22edo: Difference between revisions
simplified music section, moved first part of theory section to top |
+Temperament measures |
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"just" double harmonic - 2524252 | "just" double harmonic - 2524252 | ||
== Selected just intervals by error == | == Just approximation == | ||
=== Selected just intervals by error === | |||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
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| +4.13 | | +4.13 | ||
|- | |- | ||
! relative (%) | ! [[Relative error|relative]] (%) | ||
| 0 | | 0 | ||
| +13 | | +13 | ||
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|} | |} | ||
=== 15-odd-limit interval mappings === | ==== 15-odd-limit interval mappings ==== | ||
The following tables show how [[15-odd-limit intervals]] are represented in 22edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''. | The following tables show how [[15-odd-limit intervals]] are represented in 22edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''. | ||
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|} | |} | ||
=== Selected 17-limit intervals === | ==== Selected 17-limit intervals ==== | ||
[[File:22ed2-001e.svg|alt=alt : Your browser has no SVG support.]] | [[File:22ed2-001e.svg|alt=alt : Your browser has no SVG support.]] | ||
''See also: [[22edo Solfege]], [[22edo tetrachords]], [[22 EDO Chords]], [[22edo Modes]]'' | ''See also: [[22edo Solfege]], [[22edo tetrachords]], [[22 EDO Chords]], [[22edo Modes]]'' | ||
=== Temperament measures === | |||
The following table shows [[TE temperament measures]] (RMS normalized by the rank) of 22et. | |||
{| class="wikitable" | |||
! colspan="2" | | |||
!3-limit | |||
!5-limit | |||
!7-limit | |||
!11-limit | |||
!2.3.5.7.11.17 | |||
|- | |||
! colspan="2" |Octave stretch (¢) | |||
| -2.25 | |||
| -0.86 | |||
| -1.80 | |||
| -1.11 | |||
| -1.09 | |||
|- | |||
! rowspan="2" |Error | |||
![[TE error|absolute]] (¢) | |||
|2.25 | |||
|2.70 | |||
|2.85 | |||
|2.90 | |||
|2.65 | |||
|- | |||
![[TE simple badness|relative]] (%) | |||
|4.12 | |||
|4.94 | |||
|5.23 | |||
|5.33 | |||
|4.87 | |||
|} | |||
* 22et has a lower relative error than any previous ET in the 11-limit. The next ET that does better in this subgroup is 31. | |||
* 22et is most prominent in the 2.3.5.7.11.17 subgroup, and the next ET that does better in this is 46. | |||
== Rank Two Temperaments == | == Rank Two Temperaments == | ||