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 (''hemiluna'' temperament), which is supported by [[87edo|87EDO]], [[323edo|323EDO]], [[410edo|410EDO]], and [[733edo|733EDO]] among others.

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| | (5/4)13 = 1220703125/67108864

|}

== Harmonics ==

{{Harmonics in equal

| steps = 4

| num = 5

| denom = 4

}}

{{Harmonics in equal

| steps = 4

| num = 5

| denom = 4

| start = 12

| collapsed = 1

}}

== Related regular temperament ==

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

POTE generator: ~200/189 = 96.591

~~Vals:~~ 87, 236, 323, 410, 733

{{Optimal ET sequence|legend=1|87, 236, 323, 410, 733}}

Badness: 0.179304

'''11-limit'''

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

POTE generator: ~200/189 = 96.587

~~Vals:~~ 87, 236, 323, 410

{{Optimal ET sequence|legend=1|87, 236, 323, 410}}

Badness: 0.100077

'''13-limit'''

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

POTE generator: ~143/135 = 96.586

~~Vals:~~ 87, 236, 323, 410

{{Optimal ET sequence|legend=1|87, 236, 323, 410}}

Badness: 0.046151

[[Category:Major third]]

[[Category:Equal-step tuning]]

~~[[Category:Edonoi]]~~

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+{{Infobox ET}}
 '''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.
@@ Line 220: / Line 221: @@
 | | (5/4)<font style="vertical-align:super;font-size:0.8em;">13</font> = 1220703125/67108864
 |}
+== Harmonics ==
+{{Harmonics in equal
+| steps = 4
+| num = 5
+| denom = 4
+}}
+{{Harmonics in equal
+| steps = 4
+| num = 5
+| denom = 4
+| start = 12
+| collapsed = 1
+}}
 == Related regular temperament ==
@@ Line 230: / Line 245: @@
 Mapping: [{{val|1 4 2 -5}}, {{val|0 -30 4 97}}]<br>
 POTE generator: ~200/189 = 96.591<br>
-Vals: 87, 236, 323, 410, 733<br>
+{{Optimal ET sequence|legend=1|87, 236, 323, 410, 733}}<br>
 Badness: 0.179304<br><br>
 '''11-limit'''<br>
@@ Line 236: / Line 251: @@
 Mapping: [{{val|1 4 2 -5 7}}, {{val|0 -30 4 97 -44}}]<br>
 POTE generator: ~200/189 = 96.587<br>
-Vals: 87, 236, 323, 410<br>
+{{Optimal ET sequence|legend=1|87, 236, 323, 410}}<br>
 Badness: 0.100077<br><br>
 '''13-limit'''<br>
@@ Line 242: / Line 257: @@
 Mapping: [{{val|1 4 2 -5 7 7}}, {{val|0 -30 4 97 -44 -41}}]<br>
 POTE generator: ~143/135 = 96.586<br>
-Vals: 87, 236, 323, 410<br>
+{{Optimal ET sequence|legend=1|87, 236, 323, 410}}<br>
 Badness: 0.046151<br><br>
 [[Category:Major third]]
 [[Category:Equal-step tuning]]
-[[Category:Edonoi]]