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

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* In total, 3 to 8 tunings should be listed.
* In total, 3 to 8 tunings should be listed.
* 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 with a range of different mappings).
* The editor can choose how many decimal places to use as long as it's self-consistent.
 
; Further instructions
* Adding the comparison table at the end is optional.
* The number of decimal places to use in the comparison table is up to the user's discretion, as long as it is self-consistent within the table.


; Where this section should be placed on an edo page:
; Where this section should be placed on an edo page:
Line 48: Line 51:
''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.''


== Plan for roll-out ==
= Example (36edo) =
Edo pages which currently have  an "octave stretch", "related tunings", "zeta properties", etc. section:
== Octave stretch or compression ==
* High priority pages: {{EDOs|7, 12, 17, 19, 22, 27, 31, 36, 41, 58 & 72 edos}}.
What follows is a comparison of stretched- and compressed-octave 36edo tunings.
* Medium-high priority pages: {{EDOs|8, 13, 14, 16, 23, 99, 103, 118, & 152 edos}}.
* Low-medium priority pages: {{EDOs|32, 33, 39, 42, 45, 54, 59, 60 & 64 edos}}.
* Low priority pages: {{EDOs|111, 125, 145, 159, 166, 182, 198, 212, 243 & 247 edos}}.


; This standard will need to be rolled out to those above pages ''once this standard is ready''. (Not yet!!)
; [[21edf]]
* Step size: 33.426{{c}}, octave size: 1203.351{{c}}
Stretching the octave of 36edo by a little over 3{{c}} results in improved primes 5, 11, and 13, but worse primes 2, 3, and 7. This approximates all harmonics up to 16 within 13.4{{c}}. The tuning 21edf does this.
{{Harmonics in equal|21|3|2|columns=11|collapsed=true}}
{{Harmonics in equal|21|3|2|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 21edf (continued)}}


It can optionally be rolled out to more edo pages later.
; [[57edt]]
* Step size: 33.368{{c}}, octave size: 1201.235{{c}}
If one intends to use both 36edo's vals for 5/1 at once, stretching the octave of 36edo by about 1{{c}} optimises 36edo for that dual-5 usage, while also making slight improvements to primes 3, 7, 11, and 13. This approximates all harmonics up to 16 within 16.6{{c}}. Several almost-identical tunings do this: 57edt, [[93ed6]], [[101ed7]], [[zpi|155zpi]], and the 2.3.7.13-subgroup [[TE]] and [[WE]] tunings of 36et.
{{Harmonics in equal|57|3|1|columns=11|collapsed=true}}
{{Harmonics in equal|57|3|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 57edt (continued)}}


; Things to note:
; 36edo
* When rolling it out try not to delete existing body text but instead rework it where possible.
* Step size: 33.333{{c}}, octave size: 1200.000{{c}}
* 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>.
Pure-octaves 36edo approximates all harmonics up to 16 within 15.3{{c}}.
* It is okay to add only the descriptive text and collapsed harmonic tables to an edo page initially, and to add the full comparison  table at a later date; this should make life easier for editors on mobile devices who might want to help but find tables difficult to edit.
{{Harmonics in equal|36|2|1|intervals=integer|columns=11|collapsed=true}}
{{Harmonics in equal|36|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 36edo (continued)}}


= Example (36edo, table on top) =
; [[TE|36et, 13-limit TE tuning]]
== Octave stretch or compression ==
* Step size: 33.304{{c}}, octave size: 1198.929{{c}}
What follows is a comparison of stretched- and compressed-octave 36edo tunings.
Compressing the octave of 36edo by about 2{{c}} results in much improved primes 5 and 11, but much worse primes 7 and 13. This approximates all harmonics up to 16 within 11.6{{c}}. The 11- and 13-limit TE tunings of 36et both do this, as do their respective WE tunings.
{{Harmonics in cet|33.303596|columns=11|collapsed=true|title=Approximation of harmonics in 13-limit TE tuning of 36et}}
{{Harmonics in cet|33.303596|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 13-limit TE tuning of 36et (continued)}}


