4ed5/4: Difference between revisions

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'''4ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into four parts of 96.5784 [[cent|cents]] each, corresponding to 12.4251 [[~~edo~~]]. It is related to the temperament which tempers out 48828125/48771072 and 67108864/66976875 in the 7-limit, which is supported by [[87edo]], [[323edo]], [[410edo]], and [[733edo]] among others.

'''4ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into four parts of 96.5784 [[cent|cents]] each, corresponding to 12.4251 [[EDO]]. It is related to the temperament which tempers out 48828125/48771072 and 67108864/66976875 in the 7-limit (''hemiluna'' temperament), which is supported by [[87edo|87EDO]], [[323edo|323EDO]], [[410edo|410EDO]], and [[733edo|733EDO]] among others.

==Intervals==

== Intervals ==

{| class="wikitable"

|-

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|}

==Related regular temperament==

== Related regular temperament ==

~~===7-limit~~ 87&323~~===~~

4ED5/4 tuning is closely related to the ''hemiluna'' temperament (87&323), which tempers out 48828125/48771072 (''neptunisma'', laruruleyo) and 67108864/66976875 (''decovulture'' comma, sasabirugugu) in the 7-limit. It splits a hemithird interval into two equal parts.

~~Commas:~~ 48828125/48771072, 67108864/66976875

~~POTE generator~~: ~~~200~~/~~189 = 96.591~~

; [[Luna family #Hemiluna|Hemiluna]] (87 & 323)

'''7-limit'''

~~Map~~: [~~<~~1 4 2 -5|~~, <~~0 -30 4 97|]

Comma list: 48828125/48771072, 67108864/66976875

Mapping: [{{val|1 4 2 -5}}, {{val|0 -30 4 97}}]

~~EDOs~~: 87, 323, 410, 733

POTE generator: ~200/189 = 96.591

Vals: 87, 236, 323, 410, 733

Badness: 0.~~1793~~

Badness: 0.179304

'''11-limit'''

~~===~~11-limit ~~87&323===~~

Comma list: 5632/5625, 14641/14580, 131072/130977

~~Commas~~: 5632/5625, 14641/14580, 131072/130977

Mapping: [{{val|1 4 2 -5 7}}, {{val|0 -30 4 97 -44}}]

POTE generator: ~200/189 = 96.587

~~POTE generator: ~200/189 = 96.587~~

Vals: 87, 236, 323, 410

Badness: 0.100077

~~Map~~: [~~<~~1 4 2 -5 7|~~, <~~0 -30 4 97 -44|]

'''13-limit'''

Comma list: 676/675, 1001/1000, 4096/4095, 14641/14580

~~EDOs~~: 87, 323, 410~~, 733e~~

Mapping: [{{val|1 4 2 -5 7 7}}, {{val|0 -30 4 97 -44 -41}}]

POTE generator: ~143/135 = 96.586

Badness: 0.~~1001~~

Vals: 87, 236, 323, 410

Badness: 0.046151

~~===~~13-limit ~~87&323===~~

~~Commas~~: 676/675, 1001/1000, 4096/4095, 14641/14580

~~POTE generator: ~143/135 = 96.586~~

~~Map~~: [~~<~~1 4 2 -5 7 7|~~, <~~0 -30 4 97 -44 -41|]

~~EDOs~~: 87, 323, 410~~, 733e~~

Badness: 0.~~0462~~

[[Category:Major third]]

[[Category:Equal-step tuning]]

[[Category:Edonoi]]

@@ Line 1: / Line 1: @@
-'''4ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into four parts of 96.5784 [[cent|cents]] each, corresponding to 12.4251 [[edo]]. It is related to the temperament which tempers out 48828125/48771072 and 67108864/66976875 in the 7-limit, which is supported by [[87edo]], [[323edo]], [[410edo]], and [[733edo]] among others.
+'''4ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into four parts of 96.5784 [[cent|cents]] each, corresponding to 12.4251 [[EDO]]. It is related to the temperament which tempers out 48828125/48771072 and 67108864/66976875 in the 7-limit (''hemiluna'' temperament), which is supported by [[87edo|87EDO]], [[323edo|323EDO]], [[410edo|410EDO]], and [[733edo|733EDO]] among others.
-==Intervals==
+== Intervals ==
 {| class="wikitable"
 |-
@@ Line 221: / Line 221: @@
 |}
-==Related regular temperament==
+== Related regular temperament ==
-===7-limit 87&amp;323===
+ED5/4 tuning is closely related to the ''hemiluna'' temperament (87&amp;323), which tempers out 48828125/48771072 (''neptunisma'', laruruleyo) and 67108864/66976875 (''decovulture'' comma, sasabirugugu) in the 7-limit. It splits a hemithird interval into two equal parts.
-Commas: 48828125/48771072, 67108864/66976875
-POTE generator: ~200/189 = 96.591
+; [[Luna family #Hemiluna|Hemiluna]] (87 &amp; 323)
+'''7-limit'''<br>
-Map: [&lt;1 4 2 -5|, &lt;0 -30 4 97|]
+Comma list: 48828125/48771072, 67108864/66976875<br>
+Mapping: [{{val|1 4 2 -5}}, {{val|0 -30 4 97}}]<br>
-EDOs: 87, 323, 410, 733
+POTE generator: ~200/189 = 96.591<br>
+Vals: 87, 236, 323, 410, 733<br>
-Badness: 0.1793
+Badness: 0.179304<br><br>
+'''11-limit'''<br>
-===11-limit 87&amp;323===
+Comma list: 5632/5625, 14641/14580, 131072/130977<br>
-Commas: 5632/5625, 14641/14580, 131072/130977
+Mapping: [{{val|1 4 2 -5 7}}, {{val|0 -30 4 97 -44}}]<br>
+POTE generator: ~200/189 = 96.587<br>
-POTE generator: ~200/189 = 96.587
+Vals: 87, 236, 323, 410<br>
+Badness: 0.100077<br><br>
-Map: [&lt;1 4 2 -5 7|, &lt;0 -30 4 97 -44|]
+'''13-limit'''<br>
+Comma list: 676/675, 1001/1000, 4096/4095, 14641/14580<br>
-EDOs: 87, 323, 410, 733e
+Mapping: [{{val|1 4 2 -5 7 7}}, {{val|0 -30 4 97 -44 -41}}]<br>
+POTE generator: ~143/135 = 96.586<br>
-Badness: 0.1001
+Vals: 87, 236, 323, 410<br>
+Badness: 0.046151<br><br>
-===13-limit 87&amp;323===
-Commas: 676/675, 1001/1000, 4096/4095, 14641/14580
-POTE generator: ~143/135 = 96.586
-Map: [&lt;1 4 2 -5 7 7|, &lt;0 -30 4 97 -44 -41|]
-EDOs: 87, 323, 410, 733e
-Badness: 0.0462
 [[Category:Major third]]
 [[Category:Equal-step tuning]]
 [[Category:Edonoi]]