31edo: Difference between revisions
m typography of quoted term |
+Temperament measures |
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For a more complete list of chords, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]]. | For a more complete list of chords, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]]. | ||
== Just approximation == | |||
=== Selected just intervals === | === Selected just intervals === | ||
| Line 503: | Line 505: | ||
|- | |- | ||
! Interval, complement | ! Interval, complement | ||
! Error (abs | ! Error (abs, [[cent|¢]]) | ||
|- | |- | ||
| '''[[5/4]], [[8/5]]''' | | '''[[5/4]], [[8/5]]''' | ||
| Line 4,065: | Line 4,067: | ||
Etc. | Etc. | ||
=== Temperament measures === | |||
The following table shows [[TE temperament measures]] (RMS normalized by the rank) of 31et. | |||
{| class="wikitable center-all" | |||
! colspan="2" | | |||
! 3-limit | |||
! 5-limit | |||
! 7-limit | |||
! 11-limit | |||
! 13-limit | |||
|- | |||
! colspan="2" |Octave stretch (¢) | |||
| +1.63 | |||
| +0.98 | |||
| +0.83 | |||
| +1.21 | |||
| +0.50 | |||
|- | |||
! rowspan="2" |Error | |||
! [[TE error|absolute]] (¢) | |||
| 1.64 | |||
| 1.63 | |||
| 1.43 | |||
| 1.49 | |||
| 2.07 | |||
|- | |||
! [[TE simple badness|relative]] (%) | |||
| 4.22 | |||
| 4.20 | |||
| 3.70 | |||
| 3.84 | |||
| 5.35 | |||
|} | |||
* 31et has a lower relative error than any previous ETs in all harmonic limits from 7 to 31. | |||
== Relationship to 12-edo == | == Relationship to 12-edo == | ||