User:BudjarnLambeth/Draft related tunings section: Difference between revisions
| Line 169: | Line 169: | ||
''Done'' | ''Done'' | ||
* Done (with table): {{EDOs| 36 }}. | * Done (with table): {{EDOs| 36 }}. | ||
* Done (table not added yet): {{EDOs| 7, 8, 12, 14, 16, 17, 19, 22, 23, 27, 31, 32, 38, 41, 58, 60, 72, 99 }}. | * Done (table not added yet): {{EDOs| 7, 8, 9, 12, 14, 16, 17, 19, 22, 23, 27, 31, 32, 38, 41, 58, 60, 72, 99 }}. | ||
* Done (table & some step sizes not added yet): {{EDOs| 33, 39, 42, 45, 54, 59, 64 }}. | * Done (table & some step sizes not added yet): {{EDOs| 33, 39, 42, 45, 54, 59, 64 }}. | ||
''To-do'' | ''To-do'' | ||
* High priority: {{EDOs| 118, 103, 111, 13, 104 }}. | * High priority: {{EDOs| 118, 103, 111, 13, 104 }}. | ||
* Medium-high priority: {{EDOs| | * Medium-high priority: {{EDOs| 15, 18, 25, 26, 29, 30, 34, 35, 37, 48 }}. | ||
* Medium-low priority: {{EDOs| 10, 11, 24, 5, 6 }}. | * Medium-low priority: {{EDOs| 10, 11, 24, 5, 6 }}. | ||
* Low priority: {{EDOs| 125, 145, 152, 159, 166, 182, 198, 212, 243, 247 }}. | * Low priority: {{EDOs| 125, 145, 152, 159, 166, 182, 198, 212, 243, 247 }}. | ||
| Line 235: | Line 235: | ||
; Medium-high priority | ; Medium-high priority | ||
15edo | 15edo | ||
| Line 252: | Line 242: | ||
* 54ed12 | * 54ed12 | ||
* Nearby edf (optional) | * Nearby edf (optional) | ||
* 11lim WE | * 11lim WE (79.770) | ||
* | * 47zpi (79.715) | ||
15edo's [[prime]]s 3, 5, 11 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]]. | 15edo's [[prime]]s 3, 5, 11 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]]. | ||
| Line 261: | Line 251: | ||
* 60ed10 | * 60ed10 | ||
* 65ed12 | * 65ed12 | ||
* 7lim WE | * 7lim WE (66.148) | ||
* | * 13lim WE (66.291) | ||
* | * 60zpi (67.090) | ||
* | * 61zpi (66.228) | ||
18edo's [[prime]]s 3, 5, 7 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]]. | 18edo's [[prime]]s 3, 5, 7 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]]. | ||
| Line 271: | Line 261: | ||
* 90ed12 | * 90ed12 | ||
* Nearby edf (optional) | * Nearby edf (optional) | ||
* | * 13lim WE (47.946) | ||
* | * 95zpi (48.067) | ||
* | * 96zpi (47.642) | ||
25edo's [[prime]] 3 is very sharp, and its sharp and flat mapping of 11 and 13 are about equally bad, it can benefit from [[octave shrinking]]. | 25edo's [[prime]] 3 is very sharp, and its sharp and flat mapping of 11 and 13 are about equally bad, it can benefit from [[octave shrinking]]. | ||
| Line 283: | Line 273: | ||
* 96ed14 | * 96ed14 | ||
* Nearby edf (optional) | * Nearby edf (optional) | ||
* 13lim WE (46.249) (octave identical to 11lim within 1/20th of a cent) | |||
* 13lim WE | * 100zpi (46.268) | ||
* | |||
26edo's simple [[prime]]s with the most error - 3, 5 and 13 - are all tuned flat, so it can benefit from [[octave stretching]]. | 26edo's simple [[prime]]s with the most error - 3, 5 and 13 - are all tuned flat, so it can benefit from [[octave stretching]]. | ||
| Line 295: | Line 284: | ||
* 107ed13 | * 107ed13 | ||
* Nearby edf (optional) | * Nearby edf (optional) | ||
* 11lim WE | * 11lim WE (41.482) | ||
