User:BudjarnLambeth/Sandbox2: Difference between revisions
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= Title1 = | = Title1 = | ||
== Octave stretch or compression == | == Octave stretch or compression == | ||
38edo's approximation of [[JI]] can be improved by slightly [[octave stretch|stretching the octave]]. | |||
What follows is a comparison of stretched-octave 38edo tunings. | |||
; 38edo | |||
* Step size: 31.579{{c}}, octave size: 1200.00{{c}} | |||
Pure-octaves 38edo approximates all harmonics up to 16 within NNN{{c}}. | |||
{{Harmonics in equal|38|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 38edo}} | |||
{{Harmonics in equal|38|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 38edo (continued)}} | |||
; [[WE|38et, 13-limit WE tuning]] | |||
* Step size: 31.599{{c}}, octave size: 1200.77{{c}} | |||
Stretching the octave of 38edo by around 1{{c}} 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|31.599|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 38et, 13-limit WE tuning}} | |||
{{Harmonics in cet|31.599|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 38et, 13-limit WE tuning (continued)}} | |||
; [[ed5|88ed5]] | |||
* Step size: 31.663{{c}}, octave size: 1203.18{{c}} | |||
Stretching the octave of 38edo by around 3{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 88ed5 does this. | |||
{{Harmonics in equal|88|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 88ed5}} | |||
{{Harmonics in equal|88|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 88ed5 (continued)}} | |||
; [[zpi| | ; [[zpi|166zpi]] | ||
* Step size: | * Step size: 31.671{{c}}, octave size: 1203.48{{c}} | ||
Stretching the octave of 38edo by around 3.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 166zpi does this. | |||
{{Harmonics in cet| | {{Harmonics in cet|31.671|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 166zpi}} | ||
{{Harmonics in cet| | {{Harmonics in cet|31.671|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 166zpi (continued)}} | ||
; [[ | ; [[60edt]] | ||
* Step size: | * Step size: 31.699{{c}}, octave size: 1204.57{{c}} | ||
Stretching the octave of 38edo by around 4.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 60edt does this. | |||
{{Harmonics in equal|60| | {{Harmonics in equal|60|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 60edt}} | ||
{{Harmonics in equal|60| | {{Harmonics in equal|60|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 60edt (continued)}} | ||
= Title2 = | |||
=== Lab === | |||
Place holder | |||
<br><br><br><br><br> | |||
{{harmonics in cet | 300 | intervals=prime}} | |||
{ | |||
{{harmonics in equal | 140 | 12 | 1 | intervals=prime}} | |||
=== 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. | ||
Line 77: | Line 59: | ||
; High-priority | ; High-priority | ||
118edo (choose ZPIS) | |||
{{harmonics in equal | 118 | 2 | 1 | intervals=integer | columns=12}} | |||
* 187edt | |||
* 69edf | |||
* 13-limit WE (10.171c) | |||
* Best nearby ZPI(s) | |||
{{harmonics in equal| | |||
* | |||
* | |||
* 13-limit WE ( | |||
* | |||
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 | ||
Line 230: | Line 81: | ||
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) | ||
Line 235: | Line 87: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
13edo | |||
* | {{harmonics in equal | 13 | 2 | 1 | intervals=integer | columns=12}} | ||
* | * Main: "13edo and optimal octave stretching" | ||
* 13 | * 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) | |||
104edo | 104edo | ||
Line 249: | Line 101: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
; Medium-priority | |||
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 255: | Line 110: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 261: | Line 117: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 272: | Line 124: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 278: | Line 131: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 284: | Line 138: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 290: | Line 145: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 296: | Line 152: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 302: | Line 159: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 308: | Line 166: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 316: | Line 173: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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) | ||
* 1-2 WE tunings | * 1-2 WE tunings | ||
* Best nearby ZPI( | * Best nearby ZPI( | ||
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 328: | Line 187: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 334: | Line 194: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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) | ||
* 1-2 WE tunings | * 1-2 WE tunings | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s)s) | ||
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 346: | Line 208: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 352: | Line 215: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 358: | Line 222: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
; Low priority | |||
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 370: | Line 230: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 376: | Line 236: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
152edo | |||
* | * 241edt | ||
* | * 13-limit WE (7.894c) | ||
* Best nearby ZPI(s) | * 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 388: | Line 247: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 394: | Line 253: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 400: | Line 259: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 406: | Line 265: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 412: | Line 271: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 418: | Line 277: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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) |