blast from the past re: microtempering partch

sent from me to dave keenan Thu 1/13/00 5:26 PM . . .

You wrote,

>In earlier messages I gave the following simultaneous distribution
of the
>224:225 and 384:385 commas or "unison vectors".

Just for fun, here are the numbers of notes given by various pairs of
11-limit subdiaschismic unison vectors, keeping 224:225 and 384:385
as the other two unison vectors:

98:99, 99:100 -- 22 notes
98:99, 125:126 -- 31 notes
98:99, 242:243 -- 31 notes
98:99, 243:245 -- 22 notes
98:99, 440:441 -- 31 notes
98:99, 891:896 -- 22 notes
98:99, 1024:1029 -- 31 notes
98:99, 1323:1331 -- 31 notes
98:99, 2400:2401 -- 31 notes
98:99, 3024:3025 -- 31 notes
98:99, 3993:4000 -- 22 notes
98:99, 4374:4375 -- 53 notes
98:99, 9800:9801 -- 22 notes
99:100, 120:121 -- 22 notes
99:100, 125:126 -- 19 notes
99:100, 175:176 -- 22 notes
99:100, 242:243 -- 41 notes
99:100, 440:441 -- 41 notes
99:100, 1024:1029 -- 41 notes
99:100, 1323:1331 -- 63 notes
99:100, 2400:2401 -- 41 notes
99:100, 3024:3025 -- 41 notes
99:100, 3993:4000 -- 22 notes
99:100, 4374:4375 -- 19 notes
99:100, 5625:5632 -- 22 notes
99:100, 9800:9801 -- 22 notes
120:121, 125:126 -- 31 notes
120:121, 242:243 -- 31 notes
120:121, 243:245 -- 22 notes
120:121, 440:441 -- 31 notes
120:121, 891:896 -- 22 notes
120:121, 1024:1029 -- 31 notes
120:121, 1323:1331 -- 31 notes
120:121, 2400:2401 -- 31 notes
120:121, 3024:3025 -- 31 notes
120:121, 3993:4000 -- 22 notes
120:121, 4374:4375 -- 53 notes
120:121, 9800:9801 -- 22 notes
125:126, 175:176 -- 31 notes
125:126, 242:243 -- 31 notes
125:126, 243:245 -- 19 notes
125:126, 441:440 -- 31 notes
125:126, 891:896 -- 19 notes
125:126, 1024:1029 -- 31 notes
125:126, 1323:1331 -- 62 notes
125:126. 2400:2401 -- 31 notes
125:126, 3024:3025 -- 31 notes
125:126, 3993:4000 -- 50 notes
125:126, 4374:4375 -- 19 notes
125:126, 5625:5632 -- 31 notes
125:126, 9800:9801 -- 50 notes
175:176, 243:245 -- 22 notes
175:176, 891:896 -- 22 notes
175:176, 1024:1029 -- 31 notes
175:176, 1323:1331 -- 31 notes
175:176, 2400:2401 -- 31 notes
175:176, 3024:3025 -- 31 notes
175:176, 3993:4000 -- 22 notes
175:176, 9800:9801 -- 22 notes
242:243, 243:245 -- 41 notes
242:243, 891:896 -- 41 notes
242:243, 1323:1331 -- 31 notes
242:243, 3993:4000 -- 72 notes
242:243, 4374:4375 -- 72 notes
242:243, 5625:5632 -- 31 notes
242:243, 9800:9801 -- 72 notes
243:245, 440:441 -- 41 notes
243:245, 1024:1029 -- 41 notes
243:245, 1323:1331 -- 63 notes
243:245, 2400:2401 -- 41 notes
243:245, 3024:3025 -- 41 notes
243:245, 3993:4000 -- 22 notes
243:245, 4374:4375 -- 19 notes
243:245, 5625:5632 -- 22 notes
243:243, 9800:9801 -- 72 notes
440:441, 891:896 -- 41 notes
440:441, 1323:1331 -- 31 notes
440:441, 3993:4000 -- 72 notes
440:441, 4374:4375 -- 72 notes
440:441, 5625:5632 -- 31 notes
440:441, 9800:9801 -- 72 notes
891:896, 1024:1029 -- 41 notes
891:896, 1323:1331 -- 63 notes
891:896, 2400:2401 -- 41 notes
891:896, 3024:3025 -- 41 notes
891:896, 3993:4000 -- 22 notes
891:896, 4374:4375 -- 19 notes
891:896, 5625:5632 -- 22 notes
891:896, 9800:9801 -- 22 notes
1024:1029, 1323:1331 -- 31 notes
1024:1029, 3993:4000 -- 72 notes
1024:1029, 4374:4375 -- 72 notes
1024:1029, 5625:5632 -- 31 notes
1024:1029, 9800:9801 -- 72 notes
1323:1331, 2400:2401 -- 31 notes
1323:1331, 3024:3025 -- 31 notes
1323:1331, 3993:4000 -- 94 notes
1323:1331, 4374:4375 -- 125 notes
1323:1331, 5625:5632 -- 31 notes
1323:1331, 9800:9801 -- 94 notes
2400:2401, 3993:4000 -- 72 notes
2400:2401, 4374:4375 -- 72 notes
2400:2401, 5625:5632 -- 31 notes
2400:2401, 9801:9800 -- 72 notes
3024:3025, 3993:4000 -- 72 notes
3024:3025, 4374:4375 -- 72 notes
3024:3025, 5625:5632 -- 31 notes
3024:3025, 9800:9801 -- 72 notes
3993:4000, 4374:4375 -- 72 notes
3993:4000, 5625:5632 -- 22 notes
4374:4375, 5625:5632 -- 53 notes
4374:4375, 9800:9801 -- 72 notes
5625:5632, 9800:9801 -- 22 notes

