User:BudjarnLambeth/Sandbox2: Difference between revisions
(106 intermediate revisions by the same user not shown) | |||
Line 5: | Line 5: | ||
= Title1 = | = Title1 = | ||
== Octave stretch or compression == | == Octave stretch or compression == | ||
What follows is a comparison of stretched- and compressed-octave 42edo tunings. | |||
{{Harmonics in equal| | ; [[ed6|108ed6]] | ||
{{Harmonics in equal| | * Step size: NNN{{c}}, octave size: 1206.3{{c}} | ||
Stretching the octave of 42edo by around 6{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 108ed6 does this. So does the tuning [[97ed5]] whose octave differs by only 0.1{{c}}. | |||
{{Harmonics in equal|108|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 108ed6}} | |||
{{Harmonics in equal|108|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 108ed6 (continued)}} | |||
{{Harmonics in | ; [[zpi|189zpi]] | ||
{{Harmonics in | * Step size: 28.689{{c}}, octave size: 1204.9{{c}} | ||
Stretching the octave of 42edo by around 5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 189zpi does this. | |||
{{Harmonics in cet|28.689|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 189zpi}} | |||
{{Harmonics in cet|28.689|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 189zpi (continued)}} | |||
= | ; [[ed12|150ed12]] | ||
=== | * Step size: NNN{{c}}, octave size: 1204.5{{c}} | ||
Stretcing the octave of 42edo 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 150ed12 does this. | |||
{{Harmonics in equal|150|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 150ed12}} | |||
{{Harmonics in equal|150|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 150ed12 (continued)}} | |||
; [[equal tuning|145ed11]] | |||
* Step size: NNN{{c}}, octave size: 1202.5{{c}} | |||
Stretching the octave of 42edo by around 2.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 145ed11 does this. | |||
{{Harmonics in equal|145|11|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 145ed11}} | |||
{{Harmonics in equal|145|11|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 145ed11 (continued)}} | |||
; 42edo | |||
* Step size: NNN{{c}}, octave size: 1200.0{{c}} | |||
Pure-octaves 42edo approximates all harmonics up to 16 within NNN{{c}}. The tuning [[zpi|190zpi]] is almost exactly the same as pure-octaves 42edo, its octave differing by less than 0.05{{c}}. | |||
{{Harmonics in equal|42|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 42edo}} | |||
{{Harmonics in equal|42|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 42edo (continued)}} | |||
; [[ed7|118ed7]] | |||
* Step size: NNN{{c}}, octave size: 1199.1{{c}} | |||
Compressing the octave of 42edo by around 1{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 118ed7 does this. | |||
{{Harmonics in equal|118|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 118ed7}} | |||
{{Harmonics in equal|118|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 118ed7 (continued)}} | |||
; [[WE|42et, 13-limit WE tuning]] | |||
* Step size: 28.534{{c}}, octave size: 1198.4{{c}} | |||
Compressing the octave of 42edo by around 1.5{{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|28.534|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 42et, 13-limit WE tuning}} | |||
{{Harmonics in cet|28.534|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 42et, 13-limit WE tuning (continued)}} | |||
; [[ed12|151ed12]] | |||
* Step size: NNN{{c}}, octave size: 1196.6{{c}} | |||
Compressing the octave of 42edo 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 151ed12 does this. So do the 7-limit [[WE]] and [[TE]] tunings of 42et, whose octaves are within 0.3{{c}} of 151ed12. | |||
{{Harmonics in equal|151|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 151ed12}} | |||
{{Harmonics in equal|151|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 151ed12 (continued)}} | |||
; [[ed6|109ed6]] | |||
* Step size: NNN{{c}}, octave size: 1195.2{{c}} | |||
Compressing the octave of 42edo by around 5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 109ed6 does this. | |||
{{Harmonics in equal|109|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 109ed6}} | |||
{{Harmonics in equal|109|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 109ed6 (continued)}} | |||
; | ; [[zpi|191zpi]] | ||
* Step size: 28.444{{c}}, octave size: 1194.6{{c}} | |||
Compressing the octave of 42edo by around 5.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 191zpi does this. | |||
{{Harmonics in cet|28.444|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 191zpi}} | |||
{{Harmonics in cet|28.444|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 191zpi (continued)}} | |||
; [[67edt]] | |||
* | * Step size: NNN{{c}}, octave size: 1192.3{{c}} | ||
Compressing the octave of 42edo by around 7.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 67edt does this. | |||
{{Harmonics in equal|67|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 67edt}} | |||
{{Harmonics in equal|67|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 67edt (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 === | |||
You can remove some of these or add more that aren't listed here; this section is pretty much just brainstorming. | |||
54edo ( | (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 | ||
54edo | |||
* 139ed6 (octave is identical to 262zpi within 0.2{{c}}) | |||
* 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 | ||
* | * 140ed6 | ||
* | * 126ed5 (octave is identical to 86edt within 0.1{{c}}) | ||
* | |||
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 ( | 59edo (reduce # of edonoi or zpi) | ||
* | * 152ed6 | ||
* 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) | ||
* | * 153ed6 | ||
; 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 178: | Line 138: | ||
* 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 192: | Line 145: | ||
* 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 198: | Line 152: | ||
* 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 204: | Line 159: | ||
* 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 215: | Line 166: | ||
* 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 221: | Line 173: | ||
* 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 227: | Line 180: | ||
* 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 233: | Line 187: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 239: | Line 194: | ||
* 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 245: | Line 201: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(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 251: | 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 259: | Line 215: | ||
* 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 265: | Line 222: | ||
* 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 271: | Line 229: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 277: | Line 236: | ||
* 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) | ||
Line 283: | Line 243: | ||
* 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 289: | Line 250: | ||
* 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) | ||
Line 295: | Line 257: | ||
* 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" | |||
* 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) | |||
{{harmonics in equal | 118 | 2 | 1 | intervals=integer | columns=12}} | |||
* 187edt | |||
* 69edf | |||
* 13-limit WE (10.171c) | |||
* Best nearby ZPI(s) | |||
103edo (narrow down edonoi, choose ZPIS) | |||
{{harmonics in equal | 103 | 2 | 1 | intervals=integer | columns=12}} | |||
* 163edt | |||
* 239ed5 | |||
* 266ed6 | |||
* 289ed7 | |||
* 356ed11 | |||
* 369ed12 | |||
* 381ed13 | |||
* 421ed17 | |||
* 466ed23 | |||
* 13-limit WE (11.658c) | |||
* Best nearby ZPI(s) | |||
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 301: | Line 293: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
; 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 307: | Line 301: | ||
* Best nearby ZPI(s) | * Best nearby ZPI(s) | ||
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 313: | Line 307: | ||
* 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 319: | Line 313: | ||
* 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 331: | Line 324: | ||
* 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 337: | Line 330: | ||
* 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 343: | Line 336: | ||
* 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 349: | Line 342: | ||
* 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 355: | Line 348: | ||
* 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 361: | Line 354: | ||
* 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) |