27edo: Difference between revisions
m General cleanup |
Error table |
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For a more complete list, see [[Ups and Downs Notation #Chords and Chord Progressions]]. See also the [[22edo]] page. | For a more complete list, see [[Ups and Downs Notation #Chords and Chord Progressions]]. See also the [[22edo]] page. | ||
=== Selected just intervals by error === | |||
{| class="wikitable center-all" | |||
! colspan="2" | | |||
!prime 2 | |||
!prime 3 | |||
!prime 5 | |||
!prime 7 | |||
!prime 11 | |||
!prime 13 | |||
|- | |||
! rowspan="2" |Error | |||
!absolute (¢) | |||
|0.00 | |||
| +9.16 | |||
| +13.69 | |||
| +8.95 | |||
| -17.98 | |||
| +3.92 | |||
|- | |||
!relative (%) | |||
| 0.0 | |||
| +20.6 | |||
| +30.8 | |||
| +20.1 | |||
| -40.5 | |||
| +8.8 | |||
|} | |||
The following table shows how 15-odd-limit intervals are represented in 27edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''. | |||
{| class="wikitable center-all" | |||
|+Direct mapping (even if inconsistent) | |||
!Interval, complement | |||
!Error (abs, ¢) | |||
|- | |||
| [[7/6]], [[12/7]] | |||
| 0.204 | |||
|- | |||
| ''[[15/11]], [[22/15]]'' | |||
| ''3.617'' | |||
|- | |||
| '''[[16/13]], [[13/8]]''' | |||
| '''3.917''' | |||
|- | |||
| [[6/5]], [[5/3]] | |||
| 4.530 | |||
|- | |||
| [[10/9]], [[9/5]] | |||
| 4.626 | |||
|- | |||
| [[7/5]], [[10/7]] | |||
| 4.734 | |||
|- | |||
| [[14/13]], [[13/7]] | |||
| 5.035 | |||
|- | |||
| [[13/12]], [[24/13]] | |||
| 5.239 | |||
|- | |||
| ''[[11/9]], [[18/11]]'' | |||
| ''8.148'' | |||
|- | |||
| '''[[8/7]], [[7/4]]''' | |||
| '''8.952''' | |||
|- | |||
| '''[[4/3]], [[3/2]]''' | |||
| '''9.156''' | |||
|- | |||
| [[9/7]], [[14/9]] | |||
| 9.360 | |||
|- | |||
| [[13/10]], [[20/13]] | |||
| 9.770 | |||
|- | |||
| ''[[11/10]], [[20/11]]'' | |||
| ''12.774'' | |||
|- | |||
| '''[[5/4]], [[8/5]]''' | |||
| '''13.686''' | |||
|- | |||
| [[15/14]], [[28/15]] | |||
| 13.891 | |||
|- | |||
| [[18/13]], [[13/9]] | |||
| 14.395 | |||
|- | |||
| ''[[12/11]], [[11/6]]'' | |||
| ''17.304'' | |||
|- | |||
| ''[[14/11]], [[11/7]]'' | |||
| ''17.508'' | |||
|- | |||
| '''[[11/8]], [[16/11]]''' | |||
| '''17.985''' | |||
|- | |||
| [[9/8]], [[16/9]] | |||
| 18.312 | |||
|- | |||
| [[15/13]], [[26/15]] | |||
| 18.926 | |||
|- | |||
| ''[[16/15]], [[15/8]]'' | |||
| ''21.602'' | |||
|- | |||
| [[13/11]], [[22/13]] | |||
| 21.901 | |||
|} | |||
{| class="wikitable center-all" | |||
|+Patent val mapping | |||
!Interval, complement | |||
!Error (abs, ¢) | |||
|- | |||
| [[7/6]], [[12/7]] | |||
| 0.204 | |||
|- | |||
| '''[[16/13]], [[13/8]]''' | |||
| '''3.917''' | |||
|- | |||
| [[6/5]], [[5/3]] | |||
| 4.530 | |||
|- | |||
| [[10/9]], [[9/5]] | |||
| 4.626 | |||
|- | |||
| [[7/5]], [[10/7]] | |||
| 4.734 | |||
|- | |||
| [[14/13]], [[13/7]] | |||
| 5.035 | |||
|- | |||
| [[13/12]], [[24/13]] | |||
| 5.239 | |||
|- | |||
| '''[[8/7]], [[7/4]]''' | |||
| '''8.952''' | |||
|- | |||
| '''[[4/3]], [[3/2]]''' | |||
| '''9.156''' | |||
|- | |||
| [[9/7]], [[14/9]] | |||
| 9.360 | |||
|- | |||
| [[13/10]], [[20/13]] | |||
| 9.770 | |||
|- | |||
| '''[[5/4]], [[8/5]]''' | |||
| '''13.686''' | |||
|- | |||
| [[15/14]], [[28/15]] | |||
| 13.891 | |||
|- | |||
| [[18/13]], [[13/9]] | |||
| 14.395 | |||
|- | |||
| '''[[11/8]], [[16/11]]''' | |||
| '''17.985''' | |||
|- | |||
| [[9/8]], [[16/9]] | |||
| 18.312 | |||
|- | |||
| [[15/13]], [[26/15]] | |||
| 18.926 | |||
|- | |||
| [[13/11]], [[22/13]] | |||
| 21.901 | |||
|- | |||
| ''[[16/15]], [[15/8]]'' | |||
| ''22.842'' | |||
|- | |||
| ''[[14/11]], [[11/7]]'' | |||
| ''26.936'' | |||
|- | |||
| ''[[12/11]], [[11/6]]'' | |||
| ''27.141'' | |||
|- | |||
| ''[[11/10]], [[20/11]]'' | |||
| ''31.671'' | |||
|- | |||
| ''[[11/9]], [[18/11]]'' | |||
| ''36.297'' | |||
|- | |||
| ''[[15/11]], [[22/15]]'' | |||
| ''40.827'' | |||
|} | |||
== Rank two temperaments == | == Rank two temperaments == | ||