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; High-priority
; High-priority
64edo
* 179ed7 (octave is identical to 326zpi within 0.3{{c}})
* 165ed6
* 229ed12 (octave is identical to 221ed11 within 0.1{{c}})
* 327zpi (18.767c)
* 11-limit WE (18.755c)
''pure octaves 64edo (octave is identical to 13-limit WE within 0.13{{c}}''
* 328zpi (18.721c)
* 180ed7
* 230ed12
* 149ed5
; Medium priority


25edo
25edo

Revision as of 07:30, 2 September 2025

Quick link

User:BudjarnLambeth/Draft related tunings section

Title1

Octave stretch or compression

64edo's approximations of 3/1, 5/1, 7/1, 11/1 and 17/1 are improved by 180ed7, a compressed-octave version of 64edo. The trade-off is a slightly worse 2/1 and 13/1.

149ed5 can also be used: it is similar to 180ed7 but both the improvements and shortcomings are amplified. Most notably its 2/1 isn’t as accurate as 180ed7's.

If one prefers a stretched-octave, 64edo's approximations of 3/1, 5/1, 11/1 and 17/1 are improved by 221ed11, a stretched version of 64edo. The trade-off is a slightly worse 2/1 and 13/1.

47ed5/3 can also be used: it is similar to 221ed11 but both the improvements and shortcomings are amplified. Most notably its 2/1 is not as accurate as 221ed11's.

What follows is a comparison of stretched- and compressed-octave 64edo tunings.

179ed7
  • Octave size: 1204.50 ¢

Stretching the octave of 64edo by around 4.5 ¢ results in improved primes 3, 5, 7 and 13, but worse primes 2 and 11. This approximates all harmonics up to 16 within 8.99 ¢. The tuning 179ed7 does this. So does the tuning 326zpi whose octave is identical within 0.3 ¢.

Approximation of harmonics in 179ed7
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +4.50 -1.11 +8.99 -0.92 +3.39 +0.00 -5.33 -2.22 +3.58 +7.96 +7.88
Relative (%) +23.9 -5.9 +47.8 -4.9 +18.0 +0.0 -28.3 -11.8 +19.0 +42.3 +41.9
Steps
(reduced) 		64
(64) 		101
(101) 		128
(128) 		148
(148) 		165
(165) 		179
(0) 		191
(12) 		202
(23) 		212
(33) 		221
(42) 		229
(50)
Approximation of harmonics in 179ed7 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +1.05 +4.50 -2.02 -0.83 +7.13 +2.28 +2.78 +8.08 -1.11 -6.37 -8.04 -6.44
Relative (%) +5.6 +23.9 -10.8 -4.4 +37.9 +12.1 +14.8 +42.9 -5.9 -33.8 -42.7 -34.2
Steps
(reduced) 		236
(57) 		243
(64) 		249
(70) 		255
(76) 		261
(82) 		266
(87) 		271
(92) 		276
(97) 		280
(101) 		284
(105) 		288
(109) 		292
(113)
165ed6
  • Octave size: 1203.18 ¢

Stretching the octave of 64edo by around 3 ¢ results in improved primes 3, 5, 7, 11, 13 and 17, but a worse prime 2. This approximates all harmonics up to 16 within 9.25 ¢. The tuning 165ed6 does this.

Approximation of harmonics in 165ed6
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +3.18 -3.18 +6.37 -3.95 +0.00 -3.67 -9.25 -6.37 -0.77 +3.42 +3.18
Relative (%) +16.9 -16.9 +33.9 -21.0 +0.0 -19.5 -49.2 -33.9 -4.1 +18.2 +16.9
Steps
(reduced) 		64
(64) 		101
(101) 		128
(128) 		148
(148) 		165
(0) 		179
(14) 		191
(26) 		202
(37) 		212
(47) 		221
(56) 		229
(64)
Approximation of harmonics in 165ed6 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -3.79 -0.49 -7.14 -6.07 +1.77 -3.18 -2.79 +2.41 -6.86 +6.60 +4.85 +6.37
Relative (%) -20.2 -2.6 -38.0 -32.3 +9.4 -16.9 -14.8 +12.8 -36.5 +35.1 +25.8 +33.9
Steps
(reduced) 		236
(71) 		243
(78) 		249
(84) 		255
(90) 		261
(96) 		266
(101) 		271
(106) 		276
(111) 		280
(115) 		285
(120) 		289
(124) 		293
(128)
229ed12
  • Octave size: 1202.29 ¢

Stretching the octave of 64edo by around 2 ¢ results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 9.17 ¢. The tuning 229ed12 does this. So does the tuning 221ed11 whose octave is identical within 0.1 ¢.