{| class="wikitable sortable center-all"
{| class="wikitable sortable center-all mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Comparison of stretched and compressed tunings
|-
|-
! rowspan="2" | Tuning !! rowspan="2" | Step size<br>(cents) !! colspan="6" | Prime error (cents)  
! rowspan="2" | Tuning !! rowspan="2" | Octave size<br>(cents) !! colspan="6" | Prime error (cents)  
! rowspan="2" | Mapping of primes 2–13 (steps)
! rowspan="2" | Mapping of primes 2–13 (steps)
! rowspan="2" | Octave stretch
|-
|-
! 2 !! 3 !! 5 !! 7 !! 11  
! 2 !! 3 !! 5 !! 7 !! 11 !! 13
! 13
|-
|-
! 21edf
! 21edf
| 33.426
| 1203.351
| +3.3 || +3.3 || −12.0 || +7.2 || −6.5 || +5.1
| +3.3 || +3.3 || −12.0 || +7.2 || −6.5 || +5.1
| 36, 57, 83, 101, 124, 133
| 36, 57, 83, 101, 124, 133
| +0.275%
|-
|-
! 57edt
! 57edt
| 33.368 || +1.2 || 0.0 || +16.6 || +1.3 || −13.7 || −2.6
| 1201.235
| +1.2 || 0.0 || +16.6 || +1.3 || −13.7 || −2.6
| 36, 57, 84, 101, 124, 133
| 36, 57, 84, 101, 124, 133
| +0.001%
|-
|-
! 155zpi
! 155zpi
| 33.346
| 1200.587
| +0.6 || −1.0 || +15.1 || −0.5 || −16.0|| −5.0
| +0.6 || −1.0 || +15.1 || −0.5 || −16.0|| −5.0
| 36, 57, 83, 101, 124, 133
| 36, 57, 83, 101, 124, 133
| +0.0005%
|-
|-
! 36edo
! 36edo
| '''33.333'''
| '''1200.000'''
| '''0.0''' || '''−2.0''' || '''+13.7''' || '''−2.2''' || '''+15.3''' || '''−7.2'''
| '''0.0''' || '''−2.0''' || '''+13.7''' || '''−2.2''' || '''+15.3''' || '''−7.2'''
| '''36, 57, 84, 101, 125, 133'''
| '''36, 57, 84, 101, 125, 133'''
| '''0%'''
|-
|-
! 13-limit WE
! 13-limit TE
| 33.302
| 1198.929
| −1.1 || −3.7 || +11.1 || −5.3 || +11.4 || −11.4
| −1.1 || −3.7 || +11.2 || −5.2 || +11.6 || −11.1
| 36, 57, 84, 101, 125, 133
| 36, 57, 84, 101, 125, 133
| -0.0009%
|-
|-
! 11-limit WE
! 11-limit TE
| 33.286
| 1198.330
| −1.7 || −4.7 || +9.7 || −6.9 || +9.4 || −13.5
| −1.7 || −4.6 || +9.8 || −6.8 || +9.5 || −13.4
| 36, 57, 84, 101, 125, 133
| 36, 57, 84, 101, 125, 133
| -0.00142%
|}
|}


; [[21edf]]
= Blank template =
* Step size: 33.426{{c}}
== Octave stretch or compression ==
* Octave size: 1203.3{{c}}
What follows is a comparison of stretched- and compressed-octave EDONAME tunings.
{{Harmonics in equal|21|3|2|columns=12|collapsed=true}}
 
{{Harmonics in equal|21|3|2|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 21edf (continued)}}
; [[zpi|ZPINAME]]  
* Step size: NNN{{c}}, octave size: NNN{{c}}
_ing the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning ZPINAME does this.
{{Harmonics in cet|100|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}}
{{Harmonics in cet|100|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME (continued)}}
 
