User:BudjarnLambeth/Draft related tunings section: Difference between revisions
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''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) = | ||
== Octave stretch or compression == | |||
What follows is a comparison of stretched- and compressed-octave 36edo tunings. | |||
; [[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)}} | |||
; [[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)}} | |||
; 36edo | |||
* Step size: 33.333{{c}}, octave size: 1200.000{{c}} | |||
Pure-octaves 36edo approximates all harmonics up to 16 within 15.3{{c}}. | |||
{{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)}} | |||
; [[TE|36et, 13-limit TE tuning]] | |||
* Step size: 33.304{{c}}, octave size: 1198.929{{c}} | |||
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 mw-collapsible mw-collapsed" | |||
|+ style="white-space: nowrap;" | Comparison of stretched and compressed tunings | |||
|- | |||
! rowspan="2" | Tuning !! rowspan="2" | Octave size<br>(cents) !! colspan="6" | Prime error (cents) | |||
! rowspan="2" | Mapping of primes 2–13 (steps) | |||
|- | |||
! 2 !! 3 !! 5 !! 7 !! 11 !! 13 | |||
|- | |||
! 21edf | |||
| 1203.351 | |||
| +3.3 || +3.3 || −12.0 || +7.2 || −6.5 || +5.1 | |||
| 36, 57, 83, 101, 124, 133 | |||
|- | |||
! 57edt | |||
| 1201.235 | |||
| +1.2 || 0.0 || +16.6 || +1.3 || −13.7 || −2.6 | |||
| 36, 57, 84, 101, 124, 133 | |||
|- | |||
! 155zpi | |||
| 1200.587 | |||
| +0.6 || −1.0 || +15.1 || −0.5 || −16.0|| −5.0 | |||
| 36, 57, 83, 101, 124, 133 | |||
|- | |||
! 36edo | |||
| '''1200.000''' | |||
| '''0.0''' || '''−2.0''' || '''+13.7''' || '''−2.2''' || '''+15.3''' || '''−7.2''' | |||
| '''36, 57, 84, 101, 125, 133''' | |||
|- | |||
! 13-limit TE | |||
| 1198.929 | |||
| −1.1 || −3.7 || +11.2 || −5.2 || +11.6 || −11.1 | |||
| 36, 57, 84, 101, 125, 133 | |||
|- | |||
! 11-limit TE | |||
| 1198.330 | |||
| −1.7 || −4.6 || +9.8 || −6.8 || +9.5 || −13.4 | |||
| 36, 57, 84, 101, 125, 133 | |||
|} | |||
= Blank template = | |||
== Octave stretch or compression == | |||
What follows is a comparison of stretched- and compressed-octave EDONAME tunings. | |||
; [[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: | Edo pages which currently have an "octave stretch", "related tunings", "zeta properties", etc. section: | ||
* Done: {{EDOs|36 edo}}. | * Done (with table): {{EDOs|36 edo}}. | ||
* | * Done (table not added yet): {{EDOs|7, 12, 17, 19 edos}}. | ||
* Medium-high priority pages: {{EDOs|8, 13, 14, 16, 23, 60, 99 | -- | ||
* Low-medium priority pages: {{EDOs|32, 33, 39, 42, 45, 54, 59 | * High priority pages: {{EDOs|22, 27, 31, 41, 58, 72 edos}}. | ||
* Low priority pages: {{EDOs|111, 125, 145, 159, 166, 182, 198, 212, 243 | * 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}}. | |||
; This standard will need to be rolled out to those above pages. | ; This standard will need to be rolled out to those above pages. | ||
| Line 66: | Line 181: | ||