Approximation of harmonics in 229ed12
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +2.29 -4.59 +4.59 -6.01 -2.29 -6.16 +6.88 -9.17 -3.72 +0.35 +0.00
Relative (%) +12.2 -24.4 +24.4 -32.0 -12.2 -32.8 +36.6 -48.8 -19.8 +1.9 +0.0
Steps
(reduced) 		64
(64) 		101
(101) 		128
(128) 		148
(148) 		165
(165) 		179
(179) 		192
(192) 		202
(202) 		212
(212) 		221
(221) 		229
(0)
Approximation of harmonics in 229ed12 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -7.07 -3.87 +8.19 +9.17 -1.85 -6.88 -6.55 -1.42 +8.04 +2.64 +0.83 +2.29
Relative (%) -37.6 -20.6 +43.6 +48.8 -9.9 -36.6 -34.9 -7.6 +42.8 +14.1 +4.4 +12.2
Steps
(reduced) 		236
(7) 		243
(14) 		250
(21) 		256
(27) 		261
(32) 		266
(37) 		271
(42) 		276
(47) 		281
(52) 		285
(56) 		289
(60) 		293
(64)
327zpi
  • Step size: 18.767 ¢, octave size: 1201.09 ¢

Stretching the octave of 64edo by around 1 ¢ results in improved primes 3 and 11, but worse primes 2, 5, 7 and 13. This approximates all harmonics up to 16 within 9.23 ¢. The tuning 327zpi does this.

Approximation of harmonics in 327zpi
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +1.09 -6.49 +2.18 -8.80 -5.40 +9.23 +3.26 +5.79 -7.71 -3.81 -4.31
Relative (%) +5.8 -34.6 +11.6 -46.9 -28.8 +49.2 +17.4 +30.9 -41.1 -20.3 -23.0
Step 64 101 128 148 165 180 192 203 212 221 229
Approximation of harmonics in 327zpi (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +7.25 -8.44 +3.48 +4.35 -6.77 +6.88 +7.11 -6.62 +2.75 -2.72 -4.61 -3.22
Relative (%) +38.6 -45.0 +18.6 +23.2 -36.1 +36.7 +37.9 -35.3 +14.6 -14.5 -24.6 -17.2
Step 237 243 250 256 261 267 272 276 281 285 289 293
64et, 11-limit WE tuning
  • Step size: 18.755 ¢, octave size: 1200.32 ¢

Stretching the octave of 64edo by around a third of a cent results in slightly improved primes 3 and 11, but slightly worse primes 2, 5, 7 and 13. This approximates all harmonics up to 16 within 8.50 ¢. Its 11-limit WE tuning and 11-limit TE tuning both do this.

Approximation of harmonics in 64et, 11-limit WE tuning
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.32 -7.70 +0.64 +8.18 -7.38 +7.07 +0.96 +3.35 +8.50 -6.46 -7.06
Relative (%) +1.7 -41.1 +3.4 +43.6 -39.3 +37.7 +5.1 +17.9 +45.3 -34.5 -37.6
Step 64 101 128 149 165 180 192 203 213 221 229
Approximation of harmonics in 64et, 11-limit WE tuning (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +4.41 +7.39 +0.48 +1.28 +8.85 +3.67 +3.85 +8.82 -0.63 -6.14 -8.08 -6.74
Relative (%) +23.5 +39.4 +2.6 +6.8 +47.2 +19.6 +20.5 +47.0 -3.3 -32.8 -43.1 -35.9
Step 237 244 250 256 262 267 272 277 281 285 289 293
64edo
  • Step size: 18.750 ¢, octave size: 1200.00 ¢

Pure-octaves 64edo approximates all harmonics up to 16 within 8.21 ¢. The octave of 64edo's 13-limit WE tuning differs by only 0.13 ¢ from pure.

Approximation of harmonics in 64edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.00 -8.21 +0.00 +7.44 -8.21 +6.17 +0.00 +2.34 +7.44 -7.57 -8.21
Relative (%) +0.0 -43.8 +0.0 +39.7 -43.8 +32.9 +0.0 +12.5 +39.7 -40.4 -43.8
Steps
(reduced) 		64
(0) 		101
(37) 		128
(0) 		149
(21) 		165
(37) 		180
(52) 		192
(0) 		203
(11) 		213
(21) 		221
(29) 		229
(37)
Approximation of harmonics in 64edo (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +3.22 +6.17 -0.77 +0.00 +7.54 +2.34 +2.49 +7.44 -2.03 -7.57 +9.23 -8.21
Relative (%) +17.2 +32.9 -4.1 +0.0 +40.2 +12.5 +13.3 +39.7 -10.8 -40.4 +49.2 -43.8
Steps
(reduced) 		237
(45) 		244
(52) 		250
(58) 		256
(0) 		262
(6) 		267
(11) 		272
(16) 		277
(21) 		281
(25) 		285
(29) 		290
(34) 		293
(37)
328zpi
  • Step size: 18.721 ¢, octave size: 1198.14 ¢

Compressing the octave of 64edo by just under 2 ¢ results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 8.02 ¢. The tuning 328zpi does this.