; [[EDONOI]]
* Step size: NNN{{c}}, octave size: NNN{{c}}
_ing the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning EDONOI does this.
{{Harmonics in equal|12|2|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in EDONOI}}
{{Harmonics in equal|12|2|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in EDONOI (continued)}}
 
; [[WE|ETNAME, SUBGROUP WE tuning]]
* Step size: NNN{{c}}, octave size: NNN{{c}}
_ing the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. Its SUBGROUP WE tuning and SUBGROUP [[TE]] tuning both do this.
{{Harmonics in cet|100|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}
{{Harmonics in cet|100|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}
 
; EDONAME
* Step size: NNN{{c}}, octave size: NNN{{c}}
Pure-octaves EDONAME approximates all harmonics up to 16 within NNN{{c}}.
{{Harmonics in equal|12|2|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in EDONAME}}
{{Harmonics in equal|12|2|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in EDONAME (continued)}}
 
; [[WE|ETNAME, SUBGROUP WE tuning]]
* Step size: NNN{{c}}, octave size: NNN{{c}}
_ing the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. Its SUBGROUP WE tuning and SUBGROUP [[TE]] tuning both do this.
{{Harmonics in cet|100|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}
{{Harmonics in cet|100|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}
 
; [[EDONOI]]
* Step size: NNN{{c}}, octave size: NNN{{c}}
_ing the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning EDONOI does this.
{{Harmonics in equal|12|2|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in EDONOI}}
{{Harmonics in equal|12|2|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in EDONOI (continued)}}
 
; [[zpi|ZPINAME]]
* Step size: NNN{{c}}, octave size: NNN{{c}}
_ing the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning ZPINAME does this.
{{Harmonics in cet|100|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}}
{{Harmonics in cet|100|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME (continued)}}
 
= Plan for roll-out =
Edo pages which currently have  an "octave stretch", "related tunings", "zeta properties", etc. section:
* Done (with table): {{EDOs|36 edo}}.
* Done (table not added yet): {{EDOs|7, 12, 17, 19 edos}}.
--
* High priority pages: {{EDOs|22, 27, 31, 41, 58, 72 edos}}.
* Medium-high priority pages: {{EDOs|8, 13, 14, 16, 23, 60, 99 edos}}.
* Low-medium priority pages: {{EDOs|32, 33, 39, 42, 45, 54, 59, 64, 103, 118, 152 edos}}.
* Low priority pages: {{EDOs|111, 125, 145, 159, 166, 182, 198, 212, 243, 247 edos}}.


Stretching the octave of 36edo by a little over 3{{c}} results in improved primes 5, 11, and 13, but worse primes 2, 3, and 7. This approximates all primes up to 11 within ''12.0{{c}}''. The tuning 21edf does this.
; This standard will need to be rolled out to those above pages.


It can optionally be rolled out to other edo pages later.


; [[57edt]]
; Things to note:
* Step size: 33.368{{c}}
* When rolling it out try not to delete existing body text but instead rework it where possible.
* Octave size: 1201.2{{c}}
* 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>.
{{Harmonics in equal|57|3|1|columns=12|collapsed=true}}
 
{{Harmonics in equal|57|3|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 57edt (continued)}}
=== What to do with edonoi pages that are very close to these edos ===
* Edt and edf pages should be permanently kept
* Other edonoi pages should be temporarily kept until all [[XW:NG|notable]] information from their respective pages has been added to:
** The "octave stretch and compression" section of the edo page.
AND/OR
** A new "''N''edo and octave stretch" page (create one of these if there is too much information to squeeze into the "octave stretch and compression" section).


If one intends to use both 36edo's vals for 5/1 at once, stretching the octave of 36edo by about 1{{c}} optimises 36edo for that dual-5 usage, while also making slight improvements to primes 3, 7, 11, and 13. This approximates all primes up to 11 within ''16.6{{c}}''. Five almost-identical tunings do this: 57edt, [[101ed7]], [[zpi|155zpi]], and the [[TE]] and [[WE]] 2.3.7.13 subgroup WE tunings of 36edo.
=== 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)


; Pure-octaves 36edo
; High-priority
* Step size: 33.333{{c}}
* Octave size: 1200.0{{c}}
Pure-octaves 36edo approximates all primes up to 11 within ''15.3{{c}}''.