* 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, eg: <nowiki>"{{See also|36edo and octave stretch}}"</nowiki>. | ||
=== 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). | |||
=== Possible tunings to be used on each page === | === 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. | 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) | |||
; High-priority | ; High-priority | ||
22edo | 22edo | ||
* | * 1ed54.5c | ||
* 11-limit | * 11-limit WE (54.494c) | ||
* 13-limit | * 13-limit WE (54.546c) | ||
* | * 80zpi (54.483c) | ||
27edo | 27edo | ||
| Line 115: | Line 207: | ||
* 90ed10 | * 90ed10 | ||
* 97ed12 | * 97ed12 | ||
* 7-limit | * 7-limit WE (44.306c) | ||
* 13-limit | * 13-limit WE (44.375c) | ||
* | * 105zpi (44.674c) | ||
* 106zpi (44.302c) | |||
31edo | 31edo | ||
* 80ed6 | * 80ed6 | ||
* 111ed12 | * 111ed12 | ||
* 229ed169 | * 25ed7/4 (replaces 229ed169) | ||
* 11-limit | * 11-limit WE (38.748c) | ||
* 13-limit | * 13-limit WE (38.725c) | ||
* | * 127zpi (38.737c) | ||
41edo | 41edo | ||
| Line 131: | Line 224: | ||
* 106ed6 | * 106ed6 | ||
* 147ed12 | * 147ed12 | ||
* 11-limit | * 11-limit WE (29.277c) | ||
* 13-limit | * 13-limit WE (29.267c) | ||
* | * 184zpi (29.277c) | ||
58edo | 58edo | ||
* 92edt | * 92edt | ||
* 150ed6 | * 150ed6 | ||
* 7-limit | * 7-limit WE (20.667c) | ||
* 13-limit | * 13-limit WE (20.663c) | ||
* | * 288zpi (20.736c) | ||
* 289zpi (20.666c) | |||
72edo | 72edo | ||
* 144edt | * 144edt | ||
* 186ed6 | * 186ed6 | ||
* 11-limit | * 11-limit WE ( 16.677c) | ||
* 13-limit | * 13-limit WE (16.680c) | ||
* | * 380zpi (16.678c) | ||
; Medium-high priority | ; Medium-high priority | ||
8edo | 8edo | ||
* | * 29ed12 | ||
* | * No-7s 17-limit WE (147.895c) | ||
* No-7s 19-limit WE (148.148c) | |||
* 18zpi (153.463c) | |||
* 19zpi (147.467c) | |||
13edo | 13edo | ||
* 2.5.11.13 | * 2.5.11.13 WE (92.483c) | ||
* 2 | * 2.5.7.13 WE (92.804c) | ||
* | * 2.3 WE (91.405c) (good for opposite 7 mapping) | ||
* 38zpi (92.531c) | |||
14edo | 14edo | ||
* 22edt | * 22edt | ||
* 36ed6 | * 36ed6 | ||
* 11-limit | * 11-limit WE (85.842c) | ||
* 13-limit | * 13-limit WE (85.759c) | ||
* | * 42zpi (86.329c) | ||
16edo | 16edo | ||
| Line 171: | Line 269: | ||
* 41ed6 | * 41ed6 | ||
* 57ed12 | * 57ed12 | ||
* 2.5.7.13 | * 2.5.7.13 WE (75.105c) | ||
* 13-limit | * 13-limit WE (75.315c) | ||
* | * 15zpi (75.262c) | ||
23edo (too many edonoi) | 23edo (too many edonoi, too many ZPIs) | ||
* Main: "23edo and octave stretching" | * Main: "23edo and octave stretching" | ||
* 36edt | * 36edt | ||
| Line 183: | Line 281: | ||
* 11ed7/5 | * 11ed7/5 | ||
* 1ed33/32 | * 1ed33/32 | ||
* 2.3.5.13 | * 2.3.5.13 WE (52.447c) | ||
* 2.7.11 | * 2.7.11 WE (51.962c) | ||
* 13-limit | * 13-limit WE (52.237c) | ||
* | * 83zpi (53.105c) | ||
* 84zpi (52.615c) | |||
* 85zpi (52.114c) | |||
* 86zpi ( 51.653c) | |||
* 87zpi (51.201c) | |||
60edo (too many edonoi) | 60edo (too many edonoi, too many zpis) | ||
* 95edt | * 95edt | ||
* 139ed5 | * 139ed5 | ||
| Line 194: | Line 296: | ||
* 208ed11 | * 208ed11 | ||
