27edo: Difference between revisions
+Temperament measures |
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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. | ||
== Just approximation == | |||
=== Selected just intervals by error === | === Selected just intervals by error === | ||
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| +30.6 | | +30.6 | ||
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The following table shows how 15-odd-limit intervals are represented in 27edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''. | 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" | {| class="wikitable center-all" | ||
|+Direct mapping (even if inconsistent) | |+Direct mapping (even if inconsistent) | ||
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| ''40.827'' | | ''40.827'' | ||
|} | |} | ||
=== Temperament measures === | |||
The following table shows [[TE temperament measures]] (RMS normalized by the rank) of 27et. | |||
{| class="wikitable center-all" | |||
! colspan="2" | | |||
! 3-limit | |||
! 5-limit | |||
! 7-limit | |||
! 2.3.5.7.13 | |||
! 2.3.5.7.13.19 | |||
|- | |||
! colspan="2" |Octave stretch (¢) | |||
| -2.89 | |||
| -3.88 | |||
| -3.70 | |||
| -3.18 | |||
| -3.18 | |||
|- | |||
! rowspan="2" |Error | |||
! [[TE error|absolute]] (¢) | |||
| 2.88 | |||
| 2.74 | |||
| 2.39 | |||
| 2.39 | |||
| 2.18 | |||
|- | |||
! [[TE simple badness|relative]] (%) | |||
| 6.50 | |||
| 6.19 | |||
| 5.40 | |||
| 5.39 | |||
| 4.92 | |||
|} | |||
* 27et has a lower relative error than any previous ETs in the 2.3.5.7.13.19 subgroup. The next ET that does better in this subgroup is 53. | |||
== Rank two temperaments == | == Rank two temperaments == | ||