User:BudjarnLambeth/Draft related tunings section: Difference between revisions

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'''These are draft guidelines for what a standard "related tunings"-type section should look like on edo pages, using [[36edo]] as an example.'''
'''These are draft guidelines for what a standard "related tunings"-type section should look like on edo pages, using [[36edo]] as an example.'''


; Useful links for working on this:
* [https://sintel.pythonanywhere.com/ Temperament Calculator] by [[User:Sintel|Sintel]] (calculates WE & TE)
* [http://x31eq.com/temper/ x31eq Temperament Finder] by [[Graham Breed]] (calculates TE)


; Which tunings should be listed for any given edo:
; Which tunings should be listed for any given edo:
Line 25: Line 21:


; Where this section should be placed on an edo page:
; Where this section should be placed on an edo page:
<small><small>
* Synopsis & infobox
* Synopsis & infobox
* (Any foundational introductory subsections)
* (Any foundational introductory subsections)
Line 50: Line 47:
* External links
* External links
''Note: This particular set of headings in this order is only how most edo pages look'' at the moment'', but it might be replaced with a more intuitive standard in the future. If and when that happens, this guideline should be modified to adopt that new standard.''
''Note: This particular set of headings in this order is only how most edo pages look'' at the moment'', but it might be replaced with a more intuitive standard in the future. If and when that happens, this guideline should be modified to adopt that new standard.''
</small></small>
; Useful links for working on this:
* [https://sintel.pythonanywhere.com/ Temperament Calculator] by [[User:Sintel|Sintel]] (calculates WE & TE)
* [http://x31eq.com/temper/ x31eq Temperament Finder] by [[Graham Breed]] (calculates TE)


= Example (36edo) =
= Example (36edo) =
Line 165: Line 167:


= Plan for roll-out =
= Plan for roll-out =
Edo pages which currently have  an "octave stretch", "related tunings", "zeta properties", etc. section:
''Done''
* Done (with table): {{EDOs| 36 }}.
* Done (with table): {{EDOs| 36 }}.
* Done (table not added yet): {{EDOs| 7, 8, 12, 14, 16, 17, 19, 22, 23, 27, 31, 41, 58, 72, 99 }}.
* Done (table not added yet): {{EDOs| 7, 8, 12, 14, 16, 17, 19, 22, 23, 27, 31, 32, 41, 58, 60, 72, 99 }}.
--
* Done (table & some step sizes not added yet): {{EDOs| 33, 39, 42, 45 }}.
* High priority pages: {{EDOs| 60, 32, 33, 39, 42, 45, 54, 59, 64}}.
* Medium priority pages: {{EDOs| 118, 13, 103, 111 }}.
* Low priority pages: {{EDOs| 104, 125, 145, 152, 159, 166, 182, 198, 212, 243, 247 }}.


; This standard will need to be rolled out to those above pages.
''To-do''
 
* High priority: {{EDOs| 54, 64, 59 }}.
It can optionally be rolled out to other edo pages later:
* Medium priority pages: {{EDOs| 25, 26, 29, 30, 34, 35, 37, 38, 9, 10, 11, 15, 18, 48, 24, 5, 6, 13, 118, 103, 111 }}.
* Some that might be of interest: {{EDOs| 25, 26, 29, 30, 34, 35, 37, 5, 6, 9, 10, 11, 15, 18, 48, 20, 24, 28 }}.
* Low priority pages: {{EDOs| 104, 125, 145, 152, 159, 166, 182, 198, 212, 243, 247 }}.  


; Things to note:
; Things to note:
* When rolling it out try not to delete existing body text but instead rework it where possible.
* When rolling this out try not to delete existing body text but instead rework it where possible.
* This section will ''not'' replace any "n-edo and octave stretch" pages. Still, add this section to the relevant edo page, but also link to the "n-edo and octave stretch" page at the top of this section, using the see also Template, e.g.: <nowiki>"{{See also|36edo and octave stretch}}"</nowiki>.
* This section will ''not'' replace any "n-edo and octave stretch" pages. Still, add this section to the relevant edo page, but also link to the "n-edo and octave stretch" page at the top of this section, using the see also template, e.g.: <nowiki>"{{See also|36edo and octave stretch}}"</nowiki>.


