User:BudjarnLambeth/Sandbox2: Difference between revisions

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118edo (choose ZPIS)
118edo (choose ZPIS)
{{harmonics in equal | 118 | 2 | 1 | intervals=integer | columns=12}}
* 187edt
* 187edt
* 69edf
* 69edf
Line 67: Line 66:


103edo (narrow down edonoi, choose ZPIS)
103edo (narrow down edonoi, choose ZPIS)
{{harmonics in equal | 103 | 2 | 1 | intervals=integer | columns=12}}
* 163edt
* 163edt
* 239ed5
* 239ed5
Line 81: Line 79:


111edo (choose ZPIS)
111edo (choose ZPIS)
{{harmonics in equal | 111 | 2 | 1 | intervals=integer | columns=12}}
* Nearby edt, ed6, ed12 and/or edf
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
Line 88: Line 85:


13edo
13edo
{{harmonics in equal | 13 | 2 | 1 | intervals=integer | columns=12}}
* Main: "13edo and optimal octave stretching"
* Main: "13edo and optimal octave stretching"
* 2.5.11.13 WE (92.483c)
* 2.5.11.13 WE (92.483c)
Line 101: Line 97:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


; Medium-priority
; Medium-high priority
 
9edo
* 23ed6
* 31ed11
* 32ed12
* 11lim WE
* 13lim WE
* 2.3.5.11 WE
* Best nearby ZPI(s)
9edo's [[prime]]s 3, 7, 11 and 13 are all tuned flat, so it can benefit from [[octave stretching]].
 
15edo
* 39ed6
* 50ed10
* 52ed11
* 54ed12
* Nearby edf (optional)
* 11lim WE
* Best nearby ZPI(s)
15edo's [[prime]]s 3, 5, 11 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]].
 
18edo
* 42ed5
* 47ed6
* 60ed10
* 65ed12
* 7lim WE
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
18edo's [[prime]]s 3, 5, 7 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]].


25edo
25edo
{{harmonics in equal | 25 | 2 | 1 | intervals=integer | columns=12}}
* 65ed6
* Nearby edt, ed6, ed12 and/or edf
* 90ed12
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* Nearby edf (optional)
* 1-2 WE tunings
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
* Best nearby ZPI(s)
25edo's [[prime]] 3 is very sharp, and its sharp and flat mapping of 11 and 13 are about equally bad, it can benefit from [[octave shrinking]].


26edo
26edo
{{harmonics in equal | 26 | 2 | 1 | intervals=integer | columns=12}}
* 41edt
* Nearby edt, ed6, ed12 and/or edf
* 67ed6
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 86ed10
* 1-2 WE tunings
* 93ed12
* 96ed14
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
* Best nearby ZPI(s)
26edo's simple [[prime]]s with the most error - 3, 5 and 13 - are all tuned flat, so it can benefit from [[octave stretching]].


29edo
29edo
{{harmonics in equal | 29 | 2 | 1 | intervals=integer | columns=12}}
* 46edt
* Nearby edt, ed6, ed12 and/or edf
* 105ed12
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 96ed10
* 1-2 WE tunings
* 100ed11
* 107ed13
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
* Best nearby ZPI(s)
29edo's [[prime]]s 5, 7, 11 and 13 are all tuned flat and the 3 has relatively little error, so 29edo can benefit from [[octave stretching]].


30edo
30edo
{{harmonics in equal | 30 | 2 | 1 | intervals=integer | columns=12}}
* 78ed6
* Nearby edt, ed6, ed12 and/or edf
* 100ed10
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 104ed11
* 1-2 WE tunings
* 108ed12
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
* Best nearby ZPI(s)
30edo's simple [[prime]]s with the most error - 3, 5 and 11 - are all tuned sharp, so it can benefit from [[octave shrinking]].


35edo
34edo
{{harmonics in equal | 35 | 2 | 1 | intervals=integer | columns=12}}
* 54edt
* Nearby edt, ed6, ed12 and/or edf
* 79ed5
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 88ed6
* 1-2 WE tunings
* 108ed9
* 113ed10
* 122ed12
* 126ed13
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
* Best nearby ZPI(s)
34edo's [[prime]]s 3, 5, 11 and 13 are all tuned sharp, and it has two about equally bad mappings of 7, so 34edo can benefit from [[octave shrinking]].


