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Title1

Octave stretch or compression

152ed6
  • Octave size: NNN ¢

_ing the octave of 59edo by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning 152ed6 does this.

Approximation of harmonics in 152ed6
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +4.05 -4.05 +8.10 +9.53 +0.00 -1.57 -8.26 -8.10 -6.83 -8.58 +4.05
Relative (%) +19.8 -19.8 +39.7 +46.7 +0.0 -7.7 -40.5 -39.7 -33.5 -42.0 +19.8
Steps
(reduced) 		59
(59) 		93
(93) 		118
(118) 		137
(137) 		152
(0) 		165
(13) 		176
(24) 		186
(34) 		195
(43) 		203
(51) 		211
(59)
Approximation of harmonics in 152ed6 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +8.33 +2.48 +5.48 -4.21 -7.13 -4.05 +4.39 -2.78 -5.62 -4.53 +0.15 +8.10
Relative (%) +40.8 +12.1 +26.8 -20.7 -34.9 -19.8 +21.5 -13.6 -27.5 -22.2 +0.7 +39.7
Steps
(reduced) 		218
(66) 		224
(72) 		230
(78) 		235
(83) 		240
(88) 		245
(93) 		250
(98) 		254
(102) 		258
(106) 		262
(110) 		266
(114) 		270
(118)
294zpi
  • Step size: 20.399 ¢, octave size: NNN ¢

_ing the octave of 59edo by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning 294zpi does this.

Approximation of harmonics in 294zpi
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +3.54 -4.85 +7.08 +8.35 -1.31 -2.99 -9.78 -9.70 -8.51 +10.08 +2.23
Relative (%) +17.4 -23.8 +34.7 +40.9 -6.4 -14.7 -47.9 -47.5 -41.7 +49.4 +11.0
Step 59 93 118 137 152 165 176 186 195 204 211
Approximation of harmonics in 294zpi (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +6.45 +0.55 +3.50 -6.24 -9.20 -6.16 +2.24 -4.97 -7.84 -6.78 -2.14 +5.77
Relative (%) +31.6 +2.7 +17.2 -30.6 -45.1 -30.2 +11.0 -24.4 -38.4 -33.2 -10.5 +28.3
Step 218 224 230 235 240 245 250 254 258 262 266 270
211ed12
  • Step size: NNN ¢, octave size: NNN ¢

_ing the octave of 59edo by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning 211ed12 does this.

Approximation of harmonics in 211ed12
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +2.92 -5.83 +5.83 +6.90 -2.92 -4.74 +8.75 +8.72 +9.82 +7.92 +0.00
Relative (%) +14.3 -28.6 +28.6 +33.8 -14.3 -23.2 +42.9 +42.8 +48.1 +38.8 +0.0
Steps
(reduced) 		59
(59) 		93
(93) 		118
(118) 		137
(137) 		152
(152) 		165
(165) 		177
(177) 		187
(187) 		196
(196) 		204
(204) 		211
(0)
Approximation of harmonics in 211ed12 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +4.15 -1.82 +1.07 -8.72 +8.65 -8.75 -0.41 -7.66 +9.82 -9.55 -4.96 +2.92
Relative (%) +20.3 -8.9 +5.2 -42.8 +42.4 -42.9 -2.0 -37.6 +48.2 -46.9 -24.3 +14.3
Steps
(reduced) 		218
(7) 		224
(13) 		230
(19) 		235
(24) 		241
(30) 		245
(34) 		250
(39) 		254
(43) 		259
(48) 		262
(51) 		266
(55) 		270
(59)
ZPINAME
  • Step size: 20.342 ¢, octave size: NNN ¢

_ing the octave of 59edo by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning 295zpi does this.

