Post by fuguestate on Sept 11, 2018 18:13:45 GMT
Since it's been awfully quiet around here lately, I thought I should kick the dead horse a little to see if it's actually still alive...
Last week, I overcame a major technical hurdle in my notation software setup, and now I'm able to render MIDI in 19 EDO. That's the non-standard tuning or temperament wherein the octave is divided in 19 equal steps (19 Equal Divisions of the Octave) instead of the traditional 12 semitones (12 EDO).
Despite the scary-looking number 19, this temperament actually has several very interesting characteristics, one of which being that you can map the traditional diatonic scale to it by assigning 3 steps to each whole tone and 2 steps to each semitone (3 + 3 + 2 + 3 + 3 + 3 + 2 = 19). Applied to the C major scale, this produces a scale in which sharps and flats are distinct, except that B# = Cb and E# = Fb.
Surprisingly enough, this scale actually has a major 3rd that's much closer to Just Intonation than the 12-semitone system, and features a harmonic 7th that's very close to the 7th harmonic (e.g., C to A#), that has no equivalent in 12 EDO. The 5th is a little flatter than JI, so the overall sound is brighter in 3rds and less so in 5ths. The result is that you can translate most diatonic music to 19 EDO with no change except interpreting the notation a little differently, and it would sound satisfactorily close to the original, as long as accidentals are spelled "correctly". Enharmonicity no longer holds, though, so anything that relies on it won't work anymore.
The fact that the diatonic semitone consists of two 1/19 steps (we could call a 1/19 step a chromatic semitone) has very interesting consequences, such as an intermediate pitch between E and F (written as E# or Fb) and between B and C (B# / Cb). In the WIP fugue that I started writing last week, I take advantage of this extra pitch for ornamental purposes (as passing notes). The fact that the diatonic whole tone consists of 3 chromatic semitones also has interesting implications, such as D# and Eb being distinct, so the circle of 5ths in 19 EDO actually covers D# and Eb as distinct keys.
New harmonic possibilities also appear: for example, in addition to the major/minor distinction in your traditional triads, there's also a subminor (e.g., C-D#-G, or alternatively if you interpret the double-flat as lowering the pitch by 2 chromatic semitones, C-Ebb-G) and supermajor (C-E#-G). The supermajor sounds halfway between a susp4 and a major chord, and is an interesting sound I might employ at some point in my new piece. The subminor sounds like an "exceptionally minor" minor chord, due to the diminished 3rd (aka augmented 2nd). There's also the harmonic 7th chord (e.g., C-E-G-A#) that's quite close to the sound of the first 7 natural harmonics, which supposedly is one of the characteristics of the so-called barbershop quartet. It sounds less unstable than the diatonic 7th chord (C-E-G-Bb), and so has less of an urge to "resolve" to the subdominant. The diatonic 7th chord in 12 EDO is very sharp and unstable; the diatonic 7th in 19 EDO is less sharp but still unstable, but the harmonic 7th in 19 EDO is considerably more stable-sounding.
So far, I haven't figured out how to incorporate these new harmonies into my piece in a nice way yet (my thinking is still very much entrenched in 12 EDO; it will take a while to fully embrace the new temperament), but I'm definitely thinking about it... At the very least, new modulations are possible by "punning" certain intervals, e.g., replace the 7th scale degree with its sharpened counterpart for an even more intense "leading tone" sound, then "resolve" it by taking it a diatonic semitone up, ending up 1/19 steps above the starting key. Or equivalently, replace the relative minor chord with a subminor 1/19 steps above the relative minor, which eventually lands you 1/19 steps above the starting key. Conversely, similar "puns" can modulate you 1/19 steps below the starting key. Each of these transitions introduce a novel new sound to the harmony, which can be very useful for dramatic buildup.
Anyway, in some of my 19 EDO sketches, I let loose with the full 19 EDO chromatic semitones, and I can tell ya, it's wild. If you thought 12 EDO pantonic music was wild, this one makes it look like child's play. Unfortunately, I don't think I've quite come to grips with it yet, so it probably won't end up in my current WIP... but maybe at the shattering climax it could work... well, gotta think about it.
