### Mavila notation

Posted:

**Tue Feb 23, 2021 2:40 pm**@cmloegcmluin 's post on the porcupine notation thread got me thinking about the possibility of coming up with some general guidelines for regular temperament notation in general. One basic idea is that you can essentially use the JI notation for them, since each JI interval maps to an interval of the temperament in a regular pattern. The problem with that idea becomes clear when you try applying it to temperaments that are either too complex (such as the luna / hemithirds notation that @Dave Keenan posted about), or too far from JI.

If you want to notate mavila temperament, you can start with the generator mapping [<1 2 1|, <0 -1 3|] and easily find notations for some basic intervals like 5/3 and 5/4. Taking a 9-note chain of generators centered around D, you might end up with this notation: F 6/5, B 8/5, E 9/8, A 3/2, D 1/1, G 4/3, C 15/8, F 5/4, B 5/3. If you keep going, the obvious notation for the next note is E 10/9. But in mavila, this note is actually higher than the one labeled E 9/8. So you've got a "flat" that raises the pitch and a "sharp" that lowers the pitch! You could "fix" this by writing E 16/15 instead of E 9/8, since that doesn't change the pitch in mavila.

If you keep going, you start getting pitches that use the accidental (25/24). So one option would be to use 25/24 as the "sharp" of mavila notation, and omit the symbols since they don't change anything. You can notate up to 21 notes that way.

B E A D G C F B E A D G C F B E A D G C F

But then how do you continue the pattern if you're trying to notate a 23-note mavila scale? A 5:4 above G 25/18 is 125/72, but there's not an obvious way to notate that.

If you want to notate mavila temperament, you can start with the generator mapping [<1 2 1|, <0 -1 3|] and easily find notations for some basic intervals like 5/3 and 5/4. Taking a 9-note chain of generators centered around D, you might end up with this notation: F 6/5, B 8/5, E 9/8, A 3/2, D 1/1, G 4/3, C 15/8, F 5/4, B 5/3. If you keep going, the obvious notation for the next note is E 10/9. But in mavila, this note is actually higher than the one labeled E 9/8. So you've got a "flat" that raises the pitch and a "sharp" that lowers the pitch! You could "fix" this by writing E 16/15 instead of E 9/8, since that doesn't change the pitch in mavila.

If you keep going, you start getting pitches that use the accidental (25/24). So one option would be to use 25/24 as the "sharp" of mavila notation, and omit the symbols since they don't change anything. You can notate up to 21 notes that way.

B E A D G C F B E A D G C F B E A D G C F

But then how do you continue the pattern if you're trying to notate a 23-note mavila scale? A 5:4 above G 25/18 is 125/72, but there's not an obvious way to notate that.