=== What to do with edonoi pages that are very close to these edos ===
=== What to do with edonoi pages that are very close to these edos ===
Line 195: Line 194:


; High-priority
; High-priority
60edo
* 35edf
* 139ed5
* 301zpi (20.027c)
* 95edt
* 13-limit WE (20.013c) (155ed6 has octaves only 0.02{{c}} different)
* 215ed12
* 302zpi
* 208ed11 (ideal for catnip temperament)
* 303zpi (19.913c)
32edo
* 13-limit WE (37.481c)
* 11-limit WE (37.453c)
* 90ed7 (optimal for dual-5) (133zpi's octave only differs by 0.4{{c}})
* 51edt
* 134zpi (37.176c)
* 75ed5
33edo
* 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)
* 11-limit WE (36.349c)
* 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}})
* 2.3.5.11 WE (30.703c)
* 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}})
* 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
45edo
* 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
54edo
Line 265: Line 201:
* 263zpi (22.243c)
* 263zpi (22.243c)
* 13-limit WE (22.198c)  (octave is identical to 187ed11 within 0.1{{c}})
* 13-limit WE (22.198c)  (octave is identical to 187ed11 within 0.1{{c}})
* 2.3.7.11.13 WE (22.180c)
* 264zpi (22.175c) (octave is identical to 194ed12 within 0.01{{c}})
* 264zpi (22.175c) (octave is identical to 194ed12 within 0.01{{c}})
* 152ed7
* 152ed7
Line 271: Line 206:
* 126ed5 (octave is identical to 86edt within 0.1{{c}})
* 126ed5 (octave is identical to 86edt within 0.1{{c}})


59edo (narrow down ZPIs)
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
 
59edo (reduce # of edonoi or ZPI)
* 152ed6
* 152ed6
* 294zpi (20.399c)
* 294zpi (20.399c)
Line 278: Line 225:
''pure octaves 59edo octave is identical to 137ed5 within 0.05{{c}}''
''pure octaves 59edo octave is identical to 137ed5 within 0.05{{c}}''
* 13-limit WE (20.320c)
* 13-limit WE (20.320c)
* 11-limit WE (20.310c)
* 7-limit WE (20.301c)
* 7-limit WE (20.301c)
* 166ed7
* 166ed7
Line 284: Line 230:
* 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
* 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 edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
Line 331: Line 239:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


; Low priority
26edo
 
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 339: Line 245:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


125edo
29edo
* 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 345: Line 251:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


145edo
30edo
* 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 351: Line 257:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


152edo
34edo
* 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 362: Line 263:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


166edo
35edo
* 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 368: Line 269:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


182edo
36edo
* 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 374: Line 275:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


198edo
37edo
* 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 380: Line 281:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


212edo
38edo
{{harmonics in equal | 38 | 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 386: Line 288:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


243edo
9edo
* 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 392: Line 294:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


247edo
10edo
* 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 300:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


; Optional
11edo
 
25edo
* 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 406: Line 306:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


26edo
15edo
* 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 312:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


29edo
18edo
* 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 418: Line 318:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


30edo
48edo
* 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 424: Line 324:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


34edo
24edo
* 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 430: Line 330:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


35edo
5edo
* 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 436: Line 336:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


36edo
6edo
* 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 442: Line 342:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


37edo
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)
 
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 edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
Line 448: Line 374:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


5edo
; Low priority
 
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 454: Line 382:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


6edo
125edo
* 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 460: Line 388:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


9edo
145edo
* 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 466: Line 394:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


10edo
152edo
* Nearby edt, ed6, ed12 and/or edf
* 241edt
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 13-limit WE (7.894c)
* 1-2 WE tunings
* Best nearby ZPI(s)
* Best nearby ZPI(s)


11edo
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 478: Line 405:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


15edo
166edo
* 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 484: Line 411:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


18edo
182edo
* 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 490: Line 417:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


48edo
198edo
* 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 496: Line 423:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


20edo
212edo
* 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 502: Line 429:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


24edo
243edo
* 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 508: Line 435:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


28edo
247edo
* 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)