User:BudjarnLambeth/Sandbox2: Difference between revisions

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60edo (narrow down edonoi & ZPIs)
60edo (narrow down edonoi & ZPIs)
{{harmonics in equal | 60 | 3 | 1 | intervals=prime}}
{{harmonics in cet | 52.114 | intervals=prime}}
* 95edt
* 95edt
{{harmonics in equal | 95 | 3 | 1 | intervals=prime}}
* 35edf
* 35edf
{{harmonics in equal | 35 | 3 | 2 | intervals=prime}}
* 139ed5
* 139ed5
{{harmonics in equal | 139 | 5 | 1 | intervals=prime}}
* 155ed6
* 155ed6
{{harmonics in equal | 155 | 6 | 1 | intervals=prime}}
* 208ed11
* 208ed11
{{harmonics in equal | 208 | 11 | 1 | intervals=prime}}
* 215ed12
* 215ed12
{{harmonics in equal | 215 | 12 | 1 | intervals=prime}}
* 255ed19
* 255ed19
{{harmonics in equal | 255 | 19 | 1 | intervals=prime}}
* 272ed23 (great for catnip temperament, maybe there's a similar but simpler tuning w similar benefits?)
* 272ed23 (great for catnip temperament, maybe there's a similar but simpler tuning w similar benefits?)
{{harmonics in equal | 272 | 23 | 1 | intervals=prime}}
* 13-limit WE (20.013c)
* 13-limit WE (20.013c)
{{harmonics in cet | 20.013 | intervals=prime}}
* 299zpi (20.128c)
* 299zpi (20.128c)
{{harmonics in cet | 20.128 | intervals=prime}}
* 300zpi (20.093c)
* 300zpi (20.093c)
{{harmonics in cet | 20.093 | intervals=prime}}
* 301zpi (20.027c)
* 301zpi (20.027c)
{{harmonics in cet | 20.027 | intervals=prime}}
* 302zpi (19.962c)
* 302zpi (19.962c)
{{harmonics in cet | 19.962 | intervals=prime}}
* 303zpi (19.913c)
* 303zpi (19.913c)
{{harmonics in cet | 19.913 | intervals=prime}}
* 304zpi (19.869c)
* 304zpi (19.869c)
{{harmonics in cet | 19.869 | intervals=prime}}


32edo (narrow down ZPIs)
32edo (narrow down ZPIs)

Revision as of 05:33, 28 August 2025

Quick link

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 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: 1188.0 ¢

Compressing 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: 51.700 ¢, octave size: 1189.1 ¢

Compressing 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 60ed6 does this. So does the tuning 105ed23 whose octave is identical within 0.01 ¢.

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: 1198.6 ¢

Compressing 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 85zpi does this. So does the tuning 73ed9 whose octave is identical within 0.02 ¢.

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: 1200.0 ¢

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: 52.237 ¢, octave size: 1201.5 ¢

Stretching 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 (¢) +1.5 -21.4 +2.9 -17.8 -20.0 -25.7 +4.4 +9.4 -16.3 -24.6 -18.5
Relative (%) +2.8 -41.0 +5.6 -34.0 -38.2 -49.1 +8.3 +18.0 -31.2 -47.1 -35.5
Step 23 36 46 53 59 64 69 73 76 79 82
Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -0.4 -24.2 +13.1 +5.8 +5.3 +10.8 +21.7 -14.9 +5.2 -23.1 +4.4 -17.1
Relative (%) -0.7 -46.3 +25.0 +11.1 +10.2 +20.8 +41.6 -28.4 +9.9 -44.3 +8.4 -32.7
Step 85 87 90 92 94 96 98 99 101 102 104 105
23et, 2.3.5.13 WE tuning
  • Step size: 52.447 ¢, octave size: 1206.3 ¢

Stretching 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. So does the tuning 76ed10 whose octave is identical within 0.01 ¢.

Approximation of harmonics in ETNAME, SUBGROUP WE tuning
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +6.3 -13.9 +12.6 -6.6 -7.6 -12.2 +18.8 +24.7 -0.3 -8.0 -1.3
Relative (%) +12.0 -26.4 +24.0 -12.6 -14.5 -23.3 +35.9 +47.1 -0.7 -15.3 -2.5
Step 23 36 46 53 59 64 69 73 76 79 82
Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +17.5 -5.9 -20.5 +25.1 +25.1 -21.4 -10.2 +5.9 -26.1 -1.7 +26.2 +5.0
Relative (%) +33.3 -11.3 -39.1 +47.9 +47.8 -40.9 -19.4 +11.3 -49.7 -3.3 +50.0 +9.5
Step 85 87 89 92 94 95 97 99 100 102 104 105
59ed6
  • Step size: 52.575 ¢, octave size: 1209.2 ¢

Stretching 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 59ed6 does this. So does the tuning 53ed5 whose octave is identical within 0.01 ¢.

