44edo: Difference between revisions
Dave Keenan (talk | contribs) →Sagittal notation: Moved the explanation of ≈ to the end of the section. |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
44edo is a double of 22edo, to which it adds the ratios of 13, 19, and 23. While not the most accurate 2.3.5.7.11 tuning, 22edo is certainly a relatively compact one, and it's natural to extend it this way. The most practically useful of these additions is easily the 13th harmonic with its neutral intervals, but the 17th, 19th, and 23rd are not to be dismissed. In the 13-limit it supplies the optimal patent val for [[vigin]] temperament. The [[k*N_subgroups|2*44]] subgroup of 44edo is 2.9.5.21.11.13.17.19.23, on which 44 tempers out the same commas as the patent val for [[88edo]]. | 44edo is a double of 22edo, to which it adds the ratios of 13, 19, and 23. While not the most accurate 2.3.5.7.11 tuning, 22edo is certainly a relatively compact one, and it's natural to extend it this way. The most practically useful of these additions is easily the 13th harmonic with its neutral intervals, but the 17th, 19th, and 23rd are not to be dismissed. In the 13-limit it supplies the optimal patent val for [[vigin]] temperament. The [[k*N_subgroups|2*44]] subgroup of 44edo is 2.9.5.21.11.13.17.19.23, on which 44 tempers out the same commas as the patent val for [[88edo]]. | ||
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== Notation == | == Notation == | ||
===Sagittal notation=== | === Sagittal notation === | ||
This notation uses the same sagittal sequence as EDOs [[23edo#Second-best fifth notation|23b]], [[30edo#Sagittal notation|30]], and [[37edo#Sagittal notation|37]], and is a superset of the notations for EDOs [[22edo#Sagittal notation|22]] and [[11edo#Sagittal notation|11]]. | This notation uses the same sagittal sequence as EDOs [[23edo#Second-best fifth notation|23b]], [[30edo#Sagittal notation|30]], and [[37edo#Sagittal notation|37]], and is a superset of the notations for EDOs [[22edo#Sagittal notation|22]] and [[11edo#Sagittal notation|11]]. | ||
==== Evo flavor ==== | |||
<imagemap> | <imagemap> | ||
File:44-EDO_Evo_Sagittal.svg | File:44-EDO_Evo_Sagittal.svg | ||
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</imagemap> | </imagemap> | ||
====Revo flavor==== | ==== Revo flavor ==== | ||
<imagemap> | <imagemap> | ||
File:44-EDO_Revo_Sagittal.svg | File:44-EDO_Revo_Sagittal.svg | ||
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</imagemap> | </imagemap> | ||
====Evo-SZ flavor==== | ==== Evo-SZ flavor ==== | ||
<imagemap> | <imagemap> | ||
File:44-EDO_Evo-SZ_Sagittal.svg | File:44-EDO_Evo-SZ_Sagittal.svg | ||