--- In tuning-math@y..., "paulerlich" <paul@s...> wrote:

> Just for fun, here are the numbers of notes given by various pairs of
> 11-limit subdiaschismic unison vectors, keeping 224:225 and 384:385
> as the other two unison vectors:

Where did this list of 11-limit commas come from?

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:
>
> > Just for fun, here are the numbers of notes given by various
pairs of
> > 11-limit subdiaschismic unison vectors, keeping 224:225 and
384:385
> > as the other two unison vectors:
>
> Where did this list of 11-limit commas come from?

i'll be darned if i remember. any glaring omissions?

we haven't heard much about these 63-tone systems -- any comments on
them, gene?

--- In tuning-math@y..., "paulerlich" <paul@s...> wrote:

> we haven't heard much about these 63-tone systems -- any comments on
> them, gene?

If you wedge together 100/99^225/224^385/384 or 100/99^225/224^540/539 or 100/99^385/384^540/539 you get the
11-limit version of magic, but there doesn't seem to be any reason to prefer the 63 version over the 41. However, it extends to a different and more accurate 13-limit version of magic in the 63 form.

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:

I do get something other than magic for some combinations; for instance 100/99^225/224^1331/1323 gives a temperament with diesis-sized steps: 1/31, 2/63, 3/94 or 4/125.

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:
>
> > we haven't heard much about these 63-tone systems -- any comments
on
> > them, gene?
>
> If you wedge together 100/99^225/224^385/384 or
100/99^225/224^540/539 or 100/99^385/384^540/539 you get the
> 11-limit version of magic, but there doesn't seem to be any reason
to prefer the 63 version over the 41. However, it extends to a
different and more accurate 13-limit version of magic in the 63 form.

cool!

here's one of the 63-tone fokker periodicity blocks:

cents numerator denominator
0 1 1
14.367 121 120
38.906 45 44
53.273 33 32
80.537 22 21
84.467 21 20
119.44 15 14
123.37 189 176
150.64 12 11
165 11 10
189.54 135 121
203.91 9 8
235.1 63 55
235.68 55 48
274.58 75 64
284.45 33 28
305.78 105 88
315.64 6 5
347.41 11 9
354.55 27 22
386.31 5 4
396.18 44 35
417.51 14 11
435.08 9 7
466.85 55 42
470.78 21 16
498.04 4 3
509.69 945 704
536.95 15 11
551.32 11 8
568.15 168 121
590.22 45 32
617.49 10 7
621.42 63 44
648.68 16 11
670.76 165 112
687.59 180 121
701.96 3 2
716.32 121 80
733.15 84 55
755.23 99 64
782.49 11 7
786.42 63 40
813.69 8 5
835.76 363 224
852.59 18 11
866.96 33 20
894.22 176 105
905.87 27 16
933.13 12 7
937.06 189 110
968.83 7 4
986.4 99 56
1007.7 315 176
1017.6 9 5
1049.4 11 6
1056.5 81 44
1088.3 15 8
1098.1 66 35
1119.5 21 11
1129.3 48 25
1168.2 108 55
1168.8 55 28

it looks pretty 'fishy' . . .