Approximation of harmonics in 295zpi
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.18 -10.15 +0.36 +0.54 -9.97 +7.95 +0.53 +0.04 +0.72 -1.55 -9.79
Relative (%) +0.9 -49.9 +1.8 +2.7 -49.0 +39.1 +2.6 +0.2 +3.5 -7.6 -48.1
Step 59 93 118 137 152 166 177 187 196 204 211
Approximation of harmonics in 295zpi (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -5.97 +8.12 -9.61 +0.71 -2.53 +0.22 +8.33 +0.90 -2.20 -1.37 +3.04 -9.62
Relative (%) -29.4 +39.9 -47.2 +3.5 -12.5 +1.1 +40.9 +4.4 -10.8 -6.7 +14.9 -47.3
Step 218 225 230 236 241 246 251 255 259 263 267 270
59edo
  • Step size: 20.339 ¢, octave size: 1200.00 ¢

Pure-octaves 59edo approximates all harmonics up to 16 within NNN ¢. So does the tuning 137ed5 whose octave is identical within 0.05 ¢.

Approximation of harmonics in 59edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.00 +9.91 +0.00 +0.13 +9.91 +7.45 +0.00 -0.52 +0.13 -2.17 +9.91
Relative (%) +0.0 +48.7 +0.0 +0.6 +48.7 +36.6 +0.0 -2.6 +0.6 -10.6 +48.7
Steps
(reduced) 		59
(0) 		94
(35) 		118
(0) 		137
(19) 		153
(35) 		166
(48) 		177
(0) 		187
(10) 		196
(19) 		204
(27) 		212
(35)
Approximation of harmonics in 59edo (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -6.63 +7.45 +10.04 +0.00 -3.26 -0.52 +7.57 +0.13 -2.98 -2.17 +2.23 +9.91
Relative (%) -32.6 +36.6 +49.3 +0.0 -16.0 -2.6 +37.2 +0.6 -14.7 -10.6 +11.0 +48.7
Steps
(reduced) 		218
(41) 		225
(48) 		231
(54) 		236
(0) 		241
(5) 		246
(10) 		251
(15) 		255
(19) 		259
(23) 		263
(27) 		267
(31) 		271
(35)
59et, 13-limit WE tuning
  • Step size: 20.320 ¢, octave size: NNN ¢

_ing the octave of 59edo by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. Its 13-limit WE tuning and 13-limit TE tuning both do this.

Approximation of harmonics in 59et, 13-limit WE tuning
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -1.12 +8.12 -2.24 -2.47 +7.00 +4.29 -3.36 -4.07 -3.59 -6.04 +5.88
Relative (%) -5.5 +40.0 -11.0 -12.2 +34.5 +21.1 -16.5 -20.0 -17.7 -29.7 +29.0
Step 59 94 118 137 153 166 177 187 196 204 212
Approximation of harmonics in 59et, 13-limit WE tuning (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +9.55 +3.17 +5.65 -4.48 -7.84 -5.19 +2.81 -4.71 -7.90 -7.16 -2.83 +4.76
Relative (%) +47.0 +15.6 +27.8 -22.0 -38.6 -25.5 +13.8 -23.2 -38.9 -35.2 -13.9 +23.4
Step 219 225 231 236 241 246 251 255 259 263 267 271
59et, 7-limit WE tuning
  • Step size: 20.301 ¢, octave size: NNN ¢

_ing the octave of 59edo by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. Its 7-limit WE tuning and 7-limit TE tuning both do this.

Approximation of harmonics in ETNAME, 59et, 7-limit WE tuning
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -2.24 +6.34 -4.48 -5.08 +4.10 +1.14 -6.72 -7.62 -7.32 -9.91 +1.86
Relative (%) -11.0 +31.2 -22.1 -25.0 +20.2 +5.6 -33.1 -37.5 -36.0 -48.8 +9.1
Step 59 94 118 137 153 166 177 187 196 204 212
Approximation of harmonics in 59et, 7-limit WE tuning (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +5.39 -1.10 +1.26 -8.96 +7.89 -9.86 -1.96 -9.56 +7.48 +8.15 -7.91 -0.38
Relative (%) +26.6 -5.4 +6.2 -44.2 +38.8 -48.6 -9.7 -47.1 +36.8 +40.1 -39.0 -1.9
Step 219 225 231 236 242 246 251 255 260 264 267 271
166ed7
  • Step size: NNN ¢, octave size: NNN ¢

_ing the octave of 59edo by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning 166ed7 does this.