* 13lim WE | * 13lim WE (41.484) | ||
* | * [[116zpi]] (41.465) | ||
29edo's [[prime]]s 5, 7, 11 and 13 are all tuned flat and the 3 has relatively little error, so 29edo can benefit from [[octave stretching]]. | 29edo's [[prime]]s 5, 7, 11 and 13 are all tuned flat and the 3 has relatively little error, so 29edo can benefit from [[octave stretching]]. | ||
| Line 305: | Line 294: | ||
* 104ed11 | * 104ed11 | ||
* 108ed12 | * 108ed12 | ||
* 11lim WE | * 11lim WE (79.770) | ||
* 13lim WE | * 13lim WE (39.904) | ||
* | * 39.918zpi (39.918) | ||
30edo's simple [[prime]]s with the most error - 3, 5 and 11 - are all tuned sharp, so it can benefit from [[octave shrinking]]. | 30edo's simple [[prime]]s with the most error - 3, 5 and 11 - are all tuned sharp, so it can benefit from [[octave shrinking]]. | ||
| Line 319: | Line 308: | ||
* 126ed13 | * 126ed13 | ||
* Nearby edf (optional) | * Nearby edf (optional) | ||
* 11lim WE | * 11lim WE (35.284) | ||
* 13lim WE | * 13lim WE (35.276) | ||
* | * 144zpi (35.248) | ||
34edo's [[prime]]s 3, 5, 11 and 13 are all tuned sharp, and it has two about equally bad mappings of 7, so 34edo can benefit from [[octave shrinking]]. | 34edo's [[prime]]s 3, 5, 11 and 13 are all tuned sharp, and it has two about equally bad mappings of 7, so 34edo can benefit from [[octave shrinking]]. | ||
| Line 332: | Line 321: | ||
* 125ed12 | * 125ed12 | ||
* Nearby edf (optional) | * Nearby edf (optional) | ||
* 11lim WE | * 11lim WE (35.284) | ||
* 13lim WE | * 13lim WE (35.276) | ||
* | * [[149zpi]] (34.359) | ||
35edo's [[prime]]s 3, 5, 7 and 11 are all tuned flat, and it has two about equally bad mappings of 13, so 35edo can benefit from [[octave stretching]]. | 35edo's [[prime]]s 3, 5, 7 and 11 are all tuned flat, and it has two about equally bad mappings of 13, so 35edo can benefit from [[octave stretching]]. | ||
| Line 347: | Line 336: | ||
* 137ed13 | * 137ed13 | ||
* Nearby edf (optional) | * Nearby edf (optional) | ||
* 11lim WE | * 11lim WE (32.377) | ||
* 13lim WE | * 13lim WE (32.383) | ||
* | * [[161zpi]] (32.408) | ||
37edo's [[prime]]s 3, 5, 7, 11 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]]. | 37edo's [[prime]]s 3, 5, 7, 11 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]]. | ||
| Line 360: | Line 349: | ||
* 172ed12 | * 172ed12 | ||
* Nearby edf (optional) | * Nearby edf (optional) | ||
* 11lim WE | * 11lim WE (25.017) | ||
* 13lim WE | * 13lim WE (25.005) | ||
* | * 226zpi (25.006) | ||
Most of 48edo's simple [[prime]]s have low error, but its 5 is substantially flat, so 48edo can benefit from slight [[octave stretching]]. | Most of 48edo's simple [[prime]]s have low error, but its 5 is substantially flat, so 48edo can benefit from slight [[octave stretching]]. | ||
| Line 377: | Line 366: | ||
* 37ed13 | * 37ed13 | ||
* Nearby edf (optional) | * Nearby edf (optional) | ||
* 2.3.7.13 WE | * 2.3.7.13 WE (119.785) | ||
* 2.5.7.13 WE | * 2.5.7.13 WE (120.358) | ||
* 13lim WE | * 13lim WE (119.776) | ||
* | * 26zpi (119.899) | ||
