Semaphoresmic family: Difference between revisions

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__FORCETOC__

'''Semiphore family''' is a rank-3 temperament family of 2.3.5.7 that tempers out 49/48 and thereby identifies the septimal minor third, 7/6, and the septimal whole tone, 8/7. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". Related to this is the 2.3.7-limit 49/48 temperament called "[[~~Chromatic pairs~~ #Semaphore|semaphore]]," and the 2.3.5.7 49/48 and 81/80 temperament called "[[Meantone family #Godzilla|godzilla]]".

'''Semiphore family''' is a rank-3 temperament family of 2.3.5.7 that tempers out 49/48 and thereby identifies the septimal minor third, 7/6, and the septimal whole tone, 8/7. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". Related to this is the 2.3.7-limit 49/48 temperament called "[[Slendro clan #Semaphore|semaphore]]", and the 2.3.5.7 49/48 and 81/80 temperament called "[[Meantone family #Godzilla|godzilla]]".

= Semiphore =

Comma list: 49/48

POTE generators: ~7/6 = 250.3846, ~5/4 = 379.7035

Mapping: [{{val| 1 0 2 2 }}, {{val| 0 2 0 1 }}, {{val| 0 0 1 0 }}]

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= Selenium =

Comma list: 49/48, 56/55

POTE generators: ~7/6 = 248.2710, ~5/4 = 390.6487

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

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== 13-limit ==

Comma list: 49/48, 56/55, 91/90

POTE generators: ~7/6 = 248.7559, ~5/4 = 389.5957

Mapping: [{{val| 1 0 2 2 5 -1 }}, {{val| 0 2 0 1 1 3 }}, {{val| 0 0 1 0 -1 1 }}]

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= Negric =

Comma list: 49/48, 225/224

POTE generators: ~15/14 = 125.6080, ~11/8 = 539.2342

Mapping: [{{val| 1 2 2 3 0 }}, {{val| 0 -4 3 -2 0 }}, {{val| 0 0 0 0 1 }}]

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== 13-limit ==

Comma list: 49/48, 65/64, 91/90

POTE generators: ~14/13 = 125.5675, ~11/8 = 538.4845

Mapping: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}, {{val| 0 0 0 0 1 0 }}]

@@ Line 1: / Line 1: @@
 __FORCETOC__
-'''Semiphore family''' is a rank-3 temperament family of 2.3.5.7 that tempers out 49/48 and thereby identifies the septimal minor third, 7/6, and the septimal whole tone, 8/7. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". Related to this is the 2.3.7-limit 49/48 temperament called "[[Chromatic pairs #Semaphore|semaphore]]," and the 2.3.5.7 49/48 and 81/80 temperament called "[[Meantone family #Godzilla|godzilla]]".
+'''Semiphore family''' is a rank-3 temperament family of 2.3.5.7 that tempers out 49/48 and thereby identifies the septimal minor third, 7/6, and the septimal whole tone, 8/7. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". Related to this is the 2.3.7-limit 49/48 temperament called "[[Slendro clan #Semaphore|semaphore]]", and the 2.3.5.7 49/48 and 81/80 temperament called "[[Meantone family #Godzilla|godzilla]]".
 = Semiphore =
 Comma list: 49/48
+POTE generators: ~7/6 = 250.3846, ~5/4 = 379.7035
 Mapping: [{{val| 1 0 2 2 }}, {{val| 0 2 0 1 }}, {{val| 0 0 1 0 }}]
@@ Line 19: / Line 21: @@
 = Selenium =
 Comma list: 49/48, 56/55
+POTE generators: ~7/6 = 248.2710, ~5/4 = 390.6487
 Mapping: [{{val| 1 0 2 2 5 }}, {{val| 0 2 0 1 1 }}, {{val| 0 0 1 0 -1 }}]
@@ Line 28: / Line 32: @@
 == 13-limit ==
 Comma list: 49/48, 56/55, 91/90
+POTE generators: ~7/6 = 248.7559, ~5/4 = 389.5957
 Mapping: [{{val| 1 0 2 2 5 -1 }}, {{val| 0 2 0 1 1 3 }}, {{val| 0 0 1 0 -1 1 }}]
@@ Line 37: / Line 43: @@
 = Negric =
 Comma list: 49/48, 225/224
+POTE generators: ~15/14 = 125.6080, ~11/8 = 539.2342
 Mapping: [{{val| 1 2 2 3 0 }}, {{val| 0 -4 3 -2 0 }}, {{val| 0 0 0 0 1 }}]
@@ Line 46: / Line 54: @@
 == 13-limit ==
 Comma list: 49/48, 65/64, 91/90
+POTE generators: ~14/13 = 125.5675, ~11/8 = 538.4845
 Mapping: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}, {{val| 0 0 0 0 1 0 }}]