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: 1210.1 ¢

Stretching 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: 52.832 ¢, octave size: 1215.1 ¢

Stretching 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)
84ed13
  • Step size: 52.863 ¢, octave size: 1215.9 ¢

Stretching 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 (¢) +15.9 +1.1 -21.1 +15.4 +17.0 +14.4 -5.3 +2.3 -21.6 +24.9 -20.0
Relative (%) +30.0 +2.1 -40.0 +29.2 +32.1 +27.3 -10.0 +4.3 -40.8 +47.1 -37.9
Steps
(reduced) 		23
(23) 		36
(36) 		45
(45) 		53
(53) 		59
(59) 		64
(64) 		68
(68) 		72
(72) 		75
(75) 		79
(79) 		81
(81)
Approximation of harmonics in EDONOI (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +0.0 -22.6 +16.6 +10.6 +11.3 +18.1 -22.6 -5.7 +15.6 -12.1 +16.7 -4.2
Relative (%) +0.0 -42.7 +31.4 +20.0 +21.5 +34.3 -42.8 -10.8 +29.4 -22.9 +31.5 -7.9
Steps
(reduced) 		84
(0) 		86
(2) 		89
(5) 		91
(7) 		93
(9) 		95
(11) 		96
(12) 		98
(14) 		100
(16) 		101
(17) 		103
(19) 		104
(20)

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

60edo (narrow down edonoi & ZPIs)

