Semaphoresmic family: Difference between revisions

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'''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 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 ==

[[Subgroup]]: 2.3.5.7

Subgroup: 2.3.5.7

[[Comma list]]: 49/48

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

~~Mapping~~ generators: ~2, ~7/4, ~5

: mapping generators: ~2, ~7/4, ~5

Lattice basis:

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: Angle (7/6, 5/4) = 90 degrees

[[POTE ~~generator~~]]s: ~7/6 = 250.3846, ~5/4 = 379.7035

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 250.3846, ~5/4 = 379.7035

[[Badness]]: 0.116 × 10<sup>-3</sup>

~~</div></div>~~

== Selenium ==

Subgroup: 2.3.5.7.11

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 49/48, 56/55

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

[[POTE ~~generator~~]]s: ~7/6 = 248.2710, ~5/4 = 390.6487

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 248.2710, ~5/4 = 390.6487

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

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

Mapping: {{mapping| 1 0 2 2 5 -1 | 0 2 0 1 1 3 | 0 0 1 0 -1 1 }}

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

Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 248.7559, ~5/4 = 389.5957

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== Negric ==

[[Subgroup]]: 2.3.5.7.11

Subgroup: 2.3.5.7.11

[[Comma list]]: 49/48, 225/224

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

[[POTE ~~generator~~]]s: ~15/14 = 125.6080, ~11/8 = 539.2342

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~15/14 = 125.6080, ~11/8 = 539.2342

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

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

Mapping: {{mapping| 1 2 2 3 0 4 | 0 -4 3 -2 0 -3 | 0 0 0 0 1 0 }}

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

Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 125.5675, ~11/8 = 538.4845

@@ Line 1: / Line 1: @@
-'''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 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  ==
+[[Subgroup]]: 2.3.5.7
-Subgroup: 2.3.5.7
 [[Comma list]]: 49/48
-[[Mapping]]: [{{val| 1 0 2 2 }}, {{val| 0 2 0 1 }}, {{val| 0 0 1 0 }}]
+{{Mapping|legend=1| 1 0 2 2 | 0 2 0 1 | 0 0 1 0 }}
-Mapping generators: ~2, ~7/4, ~5
+: mapping generators: ~2, ~7/4, ~5
 Lattice basis:
@@ Line 15: / Line 14: @@
 : Angle (7/6, 5/4) = 90 degrees
-[[POTE generator]]s: ~7/6 = 250.3846, ~5/4 = 379.7035
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 250.3846, ~5/4 = 379.7035
 {{Optimal ET sequence|legend=1| 4, 5, 9, 10, 14c, 15, 19 }}
 [[Badness]]: 0.116 × 10<sup>-3</sup>
-</div></div>
 == Selenium  ==
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 49/48, 56/55
-[[Mapping]]: [{{val| 1 0 2 2 5 }}, {{val| 0 2 0 1 1 }}, {{val| 0 0 1 0 -1 }}]
+{{Mapping|legend=1| 1 0 2 2 5 | 0 2 0 1 1 | 0 0 1 0 -1 }}
-[[POTE generator]]s: ~7/6 = 248.2710, ~5/4 = 390.6487
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 248.2710, ~5/4 = 390.6487
 {{Optimal ET sequence|legend=1| 4, 5, 9, 10, 15, 19, 24, 34 }}
@@ Line 41: / Line 38: @@
 Comma list: 49/48, 56/55, 91/90
-Mapping: [{{val| 1 0 2 2 5 -1 }}, {{val| 0 2 0 1 1 3 }}, {{val| 0 0 1 0 -1 1 }}]
+Mapping: {{mapping| 1 0 2 2 5 -1 | 0 2 0 1 1 3 | 0 0 1 0 -1 1 }}
-POTE generators: ~7/6 = 248.7559, ~5/4 = 389.5957
+Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 248.7559, ~5/4 = 389.5957
 {{Optimal ET sequence|legend=1| 5, 9, 10, 15, 19, 24, 34 }}
@@ Line 50: / Line 47: @@
 == Negric  ==
+[[Subgroup]]: 2.3.5.7.11
-Subgroup: 2.3.5.7.11
 [[Comma list]]: 49/48, 225/224
-[[Mapping]]: [{{val| 1 2 2 3 0 }}, {{val| 0 -4 3 -2 0 }}, {{val| 0 0 0 0 1 }}]
+{{Mapping|legend=1| 1 2 2 3 0 | 0 -4 3 -2 0 | 0 0 0 0 1 }}
-[[POTE generator]]s: ~15/14 = 125.6080, ~11/8 = 539.2342
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~15/14 = 125.6080, ~11/8 = 539.2342
 {{Optimal ET sequence|legend=1| 9, 10, 19, 29, 38d, 67cde }}
@@ Line 69: / Line 65: @@
 Comma list: 49/48, 65/64, 91/90
-Mapping: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}, {{val| 0 0 0 0 1 0 }}]
+Mapping: {{mapping| 1 2 2 3 0 4 | 0 -4 3 -2 0 -3 | 0 0 0 0 1 0 }}
-POTE generators: ~14/13 = 125.5675, ~11/8 = 538.4845
+Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 125.5675, ~11/8 = 538.4845
 {{Optimal ET sequence|legend=1| 9, 10, 19, 29, 38df, 67cdef }}