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


= Title1 =
= Title1 =
== Octave stretch or compression ==
== Octave stretch or compression ==
99edo's approximations of harmonics 3, 5, and 7 can all be improved if slightly [[stretched and compressed tuning|compressing the octave]] is acceptable, using tunings such as [[157edt]] or [[256ed6]]. 157edt is especially performant if the 13-limit of the 99ef val is intended, but the 7-limit part is overcompressed, for which the milder 256ed6 is a better choice. If the 13-limit patent val is intended, then little to no compression, or even stretch, might be serviceable.
What follows is a comparison of stretched- and compressed-octave 33edo tunings.


What follows is a comparison of stretched- and compressed-octave 99edo tunings.
; [[ed5|76ed5]]
* Octave size: 1209.8{{c}}
Stretching the octave of 33edo by around 10{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 76ed5 does this.
{{Harmonics in equal|76|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 76ed5}}
{{Harmonics in equal|76|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 76ed5 (continued)}}


; [[zpi|567zpi]]  
; [[ed7|92ed7]]
* Step size: 12.138{{c}}, octave size: 1201.66{{c}}
* Octave size: 1208.4{{c}}
Stretching the octave of 99edo by around 1.5{{c}} results in improved primes 11, 13, 17, and 19, but worse primes 2, 3, 5 and 7. This approximates all harmonics up to 16 within 5.54{{c}}. The tuning 567zpi does this.
Stretching the octave of 33edo by around 8.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 92ed7 does this. So does the tuning [[zpi|137zpi]] whose octave differs by only 0.3{{c}}.
{{Harmonics in cet|12.138|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 567zpi}}
{{Harmonics in equal|92|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 92ed7}}
{{Harmonics in cet|12.138|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 567zpi (continued)}}
{{Harmonics in equal|92|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 92ed7 (continued)}}


; [[WE|99et, 13-limit WE tuning]]  
; [[equal tuning|114ed11]]  
* Step size: 12.123{{c}}, octave size: 1200.18{{c}}
* Octave size: 1201.7{{c}}
Stretching the octave of 99edo by around a fifth of a cent results in improved primes 11 and 13, but worse primes 2, 3, 5 and 7. This approximates all harmonics up to 16 within 5.25{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.
Stretching the octave of 33edo by around 2{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 114ed11 does this.
{{Harmonics in cet|12.123|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 99et, 13-limit WE tuning}}
{{Harmonics in equal|114|11|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 114ed11}}
{{Harmonics in cet|12.123|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 99et, 13-limit WE tuning (continued)}}
{{Harmonics in equal|114|11|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 114ed11 (continued)}}


; 99edo
; [[zpi|138zpi]]
* Step size: 12.121{{c}}, octave size: 1200.00{{c}}  
* Step size: 36.394{{c}}, octave size: 1201.0{{c}}
Pure-octaves 99edo approximates all harmonics up to 16 within 5.86{{c}}.
Stretching the octave of 33edo by around 1{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 138zpi does this. So does the tuning [[equal tuning|122ed13]] whose octave differs by only 0.1{{c}}.
{{Harmonics in equal|99|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 99edo}}
{{Harmonics in cet|36.394|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 138zpi}}
{{Harmonics in equal|99|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 99edo (continued)}}
{{Harmonics in cet|36.394|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 138zpi (continued)}}


; [[WE|99et, 7-limit WE tuning]] / [[256ed6]]
; 33edo
* Step size: 12.117{{c}}, octave size: 1199.58{{c}}
* Step size: 36.363{{c}}, octave size: 1200.0{{c}}  
Compressing the octave of 99edo by around 0.6{{c}} results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 5.71{{c}}. Its 7-limit WE tuning and 7-limit [[TE]] tuning both do this. So does the tuning 256ed6 whose octave is identical within a thousandth of a cent.
Pure-octaves 33edo approximates all harmonics up to 16 within NNN{{c}}.
{{Harmonics in cet|12.117|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 99et, 7-limit WE tuning}}
{{Harmonics in equal|33|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 33edo}}
{{Harmonics in cet|12.117|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 99et, 7-limit WE tuning (continued)}}
{{Harmonics in equal|33|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 33edo (continued)}}


; [[zpi|568zpi]]  
; [[WE|33et, 13-limit WE tuning]]
* Step size: 12.115{{c}}, octave size: 1199.39{{c}}
* Step size: 36.357{{c}}, octave size: 1199.8{{c}}
Compressing the octave of 99edo by around 0.4{{c}} results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 5.68{{c}}. The tuning 568zpi does this.
Compressing the octave of 33edo by a fifth of a cent results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.
{{Harmonics in cet|12.115|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 568zpi}}
{{Harmonics in cet|36.357|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 33et, 13-limit WE tuning}}
{{Harmonics in cet|12.115|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 568zpi (continued)}}
{{Harmonics in cet|36.357|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 33et, 13-limit WE tuning (continued)}}