36edo
35edo
{{harmonics in equal | 36 | 2 | 1 | intervals=integer | columns=12}}
* 81ed5
* Nearby edt, ed6, ed12 and/or edf
* 90ed6
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 98ed7
* 1-2 WE tunings
* 116ed10
* 121ed11
* 125ed12
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
* Best nearby ZPI(s)
35edo's [[prime]]s 3, 5, 7 and 11 are all tuned flat, and it has two about equally bad mappings of 13, so 35edo can benefit from [[octave stretching]].


37edo
37edo
{{harmonics in equal | 37 | 2 | 1 | intervals=integer | columns=12}}
* 59edt
* Nearby edt, ed6, ed12 and/or edf
* 86ed5
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 96ed6
* 1-2 WE tunings
* 104ed7
* 123ed10
* 128ed11
* 133ed12
* 137ed13
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
* Best nearby ZPI(s)
37edo's [[prime]]s 3, 5, 7, 11 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]].


15edo
48edo
{{harmonics in equal | 15 | 2 | 1 | intervals=integer | columns=12}}
* 76edt
* Nearby edt, ed6, ed12 and/or edf
* 124ed6
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 152ed9
* 1-2 WE tunings
* 159ed10
* 166ed11
* 172ed12
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
* Best nearby ZPI(s)
Most of 48edo's simple [[prime]]s have low error, but its 5 is substantially flat, so 48edo can benefit from slight [[octave stretching]].


9edo
; Medium-low priority
{{harmonics in equal | 9 | 2 | 1 | intervals=integer | columns=12}}
 
* Nearby edt, ed6, ed12 and/or edf
10edo
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 16edt
* 1-2 WE tunings
* 23ed5
* 26ed6
* 28ed7
* 32ed8
* 33ed10
* 36ed12
* 37ed13
* Nearby edf (optional)
* 2.3.7.13 WE
* 2.5.7.13 WE
* 13lim WE
* Best nearby ZPI(s)
* Best nearby ZPI(s)
If one wishes to use 10edo as a no-5s, 19-or-lower-limit tuning, then it benefits from [[octave shrinking]]. If one wishes to use 10edo as a no-3s, 13-or-lower-limit tuning, then it benefits from [[octave stretching]].


18edo
11edo
{{harmonics in equal | 18 | 2 | 1 | intervals=integer | columns=12}}
* 27ed6
* Nearby edt, ed6, ed12 and/or edf
* 28ed6
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 31ed7
* 1-2 WE tunings
* 35ed9
* 37ed10
* 38ed10
* 38ed12
* 39ed12
* 41ed13
* 2.7.11 WE
* 2.7.11.13 WE
* Best nearby ZPI(s)
* Best nearby ZPI(s)
11edo has about equally bad sharp and flat mappings of  [[prime]]s 3 and 5. The 7 and 13 are quite sharp, but the 11 is a little flat. To use it as a 2.7.11.13 tuning, slight [[octave shrinking]] is advisable. To use its primes 3 or 5, extreme octave shrinking or [[octave stretching]] can be used, at the cost of making the octaves sound significantly weaker.


24edo
24edo
{{harmonics in equal | 24 | 2 | 1 | intervals=integer | columns=12}}
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* Best nearby ZPI(
48edo
{{harmonics in equal | 48 | 2 | 1 | intervals=integer | columns=12}}
* Nearby edt, ed6, ed12 and/or edf
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* 1-2 WE tunings
* Best nearby ZPI(s)
* Best nearby ZPI(s)
If one wishes to use 24edo as a full 19-or-lower-limit tuning, then it benefits from slight [[octave stretching]], mostly to improve its [[prime]] 7. If one wishes to use 24edo as a no-7s 19-or-lower-limit tuning, then it benefits from slight [[octave shrinking]], mostly to improve its primes 5 and 13.


5edo
5edo
{{harmonics in equal | 5 | 2 | 1 | intervals=integer | columns=12}}
* 8edt
* Nearby edt, ed6, ed12 and/or edf
* 13ed6
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 14ed7
* 1-2 WE tunings
* 18ed12
* Nearby edf (optional)
* 2.3.7 WE
* Best nearby ZPI(s)
* Best nearby ZPI(s)
If one wishes to use 5edo as a  2.3.7 [[subgroup]] tuning, then it benefits from slight [[octave shrinking]] to improve its prime 3.


