User:BudjarnLambeth/Sandbox2: Difference between revisions

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* 1-2 WE tunings
* 1-2 WE tunings
* Best nearby ZPI(s)
* Best nearby ZPI(s)
; Low priority


13edo
13edo
Line 294: Line 292:
* 1-2 WE tunings
* 1-2 WE tunings
* Best nearby ZPI(s)
* Best nearby ZPI(s)
; Low priority


104edo
104edo

Revision as of 06:32, 30 August 2025

Quick link

User:BudjarnLambeth/Draft related tunings section

Octave stretch and compression

209zpi
  • Step size: 26.550 ¢, octave size: 1194.8 ¢

Compressing the octave of 45edo by around 5 ¢ results in improved primes 5 and 7, but worse primes 2, 3, 11 and 13. This approximates all harmonics up to 16 within 11.1 ¢. The tuning 209zpi does this.

Approximation of harmonics in 209zpi
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -5.2 +9.6 -10.5 +1.4 +4.4 +3.0 +10.8 -7.3 -3.8 -9.5 -0.9
Relative (%) -19.8 +36.3 -39.5 +5.4 +16.6 +11.4 +40.7 -27.3 -14.4 -35.8 -3.2
Step 45 72 90 105 117 127 136 143 150 156 162
Approximation of harmonics in 209zpi (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -6.7 -2.2 +11.1 +5.6 +6.8 -12.5 +0.1 -9.1 +12.7 +11.8 -12.1 -6.1
Relative (%) -25.2 -8.4 +41.7 +20.9 +25.6 -47.1 +0.3 -34.1 +47.7 +44.4 -45.5 -23.0
Step 167 172 177 181 185 188 192 195 199 202 204 207
45edo
  • Step size: 26.667 ¢, octave size: 1200.0 ¢

Pure-octaves 45edo approximates all harmonics up to 16 within 13.0 ¢.

Approximation of harmonics in 45edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.0 -8.6 +0.0 -13.0 -8.6 -8.8 +0.0 +9.4 -13.0 +8.7 -8.6
Relative (%) +0.0 -32.3 +0.0 -48.7 -32.3 -33.1 +0.0 +35.3 -48.7 +32.6 -32.3
Steps
(reduced) 		45
(0) 		71
(26) 		90
(0) 		104
(14) 		116
(26) 		126
(36) 		135
(0) 		143
(8) 		149
(14) 		156
(21) 		161
(26)
Approximation of harmonics in 45edo (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +12.8 -8.8 +5.1 +0.0 +1.7 +9.4 -4.2 -13.0 +9.2 +8.7 +11.7 -8.6
Relative (%) +48.0 -33.1 +19.0 +0.0 +6.4 +35.3 -15.7 -48.7 +34.6 +32.6 +44.0 -32.3
Steps
(reduced) 		167
(32) 		171
(36) 		176
(41) 		180
(0) 		184
(4) 		188
(8) 		191
(11) 		194
(14) 		198
(18) 		201
(21) 		204
(24) 		206
(26)
45et, 13-limit WE tuning
  • Step size: 26.695 ¢, octave size: 1201.3 ¢

Stretching the octave of 45edo by around 1 ¢ results in improved primes 3, 5, 7 and 13, but worse primes 2 and 11. This approximates all harmonics up to 16 within 13.2 ¢. Its 13-limit WE tuning and 13-limit TE tuning both do this.

Approximation of harmonics in 45et, 13-limit WE tuning
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +1.3 -6.6 +2.5 -10.0 -5.3 -5.3 +3.8 -13.2 -8.8 +13.1 -4.1
Relative (%) +4.8 -24.8 +9.6 -37.6 -20.0 -19.7 +14.3 -49.5 -32.8 +49.1 -15.2
Step 45 71 90 104 116 126 135 142 149 156 161
Approximation of harmonics in 45et, 13-limit WE tuning (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -9.2 -4.0 +10.1 +5.1 +6.9 -11.9 +1.2 -7.5 -11.9 -12.3 -9.2 -2.8
Relative (%) -34.3 -14.9 +37.7 +19.1 +25.9 -44.7 +4.6 -28.0 -44.4 -46.1 -34.4 -10.4
Step 166 171 176 180 184 187 191 194 197 200 203 206
161ed12
  • Step size: Octave size: 1202.4 ¢

Stretching the octave of 45edo by around 2.5 ¢ results in improved primes 3, 5, 7 and 13, but worse primes 2 and 11. This approximates all harmonics up to 16 within 12.2 ¢. The tuning 161ed12 does this.