Approximation of harmonics in 166ed7
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -2.65 +5.69 -5.29 -6.02 +3.05 +0.00 -7.94 -8.91 -8.66 +8.98 +0.40
Relative (%) -13.0 +28.1 -26.1 -29.7 +15.0 +0.0 -39.1 -43.9 -42.7 +44.2 +2.0
Steps
(reduced) 		59
(59) 		94
(94) 		118
(118) 		137
(137) 		153
(153) 		166
(0) 		177
(11) 		187
(21) 		196
(30) 		205
(39) 		212
(46)
Approximation of harmonics in 166ed7 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +3.89 -2.65 -0.32 +9.71 +6.22 +8.74 -3.69 +8.98 +5.69 +6.33 -9.74 -2.25
Relative (%) +19.2 -13.0 -1.6 +47.8 +30.7 +43.1 -18.2 +44.3 +28.1 +31.2 -48.0 -11.1
Steps
(reduced) 		219
(53) 		225
(59) 		231
(65) 		237
(71) 		242
(76) 		247
(81) 		251
(85) 		256
(90) 		260
(94) 		264
(98) 		267
(101) 		271
(105)
212ed12
  • Step size: NNN ¢, octave size: NNN ¢

_ing the octave of 59edo by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning 212ed12 does this.

Approximation of harmonics in 212ed12
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -2.76 +5.52 -5.52 -6.28 +2.76 -0.31 -8.27 -9.26 -9.03 +8.59 +0.00
Relative (%) -13.6 +27.2 -27.2 -30.9 +13.6 -1.5 -40.8 -45.6 -44.5 +42.3 +0.0
Steps
(reduced) 		59
(59) 		94
(94) 		118
(118) 		137
(137) 		153
(153) 		166
(166) 		177
(177) 		187
(187) 		196
(196) 		205
(205) 		212
(0)
Approximation of harmonics in 212ed12 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +3.47 -3.07 -0.76 +9.26 +5.77 +8.27 -4.16 +8.50 +5.20 +5.83 +10.05 -2.76
Relative (%) +17.1 -15.1 -3.8 +45.6 +28.4 +40.8 -20.5 +41.9 +25.6 +28.7 +49.5 -13.6
Steps
(reduced) 		219
(7) 		225
(13) 		231
(19) 		237
(25) 		242
(30) 		247
(35) 		251
(39) 		256
(44) 		260
(48) 		264
(52) 		268
(56) 		271
(59)
296zpi
  • Step size: 20.282 ¢, octave size: NNN ¢

_ing the octave of 59edo by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning 296zpi does this.

Approximation of harmonics in 296zpi
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -3.36 +4.55 -6.72 -7.68 +1.19 -2.01 -10.09 +9.11 +9.24 +6.49 -2.17
Relative (%) -16.6 +22.4 -33.2 -37.9 +5.9 -9.9 -49.7 +44.9 +45.6 +32.0 -10.7
Step 59 94 118 137 153 166 177 188 197 205 212
Approximation of harmonics in 296zpi (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +1.23 -5.38 -3.13 +6.83 +3.29 +5.74 -6.73 +5.88 +2.54 +3.13 +7.30 -5.53
Relative (%) +6.1 -26.5 -15.4 +33.7 +16.2 +28.3 -33.2 +29.0 +12.5 +15.4 +36.0 -27.3
Step 219 225 231 237 242 247 251 256 260 264 268 271
153ed6
  • Step size: NNN ¢, octave size: NNN ¢

_ing the octave of 59edo by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning 153ed6 does this.

