31edo: Difference between revisions
Improve infobox (precision, cent values for semitones, deprecate monotonicity) |
→Just approximation: update the tables |
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[[File:31edo Sagittal.png|800px]] | [[File:31edo Sagittal.png|800px]] | ||
== | == JI approximation == | ||
=== 15-odd-limit interval mappings === | === 15-odd-limit interval mappings === | ||
The following table shows how [[15-odd-limit intervals]] are represented in 31edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''. | The following table shows how [[15-odd-limit intervals]] are represented in 31edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''. | ||
{| class="wikitable center-all" | {| class="wikitable center-all mw-collapsible mw-collapsed" | ||
|+ | |+style=white-space:nowrap| 15-odd-limit intervals by direct mapping (even if inconsistent) | ||
|- | |- | ||
! Interval, complement | ! Interval, complement | ||
! Error (abs, [[cent| | ! Error (abs, [[Cent|¢]]) | ||
! Error (rel, [[Relative cent|%]]) | |||
|- | |- | ||
| '''[[5/4]], [[8/5]]''' | | '''[[5/4]], [[8/5]]''' | ||
| '''0.783''' | | '''0.783''' | ||
| '''2.0''' | |||
|- | |- | ||
| [[11/9]], [[18/11]] | | [[11/9]], [[18/11]] | ||
| 0.979 | | 0.979 | ||
| 2.5 | |||
|- | |- | ||
| '''[[ | | '''[[7/4]], [[8/7]]''' | ||
| '''1.084''' | | '''1.084''' | ||
| '''2.8''' | |||
|- | |- | ||
| [[7/5]], [[10/7]] | | [[7/5]], [[10/7]] | ||
| 1.867 | | 1.867 | ||
| 4.8 | |||
|- | |- | ||
| [[15/14]], [[28/15]] | | [[15/14]], [[28/15]] | ||
| 3.314 | | 3.314 | ||
| 8.6 | |||
|- | |- | ||
| [[7/6]], [[12/7]] | | [[7/6]], [[12/7]] | ||
| 4.097 | | 4.097 | ||
| 10.6 | |||
|- | |- | ||
| [[ | | [[11/6]], [[12/11]] | ||
| 4.202 | | 4.202 | ||
| 10.9 | |||
|- | |- | ||
| [[ | | [[15/8]], [[16/15]] | ||
| 4.398 | | 4.398 | ||
| 11.4 | |||
|- | |- | ||
| [[15/11]], [[22/15]] | | [[15/11]], [[22/15]] | ||
| 4.985 | | 4.985 | ||
| 12.9 | |||
|- | |- | ||
| '''[[ | | '''[[3/2]], [[4/3]]''' | ||
| '''5.181''' | | '''5.181''' | ||
| '''13.4''' | |||
|- | |- | ||
| [[ | | [[5/3]], [[6/5]] | ||
| 5.964 | | 5.964 | ||
| 15.4 | |||
|- | |- | ||
| [[ | | [[11/7]], [[14/11]] | ||
| 8.298 | | 8.298 | ||
| 21.4 | |||
|- | |- | ||
| [[9/7]], [[14/9]] | | [[9/7]], [[14/9]] | ||
| 9.278 | | 9.278 | ||
| 24.0 | |||
|- | |- | ||
| '''[[11/8]], [[16/11]]''' | | '''[[11/8]], [[16/11]]''' | ||
| '''9.382''' | | '''9.382''' | ||
| '''24.2''' | |||
|- | |- | ||
| [[11/10]], [[20/11]] | | [[11/10]], [[20/11]] | ||
| 10.166 | | 10.166 | ||
| 26.3 | |||
|- | |- | ||
| [[13/10]], [[20/13]] | | [[13/10]], [[20/13]] | ||
| 10.302 | | 10.302 | ||
| 26.6 | |||
|- | |- | ||
| [[9/8]], [[16/9]] | | [[9/8]], [[16/9]] | ||
| 10.362 | | 10.362 | ||
| 26.8 | |||
|- | |- | ||
| '''[[ | | '''[[13/8]], [[16/13]]''' | ||
| '''11.085''' | | '''11.085''' | ||
| '''28.6''' | |||
|- | |- | ||
| [[ | | [[9/5]], [[10/9]] | ||
| 11.145 | | 11.145 | ||
| 28.8 | |||
|- | |- | ||
| [[ | | [[13/7]], [[14/13]] | ||
| 12.169 | | 12.169 | ||
| 31.4 | |||
|- | |- | ||
| [[15/13]], [[26/15]] | | [[15/13]], [[26/15]] | ||
| 15.483 | | 15.483 | ||
| 40.0 | |||
|- | |- | ||
| [[13/12]], [[24/13]] | | [[13/12]], [[24/13]] | ||
| 16.266 | | 16.266 | ||
| 42.0 | |||
|- | |- | ||
| ''[[ | | ''[[13/9]], [[18/13]]'' | ||
| ''17.263'' | | ''17.263'' | ||
| ''44.6'' | |||
|- | |- | ||
| ''[[13/11]], [[22/13]]'' | | ''[[13/11]], [[22/13]]'' | ||
| ''18.242'' | | ''18.242'' | ||
| ''47.1'' | |||
|} | |} | ||
{{15-odd-limit|31}} | |||
=== Selected 19-limit intervals === | === Selected 19-limit intervals === | ||