; [[157edt]] / [[ed5|230ed5]]
; [[ed7|93ed7]]
* Step size: 12.114{{c}}, octave size: 1199.32{{c}}
* Octave size: 1196.4{{c}}
Compressing the octave of 99edo by around 0.3{{c}} results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 5.44{{c}}. The tuning 157edt does this. So does 230ed5 whose octave is identical within a hundredth of a cent.
Compressing the octave of 33edo by around 4.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. If one wishes to use both 33edo's sharp and flat fifths simultaneously (see [[dual-fifth tuning]]), then this amount of stretch is ideal, because it evenly shares error between the two fifths. The tuning 93ed7 does this. So does the tuning [[equal tuning|52ed13]] whose octave differs by only 0.1{{c}}.
{{Harmonics in equal|157|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 157edt}}
{{Harmonics in equal|93|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 93ed7}}
{{Harmonics in equal|157|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 157edt (continued)}}
{{Harmonics in equal|93|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 93ed7 (continued)}}
 
; [[ed5|77ed5]]
* Octave size: 1194.1{{c}}
Compressing the octave of 33edo by around 6{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 77ed5 does this. So does the tuning [[zpi|139zpi]] whose octave differs by only 0.2{{c}}.
{{Harmonics in equal|77|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 77ed5}}
{{Harmonics in equal|77|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 77ed5 (continued)}}
 
; [[equal tuning|115ed11]]
* Octave size: 1191.2{{c}}
Compressing the octave of 33edo by around 9{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 115ed11 does this. So do the tunings [[equal tuning|123ed13]] and [[AS|1ed47/46]] whose octaves are within 0.3{{c}} of 115ed11.
{{Harmonics in equal|115|11|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 115ed11}}
{{Harmonics in equal|115|11|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 115ed11 (continued)}}


= Title2 =
= Title2 =
=== Possible tunings to be used on each page ===
=== Lab ===
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)
Place holder


; High-priority


23edo (narrow down edonoi & ZPIs)
<br><br><br><br><br>
* Main: "23edo and octave stretching"
* 36edt
{{harmonics in equal|36|3|1|intervals=prime}}
* 59ed6
{{harmonics in equal|59|6|1|intervals=prime}}
* 60ed6
{{harmonics in equal|60|3|1|intervals=prime}}
* 2.3.5.13 WE (52.447c)
{{harmonics in cet|52.447|intervals=prime}}
* 13-limit WE (52.237c)
{{harmonics in cet|52.237|intervals=prime}}
* 84zpi (52.615c)
{{harmonics in cet| 52.615 |intervals=prime}}
* 85zpi (52.114c)
{{harmonics in cet| 52.114 |intervals=prime}}
* 86zpi (51.653c)
{{harmonics in cet| 51.653 |intervals=prime}}


60edo (narrow down edonoi & ZPIs)
* 95edt
* 35edf
* 139ed5
* 155ed6
* 208ed11
* (???)ed12
* 255ed19
* 272ed23 (great for catnip temperament, maybe there's a similar but simpler tuning w similar benefits?)
* 13-limit WE (20.013c)
* 299zpi (20.128c)
* 300zpi (20.093c)
* 301zpi (20.027c)
* 302zpi (19.962c)
* 303zpi (19.913c)
* 304zpi (19.869c)


; Medium priority
{{harmonics in cet | 300 | intervals=prime}}


13edo
{{harmonics in equal | 140 | 12 | 1 | intervals=prime}}
* 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)


32edo (narrow down ZPIs)
=== Possible tunings to be used on each page ===
* 90ed7
You can remove some of these or add more that aren't listed here; this section is pretty much just brainstorming.
* 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)
(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)
* 76ed5
* 92ed7
* 52edt
* 1ed47/46
* 114ed11
* 122ed13
* 93ed7
* 23edPhi
* 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)
; High-priority
* 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)
39edo
* 42ed257/128 (replace w something similar but simpler)
* 171zpi (30.973c) (optimised for dual-fifths use)
* AS123/121 (1ed123/121)
* 13-limit WE (30.757c) (octave of 135ed11 differs by only 0.2{{c}})
* 11ed6/5
* 101ed6 (octave of 172zpi differs by only 0.4{{c}})
* 34ed7/4
* 173zpi (30.672c) (octave of 62edt differs by only 0.2{{c}})
* 7-limit WE (28.484c)
* 110ed7 (octave of 145ed13 differs by only 0.1{{c}})
* 13-limit WE (28.534c)
* 91ed5
* 189zpi (28.689c)
* 190zpi (28.572c)
* 191zpi (28.444c)