22edo
* 1ed54.5c
* 11-limit WE (54.494c)
* 13-limit WE (54.546c)
* 80zpi (54.483c)


; [[TE|11-limit TE 36edo]]
27edo
* Step size: 33.287{{c}}
* 43edt
* Octave size: 1198.3{{c}}
* 70ed6
{{Harmonics in cet|33.287|columns=12|collapsed=true|title=Approximation of harmonics in 11lim WE-tuned 36edo}}
* 90ed10
{{Harmonics in cet|33.287|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 11lim WE-tuned 36edo (continued)}}
* 97ed12
* 7-limit WE (44.306c)
* 13-limit WE (44.375c)
* 105zpi (44.674c)
* 106zpi (44.302c)


Compressing the octave of 36edo by about 2{{c}} results in much improved primes 5 and 11, but much worse primes 7 and 13. This approximates all primes up to 11 within ''9.7{{c}}''. The 11- and 13-limit TE tunings of 36edo both do this, as do their respective WE tunings.
31edo
* 80ed6
* 111ed12
* 25ed7/4 (replaces 229ed169)
* 11-limit WE (38.748c)
* 13-limit WE (38.725c)
* 127zpi (38.737c)


= Example (36edo, table on bottom) =
41edo
== Octave stretch or compression ==
* 65edt
What follows is a comparison of stretched- and compressed-octave 36edo tunings.
* 106ed6
* 147ed12
* 11-limit WE (29.277c)
* 13-limit WE (29.267c)
* 184zpi (29.277c)


58edo
* 92edt
* 150ed6
* 7-limit WE (20.667c)
* 13-limit WE (20.663c)
* 288zpi (20.736c)
* 289zpi (20.666c)


; [[21edf]]
72edo
* Step size: 33.426{{c}}
* 144edt
* Octave size: 1203.3{{c}}
* 186ed6
{{Harmonics in equal|21|3|2|columns=12|collapsed=true}}
* 11-limit WE ( 16.677c)
{{Harmonics in equal|21|3|2|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 21edf (continued)}}
* 13-limit WE (16.680c)
* 380zpi (16.678c)


Stretching the octave of 36edo by a little over 3{{c}} results in improved primes 5, 11, and 13, but worse primes 2, 3, and 7. This approximates all primes up to 11 within ''12.0{{c}}''. The tuning 21edf does this.
; Medium-high priority


8edo
* 29ed12
* No-7s 17-limit WE (147.895c)
* No-7s 19-limit WE (148.148c)
* 18zpi (153.463c)
* 19zpi (147.467c)


; [[57edt]]
13edo
* Step size: 33.368{{c}}
* 2.5.11.13 WE (92.483c)
* Octave size: 1201.2{{c}}
* 2.5.7.13 WE (92.804c)
{{Harmonics in equal|57|3|1|columns=12|collapsed=true}}
* 2.3 WE (91.405c) (good for opposite 7 mapping)
{{Harmonics in equal|57|3|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 57edt (continued)}}
* 38zpi (92.531c)


If one intends to use both 36edo's vals for 5/1 at once, stretching the octave of 36edo by about 1{{c}} optimises 36edo for that dual-5 usage, while also making slight improvements to primes 3, 7, 11, and 13. This approximates all primes up to 11 within ''16.6{{c}}''. Five almost-identical tunings do this: 57edt, [[101ed7]], [[zpi|155zpi]], and the [[TE]] and [[WE]] 2.3.7.13 subgroup WE tunings of 36edo.
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)