Approximation of harmonics in 153ed6
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -3.82 +3.82 -7.64 -8.75 +0.00 -3.31 +8.81 +7.64 +7.71 +4.90 -3.82
Relative (%) -18.8 +18.8 -37.7 -43.1 +0.0 -16.3 +43.5 +37.7 +38.0 +24.2 -18.8
Steps
(reduced) 		59
(59) 		94
(94) 		118
(118) 		137
(137) 		153
(0) 		166
(13) 		178
(25) 		188
(35) 		197
(44) 		205
(52) 		212
(59)
Approximation of harmonics in 153ed6 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -0.47 -7.13 -4.92 +4.99 +1.40 +3.82 -8.68 +3.89 +0.52 +1.08 +5.22 -7.64
Relative (%) -2.3 -35.2 -24.3 +24.6 +6.9 +18.8 -42.8 +19.2 +2.5 +5.3 +25.7 -37.7
Steps
(reduced) 		219
(66) 		225
(72) 		231
(78) 		237
(84) 		242
(89) 		247
(94) 		251
(98) 		256
(103) 		260
(107) 		264
(111) 		268
(115) 		271
(118)

Title2

Lab

Place holder








Approximation of prime harmonics in 1ed300c
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0 -102 -86 -69 +49 +59 -105 +2 -28 -130 +55
Relative (%) +0.0 -34.0 -28.8 -22.9 +16.2 +19.8 -35.0 +0.8 -9.4 -43.2 +18.3
Step 4 6 9 11 14 15 16 17 18 19 20


Approximation of prime harmonics in 140ed12
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -1.6 +3.2 +10.0 +11.3 -3.0 +15.1 +11.6 +3.4 +10.6 +8.8 -14.5
Relative (%) -5.2 +10.4 +32.4 +36.7 -9.8 +49.0 +37.6 +11.0 +34.6 +28.6 -47.1
Steps
(reduced) 		39
(39) 		62
(62) 		91
(91) 		110
(110) 		135
(135) 		145
(5) 		160
(20) 		166
(26) 		177
(37) 		190
(50) 		193
(53)

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

64edo

  • 179ed7 (octave is identical to 326zpi within 0.3 ¢)
  • 165ed6
  • 229ed12 (octave is identical to 221ed11 within 0.1 ¢)
  • 327zpi (18.767c)
  • 11-limit WE (18.755c)

pure octaves 64edo (octave is identical to 13-limit WE within 0.13 ¢

  • 328zpi (18.721c)
  • 180ed7
  • 230ed12
  • 149ed5

59edo (reduce # of edonoi or zpi)

  • 152ed6
  • 294zpi (20.399c)
  • 211ed12
  • 295zpi (20.342c)

pure octaves 59edo octave is identical to 137ed5 within 0.05 ¢

  • 13-limit WE (20.320c)
  • 7-limit WE (20.301c)
  • 166ed7
  • 212ed12
  • 296zpi (20.282c)
  • 153ed6
Medium priority

25edo

Approximation of harmonics in 25edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +18.0 +0.0 -2.3 +18.0 -8.8 +0.0 -11.9 -2.3 -23.3 +18.0 +23.5
Relative (%) +0.0 +37.6 +0.0 -4.8 +37.6 -18.4 +0.0 -24.8 -4.8 -48.6 +37.6 +48.9
Steps
(reduced) 		25
(0) 		40
(15) 		50
(0) 		58
(8) 		65
(15) 		70
(20) 		75
(0) 		79
(4) 		83
(8) 		86
(11) 		90
(15) 		93
(18)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

26edo

Approximation of harmonics in 26edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 -9.6 +0.0 -17.1 -9.6 +0.4 +0.0 -19.3 -17.1 +2.5 -9.6 -9.8
Relative (%) +0.0 -20.9 +0.0 -37.0 -20.9 +0.9 +0.0 -41.8 -37.0 +5.5 -20.9 -21.1
Steps
(reduced) 		26
(0) 		41
(15) 		52
(0) 		60
(8) 		67
(15) 		73
(21) 		78
(0) 		82
(4) 		86
(8) 		90
(12) 		93
(15) 		96
(18)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