* 255ed19 | * 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) | |||
99edo | 99edo | ||
* 157edt | * 157edt | ||
* 256ed6 | * 256ed6 | ||
* 7-limit | * 7-limit WE (12.117c) | ||
* 13-limit WE (12.123c) | |||
* 567zpi (12.138c) | |||
* 568zpi (12.115c) | |||
* 13-limit | |||
* | |||
* | |||
; Low-medium priority | ; Low-medium priority | ||
32edo | 32edo (too many edonoi, too many zpis) | ||
* 90ed7 | * 90ed7 | ||
* 51edt | * 51edt | ||
* 75ed5 | * 75ed5 | ||
* 1ed46/45 | * 1ed46/45 | ||
* 11-limit | * 11-limit WE (37.453c) | ||
* 13-limit | * 13-limit WE (37.481c) | ||
* | * 131zpi (37.862c) | ||
* 132zpi (37.662c) | |||
* 133zpi (37.418c) | |||
* 134zpi (37.176c) | |||
33edo (too many edonoi) | 33edo (too many edonoi) | ||
| Line 255: | Line 339: | ||
* 123ed13 | * 123ed13 | ||
* 115ed11 | * 115ed11 | ||
* 11-limit | * 11-limit WE (36.349c) | ||
* 13-limit | * 13-limit WE (36.357c) | ||
* | * 137zpi (36.628c) | ||
* 138zpi (36.394c) | |||
* 139zpi (36.179c) | |||
39edo | 39edo | ||
* 62edt | * 62edt | ||
* 101ed6 | * 101ed6 | ||
* | * 18ed11/8 | ||
* 2.3.5.11 | * 2.3.5.11 WE (30.703c) | ||
* 2.3.7.11.13 | * 2.3.7.11.13 WE (30.787c) | ||
* 13-limit | * 13-limit WE (30.757c) | ||
* | * 171zpi (30.973c) | ||
* 172zpi (30.836c) | |||
* 173zpi (30.672c) | |||
42edo ( | 42edo | ||
* | * 42ed257/128 (replace w something similar but simpler) | ||
* | * AS123/121 (1ed123/121) | ||
* | * 11ed6/5 | ||
* 34ed7/4 | |||
* 7-limit | * 7-limit WE (28.484c) | ||
* 13-limit | * 13-limit WE (28.534c) | ||
* | * 189zpi (28.689c) | ||
* 190zpi (28.572c) | |||
* 191zpi (28.444c) | |||
45edo | 45edo | ||
* 126ed7 | * 126ed7 | ||
* | * 13ed11/9 | ||
* 7-limit | * 7-limit WE (26.745c) | ||
* 13-limit | * 13-limit WE (26.695c) | ||
* | * 207zpi (26.762) | ||
* 208zpi (26.646) | |||
* 209zpi (26.550) | |||
54edo | 54edo | ||
| Line 288: | Line 380: | ||
* 126ed5 | * 126ed5 | ||
* 152ed7 | * 152ed7 | ||
* | * 38ed5/3 | ||
* 2.3.7.11.13 | * 40ed5/3 | ||
* 13-limit | * 2.3.7.11.13 WE (22.180c) | ||
* | * 13-limit WE (22.198c) | ||
* 262zpi (22.313c) | |||
* 263zpi (22.243c) | |||
* 264zpi (22.175c) | |||
59edo | 59edo (too many ZPIs) | ||
* 93edt | * 93edt | ||
* 166ed7 | * 166ed7 | ||
* 203ed11 | * 203ed11 | ||
* 7-limit | * 7-limit WE (20.301c) | ||
* 11-limit | * 11-limit WE (20.310c) | ||
* 13-limit | * 13-limit WE (20.320c) | ||
* | * 293zpi (20.454c) | ||
* 294zpi (20.399c) | |||
* 295zpi (20.342c) | |||
* 296zpi (20.282c) | |||
* 297zpi (20.229c) | |||
64edo | 64edo (too many ZPIs, too many edonoi) | ||
* 149ed5 | * 149ed5 | ||
* 180ed7 | * 180ed7 | ||
* 222ed11 | * 222ed11 | ||
* | * 47ed5/3 | ||
* 11-limit | * 11-limit WE (18.755c) | ||
* 13-limit | * 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) | |||
118edo | |||
* 187edt | |||
* 69edf | |||
* 13-limit WE (10.171c) | |||
* Best nearby ZPI(s) | |||
152edo | |||
* 241edt | |||
* 13-limit WE ( 7.894c) | |||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
| Line 314: | Line 440: | ||
(add brainstorm list here) | (add brainstorm list here) | ||