If one wishes to use 10edo as a no-5s, 19-or-lower-limit tuning, then it benefits from [[octave shrinking]]. If one wishes to use 10edo as a no-3s, 13-or-lower-limit tuning, then it benefits from [[octave stretching]]. | If one wishes to use 10edo as a no-5s, 19-or-lower-limit tuning, then it benefits from [[octave shrinking]]. If one wishes to use 10edo as a no-3s, 13-or-lower-limit tuning, then it benefits from [[octave stretching]]. | ||
| Line 393: | Line 382: | ||
* 39ed12 | * 39ed12 | ||
* 41ed13 | * 41ed13 | ||
* 2.7.11.13 WE (108.821) | |||
* 2.7.11.13 WE | * 30zpi (108.722) | ||
* | |||
11edo has about equally bad sharp and flat mappings of [[prime]]s 3 and 5. The 7 and 13 are quite sharp, but the 11 is a little flat. To use it as a 2.7.11.13 tuning, slight [[octave shrinking]] is advisable. To use its primes 3 or 5, extreme octave shrinking or [[octave stretching]] can be used, at the cost of making the octaves sound significantly weaker. | 11edo has about equally bad sharp and flat mappings of [[prime]]s 3 and 5. The 7 and 13 are quite sharp, but the 11 is a little flat. To use it as a 2.7.11.13 tuning, slight [[octave shrinking]] is advisable. To use its primes 3 or 5, extreme octave shrinking or [[octave stretching]] can be used, at the cost of making the octaves sound significantly weaker. | ||
24edo | 24edo | ||
((13lim WE's octave is only 1/10th of a cent different from 24edo)) | |||
* 38edt | * 38edt | ||
* 56ed5 | * 56ed5 | ||
| Line 409: | Line 398: | ||
* 89ed13 | * 89ed13 | ||
* 14edf | * 14edf | ||
* 2.3.5.11.13 WE | * 2.3.5.11.13 WE (49.942) | ||
* 11lim WE | * 11lim WE (50.017) | ||
* | * 90zpi (49.988) | ||
If one wishes to use 24edo as a full 19-or-lower-limit tuning, then it benefits from slight [[octave stretching]], mostly to improve its [[prime]] 7. If one wishes to use 24edo as a no-7s 19-or-lower-limit tuning, then it benefits from slight [[octave shrinking]], mostly to improve its primes 5 and 13. | If one wishes to use 24edo as a full 19-or-lower-limit tuning, then it benefits from slight [[octave stretching]], mostly to improve its [[prime]] 7. If one wishes to use 24edo as a no-7s 19-or-lower-limit tuning, then it benefits from slight [[octave shrinking]], mostly to improve its primes 5 and 13. | ||
| Line 421: | Line 409: | ||
* 18ed12 | * 18ed12 | ||
* Nearby edf (optional) | * Nearby edf (optional) | ||
* 2.3.7 WE | * 2.3.7 WE (239.426) | ||
* | * 9zpi (238.357) | ||
If one wishes to use 5edo as a 2.3.7 [[subgroup]] tuning, then it benefits from slight [[octave shrinking]] to improve its prime 3. | If one wishes to use 5edo as a 2.3.7 [[subgroup]] tuning, then it benefits from slight [[octave shrinking]] to improve its prime 3. | ||
| Line 430: | Line 418: | ||
* 19ed9 | * 19ed9 | ||
* 20ed10 | * 20ed10 | ||
* 2.9.5 WE | * 2.9.5 WE (199.736) | ||
* 2.9.5.7 WE | * 2.9.5.7 WE (199.329) | ||
* | * 12zpi (198.843) | ||
If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 [[ | If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 [[sugroup]] tuning, then it benefits from [[octave shrinking]]. | ||
; Low-priority | ; Low-priority | ||