157edo: Difference between revisions
ArrowHead294 (talk | contribs) mNo edit summary |
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" |
||
| (3 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
157et [[tempers out]] 78732/78125 ([[sensipent comma]]) and {{monzo| 37 -16 -5 }} (quinticosiennic comma) in the 5-limit; [[2401/2400]], [[5120/5103]], and 110592/109375 in the 7-limit ( | 157et [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]) and {{monzo| 37 -16 -5 }} ([[quinticosiennic comma]]) in the 5-limit; [[2401/2400]], [[5120/5103]], and 110592/109375 in the 7-limit ([[support]]ing the [[hemififths]] and the [[catafourth]] temperaments). Using the [[patent val]], it tempers out [[176/175]], 1331/1323, 3773/3750 and [[8019/8000]] in the 11-limit; [[351/350]], [[352/351]], [[847/845]], [[1573/1568]], and [[2197/2187]] in the 13-limit. | ||
=== Odd harmonics === | === Odd harmonics === | ||
| Line 9: | Line 9: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
157edo is the 37th [[prime edo]]. | 157edo is the 37th [[prime edo]]. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 99: | Line 99: | ||
| 351.59 | | 351.59 | ||
| 49/40 | | 49/40 | ||
| [[Hemififths]] | | [[Hemififths]] (157eff) | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 119: | Line 119: | ||
| [[Catafourth]] | | [[Catafourth]] | ||
|} | |} | ||
<nowiki />* [[Normal | <nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||