316edo: Difference between revisions

Line 1:

~~The '''~~316 equal divisions of the octave''' ('''316edo'''), or the '''316(-tone) equal temperament''' ('''316tet''', '''316et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 316 [[equal]] parts of about 3.80 [[cent]]s each.

== Theory ==

Line 7:

It provides the [[optimal patent val]] for the rank-4 temperament tempering out 3388/3375, and [[triglav]], which also tempers out 3025/3024.

=== Prime harmonics ===

=== Subsets and supersets ===

316 factors into 22 × 79, with subset edos {{EDOs| 2, 4, 79, and 158 }}.

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

~~{{Primes in edo|316}}~~

== 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]] (¢)

Line 62:

Line 63:

{| class="wikitable center-all 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

! Temperaments

|-

Line 111:

Line 112:

|}

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

[[Category:Parakleismic]]

[[Category:Semiparakleismic]]

[[Category:Triglav]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-The '''316 equal divisions of the octave''' ('''316edo'''), or the '''316(-tone) equal temperament''' ('''316tet''', '''316et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 316 [[equal]] parts of about 3.80 [[cent]]s each.
+{{EDO intro|316}}
 == Theory ==
@@ Line 7: / Line 7: @@
 It provides the [[optimal patent val]] for the rank-4 temperament tempering out 3388/3375, and [[triglav]], which also tempers out 3025/3024.
+=== Prime harmonics ===
+{{Harmonics in equal|316}}
+=== Subsets and supersets ===
 factors into 2<sup>2</sup> × 79, with subset edos {{EDOs| 2, 4, 79, and 158 }}.
-=== Prime harmonics ===
-{{Primes in edo|316}}
 == 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 <br>stretch (¢)
+! rowspan="2" | Optimal 8ve <br>Stretch (¢)
-! colspan="2" | Tuning error
+! colspan="2" | Tuning Error
 |-
 ! [[TE error|Absolute]] (¢)
@@ Line 62: / Line 63: @@
 {| class="wikitable center-all 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
 ! Temperaments
 |-
@@ Line 111: / Line 112: @@
 |}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Parakleismic]]
 [[Category:Semiparakleismic]]
 [[Category:Triglav]]