187edo: Difference between revisions

(6 intermediate revisions by 5 users not shown)

Line 1:

~~The 187 equal temperament, which divides the octave into 187 parts of 6.417 cents each,~~ is a bit of a chimera. It has a fifth which is 2.9 ~~cents~~ flat and a major third 1.3 cents flat, but the 7, 11 and 13 are more accurate. It tempers out 78732/78125~~, the~~ sensipent comma, in the 5-limit and 225/224 in the 7-limit, providing the optimal patent val for [[~~Sensipent_family#Sensei|~~sensei ~~temperament~~]] which tempers out both. In the 11-limit it tempers out 441/440, 1375/1372 and 4000/3993 and in the 13-limit ~~1188/1183,~~ 351/350, 625/624, 1716/1715 and 2200/2197.

== Theory ==

This edo is a bit of a chimera. It has a [[3/2|fifth]] which is 2.9{{c}} flat and a [[5/4|classical major third]] 1.3 cents flat, but the [[7/1|7]], [[11/1|11]] and [[13/1|13]] are more accurate.

Using the [[patent val]], the equal temperament [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]) in the [[5-limit]] and [[225/224]] in the [[7-limit]], providing the [[optimal patent val]] for [[sensei]], which tempers out both. In the [[11-limit]] it tempers out [[441/440]], [[1375/1372]] and [[4000/3993]], and in the [[13-limit]] [[351/350]], [[625/624]], [[1188/1183]], [[1716/1715]] and [[2200/2197]].

=== Odd harmonics ===

=== Subsets and supersets ===

Since 187 factors into {{nowrap| 11 × 17 }}, 187edo contains [[11edo]] and [[17edo]] as its subsets.

== Music ==

; [[JUMBLE]]

* [https://www.youtube.com/watch?v=vrFU2J25G1Y ''Pillow(33)''] (2024) – a 187edo lullaby, using the [[22L 11s]] [[mos]]

@@ Line 1: / Line 1: @@
-The 187 equal temperament, which divides the octave into 187 parts of 6.417 cents each, is a bit of a chimera. It has a fifth which is 2.9 cents flat and a major third 1.3 cents flat, but the 7, 11 and 13 are more accurate. It tempers out 78732/78125, the sensipent comma, in the 5-limit and 225/224 in the 7-limit, providing the optimal patent val for [[Sensipent_family#Sensei|sensei temperament]] which tempers out both. In the 11-limit it tempers out 441/440, 1375/1372 and 4000/3993 and in the 13-limit 1188/1183, 351/350, 625/624, 1716/1715 and 2200/2197.
+{{Infobox ET}}
+{{ED intro}}
+== Theory ==
+This edo is a bit of a chimera. It has a [[3/2|fifth]] which is 2.9{{c}} flat and a [[5/4|classical major third]] 1.3 cents flat, but the [[7/1|7]], [[11/1|11]] and [[13/1|13]] are more accurate.
+Using the [[patent val]], the equal temperament [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]) in the [[5-limit]] and [[225/224]] in the [[7-limit]], providing the [[optimal patent val]] for [[sensei]], which tempers out both. In the [[11-limit]] it tempers out [[441/440]], [[1375/1372]] and [[4000/3993]], and in the [[13-limit]] [[351/350]], [[625/624]], [[1188/1183]], [[1716/1715]] and [[2200/2197]].
+=== Odd harmonics ===
+{{Harmonics in equal|187}}
+=== Subsets and supersets ===
+Since 187 factors into {{nowrap| 11 × 17 }}, 187edo contains [[11edo]] and [[17edo]] as its subsets.
+== Music ==
+; [[JUMBLE]]
+* [https://www.youtube.com/watch?v=vrFU2J25G1Y ''Pillow(33)''] (2024) – a 187edo lullaby, using the [[22L 11s]] [[mos]]