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[[User:BudjarnLambeth/Draft related tunings section]]
[[User:BudjarnLambeth/Draft related tunings section]]


= Title1 =
== Octave stretch and compression ==
== Octave stretch or compression ==
What follows is a comparison of stretched- and compressed-octave 60edo tunings.


; [[35edf]]  
; [[zpi|209zpi]]  
* Step size: 20.056{{c}}, octave size: 1203.35{{c}}
* Step size: 26.550{{c}}, octave size: 1194.8{{c}}
Stretching the octave of 60edo by a little over 3{{c}} results in improved primes 5, 7 and 11 but worse primes 2, 3 and 13. This approximates all harmonics up to 16 within 10.00{{c}}. The tuning 35edf does this.
Compressing the octave of 45edo by around 5{{c}} 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{{c}}. The tuning 209zpi does this.
{{Harmonics in equal|35|3|2|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 35edf}}
{{Harmonics in cet|26.550|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 209zpi}}
{{Harmonics in equal|35|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 35edf (continued)}}
{{Harmonics in cet|26.550|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 209zpi (continued)}}


; [[139ed5]]
; 45edo
* Step size: 20.045{{c}}, octave size: 1202.73{{c}}
* Step size: 26.667{{c}}, octave size: 1200.0{{c}}  
Stretching the octave of 60edo by a little under{{c}} results in improved primes 5, 7 and 11, but worse primes 2, 3 and 13. This approximates all harmonics up to 16 within 9.56{{c}}. The tuning 139ed5 does this.
Pure-octaves 45edo approximates all harmonics up to 16 within 13.0{{c}}.
{{Harmonics in equal|139|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 139ed5}}
{{Harmonics in equal|45|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 45edo}}
{{Harmonics in equal|139|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 139ed5 (continued)}}
{{Harmonics in equal|45|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 45edo (continued)}}


; [[zpi|301zpi]]  
; [[WE|45et, 13-limit WE tuning]]  
* Step size: 20.027{{c}}, octave size: 1201.62{{c}}
* Step size: 26.695{{c}}, octave size: 1201.3{{c}}
Stretching the octave of 60edo by around 1.5{{c}} results in improved primes 3, 5, 7, 11 and 13, but worse primes 2. This approximates all harmonics up to 16 within 6.48{{c}}. The tuning 301zpi does this.
Stretching the octave of 45edo by around 1{{c}} 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{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.
{{Harmonics in cet|20.027|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 301zpi}}
{{Harmonics in cet|26.695|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 45et, 13-limit WE tuning}}
{{Harmonics in cet| 20.027 |intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 301zpi (continued)}}
{{Harmonics in cet|26.695|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 45et, 13-limit WE tuning (continued)}}


; [[95edt]]  
; [[161ed12]]  
* Step size: 20.021{{c}}, octave size: 1201.23{{c}}
* Step size: Octave size: 1202.4{{c}}
Stretching the octave of 60edo by just over a cent results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 7.06{{c}}. The tuning 95edt does this.
Stretching the octave of 45edo by around 2.5{{c}} 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{{c}}. The tuning 161ed12 does this.
{{Harmonics in equal|95|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 95edt}}
{{Harmonics in equal|161|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 161ed12}}
{{Harmonics in equal|95|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 95edt (continued)}}
{{Harmonics in equal|161|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 161ed12 (continued)}}


; [[WE|60et, 13-limit WE tuning]] / [[155ed6]]
; [[116ed6]]  
* Step size: 20.013{{c}}, octave size: 1200.78{{c}}
* Step size: Octave size: 1203.3{{c}}
Stretching the octave of 60edo by just under a cent results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 8.63{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this. So does 155ed6 whose octaves differ by only 0.02{{c}}.
Stretching the octave of 45edo by around 3{{c}} 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{{c}}. The tuning 116ed6 does this. So does [[ed7|126ed7]] whose octave is identical within 0.1{{c}}.
{{Harmonics in cet|20.013|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 60et, 13-limit WE tuning}}
{{Harmonics in equal|116|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 116ed6}}
{{Harmonics in cet|20.013|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 60et, 13-limit WE tuning (continued)}}
{{Harmonics in equal|116|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 116ed6 (continued)}}


