157edo: Difference between revisions

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~~The '''157 equal divisions of the octave''' ('''157edo'''), or the '''157(-tone) equal temperament''' ('''157tet''', '''157et''') when viewed from a [[regular temperament]] perspective, is the [[~~EDO|~~equal division of the octave]] into~~ 157 ~~parts of about 7.64 [[cent]]s each.~~

== 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 (supporting 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.

~~157edo is the 37th [[prime EDO]].~~

=== Prime harmonics ===

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

=== Subsets and supersets ===

~~{{Primes in~~ edo~~|157}}~~

157edo is the 37th [[prime edo]].

== 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 8ve ~~stretch~~ (¢)

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

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

! colspan="2" | Tuning Error

|-

! [[TE error|Absolute]] (¢)

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{| class="wikitable center-all right-3 left-5"

|+Table of rank-2 temperaments by generator

! Periods per ~~octave~~

! Periods per 8ve

! Generator (~~reduced~~)

! Generator (Reduced)

! Cents (~~reduced~~)

! Cents (Reduced)

! Associated ~~ratio~~

! Associated Ratio

! Temperament

|-

Line 108:

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| 443.31

| 162/125

| [[~~Sensipent~~]]

| [[Warrior]]

|-

| 1

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| [[Catafourth]]

|}

~~[[Category:Equal divisions of the octave|###]] ~~

~~[[Category:Prime EDO]]~~

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-The '''157 equal divisions of the octave''' ('''157edo'''), or the '''157(-tone) equal temperament''' ('''157tet''', '''157et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 157 parts of about 7.64 [[cent]]s each.
+{{EDO intro|157}}
 == Theory ==
 et 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 (supporting 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.
-edo is the 37th [[prime EDO]].
+=== Prime harmonics ===
+{{Harmonics in equal|157}}
-=== Prime harmonics ===
+=== Subsets and supersets ===
-{{Primes in edo|157}}
+edo is the 37th [[prime edo]].
 == 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 74: / Line 75: @@
 {| class="wikitable center-all right-3 left-5"
 |+Table of rank-2 temperaments by generator
-! Periods<br>per octave
+! Periods<br>per 8ve
-! Generator<br>(reduced)
+! Generator<br>(Reduced)
-! Cents<br>(reduced)
+! Cents<br>(Reduced)
-! Associated<br>ratio
+! Associated<br>Ratio
 ! Temperament
 |-
@@ Line 108: / Line 109: @@
 | 443.31
 | 162/125
-| [[Sensipent]]
+| [[Warrior]]
 |-
 | 1
@@ Line 116: / Line 117: @@
 | [[Catafourth]]
 |}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
-[[Category:Prime EDO]]