Approximation of harmonics in 328zpi
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -1.86 +7.59 -3.71 +3.12 +5.73 +0.95 -5.57 -3.55 +1.26 +4.74 +3.87
Relative (%) -9.9 +40.5 -19.8 +16.6 +30.6 +5.1 -29.7 -18.9 +6.7 +25.3 +20.7
Step 64 102 128 149 166 180 192 203 213 222 230
Approximation of harmonics in 328zpi (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -3.65 -0.90 -8.02 -7.42 -0.05 -5.40 -5.40 -0.60 +8.54 +2.89 +0.82 +2.02
Relative (%) -19.5 -4.8 -42.8 -39.7 -0.3 -28.9 -28.9 -3.2 +45.6 +15.4 +4.4 +10.8
Step 237 244 250 256 262 267 272 277 282 286 290 294
180ed7
  • Octave size: 1197.80 ¢

Compressing the octave of 64edo by just over 2 ¢ results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 9.34 ¢. The tuning 180ed7 does this.

Approximation of harmonics in 180ed7
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -2.20 +7.05 -4.39 +2.33 +4.85 +0.00 -6.59 -4.62 +0.13 +3.57 +2.66
Relative (%) -11.7 +37.6 -23.5 +12.4 +25.9 +0.0 -35.2 -24.7 +0.7 +19.1 +14.2
Steps
(reduced) 		64
(64) 		102
(102) 		128
(128) 		149
(149) 		166
(166) 		180
(0) 		192
(12) 		203
(23) 		213
(33) 		222
(42) 		230
(50)
Approximation of harmonics in 180ed7 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -4.91 -2.20 -9.34 -8.78 -1.44 -6.82 -6.84 -2.06 +7.05 +1.37 -0.72 +0.46
Relative (%) -26.2 -11.7 -49.9 -46.9 -7.7 -36.4 -36.6 -11.0 +37.6 +7.3 -3.9 +2.5
Steps
(reduced) 		237
(57) 		244
(64) 		250
(70) 		256
(76) 		262
(82) 		267
(87) 		272
(92) 		277
(97) 		282
(102) 		286
(106) 		290
(110) 		294
(114)
230ed12
  • Octave size: 1197.07 ¢

Compressing the octave of 64edo by around 3 ¢ results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 8.80 ¢. The tuning 230ed12 does this.

Approximation of harmonics in 230ed12
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -2.93 +5.87 -5.87 +0.60 +2.93 -2.08 -8.80 -6.97 -2.33 +1.00 +0.00
Relative (%) -15.7 +31.4 -31.4 +3.2 +15.7 -11.1 -47.1 -37.2 -12.5 +5.4 +0.0
Steps
(reduced) 		64
(64) 		102
(102) 		128
(128) 		149
(149) 		166
(166) 		180
(180) 		192
(192) 		203
(203) 		213
(213) 		222
(222) 		230
(0)
Approximation of harmonics in 230ed12 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -7.64 -5.01 +6.47 +6.97 -4.47 +8.80 +8.72 -5.26 +3.79 -1.93 -4.07 -2.93
Relative (%) -40.9 -26.8 +34.6 +37.2 -23.9 +47.1 +46.6 -28.1 +20.3 -10.3 -21.8 -15.7
Steps
(reduced) 		237
(7) 		244
(14) 		251
(21) 		257
(27) 		262
(32) 		268
(38) 		273
(43) 		277
(47) 		282
(52) 		286
(56) 		290
(60) 		294
(64)
149ed5
  • Step size: Octave size: NNN ¢

Compressing the octave of 64edo by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning 149ed5 does this.

Approximation of harmonics in 149ed5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -3.19 +5.45 -6.39 +0.00 +2.26 -2.81 +9.12 -7.79 -3.19 +0.10 -0.93
Relative (%) -17.1 +29.2 -34.2 +0.0 +12.1 -15.0 +48.8 -41.7 -17.1 +0.5 -5.0
Steps
(reduced) 		64
(64) 		102
(102) 		128
(128) 		149
(0) 		166
(17) 		180
(31) 		193
(44) 		203
(54) 		213
(64) 		222
(73) 		230
(81)
Approximation of harmonics in 149ed5 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -8.61 -6.00 +5.45 +5.92 -5.53 +7.71 +7.61 -6.39 +2.65 -3.09 -5.25 -4.13
Relative (%) -46.0 -32.1 +29.2 +31.7 -29.6 +41.3 +40.7 -34.2 +14.1 -16.5 -28.1 -22.1
Steps
(reduced) 		237
(88) 		244
(95) 		251
(102) 		257
(108) 		262
(113) 		268
(119) 		273
(124) 		277
(128) 		282
(133) 		286
(137) 		290
(141) 		294
(145)

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

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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