harmony with 24 note scales

Question

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).

Answer 1

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.

Answer 2

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-halfflat 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.

Answer 3

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.

Answer 4

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

And

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.