45edo
45edo
* 126ed7
* 209zpi (26.550)
* 13ed11/9
* 13-limit WE (26.695c)
* 161ed12
* 116ed6 (octave identical to 126ed7 within 0.1{{c}})
* 7-limit WE (26.745c)
* 7-limit WE (26.745c)
* 13-limit WE (26.695c)
* 207zpi (26.762)
* 207zpi (26.762)
* 208zpi (26.646)
* 71edt (octave identical to 155ed11 within 0.3{{c}})
* 209zpi (26.550)


54edo (narrow down slightly)
54edo
* 86edt
* 139ed6 (octave is identical to 262zpi within 0.2{{c}})
* 126ed5
* 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
* 152ed7
* 38ed5/3
* 140ed6
* 40ed5/3
* 126ed5 (octave is identical to 86edt within 0.1{{c}})
* 2.3.7.11.13 WE (22.180c)
 
* 13-limit WE (22.198c)
64edo
* 262zpi (22.313c)
* 179ed7 (octave is identical to 326zpi within 0.3{{c}})
* 263zpi (22.243c)
* 165ed6
* 264zpi (22.175c)
* 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
 
42edo (reduce # of edonoi)
* 108ed6 (octave is identical to 97ed5 within 0.1{{c}})
* 189zpi (28.689c)
* 150ed12
* 145ed11
''190zpi's octave is within 0.05{{c}} of pure-octaves 42edo''
* 118ed7
* 13-limit WE (28.534c)
* 151ed12 (octave is identical to 7-limit WE within 0.3{{c}})
* 109ed6
* 191zpi (28.444c)
* 67edt


59edo (narrow down ZPIs)
59edo (reduce # of edonoi or zpi)
* 93edt
* 152ed6
* 166ed7
* 203ed11
* 7-limit WE (20.301c)
* 11-limit WE (20.310c)
* 13-limit WE (20.320c)
* 293zpi (20.454c)
* 294zpi (20.399c)
* 294zpi (20.399c)
* 211ed12
* 295zpi (20.342c)
* 295zpi (20.342c)
''pure octaves 59edo octave is identical to 137ed5 within 0.05{{c}}''
* 13-limit WE (20.320c)
* 7-limit WE (20.301c)
* 166ed7
* 212ed12
* 296zpi (20.282c)
* 296zpi (20.282c)
* 297zpi (20.229c)
* 153ed6


64edo (narrow down ZPIs)
; Medium priority
* 149ed5
 
* 180ed7
118edo (choose ZPIS)
* 222ed11
{{harmonics in equal | 118 | 2 | 1 | intervals=integer | columns=12}}
* 47ed5/3
* 187edt
* 11-limit WE (18.755c)
* 69edf
* 13-limit WE (18.752c)
* 13-limit WE (10.171c)
* 325zpi (18.868c)
* Best nearby ZPI(s)
* 326zpi (18.816c)
 
* 327zpi (18.767c)
13edo
* 328zpi (18.721c)
{{harmonics in equal | 13 | 2 | 1 | intervals=integer | columns=12}}
* 329zpi (18.672c)
* Main: "13edo and optimal octave stretching"
* 330zpi (18.630c)
* 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)
103edo (narrow down edonoi, choose ZPIS)
{{harmonics in equal | 103 | 2 | 1 | intervals=integer | columns=12}}
* 163edt
* 163edt
* 239ed5
* 239ed5
* (???)ed6
* 266ed6
* 289ed7
* 289ed7
* 356ed11
* 356ed11
* (???)ed12
* 369ed12
* 381ed13
* 381ed13
* 421ed17
* 421ed17
Line 212: Line 179:


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)
* 1-2 WE tunings
* 1-2 WE tunings
* Best nearby ZPI(s)
118edo (choose ZPIS)
* 187edt
* 69edf
* 13-limit WE (10.171c)
* Best nearby ZPI(s)
* Best nearby ZPI(s)


Line 293: Line 255:


25edo
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 299: Line 262:


26edo
26edo
{{harmonics in equal | 26 | 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 305: Line 269:


29edo
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 311: Line 276:


30edo
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 317: Line 283:


34edo
34edo
{{harmonics in equal | 34 | 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 323: Line 290:


35edo
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 329: Line 297:


36edo
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 335: Line 304:


37edo
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 340: Line 310:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


5edo
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 346: Line 317:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


6edo
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 352: Line 324:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


9edo
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 358: Line 331:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


10edo
15edo
{{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 364: Line 338:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


11edo
18edo
{{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 370: Line 345:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


15edo
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)
Line 376: Line 352:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


18edo
5edo
{{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 382: Line 359:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


48edo
6edo
{{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 389: Line 367:


20edo
20edo
{{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 395: Line 374:


24edo
24edo
{{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 401: Line 381:


28edo
28edo
{{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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