; [[ed12|215ed12]]  
; [[WE|45et, 7-limit WE tuning]]  
* Step size: 20.009{{c}}, octave size: 1200.55{{c}}
* Step size: 26.745{{c}}, octave size: 1203.5{{c}}
Stretching the octave of 215ed12 by around half a cent results in improved primes 3, 5 and 7, but worse primes 2, 11 and 13. This approximates all harmonics up to 16 within 9.44{{c}}. The tuning 215ed12 does this.
Stretching the octave of 45edo by around 3.5{{c}} 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{{c}}. Its 7-limit WE tuning and 7-limit [[TE]] tuning both do this.
{{Harmonics in equal|215|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 215ed12}}
{{Harmonics in cet|26.745|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 45et, 7-limit WE tuning}}
{{Harmonics in equal|215|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 215ed12 (continued)}}
{{Harmonics in cet|26.745|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 45et, 7-limit WE tuning (continued)}}


; 60edo
; [[zpi|207zpi]]
* Step size: 20.000{{c}}, octave size: 1200.00{{c}}  
* Step size: 26.762{{c}}, octave size: 1204.3{{c}}
Pure-octaves 60edo approximates all harmonics up to 16 within 8.83{{c}}.
Stretching the octave of 45edo by around 4{{c}} 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{{c}}. The tuning 207zpi does this.
{{Harmonics in equal|60|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 60edo}}
{{Harmonics in cet|26.762|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 207zpi}}
{{Harmonics in equal|60|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 60edo (continued)}}
{{Harmonics in cet|26.762|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 207zpi (continued)}}


; [[zpi|302zpi]]  
; [[71edt]]  
* Step size: 19.962{{c}}, octave size: 1197.72{{c}}
* Step size: 26.788{{c}}, octave size: 1205.5{{c}}
Compressing the octave of 60edo by around 2{{c}} results in improved primes 7 and 11, but worse primes 2, 3, 5 and 13. This approximates all harmonics up to 16 within 9.84{{c}}. The tuning 202zpi does this. So does the tuning [[equal tuning|208ed11]] whose octave is identical within 0.3{{c}}.
Stretching the octave of 45edo by around 5.5{{c}} 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{{c}}. The tuning 71edt does this. So does the tuning [[equal tuning|155ed11]] whose octave is identical within 0.3{{c}}.
{{Harmonics in cet|19.962|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 302zpi}}
{{Harmonics in equal|71|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 71edt}}
{{Harmonics in cet|19.962|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 302zpi (continued)}}
{{Harmonics in equal|71|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 71edt (continued)}}
 
302zpi is particularly well suited to [[catnip]] temperament specifically: in 60edo, catnip's mappings of 5 and 13 both differ from the [[patent val]]s, but in 19.95cet, only it's mapping of 7 differs. The tuning 169ed7 also does this, but 302zpi approximates most simple harmonics better than 169ed7.
 
; [[ed7|169ed7]]
* Step size: 19.958{{c}}, octave size: 1197.50{{c}}
Compressing the octave of 60edo by around 2.5{{c}} results in improved primes 7 and 11, but worse primes 2, 3, 5 and 13. This approximates all harmonics up to 16 within 9.94{{c}}. The tuning 169ed7 does this.
{{Harmonics in equal|169|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 169ed7}}
{{Harmonics in equal|169|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 169ed7 (continued)}}
 
; [[zpi|303zpi]]
* Step size: 19.913{{c}}, octave size: 1194.78{{c}}
Compressing the octave of 60edo by around 5{{c}} results in improved primes 5, 7 and 13, but worse primes 2, 3 and 11. This approximates all harmonics up to 16 within 8.75{{c}}. The tuning 303zpi does this. So does [[equal tuning|223ed13]] whose octave is identical within 0.03{{c}}.
{{Harmonics in cet|19.913|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 303zpi}}
{{Harmonics in cet|19.913|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 303zpi (continued)}}


