253edo: Difference between revisions
ArrowHead294 (talk | contribs) mNo edit summary |
m + category |
||
| (5 intermediate revisions by 5 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
253edo is [[consistent]] to the [[17-odd-limit]], approximating the fifth by 148\253 (0.021284 cents sharper than the just 3/2), and the [[prime harmonic]]s from 5 to 17 are all slightly flat. | 253edo is [[consistent]] to the [[17-odd-limit]], approximating the fifth by 148\253 (0.021284 cents sharper than the just 3/2), and the [[prime harmonic]]s from 5 to 17 are all slightly flat. As an equal temperament, it [[tempering out|tempers out]] [[32805/32768]] in the [[5-limit]]; [[2401/2400]] in the [[7-limit]]; [[385/384]], [[1375/1372]] and [[4000/3993]] in the [[11-limit]]; [[325/324]], [[1575/1573]] and [[2200/2197]] in the [[13-limit]]; [[375/374]] and [[595/594]] in the [[17-limit]]. It provides the [[optimal patent val]] for the [[tertiaschis]] temperament, and a good tuning for the [[sesquiquartififths]] temperament in the higher limits. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 9: | Line 9: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 253 factors into | Since 253 factors into 11 × 23, and has subset edos [[11edo]] and [[23edo]]. [[1012edo]] divides 253edo's step size into 4 equal parts and provides a good approximation of the 13-limit. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 92: | Line 92: | ||
| 498.02 | | 498.02 | ||
| 4/3 | | 4/3 | ||
| [[Helmholtz]] | | [[Helmholtz (temperament)|Helmholtz]] | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 104: | Line 104: | ||
== Scales == | == Scales == | ||
* 63 32 63 63 32: One of many [[3L 2s|pentic]] scales available | * 63 32 63 63 32: One of many [[3L 2s|pentic]] scales available | ||
* 43 43 19 43 43 43 19: [[Helmholtz]][7] | * 43 43 19 43 43 43 19: [[Helmholtz (temperament)|Helmholtz]][7] | ||
* 41 41 24 41 41 41 24: [[Meantone]][7] | * 41 41 24 41 41 41 24: [[Meantone]][7] | ||
* 35 35 35 35 35 35 35 8: [[Porcupine]][8] | * 35 35 35 35 35 35 35 8: [[Porcupine]][8] | ||
| Line 112: | Line 112: | ||
* 20 20 20 11 20 20 20 20 11 20 20 20 20 11: [[11L 3s|Ketradektriatoh scale]] | * 20 20 20 11 20 20 20 20 11 20 20 20 20 11: [[11L 3s|Ketradektriatoh scale]] | ||
[[Category:3-limit record edos|###]] <!-- 3-digit number --> | |||
[[Category:Tertiaschis]] | [[Category:Tertiaschis]] | ||