308edo: Difference between revisions

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== Theory ==

~~308et~~ only is consistent in the 5-limit. Ignoring the ~~harmonics~~ 7, 11 and 13, ~~308et~~ is strong in the 2.3.5.17.19.23.29.31 subgroup.

308edo only is [[consistent]] in the [[5-odd-limit]]. Ignoring the [[harmonic]]s [[7/1|7]], [[11/1|11]] and [[13/1|13]], it is strong in the 2.3.5.17.19.23.29.31 [[subgroup]].

~~308et tempers out following commas:~~

Using the [[patent val]] nonetheless, the equal temperament [[tempering out|tempers out]] [[19683/19600]], [[65625/65536]], and [[390625/388962]] in the 7-limit, and [[243/242]], 1375/1372, [[6250/6237]], [[9801/9800]], and 14700/14641 in the 11-limit.

~~7-limit commas: 4096000/4084101,~~ [[~~390625/388962~~]], ~~26873856/26796875,~~ [[~~19683/19600~~]], [[~~78125000~~/~~78121827~~]], [[65625/65536]], [[~~1640558367~~/~~1638400000~~]]

11-limit ~~commas: 806736/805255, 1835008/1830125, 14700/14641, 26214400/26198073, 166698/166375~~, [[243/242]], ~~[[131072~~/~~130977]]~~, [[6250/6237]]~~, 107495424/107421875, 9765625/9732096, 137781/137500, 180224/180075, 1375/1372, 17537553/17500000, 47265625/47258883~~, [[9801/9800]], ~~539055~~/~~537824, 202397184/201768035~~

Using the 308d val, it supports [[unidec]] and [[gammic]].

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=== Subsets and supersets ===

308 factors into 22 x 7 x 11, ~~with~~ subset edos {{EDOs| 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154}}.

Since 308 factors into {{nowrap|22 × 7 × 11}}, 308edo has subset edos {{EDOs| 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154 }}.

==Regular temperament properties==

== Regular temperament properties ==

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

|-

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

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

! rowspan="2" | [[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]] (¢)

! [[TE error|Absolute]] (¢)

![[TE simple badness|Relative]] (%)

! [[TE simple badness|Relative]] (%)

|-

| 2.3

| {{monzo| -122 77 }}

| {{~~val~~| 308 488 }}

| {{mapping| 308 488 }}

| 0.2070

| +0.2070

| 0.2071

| 5.32

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| 2.3.5

| {{monzo| -36 11 8 }}, {{monzo| -7 22 -12 }}

| {{~~val~~| 308 488 715 }}

| {{mapping| 308 488 715 }}

| 0.2241

| +0.2241

| 0.1708

| 4.38

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=== Rank-2 temperaments ===

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

|+Table of rank-2 temperaments by generator

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

! Periods per 8ve

|-

! Generator~~ (Reduced)~~

! Periods per 8ve

! Cents~~ (Reduced)~~

! Generator*

! Associated ~~Ratio~~

! Cents*

! Associated ratio*

! Temperaments

|-

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|-

| 28

| 128\308 (4\308)

| 128\308 (4\308)

| 498.70 (15.58)

| 498.70 (15.58)

| 4/3 (~~2048~~/~~2025~~)

| 4/3 (126/125)

| [[Oquatonic]]

| [[Oquatonic]] (308)

|}

<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct

~~{{Todo~~| ~~review }}~~

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|308}}
+{{ED intro}}
 == Theory ==
-et only is consistent in the 5-limit. Ignoring the harmonics 7, 11 and 13, 308et is strong in the 2.3.5.17.19.23.29.31 subgroup.
+edo only is [[consistent]] in the [[5-odd-limit]]. Ignoring the [[harmonic]]s [[7/1|7]], [[11/1|11]] and [[13/1|13]], it is strong in the 2.3.5.17.19.23.29.31 [[subgroup]].
-et tempers out following commas:
+Using the [[patent val]] nonetheless, the equal temperament [[tempering out|tempers out]] [[19683/19600]], [[65625/65536]], and [[390625/388962]] in the 7-limit, and [[243/242]], 1375/1372, [[6250/6237]], [[9801/9800]], and 14700/14641 in the 11-limit.
--limit commas: 4096000/4084101, [[390625/388962]], 26873856/26796875, [[19683/19600]], [[78125000/78121827]], [[65625/65536]], [[1640558367/1638400000]]
--limit commas: 806736/805255, 1835008/1830125, 14700/14641, 26214400/26198073, 166698/166375, [[243/242]], [[131072/130977]], [[6250/6237]], 107495424/107421875, 9765625/9732096, 137781/137500, 180224/180075, 1375/1372, 17537553/17500000, 47265625/47258883, [[9801/9800]], 539055/537824, 202397184/201768035
 Using the 308d val, it supports [[unidec]] and [[gammic]].
@@ Line 17: / Line 13: @@
 === Subsets and supersets ===
-factors into 2<sup>2</sup> x 7 x 11, with subset edos {{EDOs| 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154}}.
+Since 308 factors into {{nowrap|2<sup>2</sup> × 7 × 11}}, 308edo has subset edos {{EDOs| 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154 }}.
-==Regular temperament properties==
+== Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[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]] (¢)
+! [[TE error|Absolute]] (¢)
-![[TE simple badness|Relative]] (%)
+! [[TE simple badness|Relative]] (%)
 |-
 | 2.3
 | {{monzo| -122 77 }}
-| {{val| 308 488 }}
+| {{mapping| 308 488 }}
-| 0.2070
+| +0.2070
 | 0.2071
 | 5.32
@@ Line 39: / Line 36: @@
 | 2.3.5
 | {{monzo| -36 11 8 }}, {{monzo| -7 22 -12 }}
-| {{val| 308 488 715 }}
+| {{mapping| 308 488 715 }}
-| 0.2241
+| +0.2241
 | 0.1708
 | 4.38
@@ Line 47: / Line 44: @@
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
-|+Table of rank-2 temperaments by generator
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Periods<br>per 8ve
+|-
-! Generator<br>(Reduced)
+! Periods<br />per 8ve
-! Cents<br>(Reduced)
+! Generator*
-! Associated<br>Ratio
+! Cents*
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 61: / Line 59: @@
 |-
 | 28
-| 128\308<br>(4\308)
+| 128\308<br />(4\308)
-| 498.70<br>(15.58)
+| 498.70<br />(15.58)
-| 4/3<br>(2048/2025)
+| 4/3<br />(126/125)
-| [[Oquatonic]]
+| [[Oquatonic]] (308)
 |}
+<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
-{{Todo| review }}