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User:BudjarnLambeth/Draft related tunings section

Title1

Octave stretch or compression

Main article: 23edo and octave stretching

23edo is not typically taken seriously as a tuning except by those interested in extreme xenharmony. Its fifths are significantly flat, and is neighbors 22edo and 24edo generally get more attention.

However, when using a slightly stretched octave of around 1216 cents, 23edo looks much better, and it approximates the perfect fifth (and various other intervals involving the 5th, 7th, 11th, and 13th harmonics) to within 18 cents or so. If we can tolerate errors around this size in 12edo, we can probably tolerate them in stretched-23 as well.

Stretched 23edo is one of the best tunings to use for exploring the antidiatonic scale (and its 9-note extension, the superantidiatonic scale), since its fifth is more consonant and less "wolfish" than fifths in other pelogic family temperaments.

What follows is a comparison of stretched- and compressed-octave 23edo tunings.

86zpi
  • Step size: 51.653 ¢, octave size: NNN ¢

_ing the octave of EDONAME by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning ZPINAME does this.

Approximation of harmonics in ZPINAME
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -12.0 +9.2 -24.0 +2.9 -2.8 -11.4 +15.7 +18.4 -9.0 -19.1 -14.8
Relative (%) -23.2 +17.8 -46.4 +5.7 -5.4 -22.0 +30.4 +35.6 -17.5 -36.9 -28.6
Step 23 37 46 54 60 65 70 74 77 80 83
Approximation of harmonics in ZPINAME (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +1.6 -23.4 +12.2 +3.7 +2.1 +6.4 +16.1 -21.0 -2.2 +20.6 -4.7 +24.9
Relative (%) +3.2 -45.2 +23.5 +7.2 +4.0 +12.5 +31.2 -40.7 -4.2 +39.9 -9.1 +48.2
Step 86 88 91 93 95 97 99 100 102 104 105 107
60ed6
  • Step size: NNN ¢, octave size: NNN ¢

_ing the octave of EDONAME by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning EDONOI does this.

Approximation of harmonics in EDONOI
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -10.9 +10.9 -21.8 +5.4 +0.0 -8.4 +18.9 +21.8 -5.5 -15.4 -10.9
Relative (%) -21.1 +21.1 -42.2 +10.5 +0.0 -16.2 +36.6 +42.2 -10.6 -29.7 -21.1
Steps
(reduced) 		23
(23) 		37
(37) 		46
(46) 		54
(54) 		60
(0) 		65
(5) 		70
(10) 		74
(14) 		77
(17) 		80
(20) 		83
(23)
Approximation of harmonics in EDONOI (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +5.6 -19.3 +16.4 +8.0 +6.5 +10.9 +20.7 -16.4 +2.5 +25.4 +0.1 -21.8
Relative (%) +10.8 -37.3 +31.7 +15.5 +12.5 +21.1 +40.1 -31.7 +4.9 +49.1 +0.3 -42.2
Steps
(reduced) 		86
(26) 		88
(28) 		91
(31) 		93
(33) 		95
(35) 		97
(37) 		99
(39) 		100
(40) 		102
(42) 		104
(44) 		105
(45) 		106
(46)
85zpi
  • Step size: 52.114 ¢, octave size: NNN ¢

_ing the octave of EDONAME by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning ZPINAME does this.

Approximation of harmonics in ZPINAME
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -1.4 -25.9 -2.8 -24.3 +24.9 +18.6 -4.1 +0.4 -25.6 +17.8 +23.5
Relative (%) -2.6 -49.6 -5.3 -46.6 +47.8 +35.7 -7.9 +0.8 -49.2 +34.2 +45.1
Step 23 36 46 53 60 65 69 73 76 80 83
Approximation of harmonics in ZPINAME (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -10.8 +17.2 +2.0 -5.5 -6.2 -1.0 +9.7 +25.1 -7.3 +16.4 -8.4 +22.1
Relative (%) -20.8 +33.0 +3.8 -10.6 -12.0 -1.9 +18.5 +48.1 -13.9 +31.5 -16.2 +42.5
Step 85 88 90 92 94 96 98 100 101 103 104 106
23edo
  • Step size: NNN ¢, octave size: NNN ¢

Pure-octaves EDONAME approximates all harmonics up to 16 within NNN ¢.