6edo
6edo
{{harmonics in equal | 6 | 2 | 1 | intervals=integer | columns=12}}
* 14ed5
* Nearby edt, ed6, ed12 and/or edf
* 17ed7
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 19ed9
* 1-2 WE tunings
* 20ed10
* Best nearby ZPI(s)s)
* 2.9.5 WE
 
* 2.9.5.7 WE
10edo
{{harmonics in equal | 10 | 2 | 1 | intervals=integer | columns=12}}
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* Best nearby ZPI(s)
 
11edo
{{harmonics in equal | 11 | 2 | 1 | intervals=integer | columns=12}}
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* Best nearby ZPI(s)
 
34edo
{{harmonics in equal | 34 | 2 | 1 | intervals=integer | columns=12}}
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* Best nearby ZPI(s)
* Best nearby ZPI(s)
If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 [[sugroup]] tuning, then it benefits from [[octave shrinking]].


; Low priority
; Low-priority


125edo
125edo

Revision as of 00:55, 11 September 2025

Quick link

User:BudjarnLambeth/Draft related tunings section

Title1

Octave stretch or compression

38edo's approximation of JI can be improved by slightly stretching the octave.

What follows is a comparison of stretched-octave 38edo tunings.

38edo
  • Step size: 31.579 ¢, octave size: 1200.00 ¢

Pure-octaves 38edo approximates all harmonics up to 16 within NNN ¢.

Approximation of harmonics in 38edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.0 -7.2 +0.0 -7.4 -7.2 +10.1 +0.0 -14.4 -7.4 -14.5 -7.2
Relative (%) +0.0 -22.9 +0.0 -23.3 -22.9 +32.1 +0.0 -45.7 -23.3 -45.8 -22.9
Steps
(reduced) 		38
(0) 		60
(22) 		76
(0) 		88
(12) 		98
(22) 		107
(31) 		114
(0) 		120
(6) 		126
(12) 		131
(17) 		136
(22)
Approximation of harmonics in 38edo (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +12.1 +10.1 -14.6 +0.0 -10.2 -14.4 -13.3 -7.4 +2.9 -14.5 +3.3 -7.2
Relative (%) +38.3 +32.1 -46.2 +0.0 -32.4 -45.7 -42.1 -23.3 +9.2 -45.8 +10.5 -22.9
Steps
(reduced) 		141
(27) 		145
(31) 		148
(34) 		152
(0) 		155
(3) 		158
(6) 		161
(9) 		164
(12) 		167
(15) 		169
(17) 		172
(20) 		174
(22)
38et, 13-limit WE tuning
  • Step size: 31.599 ¢, octave size: 1200.77 ¢

Stretching the octave of 38edo by around 1 ¢ 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 38et, 13-limit WE tuning
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.8 -6.0 +1.5 -5.6 -5.3 +12.3 +2.3 -12.0 -4.8 -11.8 -4.5
Relative (%) +2.4 -19.0 +4.8 -17.7 -16.6 +38.8 +7.2 -38.1 -15.3 -37.5 -14.2
Step 38 60 76 88 98 107 114 120 126 131 136
Approximation of harmonics in 38et, 13-limit WE tuning (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +14.9 +13.0 -11.6 +3.0 -7.1 -11.3 -10.1 -4.1 +6.3 -11.1 +6.8 -3.7
Relative (%) +47.3 +41.2 -36.8 +9.6 -22.5 -35.7 -31.9 -12.9 +19.8 -35.1 +21.4 -11.8
Step 141 145 148 152 155 158 161 164 167 169 172 174
88ed5
  • Step size: 31.663 ¢, octave size: 1203.18 ¢

Stretching the octave of 38edo by around 3 ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning 88ed5 does this.

Approximation of harmonics in 88ed5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +3.2 -2.2 +6.4 +0.0 +1.0 -12.6 +9.5 -4.4 +3.2 -3.5 +4.2
Relative (%) +10.0 -6.9 +20.1 +0.0 +3.1 -39.7 +30.1 -13.9 +10.0 -11.1 +13.2
Steps
(reduced) 		38
(38) 		60
(60) 		76
(76) 		88
(0) 		98
(10) 		106
(18) 		114
(26) 		120
(32) 		126
(38) 		131
(43) 		136
(48)
Approximation of harmonics in 88ed5 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -7.8 -9.4 -2.2 +12.7 +2.8 -1.2 +0.2 +6.4 -14.8 -0.3 -14.0 +7.3
Relative (%) -24.5 -29.7 -6.9 +40.2 +8.7 -3.8 +0.6 +20.1 -46.7 -1.0 -44.1 +23.2
Steps
(reduced) 		140
(52) 		144
(56) 		148
(60) 		152
(64) 		155
(67) 		158
(70) 		161
(73) 		164
(76) 		166
(78) 		169
(81) 		171
(83) 		174
(86)
166zpi
  • Step size: 31.671 ¢, octave size: 1203.48 ¢

Stretching the octave of 38edo by around 3.5 ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning 166zpi does this.