29edo

Approximation of harmonics in 29edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +1.5 +0.0 -13.9 +1.5 -17.1 +0.0 +3.0 -13.9 -13.4 +1.5 -12.9
Relative (%) +0.0 +3.6 +0.0 -33.6 +3.6 -41.3 +0.0 +7.2 -33.6 -32.4 +3.6 -31.3
Steps
(reduced) 		29
(0) 		46
(17) 		58
(0) 		67
(9) 		75
(17) 		81
(23) 		87
(0) 		92
(5) 		96
(9) 		100
(13) 		104
(17) 		107
(20)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

30edo

Approximation of harmonics in 30edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +18.0 +0.0 +13.7 +18.0 -8.8 +0.0 -3.9 +13.7 +8.7 +18.0 -0.5
Relative (%) +0.0 +45.1 +0.0 +34.2 +45.1 -22.1 +0.0 -9.8 +34.2 +21.7 +45.1 -1.3
Steps
(reduced) 		30
(0) 		48
(18) 		60
(0) 		70
(10) 		78
(18) 		84
(24) 		90
(0) 		95
(5) 		100
(10) 		104
(14) 		108
(18) 		111
(21)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

34edo

Approximation of harmonics in 34edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +3.9 +0.0 +1.9 +3.9 -15.9 +0.0 +7.9 +1.9 +13.4 +3.9 +6.5
Relative (%) +0.0 +11.1 +0.0 +5.4 +11.1 -45.0 +0.0 +22.3 +5.4 +37.9 +11.1 +18.5
Steps
(reduced) 		34
(0) 		54
(20) 		68
(0) 		79
(11) 		88
(20) 		95
(27) 		102
(0) 		108
(6) 		113
(11) 		118
(16) 		122
(20) 		126
(24)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

35edo

Approximation of harmonics in 35edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 -16.2 +0.0 -9.2 -16.2 -8.8 +0.0 +1.8 -9.2 -2.7 -16.2 +16.6
Relative (%) +0.0 -47.4 +0.0 -26.7 -47.4 -25.7 +0.0 +5.3 -26.7 -8.0 -47.4 +48.5
Steps
(reduced) 		35
(0) 		55
(20) 		70
(0) 		81
(11) 		90
(20) 		98
(28) 		105
(0) 		111
(6) 		116
(11) 		121
(16) 		125
(20) 		130
(25)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

36edo

Approximation of harmonics in 36edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 -2.0 +0.0 +13.7 -2.0 -2.2 +0.0 -3.9 +13.7 +15.3 -2.0 -7.2
Relative (%) +0.0 -5.9 +0.0 +41.1 -5.9 -6.5 +0.0 -11.7 +41.1 +46.0 -5.9 -21.6
Steps
(reduced) 		36
(0) 		57
(21) 		72
(0) 		84
(12) 		93
(21) 		101
(29) 		108
(0) 		114
(6) 		120
(12) 		125
(17) 		129
(21) 		133
(25)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

37edo

Approximation of harmonics in 37edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +11.6 +0.0 +2.9 +11.6 +4.1 +0.0 -9.3 +2.9 +0.0 +11.6 +2.7
Relative (%) +0.0 +35.6 +0.0 +8.9 +35.6 +12.8 +0.0 -28.7 +8.9 +0.1 +35.6 +8.4
Steps
(reduced) 		37
(0) 		59
(22) 		74
(0) 		86
(12) 		96
(22) 		104
(30) 		111
(0) 		117
(6) 		123
(12) 		128
(17) 		133
(22) 		137
(26)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

38edo

Approximation of harmonics in 38edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 -7.2 +0.0 -7.4 -7.2 +10.1 +0.0 -14.4 -7.4 -14.5 -7.2 +12.1
Relative (%) +0.0 -22.9 +0.0 -23.3 -22.9 +32.1 +0.0 -45.7 -23.3 -45.8 -22.9 +38.3
Steps
(reduced) 		38
(0) 		60
(22) 		76
(0) 		88
(12) 		98
(22) 		107
(31) 		114
(0) 		120
(6) 		126
(12) 		131
(17) 		136
(22) 		141
(27)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

