187edo: Difference between revisions

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This edo is a bit of a chimera. It has a [[3/2|fifth]] which is 2.9 ~~cents~~ 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. ~~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]].

== 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 ===

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=== Subsets and supersets ===

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

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

=== Music ===

== Music ==

* ''[https://www.youtube.com/watch?v=vrFU2J25G1Y Pillow(33) ~~(187edo lullaby)]~~'' ~~by [[JUMBLE]~~] (~~Dec~~ 2024, ~~uses MOS~~ [[22L 11s]])

; [[JUMBLE]]

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

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 {{Infobox ET}}
-{{EDO intro}}
+{{ED intro}}
-This edo is a bit of a chimera. It has a [[3/2|fifth]] which is 2.9 cents 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. 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]].
+== 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 ===
@@ Line 8: / Line 11: @@
 === Subsets and supersets ===
-Since 187 factors into {{factorization|187}}, 187edo contains [[11edo]] and [[17edo]] as its subsets.
+Since 187 factors into {{nowrap| 11 × 17 }}, 187edo contains [[11edo]] and [[17edo]] as its subsets.
-=== Music ===
+== Music ==
-* ''[https://www.youtube.com/watch?v=vrFU2J25G1Y Pillow(33) (187edo lullaby)]'' by [[JUMBLE]] (Dec 2024, uses MOS [[22L 11s]])
+; [[JUMBLE]]
+* [https://www.youtube.com/watch?v=vrFU2J25G1Y ''Pillow(33)''] (2024) – a 187edo lullaby, using the [[22L 11s]] [[mos]]