Approximation of harmonics in 166zpi
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +3.5 -1.7 +7.0 +0.7 +1.8 -11.7 +10.5 -3.4 +4.2 -2.4 +5.3
Relative (%) +11.0 -5.4 +22.1 +2.3 +5.7 -36.9 +33.1 -10.7 +13.4 -7.6 +16.7
Step 38 60 76 88 98 106 114 120 126 131 136
Approximation of harmonics in 166zpi (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -6.6 -8.2 -1.0 +14.0 +4.0 +0.1 +1.5 +7.7 -13.4 +1.1 -12.5 +8.8
Relative (%) -20.8 -25.9 -3.0 +44.2 +12.8 +0.3 +4.8 +24.4 -42.3 +3.4 -39.6 +27.8
Step 140 144 148 152 155 158 161 164 166 169 171 174
60edt
  • Step size: 31.699 ¢, octave size: 1204.57 ¢

Stretching the octave of 38edo by around 4.5 ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning 60edt does this.

Approximation of harmonics in 60edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +4.6 +0.0 +9.1 +3.2 +4.6 -8.7 +13.7 +0.0 +7.8 +1.3 +9.1
Relative (%) +14.4 +0.0 +28.8 +10.2 +14.4 -27.5 +43.3 +0.0 +24.6 +4.0 +28.8
Steps
(reduced) 		38
(38) 		60
(0) 		76
(16) 		88
(28) 		98
(38) 		106
(46) 		114
(54) 		120
(0) 		126
(6) 		131
(11) 		136
(16)
Approximation of harmonics in 60edt (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -2.6 -4.1 +3.2 -13.4 +8.4 +4.6 +6.1 +12.4 -8.7 +5.9 -7.7 +13.7
Relative (%) -8.3 -13.0 +10.2 -42.3 +26.6 +14.4 +19.1 +39.0 -27.5 +18.5 -24.3 +43.3
Steps
(reduced) 		140
(20) 		144
(24) 		148
(28) 		151
(31) 		155
(35) 		158
(38) 		161
(41) 		164
(44) 		166
(46) 		169
(49) 		171
(51) 		174
(54)

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

118edo (choose ZPIS)

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

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)

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)

104edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)
Medium-high priority

9edo

  • 23ed6
  • 31ed11
  • 32ed12
  • 11lim WE
  • 13lim WE
  • 2.3.5.11 WE
  • Best nearby ZPI(s)

9edo's primes 3, 7, 11 and 13 are all tuned flat, so it can benefit from octave stretching.

15edo

  • 39ed6
  • 50ed10
  • 52ed11
  • 54ed12
  • Nearby edf (optional)
  • 11lim WE
  • Best nearby ZPI(s)

15edo's primes 3, 5, 11 and 13 are all tuned sharp, so it can benefit from octave shrinking.

18edo

  • 42ed5
  • 47ed6
  • 60ed10
  • 65ed12
  • 7lim WE
  • 11lim WE
  • 13lim WE
  • Best nearby ZPI(s)

18edo's primes 3, 5, 7 and 13 are all tuned sharp, so it can benefit from octave shrinking.

25edo

  • 65ed6
  • 90ed12
  • Nearby edf (optional)
  • 11lim WE
  • 13lim WE
  • Best nearby ZPI(s)

25edo's prime 3 is very sharp, and its sharp and flat mapping of 11 and 13 are about equally bad, it can benefit from octave shrinking.

26edo

  • 41edt
  • 67ed6
  • 86ed10
  • 93ed12
  • 96ed14
  • Nearby edf (optional)
  • 11lim WE
  • 13lim WE
  • Best nearby ZPI(s)

26edo's simple primes with the most error - 3, 5 and 13 - are all tuned flat, so it can benefit from octave stretching.

