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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 17: Line 13:


Additional guidelines for selecting tunings:
Additional guidelines for selecting tunings:
* In total, 3 to 8 tunings should be listed.
* In total, roughly 6 tunings should be listed, give or take a few.
* The selection of tunings should cover a range of meaningfully different tunings (eg with a range of different mappings).
* The selection of tunings should cover a range of meaningfully different tunings (eg they cover a range of different mappings and/or they approximate different harmonics well or badly).


; Further instructions
; Further instructions
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 166: Line 168:
= Plan for roll-out =
= Plan for roll-out =
Edo pages which currently have  an "octave stretch", "related tunings", "zeta properties", etc. section:
Edo pages which currently have  an "octave stretch", "related tunings", "zeta properties", etc. section:
* Done (with table): {{EDOs|36 edo}}.
* Done (with table): {{EDOs| 36 }}.
* Done (table not added yet): {{EDOs|7, 8, 12, 17, 19, 22, 27, 31, 41, 58, 72 edos}}.
* Done (table not added yet): {{EDOs| 7, 8, 12, 14, 16, 17, 19, 22, 23, 27, 31, 41, 58, 72, 99 }}.
--
--
* High priority pages: {{EDOs|13, 14, 16, 99, 23, 60 edos}}.
* High priority pages: {{EDOs| 60, 32, 33, 39, 42, 45, 54, 59, 64}}.
* Medium priority pages: {{EDOs|32, 33, 39, 42, 45, 54, 59, 64, 103, 118, 152 edos}}.
* Medium priority pages: {{EDOs| 118, 13, 103, 111 }}.
* Low priority pages: {{EDOs|111, 125, 145, 159, 166, 182, 198, 212, 243, 247 edos}}.
* 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.
; This standard will need to be rolled out to those above pages.


It can optionally be rolled out to other edo pages later:
It can optionally be rolled out to other edo pages later:
* Some that might be of interest: <small>{{EDOs|5, 6, 9, 10, 11, 15, 18, 25, 26, 29, 30, 34, 35, 36, 37, 48, 20, 24, 28 edos}}</small>.
* Some that might be of interest: {{EDOs| 25, 26, 29, 30, 34, 35, 37, 9, 10, 11, 15, 18, 48, 5, 6, 20, 24, 28 }}.


; 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 it 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, eg: <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 196: Line 198:
; High-priority
; High-priority


13edo
60edo
* Main: "13edo and optimal octave stretching"
* 35edf
* 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)
 
14edo
* 22edt
* 36ed6
* 11-limit WE (85.842c)
* 13-limit WE (85.759c)
* 42zpi (86.329c)
 
16edo
* 25edt
* 41ed6
* 57ed12
* 2.5.7.13 WE (75.105c)
* 13-limit WE (75.315c)
* 15zpi (75.262c)
 
99edo
* 157edt
* 256ed6
* 7-limit WE (12.117c)
* 13-limit WE (12.123c)
* 567zpi (12.138c)
* 568zpi (12.115c)
 
23edo (narrow down edonoi & ZPIs)
* Main: "23edo and octave stretching"
* 36edt
* 59ed6
* 60ed6
* 68ed8
* 11ed7/5
* 1ed33/32
* 2.3.5.13 WE (52.447c)
* 2.7.11 WE (51.962c)
* 13-limit WE (52.237c)
* 83zpi (53.105c)
* 84zpi (52.615c)
* 85zpi (52.114c)
* 86zpi (51.653c)
* 87zpi (51.201c)
 
60edo (narrow down edonoi & ZPIs)
* 95edt
* 139ed5
* 139ed5
* 155ed6
* 208ed11
* 255ed19
* 272ed23 (great for catnip temperament)
* 13-limit WE (20.013c)
* 299zpi (20.128c)
* 300zpi (20.093c)
* 301zpi (20.027c)
* 301zpi (20.027c)
* 302zpi (19.962c)
* 95edt
* 13-limit WE (20.013c) (155ed6 has octaves only 0.02{{c}} different)
* 215ed12
* 302zpi
* 208ed11 (ideal for catnip temperament)
* 303zpi (19.913c)
* 303zpi (19.913c)
* 304zpi (19.869c)


