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User:BudjarnLambeth/Sandbox2

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Revision as of 02:55, 28 August 2025 by BudjarnLambeth (talk | contribs) (→Octave stretch or compression)

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User:BudjarnLambeth/Draft related tunings section

Title1

Octave stretch or compression

Approximation of harmonics in 99edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.00 -1.96 +0.00 -6.31 -1.96 -8.83 +0.00 -3.91 -6.31 +8.68 -1.96
Relative (%) +0.0 -9.8 +0.0 -31.6 -9.8 -44.1 +0.0 -19.6 -31.6 +43.4 -9.8
Steps
(reduced) 		60
(0) 		95
(35) 		120
(0) 		139
(19) 		155
(35) 		168
(48) 		180
(0) 		190
(10) 		199
(19) 		208
(28) 		215
(35)
Approximation of harmonics in 99edo (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -0.53 -8.83 -8.27 +0.00 -4.96 -3.91 +2.49 -6.31 +9.22 +8.68 -8.27 -1.96
Relative (%) -2.6 -44.1 -41.3 +0.0 -24.8 -19.6 +12.4 -31.6 +46.1 +43.4 -41.4 -9.8
Steps
(reduced) 		222
(42) 		228
(48) 		234
(54) 		240
(0) 		245
(5) 		250
(10) 		255
(15) 		259
(19) 		264
(24) 		268
(28) 		271
(31) 		275
(35)


Approximation of harmonics in 99edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.00 -2.93 +0.00 -1.85 -2.93 -1.84 +0.00 +5.80 -1.85 -3.75 -2.93
Relative (%) +0.0 -25.1 +0.0 -15.9 -25.1 -15.8 +0.0 +49.8 -15.9 -32.1 -25.1
Steps
(reduced) 		103
(0) 		163
(60) 		206
(0) 		239
(33) 		266
(60) 		289
(83) 		309
(0) 		327
(18) 		342
(33) 		356
(47) 		369
(60)
Approximation of harmonics in 99edo (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -1.69 -1.84 -4.77 +0.00 -0.10 +5.80 +5.40 -1.85 -4.76 -3.75 +0.85 -2.93
Relative (%) -14.5 -15.8 -41.0 +0.0 -0.9 +49.8 +46.3 -15.9 -40.9 -32.1 +7.3 -25.1
Steps
(reduced) 		381
(72) 		392
(83) 		402
(93) 		412
(0) 		421
(9) 		430
(18) 		438
(26) 		445
(33) 		452
(40) 		459
(47) 		466
(54) 		472
(60)

Title2

Possible tunings to be used on each page

You can remove some of these or add more that aren't listed here; this section is pretty much just brainstorming.

(Used https://x31eq.com/temper-pyscript/net.html, used WE instead of TE cause it kept defaulting to WE and I kept not remembering to switch it)

High-priority

23edo (narrow down edonoi & ZPIs)

  • Main: "23edo and octave stretching"
  • 36edt
Approximation of prime harmonics in 36edt
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +15.1 +0.0 +13.8 +12.4 +22.4 -2.6 +8.4 -25.6 +13.4 -18.0 +25.0
Relative (%) +28.7 +0.0 +26.1 +23.5 +42.4 -5.0 +16.0 -48.5 +25.4 -34.2 +47.3
Steps
(reduced) 		23
(23) 		36
(0) 		53
(17) 		64
(28) 		79
(7) 		84
(12) 		93
(21) 		96
(24) 		103
(31) 		110
(2) 		113
(5)
  • 59ed6
Approximation of prime harmonics in 59ed6
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +9.2 -9.2 +0.2 -4.0 +2.1 -24.2 -15.4 +2.3 -13.0 +6.3 -4.0
Relative (%) +17.6 -17.6 +0.4 -7.6 +4.1 -46.0 -29.4 +4.4 -24.7 +12.0 -7.6
Steps
(reduced) 		23
(23) 		36
(36) 		53
(53) 		64
(5) 		79
(20) 		84
(25) 		93
(34) 		97
(38) 		103
(44) 		111
(52) 		113
(54)
  • 60ed6
Approximation of prime harmonics in 60ed6
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -10.9 +10.9 +5.4 -8.4 -15.4 +5.6 +6.5 +20.7 +0.1 +12.4 +0.4
Relative (%) -21.1 +21.1 +10.5 -16.2 -29.7 +10.8 +12.5 +40.1 +0.3 +24.1 +0.7
Steps
(reduced) 		23
(23) 		37
(37) 		54
(54) 		65
(5) 		80
(20) 		86
(26) 		95
(35) 		99
(39) 		105
(45) 		113
(53) 		115
(55)
  • 2.3.5.13 WE (52.447c)
Approximation of prime harmonics in 1ed52.447c
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +6.3 -13.9 -6.6 -12.2 -8.0 +17.5 +25.1 -10.2 +26.2 -8.0 -18.5
Relative (%) +12.0 -26.4 -12.6 -23.3 -15.3 +33.3 +47.8 -19.4 +50.0 -15.2 -35.3
Step 23 36 53 64 79 85 94 97 104 111 113
  • 13-limit WE (52.237c)
Approximation of prime harmonics in 1ed52.237c
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +1.5 -21.4 -17.8 -25.7 -24.6 -0.4 +5.3 +21.7 +4.4 +21.0 +10.0
Relative (%) +2.8 -41.0 -34.0 -49.1 -47.1 -0.7 +10.2 +41.6 +8.4 +40.1 +19.1
Step 23 36 53 64 79 85 94 98 104 112 114
  • 84zpi (52.615c)
Approximation of prime harmonics in 1ed52.615c
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +10.1 -7.8 +2.3 -1.5 +5.3 -20.9 -11.8 +6.1 -8.9 +10.7 +0.5
Relative (%) +19.3 -14.9 +4.3 -2.8 +10.0 -39.7 -22.4 +11.7 -17.0 +20.3 +0.9
Step 23 36 53 64 79 84 93 97 103 111 113
  • 85zpi (52.114c)
Approximation of prime harmonics in 1ed52.114c
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -1.4 -25.9 -24.3 +18.6 +17.8 -10.8 -6.2 +9.7 -8.4 +7.2 -4.0
Relative (%) -2.6 -49.6 -46.6 +35.7 +34.2 -20.8 -12.0 +18.5 -16.2 +13.8 -7.8
Step 23 36 53 65 80 85 94 98 104 112 114
  • 86zpi (51.653c)
Approximation of prime harmonics in 1ed51.653c
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -12.0 +9.2 +2.9 -11.4 -19.1 +1.6 +2.1 +16.1 -4.7 +7.2 -4.9
Relative (%) -23.2 +17.8 +5.7 -22.0 -36.9 +3.2 +4.0 +31.2 -9.1 +14.0 -9.6
Step 23 37 54 65 80 86 95 99 105 113 115

