152edo: Difference between revisions

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~~The '''~~152 equal divisions of the octave''' ('''152edo''') or '''152(-tone) equal temperament''' ('''152tet''', '''152et''') when viewed from a [[regular temperament]] perspective, is the tuning system derived by dividing the [[octave]] into 152 [[equal]]ly sized parts of about 7.89 [[cent]]s each.

== Theory ==

152et is a strong 11-limit system, with the 3, 5, 7, and 11 slightly sharp. It tempers out 1600000/1594323~~, the~~ [[amity comma]], in the 5-limit; [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[Mirkwai comma|16875/16807]] in the 7-limit; [[540/539]], 1375/1372, [[4000/3993]], 5632/5625 and [[9801/9800]] in the 11-limit.

152et is a strong 11-limit system, with the 3, 5, 7, and 11 slightly sharp. It tempers out 1600000/1594323 ([[amity comma]]) and {{monzo| 32 -7 -9 }} ([[escapade comma]]) in the 5-limit; [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[Mirkwai comma|16875/16807]] in the 7-limit; [[540/539]], 1375/1372, [[3025/3024]], [[4000/3993]], [[5632/5625]] and [[9801/9800]] in the 11-limit.

It has two reasonable mappings for 13, with the 152f val scoring much better. The patent val tempers out [[169/168]], [[325/324]], [[351/350]], [[364/363]], [[1001/1000]], [[1573/1568]], and [[4096/4095]]. The 152f val tempers out [[352/351]], [[625/624]], [[640/637]], [[729/728]], [[847/845]], [[1188/1183]], [[1575/1573]], [[1716/1715]] and [[2080/2079]].

It has two reasonable mappings for 13, with the 152f val scoring much better. The [[patent val]] tempers out [[169/168]], [[325/324]], [[351/350]], [[364/363]], [[1001/1000]], [[1573/1568]], and [[4096/4095]]. The 152f val tempers out [[352/351]], [[625/624]], [[640/637]], [[729/728]], [[847/845]], [[1188/1183]], [[1575/1573]], [[1716/1715]] and [[2080/2079]].

It provides the [[optimal patent val]] for the 11-limit [[~~Mirkwai clan #Grendel|~~grendel]] and [[~~Mirkwai clan #Kwai|~~kwai]] linear temperaments, the 13-limit rank ~~two~~ temperament [[Ragismic microtemperaments #Octoid-Octopus|octopus]], the 11-limit planar temperament [[~~Hemifamity family #Laka|~~laka]], and the rank ~~five~~ temperament tempering out 169/168.

It provides the [[optimal patent val]] for the 11-limit [[grendel]] and [[kwai]] linear temperaments, the 13-limit rank-2 temperament [[Ragismic microtemperaments #Octoid-Octopus|octopus]], the 11-limit planar temperament [[laka]], and the rank-5 temperament tempering out 169/168.

[[Paul Erlich]] has suggested that 152edo could be considered a sort of [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3038.html#3041 universal tuning].

152 ~~= 8 × 19, with divisors 2, 4, 8, 19, 38, 76.~~

=== Prime harmonics ===

=== ~~Prime harmonics~~ ===

=== Subsets and supersets ===

Since 152 factors into 2<sup>3</sup> × 19, 152edo has subset edos {{EDOs| 2, 4, 8, 19, 38, 76 }}.

== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

! rowspan="2" | Subgroup

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Comma list|Comma List]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal<br>8ve ~~stretch~~ (¢)

! rowspan="2" | Optimal<br>8ve Stretch (¢)

! colspan="2" | Tuning ~~error~~

! colspan="2" | Tuning Error

|-

! [[TE error|Absolute]] (¢)

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-The '''152 equal divisions of the octave''' ('''152edo''') or '''152(-tone) equal temperament''' ('''152tet''', '''152et''') when viewed from a [[regular temperament]] perspective, is the tuning system derived by dividing the [[octave]] into 152 [[equal]]ly sized parts of about 7.89 [[cent]]s each.
+{{EDO intro|152}}
 == Theory ==
-et is a strong 11-limit system, with the 3, 5, 7, and 11 slightly sharp. It tempers out 1600000/1594323, the [[amity comma]], in the 5-limit; [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[Mirkwai comma|16875/16807]] in the 7-limit; [[540/539]], 1375/1372, [[4000/3993]], 5632/5625 and [[9801/9800]] in the 11-limit.
+et is a strong 11-limit system, with the 3, 5, 7, and 11 slightly sharp. It tempers out 1600000/1594323 ([[amity comma]]) and {{monzo| 32 -7 -9 }} ([[escapade comma]]) in the 5-limit; [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[Mirkwai comma|16875/16807]] in the 7-limit; [[540/539]], 1375/1372, [[3025/3024]], [[4000/3993]], [[5632/5625]] and [[9801/9800]] in the 11-limit.
-It has two reasonable mappings for 13, with the 152f val scoring much better. The patent val tempers out [[169/168]], [[325/324]], [[351/350]], [[364/363]], [[1001/1000]], [[1573/1568]], and [[4096/4095]]. The 152f val tempers out [[352/351]], [[625/624]], [[640/637]], [[729/728]], [[847/845]], [[1188/1183]], [[1575/1573]], [[1716/1715]] and [[2080/2079]].
+It has two reasonable mappings for 13, with the 152f val scoring much better. The [[patent val]] tempers out [[169/168]], [[325/324]], [[351/350]], [[364/363]], [[1001/1000]], [[1573/1568]], and [[4096/4095]]. The 152f val tempers out [[352/351]], [[625/624]], [[640/637]], [[729/728]], [[847/845]], [[1188/1183]], [[1575/1573]], [[1716/1715]] and [[2080/2079]].
-It provides the [[optimal patent val]] for the 11-limit [[Mirkwai clan #Grendel|grendel]] and [[Mirkwai clan #Kwai|kwai]] linear temperaments, the 13-limit rank two temperament [[Ragismic microtemperaments #Octoid-Octopus|octopus]], the 11-limit planar temperament [[Hemifamity family #Laka|laka]], and the rank five temperament tempering out 169/168.
+It provides the [[optimal patent val]] for the 11-limit [[grendel]] and [[kwai]] linear temperaments, the 13-limit rank-2 temperament [[Ragismic microtemperaments #Octoid-Octopus|octopus]], the 11-limit planar temperament [[laka]], and the rank-5 temperament tempering out 169/168.
 [[Paul Erlich]] has suggested that 152edo could be considered a sort of [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3038.html#3041 universal tuning].
-= 8 × 19, with divisors 2, 4, 8, 19, 38, 76.
+=== Prime harmonics ===
+{{Harmonics in equal|152}}
-=== Prime harmonics ===
+=== Subsets and supersets ===
-{{Harmonics in equal|152|columns=11}}
+Since 152 factors into 2<sup>3</sup> × 19, 152edo has subset edos {{EDOs| 2, 4, 8, 19, 38, 76 }}.
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
-! rowspan="2" | Subgroup
+! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Comma list|Comma List]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br>8ve stretch (¢)
+! rowspan="2" | Optimal<br>8ve Stretch (¢)
-! colspan="2" | Tuning error
+! colspan="2" | Tuning Error
 |-
 ! [[TE error|Absolute]] (¢)