19edo: Difference between revisions
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== Theory == | == Theory == | ||
In music, '''19 equal temperament''', called 19-TET, 19-[[EDO]], or 19-ET, is the scale derived by dividing the [[ | In music, '''19 equal temperament''', called 19-TET, 19-[[EDO]], or 19-ET, is the scale derived by dividing the [[octave]] into 19 [[Equal]]ly large steps. Each step represents a frequency ratio of the 19th root of 2, or 63.16 [[cent|cents]]. It is the 8th [[prime numbers|prime]] [[prime EDO|edo]], following [[17edo]] and coming before [[23edo]]. | ||
=== History === | === History === | ||
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For a more complete list, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]]. | For a more complete list, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]]. | ||
== Selected just intervals by error == | == Just approximation == | ||
=== Selected just intervals by error === | |||
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=== 15-odd-limit interval mappings === | ==== 15-odd-limit interval mappings ==== | ||
The following table shows how [[15-odd-limit intervals]] are represented in 19edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''. | The following table shows how [[15-odd-limit intervals]] are represented in 19edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''. | ||
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=== Selected 17-limit intervals === | ==== Selected 17-limit intervals ==== | ||
[[File:19ed2-001.svg|alt=alt : Your browser has no SVG support.]] | [[File:19ed2-001.svg|alt=alt : Your browser has no SVG support.]] | ||
=== Temperament measures === | |||
The following table shows [[TE temperament measures]] (RMS normalized by the rank) of 19et. | |||
{| class="wikitable center-all" | |||
! colspan="2" | | |||
!3-limit | |||
!5-limit | |||
!7-limit | |||
!2.3.5.7.13 | |||
|- | |||
! colspan="2" |Octave stretch (¢) | |||
| +2.28 | |||
| +2.58 | |||
| +3.85 | |||
| +4.14 | |||
|- | |||
! rowspan="2" |Error | |||
![[TE error|absolute]] (¢) | |||
|2.28 | |||
|1.91 | |||
|2.76 | |||
|2.53 | |||
|- | |||
![[TE simple badness|relative]] (%) | |||
|3.61 | |||
|3.02 | |||
|4.35 | |||
|3.99 | |||
|} | |||
* 19-et has a lower relative error than any previous ETs in the 5- and 7-limit. The next ET that does better in these subgroups is 34 and 31, respectively. | |||
* 19-et is most prominent in the 2.3.5.7.13 subgroup, and the next ET that does better in this is 53. | |||
== Commas == | == Commas == | ||