Approximation of harmonics in 161ed12
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +2.4 -4.8 +4.8 -7.4 -2.4 -2.1 +7.2 -9.6 -5.0 -9.7 +0.0
Relative (%) +9.0 -18.0 +18.0 -27.7 -9.0 -7.8 +27.1 -36.1 -18.7 -36.2 +0.0
Steps
(reduced) 		45
(45) 		71
(71) 		90
(90) 		104
(104) 		116
(116) 		126
(126) 		135
(135) 		142
(142) 		149
(149) 		155
(155) 		161
(0)
Approximation of harmonics in 161ed12 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -5.0 +0.3 -12.2 +9.6 +11.6 -7.2 +6.0 -2.6 -6.9 -7.3 -4.1 +2.4
Relative (%) -18.6 +1.2 -45.8 +36.1 +43.3 -27.1 +22.6 -9.7 -25.8 -27.2 -15.2 +9.0
Steps
(reduced) 		166
(5) 		171
(10) 		175
(14) 		180
(19) 		184
(23) 		187
(26) 		191
(30) 		194
(33) 		197
(36) 		200
(39) 		203
(42) 		206
(45)
116ed6
  • Step size: Octave size: 1203.3 ¢

Stretching the octave of 45edo by around 3 ¢ results in improved primes 3, 5, 7, 11 and 13, but a worse prime 2. This approximates all harmonics up to 16 within 13.4 ¢. The tuning 116ed6 does this. So does 126ed7 whose octave is identical within 0.1 ¢.

Approximation of harmonics in 116ed6
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +3.3 -3.3 +6.7 -5.3 +0.0 +0.5 +10.0 -6.7 -1.9 -6.5 +3.3
Relative (%) +12.5 -12.5 +25.0 -19.6 +0.0 +2.0 +37.5 -25.0 -7.1 -24.2 +12.5
Steps
(reduced) 		45
(45) 		71
(71) 		90
(90) 		104
(104) 		116
(0) 		126
(10) 		135
(19) 		142
(26) 		149
(33) 		155
(39) 		161
(45)
Approximation of harmonics in 116ed6 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -1.5 +3.9 -8.6 -13.4 -11.4 -3.3 +10.0 +1.4 -2.8 -3.1 +0.1 +6.7
Relative (%) -5.7 +14.5 -32.1 -50.0 -42.5 -12.5 +37.5 +5.4 -10.5 -11.7 +0.5 +25.0
Steps
(reduced) 		166
(50) 		171
(55) 		175
(59) 		179
(63) 		183
(67) 		187
(71) 		191
(75) 		194
(78) 		197
(81) 		200
(84) 		203
(87) 		206
(90)
45et, 7-limit WE tuning
  • Step size: 26.745 ¢, octave size: 1203.5 ¢

Stretching the octave of 45edo by around 3.5 ¢ results in improved primes 3, 5, 7, 11 and 13, but a worse prime 2. This approximates all harmonics up to 16 within 12.6 ¢. Its 7-limit WE tuning and 7-limit TE tuning both do this.

Approximation of harmonics in 45et, 7-limit WE tuning
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +3.5 -3.1 +7.1 -4.8 +0.5 +1.0 +10.6 -6.1 -1.3 -5.8 +4.0
Relative (%) +13.2 -11.4 +26.4 -18.1 +1.7 +3.9 +39.5 -22.9 -4.9 -21.8 +14.9
Step 45 71 90 104 116 126 135 142 149 155 161
Approximation of harmonics in 45et, 7-limit WE tuning (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -0.9 +4.6 -7.9 -12.6 -10.6 -2.6 +10.8 +2.2 -2.0 -2.3 +1.0 +7.5
Relative (%) -3.2 +17.1 -29.5 -47.3 -39.7 -9.7 +40.3 +8.3 -7.5 -8.7 +3.6 +28.1
Step 166 171 175 179 183 187 191 194 197 200 203 206
207zpi
  • Step size: 26.762 ¢, octave size: 1204.3 ¢

Stretching the octave of 45edo by around 4 ¢ results in improved primes 3, 5, 7, 11 and 13, but a worse prime 2. This approximates all harmonics up to 16 within 12.9 ¢. The tuning 207zpi does this.