; Pure-octaves 36edo
23edo (too many edonoi, too many ZPIs)
* Step size: 33.333{{c}}
* Main: "23edo and octave stretching"
* Octave size: 1200.0{{c}}
* 36edt
Pure-octaves 36edo approximates all primes up to 11 within ''15.3{{c}}''.
* 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 (too many edonoi, too many zpis)
* 95edt
* 139ed5
* 155ed6
* 208ed11
* 255ed19
* 272ed23 (great for catnip temperament)
* 13-limit WE (20.013c)
* 299zpi (20.128c)
* 300zpi (20.093c)
* 301zpi (20.027c)
* 302zpi (19.962c)
* 303zpi (19.913c)
* 304zpi (19.869c)


; [[TE|11-limit TE 36edo]]
99edo
* Step size: 33.287{{c}}
* 157edt
* Octave size: 1198.3{{c}}
* 256ed6
{{Harmonics in cet|33.287|columns=12|collapsed=true|title=Approximation of harmonics in 11lim WE-tuned 36edo}}
* 7-limit WE (12.117c)
{{Harmonics in cet|33.287|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 11lim WE-tuned 36edo (continued)}}
* 13-limit WE (12.123c)
* 567zpi (12.138c)
* 568zpi (12.115c)


Compressing the octave of 36edo by about 2{{c}} results in much improved primes 5 and 11, but much worse primes 7 and 13. This approximates all primes up to 11 within ''9.7{{c}}''. The 11- and 13-limit TE tunings of 36edo both do this, as do their respective WE tunings.
; Low-medium priority


32edo (too many edonoi, too many zpis)
* 90ed7
* 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)


{| class="wikitable sortable center-all"
33edo (too many edonoi)
|-
* 76ed5
! rowspan="2" | Tuning !! rowspan="2" | Step size<br>(cents) !! colspan="6" | Prime error (cents)  
* 92ed7
! rowspan="2" | Mapping of primes 2–13 (steps)
* 52edt
! rowspan="2" | Octave stretch
* 1ed47/46
|-
* 114ed11
! 2 !! 3 !! 5 !! 7 !! 11
* 122ed13
! 13
* 93ed7
|-
* 23edPhi
! 21edf
* 77ed5
| 33.426
* 123ed13
| +3.3 || +3.3 || −12.0 || +7.2 || −6.5 || +5.1
* 115ed11
| 36, 57, 83, 101, 124, 133
* 11-limit WE (36.349c)
| +0.275%
* 13-limit WE (36.357c)
|-
* 137zpi (36.628c)
! 57edt
* 138zpi (36.394c)
| 33.368 || +1.2 || 0.0 || +16.6 || +1.3 || −13.7 || −2.6
* 139zpi (36.179c)
| 36, 57, 84, 101, 124, 133
| +0.001%
|-
! 155zpi
| 33.346
| +0.6 || −1.0 || +15.1 || −0.5 || −16.0|| −5.0
| 36, 57, 83, 101, 124, 133
| +0.0005%
|-
! 36edo
| '''33.333'''
| '''0.0''' || '''−2.0''' || '''+13.7''' || '''−2.2''' || '''+15.3''' || '''−7.2'''
| '''36, 57, 84, 101, 125, 133'''
| '''0%'''
|-
! 13-limit WE
| 33.302
| −1.1 || −3.7 || +11.1 || −5.3 || +11.4 || −11.4
| 36, 57, 84, 101, 125, 133
| -0.0009%
|-
! 11-limit WE
| 33.286
| −1.7 || −4.7 || +9.7 || −6.9 || +9.4 || −13.5
| 36, 57, 84, 101, 125, 133
| -0.00142%
|}


= Example (36edo, no table) =
39edo
== Octave stretch or compression ==
* 62edt
What follows is a comparison of stretched- and compressed-octave 36edo tunings.
* 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)