= Title2 =
= Title2 =
Line 89: Line 73:
; High-priority
; High-priority


60edo (narrow down edonoi & ZPIs)
54edo
* 35edf
* 139ed6 (octave is identical to 262zpi within 0.2{{c}})
* 139ed5
* 151ed7
* 301zpi (20.027c)
* 193ed12
* 95edt
* 263zpi (22.243c)
* 13-limit WE (20.013c) (155ed6 has octaves only 0.02{{c}} different)
* 13-limit WE (22.198c) (octave is identical to 187ed11 within 0.1{{c}})
* 215ed12
* 264zpi (22.175c) (octave is identical to 194ed12 within 0.01{{c}})
* 302zpi (19.962c)
* 152ed7
* 208ed11 (ideal for catnip temperament)
* 140ed6
* 303zpi (19.913c)
* 126ed5 (octave is identical to 86edt within 0.1{{c}})


32edo
64edo
* 13-limit WE (37.481c)
* 179ed7 (octave is identical to 326zpi within 0.3{{c}})
* 11-limit WE (37.453c)
* 165ed6
* 90ed7 (optimal for dual-5) (133zpi's octave only differs by 0.4{{c}})
* 229ed12 (octave is identical to 221ed11 within 0.1{{c}})
* 51edt
* 327zpi (18.767c)
* 134zpi (37.176c)
* 11-limit WE (18.755c)
* 75ed5
''pure octaves 64edo (octave is identical to 13-limit WE within 0.13{{c}}''
* 328zpi (18.721c)
* 180ed7
* 230ed12
* 149ed5


33edo
42edo (reduce # of edonoi)
* 76ed5
* 92ed7 (137zpi's octave differs by only 0.3{{c}})
* 52ed13
* 114ed11
* 138zpi (36.394c) (122ed13's octave differs by only 0.1{{c}})
* 13-limit WE (36.357c)
* 93ed7 (optimised for dual-fifths)
* 77ed5 (139zpi's octave differs by only 0.2{{c}})
* 123ed13 / 1ed47/46 (identical within <0.1{{c}})
* 115ed11
 
39edo
* 171zpi (30.973c) (optimised for dual-fifths use)
* 13-limit WE (30.757c) (octave of 135ed11 differs by only 0.2{{c}})
* 101ed6 (octave of 172zpi differs by only 0.4{{c}})
* 173zpi (30.672c) (octave of 62edt differs by only 0.2{{c}})
* 110ed7 (octave of 145ed13 differs by only 0.1{{c}})
* 91ed5
 
42edo
* 108ed6 (octave is identical to 97ed5 within 0.1{{c}})
* 108ed6 (octave is identical to 97ed5 within 0.1{{c}})
* 189zpi (28.689c)
* 189zpi (28.689c)
Line 141: Line 109:
* 67edt
* 67edt


45edo
59edo (reduce # of edonoi or zpi)
* 209zpi (26.550)
* 13-limit WE (26.695c)
* 161ed12
* 116ed6 (octave identical to 126ed7 within 0.1{{c}})
* 7-limit WE (26.745c)
* 207zpi (26.762)
* 71edt (octave identical to 155ed11 within 0.3{{c}})
 
54edo
* 139ed6 (octave is identical to 262zpi within 0.2{{c}})
* 151ed7
* 193ed12
* 263zpi (22.243c)
* 13-limit WE (22.198c) (octave is identical to 187ed11 within 0.1{{c}})
* 264zpi (22.175c) (octave is identical to 194ed12 within 0.01{{c}})
* 152ed7
* 140ed6
* 126ed5 (octave is identical to 86edt within 0.1{{c}})
 
59edo
* 152ed6
* 152ed6
* 294zpi (20.399c)
* 294zpi (20.399c)
Line 173: Line 121:
* 296zpi (20.282c)
* 296zpi (20.282c)
* 153ed6
* 153ed6
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
; Medium priority


118edo (choose ZPIS)
25edo
{{harmonics in equal | 118 | 2 | 1 | intervals=integer | columns=12}}
{{harmonics in equal | 25 | 2 | 1 | intervals=integer | columns=12}}
* 187edt
* 69edf
* 13-limit WE (10.171c)
* Best nearby ZPI(s)
 
13edo
{{harmonics in equal | 13 | 2 | 1 | intervals=integer | columns=12}}
* 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)
{{harmonics in equal | 103 | 2 | 1 | intervals=integer | columns=12}}
* 163edt
* 239ed5
* 266ed6
* 289ed7
* 356ed11
* 369ed12
* 381ed13
* 421ed17
* 466ed23
* 13-limit WE (11.658c)
* Best nearby ZPI(s)
 
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 224: Line 131:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