60edo (narrow down edonoi & ZPIs)

  • 95edt
  • 35edf
  • 139ed5
  • 155ed6
  • 208ed11
  • (???)ed12
  • 255ed19
  • 272ed23 (great for catnip temperament, maybe there's a similar but simpler tuning w similar benefits?)
  • 13-limit WE (20.013c)
  • 299zpi (20.128c)
  • 300zpi (20.093c)
  • 301zpi (20.027c)
  • 302zpi (19.962c)
  • 303zpi (19.913c)
  • 304zpi (19.869c)
Medium priority

13edo

  • Main: "13edo and optimal octave stretching"
  • 2.5.11.13 WE (92.483c)
  • 2.5.7.13 WE (92.804c)
  • 2.3 WE (91.405c) (good for opposite 7 mapping)
  • 38zpi (92.531c)

32edo (narrow down ZPIs)

  • 90ed7
  • 51edt
  • 75ed5
  • 1ed46/45
  • 11-limit WE (37.453c)
  • 13-limit WE (37.481c)
  • 131zpi (37.862c)
  • 132zpi (37.662c)
  • 133zpi (37.418c)
  • 134zpi (37.176c)

33edo (narrow down edonoi)

  • 76ed5
  • 92ed7
  • 52edt
  • 1ed47/46
  • 114ed11
  • 122ed13
  • 93ed7
  • 23edPhi
  • 77ed5
  • 123ed13
  • 115ed11
  • 11-limit WE (36.349c)
  • 13-limit WE (36.357c)
  • 137zpi (36.628c)
  • 138zpi (36.394c)
  • 139zpi (36.179c)

39edo (narrow down slightly)

  • 62edt
  • 101ed6
  • 18ed11/8
  • 2.3.5.11 WE (30.703c)
  • 2.3.7.11.13 WE (30.787c)
  • 13-limit WE (30.757c)
  • 171zpi (30.973c)
  • 172zpi (30.836c)
  • 173zpi (30.672c)

42edo (narrow down slightly)

  • 42ed257/128 (replace w something similar but simpler)
  • AS123/121 (1ed123/121)
  • 11ed6/5
  • 34ed7/4
  • 7-limit WE (28.484c)
  • 13-limit WE (28.534c)
  • 189zpi (28.689c)
  • 190zpi (28.572c)
  • 191zpi (28.444c)

45edo

  • 126ed7
  • 13ed11/9
  • 7-limit WE (26.745c)
  • 13-limit WE (26.695c)
  • 207zpi (26.762)
  • 208zpi (26.646)
  • 209zpi (26.550)

54edo (narrow down slightly)

  • 86edt
  • 126ed5
  • 152ed7
  • 38ed5/3
  • 40ed5/3
  • 2.3.7.11.13 WE (22.180c)
  • 13-limit WE (22.198c)
  • 262zpi (22.313c)
  • 263zpi (22.243c)
  • 264zpi (22.175c)

59edo (narrow down ZPIs)

  • 93edt
  • 166ed7
  • 203ed11
  • 7-limit WE (20.301c)
  • 11-limit WE (20.310c)
  • 13-limit WE (20.320c)
  • 293zpi (20.454c)
  • 294zpi (20.399c)
  • 295zpi (20.342c)
  • 296zpi (20.282c)
  • 297zpi (20.229c)

64edo (narrow down ZPIs)

  • 149ed5
  • 180ed7
  • 222ed11
  • 47ed5/3
  • 11-limit WE (18.755c)
  • 13-limit WE (18.752c)
  • 325zpi (18.868c)
  • 326zpi (18.816c)
  • 327zpi (18.767c)
  • 328zpi (18.721c)
  • 329zpi (18.672c)
  • 330zpi (18.630c)

103edo (narrow down edonoi, choose ZPIS)

  • 163edt
  • 239ed5
  • (???)ed6
  • 289ed7
  • 356ed11
  • (???)ed12
  • 381ed13
  • 421ed17
  • 466ed23
  • 13-limit WE (11.658c)
  • Best nearby ZPI(s)

111edo (choose ZPIS)

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

118edo (choose ZPIS)

  • 187edt
  • 69edf
  • 13-limit WE (10.171c)
  • Best nearby ZPI(s)
Low priority

104edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

125edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

145edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

152edo

  • 241edt
  • 13-limit WE (7.894c)
  • Best nearby ZPI(s)

159edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

166edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

182edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

198edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

212edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

243edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

247edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)
Optional

25edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

26edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

29edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

30edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

34edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

35edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

36edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

37edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

5edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

6edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

9edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

10edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

11edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

15edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

18edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

48edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

20edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

24edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

28edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)
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