; [[21edf]]
42edo
* Step size: 33.426{{c}}
* 42ed257/128 (replace w something similar but simpler)
* Octave size: 1203.3{{c}}
* AS123/121 (1ed123/121)
{{Harmonics in equal|21|3|2|columns=12|collapsed=true}}
* 11ed6/5
{{Harmonics in equal|21|3|2|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 21edf (continued)}}
* 34ed7/4
* 7-limit WE (28.484c)
* 13-limit WE (28.534c)
* 189zpi (28.689c)
* 190zpi (28.572c)
* 191zpi (28.444c)


Stretching the octave of 36edo by a little over 3{{c}} results in improved primes 5, 11, and 13, but worse primes 2, 3, and 7. This approximates all primes up to 11 within ''12.0{{c}}''. The tuning 21edf does this.
45edo
* 126ed7
* 13ed11/9
* 7-limit WE (26.745c)
* 13-limit WE (26.695c)
* 207zpi (26.762)
* 208zpi (26.646)
* 209zpi (26.550)


54edo
* 86edt
* 126ed5
* 152ed7
* 38ed5/3
* 40ed5/3
* 2.3.7.11.13 WE (22.180c)
* 13-limit WE (22.198c)
* 262zpi (22.313c)
* 263zpi (22.243c)
* 264zpi (22.175c)


; [[57edt]]
59edo (too many ZPIs)
* Step size: 33.368{{c}}
* 93edt
* Octave size: 1201.2{{c}}
* 166ed7
{{Harmonics in equal|57|3|1|columns=12|collapsed=true}}
* 203ed11
{{Harmonics in equal|57|3|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 57edt (continued)}}
* 7-limit WE (20.301c)
* 11-limit WE (20.310c)
* 13-limit WE (20.320c)
* 293zpi (20.454c)
* 294zpi (20.399c)
* 295zpi (20.342c)
* 296zpi (20.282c)
* 297zpi (20.229c)


If one intends to use both 36edo's vals for 5/1 at once, stretching the octave of 36edo by about 1{{c}} optimises 36edo for that dual-5 usage, while also making slight improvements to primes 3, 7, 11, and 13. This approximates all primes up to 11 within ''16.6{{c}}''. Five almost-identical tunings do this: 57edt, [[101ed7]], [[zpi|155zpi]], and the [[TE]] and [[WE]] 2.3.7.13 subgroup WE tunings of 36edo.
64edo (too many ZPIs, too many edonoi)
* 149ed5
* 180ed7
* 222ed11
* 47ed5/3
* 11-limit WE (18.755c)
* 13-limit WE (18.752c)
* 325zpi (18.868c)
* 326zpi (18.816c)
* 327zpi (18.767c)
* 328zpi (18.721c)
* 329zpi (18.672c)
* 330zpi (18.630c)


103edo (too many edonoi)
* 163edt
* 239ed5
* 289ed7
* 356ed11
* 381ed13
* 421ed17
* 466ed23
* 13-limit WE (11.658c)
* Best nearby ZPI(s)


; Pure-octaves 36edo
118edo
* Step size: 33.333{{c}}
* 187edt
* Octave size: 1200.0{{c}}
* 69edf
Pure-octaves 36edo approximates all primes up to 11 within ''15.3{{c}}''.
* 13-limit WE (10.171c)
{{Harmonics in equal|36|2|1|columns=12|collapsed=true}}
* Best nearby ZPI(s)
{{Harmonics in equal|36|2|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 36edo (continued)}}


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


; [[TE|11-limit TE 36edo]]
; Low priority
* Step size: 33.287{{c}}
* Octave size: 1198.3{{c}}
{{Harmonics in cet|33.287|columns=12|collapsed=true|title=Approximation of harmonics in 11lim WE-tuned 36edo}}
{{Harmonics in cet|33.287|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 11lim WE-tuned 36edo (continued)}}


Compressing the octave of 36edo by about 2{{c}} results in much improved primes 5 and 11, but much worse primes 7 and 13. This approximates all primes up to 11 within ''9.7{{c}}''. The 11- and 13-limit TE tunings of 36edo both do this, as do their respective WE tunings.
(add brainstorm list here)
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