9edo

Approximation of harmonics in 9edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 -35.3 +0.0 +13.7 -35.3 -35.5 +0.0 +62.8 +13.7 -18.0 -35.3 -40.5
Relative (%) +0.0 -26.5 +0.0 +10.3 -26.5 -26.6 +0.0 +47.1 +10.3 -13.5 -26.5 -30.4
Steps
(reduced) 		9
(0) 		14
(5) 		18
(0) 		21
(3) 		23
(5) 		25
(7) 		27
(0) 		29
(2) 		30
(3) 		31
(4) 		32
(5) 		33
(6)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

10edo

Approximation of harmonics in 10edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +18.0 +0.0 -26.3 +18.0 -8.8 +0.0 +36.1 -26.3 +48.7 +18.0 -0.5
Relative (%) +0.0 +15.0 +0.0 -21.9 +15.0 -7.4 +0.0 +30.1 -21.9 +40.6 +15.0 -0.4
Steps
(reduced) 		10
(0) 		16
(6) 		20
(0) 		23
(3) 		26
(6) 		28
(8) 		30
(0) 		32
(2) 		33
(3) 		35
(5) 		36
(6) 		37
(7)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

11edo

Approximation of harmonics in 11edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 -47.4 +0.0 +50.0 -47.4 +13.0 +0.0 +14.3 +50.0 -5.9 -47.4 +32.2
Relative (%) +0.0 -43.5 +0.0 +45.9 -43.5 +11.9 +0.0 +13.1 +45.9 -5.4 -43.5 +29.5
Steps
(reduced) 		11
(0) 		17
(6) 		22
(0) 		26
(4) 		28
(6) 		31
(9) 		33
(0) 		35
(2) 		37
(4) 		38
(5) 		39
(6) 		41
(8)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

15edo

Approximation of harmonics in 15edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +18.0 +0.0 +13.7 +18.0 -8.8 +0.0 +36.1 +13.7 +8.7 +18.0 +39.5
Relative (%) +0.0 +22.6 +0.0 +17.1 +22.6 -11.0 +0.0 +45.1 +17.1 +10.9 +22.6 +49.3
Steps
(reduced) 		15
(0) 		24
(9) 		30
(0) 		35
(5) 		39
(9) 		42
(12) 		45
(0) 		48
(3) 		50
(5) 		52
(7) 		54
(9) 		56
(11)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

18edo

Approximation of harmonics in 18edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +31.4 +0.0 +13.7 +31.4 +31.2 +0.0 -3.9 +13.7 -18.0 +31.4 +26.1
Relative (%) +0.0 +47.1 +0.0 +20.5 +47.1 +46.8 +0.0 -5.9 +20.5 -27.0 +47.1 +39.2
Steps
(reduced) 		18
(0) 		29
(11) 		36
(0) 		42
(6) 		47
(11) 		51
(15) 		54
(0) 		57
(3) 		60
(6) 		62
(8) 		65
(11) 		67
(13)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

48edo

Approximation of harmonics in 48edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 -2.0 +0.0 -11.3 -2.0 +6.2 +0.0 -3.9 -11.3 -1.3 -2.0 +9.5
Relative (%) +0.0 -7.8 +0.0 -45.3 -7.8 +24.7 +0.0 -15.6 -45.3 -5.3 -7.8 +37.9
Steps
(reduced) 		48
(0) 		76
(28) 		96
(0) 		111
(15) 		124
(28) 		135
(39) 		144
(0) 		152
(8) 		159
(15) 		166
(22) 		172
(28) 		178
(34)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

24edo

Approximation of harmonics in 24edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 -2.0 +0.0 +13.7 -2.0 -18.8 +0.0 -3.9 +13.7 -1.3 -2.0 +9.5
Relative (%) +0.0 -3.9 +0.0 +27.4 -3.9 -37.7 +0.0 -7.8 +27.4 -2.6 -3.9 +18.9
Steps
(reduced) 		24
(0) 		38
(14) 		48
(0) 		56
(8) 		62
(14) 		67
(19) 		72
(0) 		76
(4) 		80
(8) 		83
(11) 		86
(14) 		89
(17)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