Approximation of harmonics in EDONAME
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.0 -23.7 +0.0 -21.1 -23.7 +22.5 +0.0 +4.8 -21.1 +22.6 -23.7
Relative (%) +0.0 -45.4 +0.0 -40.4 -45.4 +43.1 +0.0 +9.2 -40.4 +43.3 -45.4
Steps
(reduced) 		23
(0) 		36
(13) 		46
(0) 		53
(7) 		59
(13) 		65
(19) 		69
(0) 		73
(4) 		76
(7) 		80
(11) 		82
(13)
Approximation of harmonics in EDONAME (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -5.7 +22.5 +7.4 +0.0 -0.6 +4.8 +15.5 -21.1 -1.2 +22.6 -2.2 -23.7
Relative (%) -11.0 +43.1 +14.2 +0.0 -1.2 +9.2 +29.8 -40.4 -2.3 +43.3 -4.2 -45.4
Steps
(reduced) 		85
(16) 		88
(19) 		90
(21) 		92
(0) 		94
(2) 		96
(4) 		98
(6) 		99
(7) 		101
(9) 		103
(11) 		104
(12) 		105
(13)
23et, 13-limit WE tuning
  • Step size: 53.237 ¢, octave size: NNN ¢

_ing the octave of EDONAME by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. Its SUBGROUP WE tuning and SUBGROUP TE tuning both do this.

Approximation of harmonics in ETNAME, SUBGROUP WE tuning
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +24.5 +14.6 -4.3 -18.0 -14.2 -14.9 +20.1 -24.1 +6.5 +1.2 +10.2
Relative (%) +45.9 +27.4 -8.1 -33.8 -26.7 -28.0 +37.8 -45.2 +12.1 +2.2 +19.2
Step 23 36 45 52 58 63 68 71 75 78 81
Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -21.9 +9.6 -3.4 -8.7 -7.2 +0.4 +13.2 -22.3 -0.3 +25.6 +1.9 -18.5
Relative (%) -41.1 +18.0 -6.4 -16.3 -13.4 +0.7 +24.9 -41.9 -0.6 +48.1 +3.6 -34.8
Step 83 86 88 90 92 94 96 97 99 101 102 103
23et, 2.3.5.13 WE tuning
  • Step size: 53.447 ¢, octave size: NNN ¢

_ing the octave of EDONAME by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. Its SUBGROUP WE tuning and SUBGROUP TE tuning both do this.

Approximation of harmonics in ETNAME, SUBGROUP WE tuning
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -24.2 +22.1 +5.1 -7.1 -2.0 -1.7 -19.1 -9.2 +22.2 +17.5 -26.2
Relative (%) -45.2 +41.4 +9.6 -13.2 -3.8 -3.1 -35.6 -17.2 +41.6 +32.8 -49.0
Step 22 36 45 52 58 63 67 71 75 78 80
Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -4.4 -25.8 +15.1 +10.2 +12.2 +20.1 -20.0 -2.0 +20.5 -6.6 +23.3 +3.1
Relative (%) -8.3 -48.3 +28.2 +19.1 +22.8 +37.6 -37.5 -3.7 +38.3 -12.4 +43.6 +5.8
Step 83 85 88 90 92 94 95 97 99 100 102 103
59ed6
  • Step size: NNN ¢, octave size: NNN ¢

_ing the octave of EDONAME by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning EDONOI does this.