; Medium priority
32edo
 
* 13-limit WE (37.481c)
32edo (narrow down ZPIs)
* 11-limit WE (37.453c)
* 90ed7
* 90ed7 (optimal for dual-5) (133zpi's octave only differs by 0.4{{c}})
* 51edt
* 51edt
* 134zpi (37.176c)
* 75ed5
* 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)
33edo
* 76ed5
* 76ed5
* 92ed7
* 92ed7 (137zpi's octave differs by only 0.3{{c}})
* 52edt
* 52ed13
* 1ed47/46
* 114ed11
* 114ed11
* 122ed13
* 138zpi (36.394c) (122ed13's octave differs by only 0.1{{c}})
* 93ed7
* 13-limit WE (36.357c)
* 23edPhi
* 93ed7 (optimised for dual-fifths)
* 77ed5
* 77ed5 (139zpi's octave differs by only 0.2{{c}})
* 123ed13
* 123ed13 / 1ed47/46 (identical within <0.1{{c}})
* 115ed11
* 115ed11
* 11-limit WE (36.349c)
* 13-limit WE (36.357c)
* 137zpi (36.628c)
* 138zpi (36.394c)
* 139zpi (36.179c)


39edo
39edo
* 62edt
* 171zpi (30.973c) (optimised for dual-fifths use)
* 101ed6
* 13-limit WE (30.757c) (octave of 135ed11 differs by only 0.2{{c}})
* 18ed11/8
* 101ed6 (octave of 172zpi differs by only 0.4{{c}})
* 2.3.5.11 WE (30.703c)
* 2.3.5.11 WE (30.703c)
* 2.3.7.11.13 WE (30.787c)
* 173zpi (30.672c) (octave of 62edt differs by only 0.2{{c}})
* 13-limit WE (30.757c)
* 110ed7 (octave of 145ed13 differs by only 0.1{{c}})
* 171zpi (30.973c)
* 91ed5
* 172zpi (30.836c)
* 173zpi (30.672c)


42edo
42edo
* 42ed257/128 (replace w something similar but simpler)
* 108ed6 (octave is identical to 97ed5 within 0.1{{c}})
* AS123/121 (1ed123/121)
* 189zpi (28.689c)
* 11ed6/5
* 150ed12
* 34ed7/4
* 145ed11
* 7-limit WE (28.484c)
''190zpi's octave is within 0.05{{c}} of pure-octaves 42edo''
* 118ed7
* 13-limit WE (28.534c)
* 13-limit WE (28.534c)
* 189zpi (28.689c)
* 151ed12 (octave is identical to 7-limit WE within 0.3{{c}})
* 190zpi (28.572c)
* 109ed6
* 191zpi (28.444c)
* 191zpi (28.444c)
* 67edt


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
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)
* 262zpi (22.313c)
* 263zpi (22.243c)
* 264zpi (22.175c)


59edo (narrow down ZPIs)
59edo (narrow down ZPIs)
* 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)
64edo
* 149ed5
* 179ed7 (octave is identical to 326zpi within 0.3{{c}})
* 180ed7
* 165ed6
* 222ed11
* 229ed12 (octave is identical to 221ed11 within 0.1{{c}})
* 47ed5/3
* 327zpi (18.767c)
* 11-limit WE (18.755c)
* 11-limit WE (18.755c)
* 13-limit WE (18.752c)
''pure octaves 64edo (octave is identical to 13-limit WE within 0.13{{c}}''
* 325zpi (18.868c)
* 326zpi (18.816c)
* 327zpi (18.767c)
* 328zpi (18.721c)
* 328zpi (18.721c)
* 329zpi (18.672c)
* 180ed7
* 330zpi (18.630c)
* 230ed12
* 149ed5
 
; 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)
103edo (narrow down edonoi, choose ZPIS)
* 163edt
* 163edt
* 239ed5
* 239ed5
* 266ed6
* 289ed7
* 289ed7
* 356ed11
* 356ed11
* 369ed12
* 381ed13
* 381ed13
* 421ed17
* 421ed17
Line 371: Line 324:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


118edo (choose ZPIS)
111edo (choose ZPIS)
* 187edt
* Nearby edt, ed6, ed12 and/or edf
* 69edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 13-limit WE (10.171c)
* 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)
* Best nearby ZPI(s)


152edo (choose ZPIS)
152edo
* 241edt
* 241edt
* 13-limit WE (7.894c)
* 13-limit WE (7.894c)
* Best nearby ZPI(s)
* Best nearby ZPI(s)


; Low priority
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)
 
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)
 
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)
 
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)


(list more here)
28edo
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* Best nearby ZPI(s)
Retrieved from "https://en.xen.wiki/w/User:BudjarnLambeth/Draft_related_tunings_section"