Last week, I overcame a major technical hurdle in my notation software setup, and now I'm able to render MIDI in 19 EDO. That's the non-standard tuning or temperament wherein the octave is divided in 19 equal steps (19 Equal Divisions of the Octave) instead of the traditional 12 semitones (12 EDO).
Despite the scary-looking number 19, this temperament actually has several very interesting characteristics, one of which being that you can map the traditional diatonic scale to it by assigning 3 steps to each whole tone and 2 steps to each semitone (3 + 3 + 2 + 3 + 3 + 3 + 2 = 19). Applied to the C major scale, this produces a scale in which sharps and flats are distinct, except that B# = Cb and E# = Fb.
Surprisingly enough, this scale actually has a major 3rd that's much closer to Just Intonation than the 12-semitone system, and features a harmonic 7th that's very close to the 7th harmonic (e.g., C to A#), that has no equivalent in 12 EDO. The 5th is a little flatter than JI, so the overall sound is brighter in 3rds and less so in 5ths. The result is that you can translate most diatonic music to 19 EDO with no change except interpreting the notation a little differently, and it would sound satisfactorily close to the original, as long as accidentals are spelled "correctly". Enharmonicity no longer holds, though, so anything that relies on it won't work anymore.
The fact that the diatonic semitone consists of two 1/19 steps (we could call a 1/19 step a chromatic semitone) has very interesting consequences, such as an intermediate pitch between E and F (written as E# or Fb) and between B and C (B# / Cb). In the WIP fugue that I started writing last week, I take advantage of this extra pitch for ornamental purposes (as passing notes). The fact that the diatonic whole tone consists of 3 chromatic semitones also has interesting implications, such as D# and Eb being distinct, so the circle of 5ths in 19 EDO actually covers D# and Eb as distinct keys.
New harmonic possibilities also appear: for example, in addition to the major/minor distinction in your traditional triads, there's also a subminor (e.g., C-D#-G, or alternatively if you interpret the double-flat as lowering the pitch by 2 chromatic semitones, C-Ebb-G) and supermajor (C-E#-G). The supermajor sounds halfway between a susp4 and a major chord, and is an interesting sound I might employ at some point in my new piece. The subminor sounds like an "exceptionally minor" minor chord, due to the diminished 3rd (aka augmented 2nd). There's also the harmonic 7th chord (e.g., C-E-G-A#) that's quite close to the sound of the first 7 natural harmonics, which supposedly is one of the characteristics of the so-called barbershop quartet. It sounds less unstable than the diatonic 7th chord (C-E-G-Bb), and so has less of an urge to "resolve" to the subdominant. The diatonic 7th chord in 12 EDO is very sharp and unstable; the diatonic 7th in 19 EDO is less sharp but still unstable, but the harmonic 7th in 19 EDO is considerably more stable-sounding.
So far, I haven't figured out how to incorporate these new harmonies into my piece in a nice way yet (my thinking is still very much entrenched in 12 EDO; it will take a while to fully embrace the new temperament), but I'm definitely thinking about it... At the very least, new modulations are possible by "punning" certain intervals, e.g., replace the 7th scale degree with its sharpened counterpart for an even more intense "leading tone" sound, then "resolve" it by taking it a diatonic semitone up, ending up 1/19 steps above the starting key. Or equivalently, replace the relative minor chord with a subminor 1/19 steps above the relative minor, which eventually lands you 1/19 steps above the starting key. Conversely, similar "puns" can modulate you 1/19 steps below the starting key. Each of these transitions introduce a novel new sound to the harmony, which can be very useful for dramatic buildup.
Anyway, in some of my 19 EDO sketches, I let loose with the full 19 EDO chromatic semitones, and I can tell ya, it's wild. If you thought 12 EDO pantonic music was wild, this one makes it look like child's play. Unfortunately, I don't think I've quite come to grips with it yet, so it probably won't end up in my current WIP... but maybe at the shattering climax it could work... well, gotta think about it.