5edo

Approximation of harmonics in 5edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0 +18 +0 +94 +18 -9 +0 +36 +94 -71 +18 +119
Relative (%) +0.0 +7.5 +0.0 +39.0 +7.5 -3.7 +0.0 +15.0 +39.0 -29.7 +7.5 +49.8
Steps
(reduced) 		5
(0) 		8
(3) 		10
(0) 		12
(2) 		13
(3) 		14
(4) 		15
(0) 		16
(1) 		17
(2) 		17
(2) 		18
(3) 		19
(4)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

6edo

Approximation of harmonics in 6edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +98.0 +0.0 +13.7 +98.0 +31.2 +0.0 -3.9 +13.7 +48.7 +98.0 -40.5
Relative (%) +0.0 +49.0 +0.0 +6.8 +49.0 +15.6 +0.0 -2.0 +6.8 +24.3 +49.0 -20.3
Steps
(reduced) 		6
(0) 		10
(4) 		12
(0) 		14
(2) 		16
(4) 		17
(5) 		18
(0) 		19
(1) 		20
(2) 		21
(3) 		22
(4) 		22
(4)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

13edo

Approximation of harmonics in 13edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +36.5 +0.0 -17.1 +36.5 -45.7 +0.0 -19.3 -17.1 +2.5 +36.5 -9.8
Relative (%) +0.0 +39.5 +0.0 -18.5 +39.5 -49.6 +0.0 -20.9 -18.5 +2.7 +39.5 -10.6
Steps
(reduced) 		13
(0) 		21
(8) 		26
(0) 		30
(4) 		34
(8) 		36
(10) 		39
(0) 		41
(2) 		43
(4) 		45
(6) 		47
(8) 		48
(9)
  • 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)

118edo (choose ZPIS)

Approximation of harmonics in 118edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.00 -0.26 +0.00 +0.13 -0.26 -2.72 +0.00 -0.52 +0.13 -2.17 -0.26 +3.54
Relative (%) +0.0 -2.6 +0.0 +1.2 -2.6 -26.8 +0.0 -5.1 +1.2 -21.3 -2.6 +34.8
Steps
(reduced) 		118
(0) 		187
(69) 		236
(0) 		274
(38) 		305
(69) 		331
(95) 		354
(0) 		374
(20) 		392
(38) 		408
(54) 		423
(69) 		437
(83)
  • 187edt
  • 69edf
  • 13-limit WE (10.171c)
  • Best nearby ZPI(s)

103edo (narrow down edonoi, choose ZPIS)

Approximation of harmonics in 103edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.00 -2.93 +0.00 -1.85 -2.93 -1.84 +0.00 +5.80 -1.85 -3.75 -2.93 -1.69
Relative (%) +0.0 -25.1 +0.0 -15.9 -25.1 -15.8 +0.0 +49.8 -15.9 -32.1 -25.1 -14.5
Steps
(reduced) 		103
(0) 		163
(60) 		206
(0) 		239
(33) 		266
(60) 		289
(83) 		309
(0) 		327
(18) 		342
(33) 		356
(47) 		369
(60) 		381
(72)
  • 163edt
  • 239ed5
  • 266ed6
  • 289ed7
  • 356ed11
  • 369ed12
  • 381ed13
  • 421ed17
  • 466ed23
  • 13-limit WE (11.658c)
  • Best nearby ZPI(s)

111edo (choose ZPIS)

Approximation of harmonics in 111edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.00 +0.75 +0.00 +2.88 +0.75 +4.15 +0.00 +1.50 +2.88 +0.03 +0.75 +2.72
Relative (%) +0.0 +6.9 +0.0 +26.6 +6.9 +38.4 +0.0 +13.8 +26.6 +0.3 +6.9 +25.1
Steps
(reduced) 		111
(0) 		176
(65) 		222
(0) 		258
(36) 		287
(65) 		312
(90) 		333
(0) 		352
(19) 		369
(36) 		384
(51) 		398
(65) 		411
(78)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • 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)
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