; Low priority
26edo
 
{{harmonics in equal | 26 | 2 | 1 | intervals=integer | columns=12}}
104edo
* 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 232: Line 138:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


125edo
29edo
{{harmonics in equal | 29 | 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 238: Line 145:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


145edo
30edo
{{harmonics in equal | 30 | 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 244: Line 152:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


152edo
34edo
* 241edt
{{harmonics in equal | 34 | 2 | 1 | intervals=integer | columns=12}}
* 13-limit WE (7.894c)
* Best nearby ZPI(s)
 
159edo
* 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 255: Line 159:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


166edo
35edo
{{harmonics in equal | 35 | 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 261: Line 166:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


182edo
36edo
{{harmonics in equal | 36 | 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 267: Line 173:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


198edo
37edo
{{harmonics in equal | 37 | 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 273: Line 180:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


212edo
9edo
{{harmonics in equal | 9 | 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 279: Line 187:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


243edo
10edo
{{harmonics in equal | 10 | 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 285: Line 194:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


247edo
11edo
{{harmonics in equal | 11 | 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 291: Line 201:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


; Optional
15edo
 
{{harmonics in equal | 15 | 2 | 1 | intervals=integer | columns=12}}
25edo
{{harmonics in equal | 25 | 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 300: Line 208:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


26edo
18edo
{{harmonics in equal | 26 | 2 | 1 | intervals=integer | columns=12}}
{{harmonics in equal | 18 | 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 307: Line 215:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


29edo
48edo
{{harmonics in equal | 29 | 2 | 1 | intervals=integer | columns=12}}
{{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)
Line 314: Line 222:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


30edo
5edo
{{harmonics in equal | 30 | 2 | 1 | intervals=integer | columns=12}}
{{harmonics in equal | 5 | 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 321: Line 229:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


34edo
6edo
{{harmonics in equal | 34 | 2 | 1 | intervals=integer | columns=12}}
{{harmonics in equal | 6 | 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 328: Line 236:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


35edo
20edo
{{harmonics in equal | 35 | 2 | 1 | intervals=integer | columns=12}}
{{harmonics in equal | 20 | 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 335: Line 243:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


36edo
24edo
{{harmonics in equal | 36 | 2 | 1 | intervals=integer | columns=12}}
{{harmonics in equal | 24 | 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 342: Line 250:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


37edo
28edo
{{harmonics in equal | 37 | 2 | 1 | intervals=integer | columns=12}}
{{harmonics in equal | 28 | 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 349: Line 257:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


9edo
; Low priority
{{harmonics in equal | 9 | 2 | 1 | intervals=integer | columns=12}}
 
13edo
{{harmonics in equal | 13 | 2 | 1 | intervals=integer | columns=12}}
* 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)
{{harmonics in equal | 118 | 2 | 1 | intervals=integer | columns=12}}
* 187edt
* 69edf
* 13-limit WE (10.171c)
* Best nearby ZPI(s)
 
103edo (narrow down edonoi, choose ZPIS)
{{harmonics in equal | 103 | 2 | 1 | intervals=integer | columns=12}}
* 163edt
* 239ed5
* 266ed6
* 289ed7
* 356ed11
* 369ed12
* 381ed13
* 421ed17
* 466ed23
* 13-limit WE (11.658c)
* Best nearby ZPI(s)
 
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 356: Line 295:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


10edo
104edo
{{harmonics in equal | 10 | 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 363: Line 301:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


11edo
125edo
{{harmonics in equal | 11 | 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 370: Line 307:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


15edo
145edo
{{harmonics in equal | 15 | 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 377: Line 313:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


18edo
152edo
{{harmonics in equal | 18 | 2 | 1 | intervals=integer | columns=12}}
* 241edt
* 13-limit WE (7.894c)
* Best nearby ZPI(s)
 
159edo
* 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 384: Line 324:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


48edo
166edo
{{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)
Line 391: Line 330:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


5edo
182edo
{{harmonics in equal | 5 | 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 398: Line 336:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


6edo
198edo
{{harmonics in equal | 6 | 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 405: Line 342:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


20edo
212edo
{{harmonics in equal | 20 | 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 412: Line 348:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


24edo
243edo
{{harmonics in equal | 24 | 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 419: Line 354:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


28edo
247edo
{{harmonics in equal | 28 | 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)
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