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 "[[Chromatic pairs #Semaphore|semaphore]]," and the 2.3.5.7 49/48 and 81/80 temperament called "[[Meantone family #Godzilla|godzilla]]".
-Semiphore is a rank-3 temperament 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"]].
+= Semiphore =
+Comma list: 49/48
-Comma: 49/48
+Mapping: [{{val| 1 0 2 2 }}, {{val| 0 2 0 1 }}, {{val| 0 0 1 0 }}]
-Lattice basis: 7/6 0.7627 5/4 2.322
+Mapping: Generators: 2, 7/4, 5
-Angle(7/6, 5/4) = 90 degrees
+Lattice basis:
+: 7/6 length = 0.7627, 5/4 length = 2.322
+: Angle (7/6, 5/4) = 90 degrees
-Map: [&lt;1 0 2 2|, &lt;0 2 0 1|, &lt;0 0 1 0|]
+{{Val list|legend=1| 4, 5, 9, 10, 15, 19 }}
-Generators: 2, 7/4, 5
-EDOs: 4, 5, 9, 10, 15, 19
 Badness: 0.000116
-=Selenium=
+= Selenium =
-Commas: 49/48, 56/55
+Comma list: 49/48, 56/55
-Map: [&lt;1 0 2 2 5|, &lt;0 2 0 1 1|, &lt;0 0 1 0 -1|]
+Mapping: [{{val| 1 0 2 2 5 }}, {{val| 0 2 0 1 1 }}, {{val| 0 0 1 0 -1 }}]
-EDOs: 4, 5, 9, 10, 15, 19, 24, 34
+{{Val list|legend=1| 4, 5, 9, 10, 15, 19, 24, 34 }}
 Badness: 0.000665
-==13-limit==
+== 13-limit ==
-Commas: 49/48, 56/55, 91/90
+Comma list: 49/48, 56/55, 91/90
-Map: [&lt;1 0 2 2 5 -1|, &lt;0 2 0 1 1 3|, &lt;0 0 1 0 -1 1|]
+Mapping: [{{val| 1 0 2 2 5 -1 }}, {{val| 0 2 0 1 1 3 }}, {{val| 0 0 1 0 -1 1 }}]
-EDOs: 5, 9, 10, 15, 19, 24, 34
+{{Val list|legend=1| 5, 9, 10, 15, 19, 24, 34 }}
 Badness: 0.000787
-=Negric=
+= Negric =
-Commas: 49/48, 225/224
+Comma list: 49/48, 225/224
-Map: [&lt;1 2 2 3 0|, &lt;0 -4 3 -2 0|, &lt;0 0 0 0 1|]
+Mapping: [{{val| 1 2 2 3 0 }}, {{val| 0 -4 3 -2 0 }}, {{val| 0 0 0 0 1 }}]
-EDOs: 9, 10, 19, 29, 38d, 67cde
+{{Val list|legend=1| 9, 10, 19, 29, 38d, 67cde }}
 Badness: 0.001087
-==13-limit==
+== 13-limit ==
-Commas: 49/48, 65/64, 91/90
+Comma list: 49/48, 65/64, 91/90
-Map: [&lt;1 2 2 3 0 4|, &lt;0 -4 3 -2 0 -3|, &lt;0 0 0 0 1 0|]
+Mapping: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}, {{val| 0 0 0 0 1 0 }}]
-EDOs: 9, 10, 19, 29, 38df, 67cdef
+{{Val list|legend=1| 9, 10, 19, 29, 38df, 67cdef }}
 Badness: 80.756
+[[Category:Theory]]
+[[Category:Temperament family]]
+[[Category:Semiphore]]
+[[Category:Rank 3]]