tunes to. – leftaroundabout Jan 1 at 15:46
  • it kind of depends on whether there are guitars, bass guitar, or pianos prominent. as an example ... bits of Umm Kulthum's Daret El Ayam gets covered a lot of people. some of them are intonated differently. if you have a fretted bass guitar, it can stick to pentatonic scales, as the special notes land in between its minor thirds. – Rob Jan 4 at 17:39
  • also, i have an oud, and a few (exactly) quartertone-fretted electric guitars. the Bayati notes (3/4 tone higher than root) are slightly sharper than what they should be. but minor thirds are slightly flatter than they need to be (so I can bend up a little). i deal with major third intervals by bending the root note a little - to at least get the interval between them correct. i just kind of live with the 3/4 tone above root note being a little sharp; as it's close enough for most purposes. – Rob Jan 4 at 17:44

Yes - I've written in various tunings. Live performances are elusive though, as the musicians can't tell if they're hitting the right notes!

I did write something for two sopranos and a piano where one of the singers had the 'in-tune' accompaniment in her cans and the other an 'out-of-tune' accompaniment. Crucially neither singer could hear the other! The out-of-tune piano wasn't in the final mix.

For virtual instruments the best fun I've had was a big-band piece that used mostly these tunings:

06-41 Hexatonic scale in 41-tet:
    0: 1/1 0.000 unison, perfect prime
    1: 321.951 cents
    2: 380.488 cents
    3: 702.439 cents
    4: 760.976 cents
    5: 1141.463 cents
    6: 2/1 1200.000 octave


07-37 Miller's Porcupine-7:
    0: 1/1 0.000 unison, perfect prime
    1: 162.162 cents
    2: 324.324 cents
    3: 486.486 cents
    4: 648.649 cents
    5: 810.811 cents
    6: 972.973 cents
    7: 2/1 1200.000 octave 

There's plenty of quartertone music out there. But it seems to me the most interesting way to go is to generate the pitches for, say, 37-tet, and then to choose a promising gamut from those.

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  • Shouldn't it be at least theoretically more interesting if you could choose tunings for all notes on the fly, like a "fretless piano"? – piiperi Reinstate Monica Jan 1 at 14:55

Yes, it is called microtonal music. https://en.m.wikipedia.org/wiki/Microtonal_music

Though in practice I don’t think anyone really uses all possible notes. A lot of the ”usual 12 notes” music uses only a subset of the 12 pitches. And then again e.g. violin and wind instrument players and singers produce pitches that are not exactly on the equal-temperament frequencies.

There's also something called "polychromatic" music. I know nothing about it, but here is a polychromatic composition by Dolores Catherino:

I think this introduction video should give you an idea:

There's lots of non-12TET pitches there. 106 pitches per octave etc.

If I understand it correctly, the difference between microtonal and polychromatic instruments is:

  • Microtonal instruments: a regular keyboard with e.g. 12 keys per octave, or at least a linear organization of keys on a "pitch line". Microtonality is supported by letting the user tune each key individually.
  • Polychromatic instruments: in addition to the horizontal left/right low/high dimension, you have a vertical top/bottom dimension, letting you choose a different tuning for each note and even play several of them at the same time.

You could achieve the same thing with a regular keyboard by ditching the 12 keys per octave system and have an octave that's, say, 24 keys wide. This just spreads the 2-dimensional "polychromatic" keyboard onto a 1-dimensional one. Possible, but more cumbersome. Then a full-size piano keyboard would have 88/24 = 3 2/3 octaves range. Or use all 88 keys for a single semitone if you want. This is possible in many synthesizers with a "key/pitch scaling" parameter or similar.

There might be polychromatic synth apps for mobile devices, tablets and other devices which have a multitouch display.

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