7n edos

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Dave Keenan
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7n edos

Postby Dave Keenan » Fri Sep 30, 2016 9:20 am

Rescued from facebook oblivion:

George Secor wrote:Dave Keenan I'm still working my way thru ᔣᗅᘹᖇᕦᖱ ᔤᖽᐸᕧᒷᕧᖶᓋᘘ's paper. I think you should get a copy of it so that the 3 of us can discuss possible revision of symbol sets for some of the more difficult and/or obscure EDOs.

I have already revisited the 7n-EDO stack, for which we had only done native notations for 7, 14, and 21. Here's the new stack, which includes a symbol for the limma, |||~), that's valid across the entire stack:
7: |||~) with naturals F C G D A E B
14: )||~ |||~) with naturals F C G D A E B
21: /|\ )||~ |||~) with naturals F C G D A E B
28: /|\ )||~ )//|| |||~) with naturals F C G D A E B
35: /|\ )||~ )//|| (|| |||~) with naturals F C G D A E B
Observe that only 5 different symbols are used in the entire stack, and all of them are valid for each EDO.

The |||~) symbol (157c), seems to be an appropriate choice to represent the (171c) "limma" in this stack, since its size is reasonably close to the actual alteration of pitch. However, I didn't expect that it would find much use in actual practice, but since I found that it would work, I decided to include it for the sake of completeness.

OOPS! I just realized that I made a mistake in the 35-EDO set in that )||~ is not valid as 2\35, but 3\35 instead, so I would have to use something else, such as )||(, for 2\35, in which case either )||~ or )//|| could be used for 3\35:
35a: /|\ )||( )||~ (|| |||~) with naturals F C G D A E B
35b: /|\ )||( )//|| (|| |||~) with naturals F C G D A E B
Since there could be additional alternatives for the entire stack, I think I'll revisit the 5n-EDO stack and then compare that with the 7-EDO stack to determine which choices would facilitate translation between temperaments.

Here I have added colons either side of each ASCII representation of a symbol (and added spaces between any consecutive slashes or back-slashes) so that the forum software would treat them as "smilies" and render them as the appropriate symbols.

7: :|||~): with naturals F C G D A E B
14: :)||~: :|||~): with naturals F C G D A E B
21: :/|\: :)||~: :|||~): with naturals F C G D A E B
28: :/|\: :)||~: :)/ /||: :|||~): with naturals F C G D A E B
35a: :/|\: :)||(: :)||~: :(||: :|||~): with naturals F C G D A E B
35b: :/|\: :)||(: :)/ /||: :(||: :|||~): with naturals F C G D A E B

At first I thought the failure to correctly render |||~) was merely because I have not yet installed any smilies for triple-shaft symbols beyond the Spartan set. But in fact, no symbol resembling |||~) or |~) exists in any Sagittal set. See page 24 of http://sagittal.org/sagittal.pdf. So what did you really mean here, George?

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Dave Keenan
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Re: 7n edos

Postby Dave Keenan » Fri Jun 02, 2017 9:16 am

George wrote in email (on 2016-Sep-30):
George Secor wrote:Oops, you're right! |||~) would have been 7:23S (45927:47104) + an apotome, which we might have been considering at one time, but we chose 5:13M (405:416) instead. For some reason I never updated my EDO-degrees spreadsheet with the change. Fortunately, a symbol to represent the limma isn't really necessary in the 7n stack.

But since then we have come up with a better rationale for 7n-edo notations (and other "bad fifth" EDOs), thanks to suggestions by Cryptic Ruse / Igliashon Jones. See this thread:
http://forum.sagittal.org/viewtopic.php?f=5&t=256

The proposal looks like this for 7n-edos:
7n-edos: A:B C:D D:E F:G G:A = 1\7, B:C E:F = 1\7, # b = 0 (Must use multi-shafts for >3/4-limma. Can't use # or b.)
 7-edo :h: :||\: 7-edo
14-edo :h: :|\: :||\: 14-edo
21-edo :h: :|): :(|\: :||\: 21-edo
28-edo :h: :|): :|\: :(|\: :||\: 28-edo
35-edo :h: :|(: :|): :(|\: :||): :||\: 35-edo
Limma fractions: 1/5 1/4 1/3 2/5 1/2 3/5 2/3 3/4 4/5 1 limma

Use the horizontal scroll bar below to see the rest of the figure above.


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