29edo

  • 46edt
  • 105ed12
  • 96ed10
  • 100ed11
  • 107ed13
  • Nearby edf (optional)
  • 11lim WE
  • 13lim WE
  • Best nearby ZPI(s)

29edo's primes 5, 7, 11 and 13 are all tuned flat and the 3 has relatively little error, so 29edo can benefit from octave stretching.

30edo

  • 78ed6
  • 100ed10
  • 104ed11
  • 108ed12
  • 11lim WE
  • 13lim WE
  • Best nearby ZPI(s)

30edo's simple primes with the most error - 3, 5 and 11 - are all tuned sharp, so it can benefit from octave shrinking.

34edo

  • 54edt
  • 79ed5
  • 88ed6
  • 108ed9
  • 113ed10
  • 122ed12
  • 126ed13
  • Nearby edf (optional)
  • 11lim WE
  • 13lim WE
  • Best nearby ZPI(s)

34edo's primes 3, 5, 11 and 13 are all tuned sharp, and it has two about equally bad mappings of 7, so 34edo can benefit from octave shrinking.

35edo

  • 81ed5
  • 90ed6
  • 98ed7
  • 116ed10
  • 121ed11
  • 125ed12
  • Nearby edf (optional)
  • 11lim WE
  • 13lim WE
  • Best nearby ZPI(s)

35edo's primes 3, 5, 7 and 11 are all tuned flat, and it has two about equally bad mappings of 13, so 35edo can benefit from octave stretching.

37edo

  • 59edt
  • 86ed5
  • 96ed6
  • 104ed7
  • 123ed10
  • 128ed11
  • 133ed12
  • 137ed13
  • Nearby edf (optional)
  • 11lim WE
  • 13lim WE
  • Best nearby ZPI(s)

37edo's primes 3, 5, 7, 11 and 13 are all tuned sharp, so it can benefit from octave shrinking.

48edo

  • 76edt
  • 124ed6
  • 152ed9
  • 159ed10
  • 166ed11
  • 172ed12
  • Nearby edf (optional)
  • 11lim WE
  • 13lim WE
  • Best nearby ZPI(s)

Most of 48edo's simple primes have low error, but its 5 is substantially flat, so 48edo can benefit from slight octave stretching.

Medium-low priority

10edo

  • 16edt
  • 23ed5
  • 26ed6
  • 28ed7
  • 32ed8
  • 33ed10
  • 36ed12
  • 37ed13
  • Nearby edf (optional)
  • 2.3.7.13 WE
  • 2.5.7.13 WE
  • 13lim WE
  • Best nearby ZPI(s)

If one wishes to use 10edo as a no-5s, 19-or-lower-limit tuning, then it benefits from octave shrinking. If one wishes to use 10edo as a no-3s, 13-or-lower-limit tuning, then it benefits from octave stretching.

11edo

  • 27ed6
  • 28ed6
  • 31ed7
  • 35ed9
  • 37ed10
  • 38ed10
  • 38ed12
  • 39ed12
  • 41ed13
  • 2.7.11 WE
  • 2.7.11.13 WE
  • Best nearby ZPI(s)

11edo has about equally bad sharp and flat mappings of primes 3 and 5. The 7 and 13 are quite sharp, but the 11 is a little flat. To use it as a 2.7.11.13 tuning, slight octave shrinking is advisable. To use its primes 3 or 5, extreme octave shrinking or octave stretching can be used, at the cost of making the octaves sound significantly weaker.

24edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

If one wishes to use 24edo as a full 19-or-lower-limit tuning, then it benefits from slight octave stretching, mostly to improve its prime 7. If one wishes to use 24edo as a no-7s 19-or-lower-limit tuning, then it benefits from slight octave shrinking, mostly to improve its primes 5 and 13.

5edo

  • 8edt
  • 13ed6
  • 14ed7
  • 18ed12
  • Nearby edf (optional)
  • 2.3.7 WE
  • Best nearby ZPI(s)

If one wishes to use 5edo as a 2.3.7 subgroup tuning, then it benefits from slight octave shrinking to improve its prime 3.

6edo

  • 14ed5
  • 17ed7
  • 19ed9
  • 20ed10
  • 2.9.5 WE
  • 2.9.5.7 WE
  • Best nearby ZPI(s)

If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 sugroup tuning, then it benefits from octave shrinking.

Low-priority

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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