  • 95edt
Approximation of prime harmonics in 95edt
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +1.23 +0.00 -3.45 -5.37 -7.06 +4.04 +0.09 +7.73 -2.70 -3.59 +1.08
Relative (%) +6.2 +0.0 -17.2 -26.8 -35.3 +20.2 +0.4 +38.6 -13.5 -17.9 +5.4
Steps
(reduced) 		60
(60) 		95
(0) 		139
(44) 		168
(73) 		207
(17) 		222
(32) 		245
(55) 		255
(65) 		271
(81) 		291
(6) 		297
(12)
  • 35edf
Approximation of prime harmonics in 35edf
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +3.35 +3.35 +1.45 +0.56 +0.24 -8.18 +8.73 -3.33 +6.86 +6.68 -8.50
Relative (%) +16.7 +16.7 +7.2 +2.8 +1.2 -40.8 +43.5 -16.6 +34.2 +33.3 -42.4
Steps
(reduced) 		60
(25) 		95
(25) 		139
(34) 		168
(28) 		207
(32) 		221
(11) 		245
(0) 		254
(9) 		271
(26) 		291
(11) 		296
(16)
  • 139ed5
Approximation of prime harmonics in 139ed5
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +2.73 +2.36 +0.00 -1.19 -1.92 +9.56 +6.17 -5.98 +4.04 +3.64 +8.45
Relative (%) +13.6 +11.8 +0.0 -6.0 -9.6 +47.7 +30.8 -29.8 +20.1 +18.2 +42.2
Steps
(reduced) 		60
(60) 		95
(95) 		139
(0) 		168
(29) 		207
(68) 		222
(83) 		245
(106) 		254
(115) 		271
(132) 		291
(13) 		297
(19)
  • 155ed6
Approximation of prime harmonics in 155ed6
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.76 -0.76 -4.56 -6.71 -8.71 +2.27 -1.87 +5.70 -4.86 -5.91 -1.29
Relative (%) +3.8 -3.8 -22.8 -33.5 -43.5 +11.4 -9.3 +28.5 -24.3 -29.5 -6.4
Steps
(reduced) 		60
(60) 		95
(95) 		139
(139) 		168
(13) 		207
(52) 		222
(67) 		245
(90) 		255
(100) 		271
(116) 		291
(136) 		297
(142)
  • 208ed11
Approximation of prime harmonics in 208ed11
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -2.50 -5.92 +7.84 +4.12 +0.00 -9.79 +4.78 -8.16 +0.37 -1.77 +2.53
Relative (%) -12.5 -29.7 +39.3 +20.6 +0.0 -49.1 +23.9 -40.9 +1.9 -8.8 +12.7
Steps
(reduced) 		60
(60) 		95
(95) 		140
(140) 		169
(169) 		208
(0) 		222
(14) 		246
(38) 		255
(47) 		272
(64) 		292
(84) 		298
(90)
  • 215ed12
Approximation of prime harmonics in 215ed12
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.55 -1.09 -5.05 -7.30 -9.44 +1.49 -2.73 +4.81 -5.81 -6.93 -2.33
Relative (%) +2.7 -5.5 -25.2 -36.5 -47.2 +7.5 -13.6 +24.0 -29.0 -34.6 -11.7
Steps
(reduced) 		60
(60) 		95
(95) 		139
(139) 		168
(168) 		207
(207) 		222
(7) 		245
(30) 		255
(40) 		271
(56) 		291
(76) 		297
(82)
  • 255ed19
Approximation of prime harmonics in 255ed19
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -0.59 -2.88 -7.67 +9.53 +6.65 -2.69 -7.34 +0.00 +9.07 +7.57 -7.93
Relative (%) -2.9 -14.4 -38.4 +47.7 +33.3 -13.5 -36.7 +0.0 +45.4 +37.9 -39.7
Steps
(reduced) 		60
(60) 		95
(95) 		139
(139) 		169
(169) 		208
(208) 		222
(222) 		245
(245) 		255
(0) 		272
(17) 		292
(37) 		297
(42)
  • 272ed23 (great for catnip temperament, maybe there's a similar but simpler tuning w similar benefits?)
Approximation of prime harmonics in 272ed23
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -2.59 -6.05 +7.65 +3.89 -0.28 +9.86 +4.44 -8.51 +0.00 -2.17 +2.12
Relative (%) -13.0 -30.3 +38.3 +19.5 -1.4 +49.4 +22.2 -42.6 +0.0 -10.8 +10.6
Steps
(reduced) 		60
(60) 		95
(95) 		140
(140) 		169
(169) 		208
(208) 		223
(223) 		246
(246) 		255
(255) 		272
(0) 		292
(20) 		298
(26)
  • 13-limit WE (20.013c)
Approximation of prime harmonics in 1ed20.013c
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.78 -0.72 -4.51 -6.64 -8.63 +2.36 -1.77 +5.80 -4.75 -5.79 -1.17
Relative (%) +3.9 -3.6 -22.5 -33.2 -43.1 +11.8 -8.8 +29.0 -23.7 -29.0 -5.9
Step 60 95 139 168 207 222 245 255 271 291 297
  • 299zpi (20.128c)
Approximation of prime harmonics in 1ed20.128c
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +7.68 -9.92 -8.65 -7.45 -4.95 +7.76 +6.28 -5.13 +6.29 +7.54 -7.28
Relative (%) +38.2 -49.3 -43.0 -37.0 -24.6 +38.6 +31.2 -25.5 +31.2 +37.5 -36.1
Step 60 94 138 167 206 221 244 253 270 290 295
  • 300zpi (20.093c)
Approximation of prime harmonics in 1ed20.093c
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +5.58 +6.88 +6.61 +6.80 +7.93 +0.03 -2.26 +6.11 -3.16 -2.61 +2.49
Relative (%) +27.8 +34.2 +32.9 +33.8 +39.5 +0.1 -11.3 +30.4 -15.7 -13.0 +12.4
Step 60 95 139 168 207 221 244 254 270 290 296
  • 301zpi (20.027c)
Approximation of prime harmonics in 1ed20.027c
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +1.62 +0.61 -2.56 -4.29 -5.73 +5.47 +1.66 +9.37 -0.96 -1.72 +2.98
Relative (%) +8.1 +3.0 -12.8 -21.4 -28.6 +27.3 +8.3 +46.8 -4.8 -8.6 +14.9
Step 60 95 139 168 207 222 245 255 271 291 297
  • 302zpi (19.962c)
Approximation of prime harmonics in 1ed19.962c
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -2.28 -5.57 +8.37 +4.75 +0.78 -8.96 +5.70 -7.20 +1.39 -0.67 +3.64
Relative (%) -11.4 -27.9 +41.9 +23.8 +3.9 -44.9 +28.5 -36.1 +7.0 -3.4 +18.2
Step 60 95 140 169 208 222 246 255 272 292 298
  • 303zpi (19.913c)
Approximation of prime harmonics in 1ed19.913c
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -5.22 +9.69 +1.51 -3.53 -9.41 +0.07 -6.36 +0.21 +7.97 +4.93 +8.95
Relative (%) -26.2 +48.7 +7.6 -17.7 -47.3 +0.4 -31.9 +1.1 +40.0 +24.8 +45.0
Step 60 96 140 169 208 223 246 256 273 293 299
  • 304zpi (19.869c)
Approximation of prime harmonics in 1ed19.869c
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -7.86 +5.47 -4.65 +8.90 +1.30 -9.74 +2.69 +8.82 -4.04 -7.96 -4.20
Relative (%) -39.6 +27.5 -23.4 +44.8 +6.6 -49.0 +13.5 +44.4 -20.3 -40.1 -21.2
Step 60 96 140 170 209 223 247 257 273 293 299

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
  • 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)
Medium priority

118edo (choose ZPIS)

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

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)

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)
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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