Approximation of harmonics in EDONOI
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +9.2 -9.2 +18.5 +0.2 +0.0 -4.0 -24.9 -18.5 +9.4 +2.1 +9.2
Relative (%) +17.6 -17.6 +35.1 +0.4 +0.0 -7.6 -47.3 -35.1 +17.9 +4.1 +17.6
Steps
(reduced) 		23
(23) 		36
(36) 		46
(46) 		53
(53) 		59
(0) 		64
(5) 		68
(9) 		72
(13) 		76
(17) 		79
(20) 		82
(23)
Approximation of harmonics in EDONOI (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -24.2 +5.2 -9.0 -15.6 -15.4 -9.2 +2.3 +18.7 -13.2 +11.4 -13.0 +18.5
Relative (%) -46.0 +10.0 -17.2 -29.7 -29.4 -17.6 +4.4 +35.5 -25.2 +21.7 -24.7 +35.1
Steps
(reduced) 		84
(25) 		87
(28) 		89
(30) 		91
(32) 		93
(34) 		95
(36) 		97
(38) 		99
(40) 		100
(41) 		102
(43) 		103
(44) 		105
(46)
84zpi
  • Step size: 52.615 ¢, octave size: NNN ¢

_ing the octave of EDONAME by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning ZPINAME does this.

Approximation of harmonics in ZPINAME
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +10.1 -7.8 +20.3 +2.3 +2.3 -1.5 -22.2 -15.6 +12.4 +5.3 +12.5
Relative (%) +19.3 -14.9 +38.6 +4.3 +4.4 -2.8 -42.2 -29.7 +23.6 +10.0 +23.7
Step 23 36 46 53 59 64 68 72 76 79 82
Approximation of harmonics in ZPINAME (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -20.9 +8.7 -5.5 -12.0 -11.8 -5.5 +6.1 +22.6 -9.3 +15.4 -8.9 +22.6
Relative (%) -39.7 +16.5 -10.5 -22.9 -22.4 -10.4 +11.7 +42.9 -17.6 +29.3 -17.0 +43.0
Step 84 87 89 91 93 95 97 99 100 102 103 105
36edt
  • Step size: NNN ¢, octave size: NNN ¢

_ing the octave of EDONAME by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning EDONOI does this.

Approximation of harmonics in EDONOI
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +15.1 +0.0 -22.6 +13.8 +15.1 +12.4 -7.4 +0.0 -23.9 +22.4 -22.6
Relative (%) +28.7 +0.0 -42.7 +26.1 +28.7 +23.5 -14.0 +0.0 -45.3 +42.4 -42.7
Steps
(reduced) 		23
(23) 		36
(0) 		45
(9) 		53
(17) 		59
(23) 		64
(28) 		68
(32) 		72
(0) 		75
(3) 		79
(7) 		81
(9)
Approximation of harmonics in EDONOI (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -2.6 -25.3 +13.8 +7.7 +8.4 +15.1 -25.6 -8.8 +12.4 -15.3 +13.4 -7.4
Relative (%) -5.0 -47.8 +26.1 +14.6 +16.0 +28.7 -48.5 -16.6 +23.5 -28.9 +25.4 -14.0
Steps
(reduced) 		84
(12) 		86
(14) 		89
(17) 		91
(19) 		93
(21) 		95
(23) 		96
(24) 		98
(26) 		100
(28) 		101
(29) 		103
(31) 		104
(32)

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

  • Main: "23edo and octave stretching"
  • 36edt
  • 84zpi (52.615c)
  • 59ed6
  • 2.3.5.13 WE (52.447c)
  • 13-limit WE (52.237c)
  • 85zpi (52.114c)
  • 60ed6
  • 86zpi (51.653c)

60edo (narrow down edonoi & ZPIs)

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)
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
  • 95edt
  • 35edf
  • 139ed5
  • 155ed6
  • 208ed11
  • 215ed12
  • 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
  • 266ed6
  • 289ed7
  • 356ed11
  • 369ed12
  • 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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