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Paul Erlich commented:

I didn't come up with it but I like it because each of the four consonant triads in porcupine-7 gets a conventional spellings for its quality. D-F-A and E-G-B are minor, and F-A-C and G-B-D are major. Also the minor seventh chords D-F-A-C and E-G-B-D.~ ~ ~Mike added:

BTW with this notation system, one question is - how many lines do you use in a staff? I guess you'd have to have "staff switches" in the middle of a score if you want to switch into a porcupine[8]-oriented notation or what have you. ... Actually, forget staff changes, why not clef changes? 5 lines can accommodate 1 octave of both porcupine[7] and porcupine[8], so there you go.~ ~ ~## William Lynch generally likes to reinvent the wheel. He proposed a system of notation for 15 EDO based on porcupine[8] as the fundamental scale.

I think it's worthwhile to explore these scales from scratch with no previous associations. I chose this old-english based alphabet as the nominals of porcupine[8]. They work for porcupine[7] as well if you leave out "ð" from the scale.Porcupine 8 alphabet: b c d ðe f þ æPorcupine 7 alphabet:b c d e f þ æ------------Some diagrams by Andrew Heathwaite to illustrate:

Andrew added:

Yikes, so #v (sharp-down) is 40/39 and b^^ (flat-double-up) is 65/64 -- and in a 13-limit Porcupine musical setting, unless you're in 37edo, they're not the same, and they're both necessary if you want to spell your scales logically!Let's say you want an 8:9:10:11:12:13:14 chord with letter names A B C D E F G. If you start it on Av, it's:Av B C D E Fb^ G...with the flat-up turning a 5/3 into 13/8 by subtracting 40/39.But if I start it on A natural, I get:A B^ C^ D^ E^ Fb^^ G^...with the flat-double-up turning an 8/5 into 13/8 by adding 65/64!To summarize:#v is the chroma in Porcupine[15].In a 13-limit setting, it's 40/39.In 15edo it's tempered out.In 22edo, it's one degree, which would mean, for example, A#v=A^; so we don't need it to describe all the pitches.In 37edo, it's one degree, but A#v != A^, because ^ is two degrees.b^^ is the chroma in Porcupine[22].In a 13-limit setting, it's 65/64.In 15edo, it's equivalent to ^ and # and therefore totally unnecessary.In 22edo, it's tempered out.In 37edo, it's one degree, which means that #v and bvv are in fact the same, and only one accidental would be needed.In other Porcupinefish systems (like 59edo, for instance), it's smaller than #v, and therefore needs a distinct and preferably smaller symbol.That's my proposal for expanding the Porcupine notation Mike Battaglia has described into the 13-limit. Does this make sense to people?BTW with this notation system, one question is - how many lines do you use in a staff? I guess you'd have to have "staff switches" in the middle of a score if you want to switch into a porcupine[8]-oriented notation or what have you.## Kite Giedraitis's approach

Ups and downs notation can be used even though we don't know which edo we are in. We know that porcupine divides the perfect 4th into 3 equal steps. Also the aug 4th is always 3 major 2nds by definition. And from P4 to A4 is A1. So any edo which divides the aug1 into 3 equal steps will temper out porcupine. These are the edos marked on the scale tree on the linked page as sharp-3, sharp-6, etc. For sharp-3 edos (15, 22, 29, etc.), A1 = triple-up unison, and the generator is

generator = P4 / 3 = (A4 - A1) / 3 = A4 / 3 - A1 / 3 = M2 - ^31 / 3 = M2 - ^1 = vM2

For sharp-6 edos (e.g. 30 or 72), the generator is vvM2. Sharp-9 edos are rarely used, but the generator would be v3M2.

For sharp-3 edos, the genchain is ^1 - M2 - vM3 - ^4 - P5 - vM6 - ^m7 -

- vM2 - ^m3 - P4 - v5 - ^m6 - m7 - v8.P1In C, this would be C^ - D - Ev - F^ - G - Av - Bb^ -

- Dv - Eb^ - F - Gv - Ab^ - Bb - Cv.CFor sharp-6 edos, simply double all ups and downs: P1 - vvM2 - ^^m3 - P4 - vv5... and C - Dvv - Eb^^ - F - Gvv...

This assumes a mapping of 5/4 that results in 250/243 mapping to zero edosteps. Since 10/9 should be vM2, 5/4 should be 10/9 + 9/8 = vM2 +M2 = vM3. The obvious mapping often suffices, but sometimes the mapping needs tweaking, as with edos 36c, 43c, 57cc, 58c, 64ccc, 65c and 72cc. If the edo isn't tweaked, the generator won't map to 10/9, and two generators won't map to 6/5. (Arguably, the generated scale is still porcupine-like.)

If we're not in an edo at all, but in a rank-2 tuning with a generator of indeterminate cents, use the sharp-3 notation.