Approximation of harmonics in 207zpi
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +4.3 -1.9 +8.6 -3.1 +2.4 +3.2 +12.9 -3.7 +1.2 -3.2 +6.7
Relative (%) +16.0 -6.9 +32.1 -11.5 +9.1 +11.9 +48.1 -13.8 +4.6 -12.0 +25.1
Step 45 71 90 104 116 126 135 142 149 155 161
Approximation of harmonics in 207zpi (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +2.0 +7.5 -4.9 -9.6 -7.5 +0.6 -12.7 +5.5 +1.3 +1.1 +4.4 +11.0
Relative (%) +7.3 +27.9 -18.4 -35.9 -28.1 +2.2 -47.6 +20.6 +5.0 +4.0 +16.5 +41.2
Step 166 171 175 179 183 187 190 194 197 200 203 206
71edt
  • Step size: 26.788 ¢, octave size: 1205.5 ¢

Stretching the octave of 45edo by around 5.5 ¢ results in improved primes 3, 5, 7, 11 and 13, but a worse prime 2. This approximates all harmonics up to 16 within 11.9 ¢. The tuning 71edt does this. So does the tuning 155ed11 whose octave is identical within 0.3 ¢.

Approximation of harmonics in 71edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +5.5 +0.0 +10.9 -0.4 +5.5 +6.5 -10.4 +0.0 +5.1 +0.8 +10.9
Relative (%) +20.4 +0.0 +40.8 -1.3 +20.4 +24.2 -38.8 +0.0 +19.1 +3.1 +40.8
Steps
(reduced) 		45
(45) 		71
(0) 		90
(19) 		104
(33) 		116
(45) 		126
(55) 		134
(63) 		142
(0) 		149
(7) 		155
(13) 		161
(19)
Approximation of harmonics in 71edt (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +6.3 +11.9 -0.4 -4.9 -2.7 +5.5 -7.8 +10.6 +6.5 +6.3 +9.7 -10.4
Relative (%) +23.5 +44.6 -1.3 -18.4 -10.2 +20.4 -29.0 +39.5 +24.2 +23.5 +36.2 -38.8
Steps
(reduced) 		166
(24) 		171
(29) 		175
(33) 		179
(37) 		183
(41) 		187
(45) 		190
(48) 		194
(52) 		197
(55) 		200
(58) 		203
(61) 		205
(63)

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

54edo

  • 139ed6 (octave is identical to 262zpi within 0.2 ¢)
  • 151ed7
  • 193ed12
  • 263zpi (22.243c)
  • 13-limit WE (22.198c) (octave is identical to 187ed11 within 0.1 ¢)
  • 264zpi (22.175c) (octave is identical to 194ed12 within 0.01 ¢)
  • 152ed7
  • 140ed6
  • 126ed5 (octave is identical to 86edt within 0.1 ¢)

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

42edo (reduce # of edonoi)

  • 108ed6 (octave is identical to 97ed5 within 0.1 ¢)
  • 189zpi (28.689c)
  • 150ed12
  • 145ed11

190zpi's octave is within 0.05 ¢ of pure-octaves 42edo

  • 118ed7
  • 13-limit WE (28.534c)
  • 151ed12 (octave is identical to 7-limit WE within 0.3 ¢)
  • 109ed6
  • 191zpi (28.444c)
  • 67edt

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)

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)

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)

20edo

Approximation of harmonics in 20edo
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 -23.9 -26.3 -11.3 +18.0 -0.5
Relative (%) +0.0 +30.1 +0.0 -43.9 +30.1 -14.7 +0.0 -39.9 -43.9 -18.9 +30.1 -0.9
Steps
(reduced) 		20
(0) 		32
(12) 		40
(0) 		46
(6) 		52
(12) 		56
(16) 		60
(0) 		63
(3) 		66
(6) 		69
(9) 		72
(12) 		74
(14)
  • 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)

28edo

Approximation of harmonics in 28edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 -16.2 +0.0 -0.6 -16.2 +16.9 +0.0 +10.4 -0.6 +5.8 -16.2 +16.6
Relative (%) +0.0 -37.9 +0.0 -1.4 -37.9 +39.4 +0.0 +24.2 -1.4 +13.6 -37.9 +38.8
Steps
(reduced) 		28
(0) 		44
(16) 		56
(0) 		65
(9) 		72
(16) 		79
(23) 		84
(0) 		89
(5) 		93
(9) 		97
(13) 		100
(16) 		104
(20)
  • 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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