Semaphoresmic family: Difference between revisions

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The '''semaphoresmic family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] [[49/48]] in the full [[7-limit]], 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-subgroup {49/48} temperament [[Semaphoresmic clan #Semaphore|semaphore]], and the 7-limit {49/48, 81/80} temperament [[Semaphoresmic clan #Godzilla|godzilla]].

== ~~Semiphore~~ ==

== Semaphoresmic a.k.a. semiphore ==

~~This temperament is also known as '''semaphoresmic'''.~~

[[Subgroup]]: 2.3.5.7

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: error map: {{val| 0.000 -0.577 -3.962 -18.137 }}

{{Optimal ET sequence|legend=1| 4, 5, 9, 10, 14c, 15, 19, 48d, 53d, 67cdd, 86cdd }}

[[Badness]] (Sintel): 0.510

=== 2.3.5.7.13 subgroup ===

Subgroup: 2.3.5.7.13

Comma list: 49/48, 91/90

Sval mapping: {{mapping| 1 0 0 2 -1 | 0 2 0 1 3 | 0 0 1 0 1 }}

Optimal tunings:

* WE: ~2 = 1202.7771, ~7/4 = 951.9629, ~5/4 = 381.0131

* CWE: ~2 = 1200.0000, ~7/4 = 950.6703, ~5/4 = 382.2972

{{Optimal ET sequence|legend=0| 5, 9, 10, 14cf, 15, 19, 48df, 53d, 67cddf, 72dd }}

Badness (Sintel): 0.380

== Selenium ==

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 The '''semaphoresmic family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] [[49/48]] in the full [[7-limit]], 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-subgroup {49/48} temperament [[Semaphoresmic clan #Semaphore|semaphore]], and the 7-limit {49/48, 81/80} temperament [[Semaphoresmic clan #Godzilla|godzilla]].
-== Semiphore ==
+== Semaphoresmic a.k.a. semiphore ==
-This temperament is also known as '''semaphoresmic'''.
 [[Subgroup]]: 2.3.5.7
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 : error map: {{val| 0.000 -0.577 -3.962 -18.137 }}
-{{Optimal ET sequence|legend=1| 4, 5, 9, 10, 14c, 15, 19 }}
+{{Optimal ET sequence|legend=1| 4, 5, 9, 10, 14c, 15, 19, 48d, 53d, 67cdd, 86cdd }}
 [[Badness]] (Sintel): 0.510
+=== 2.3.5.7.13 subgroup ===
+Subgroup: 2.3.5.7.13
+Comma list: 49/48, 91/90
+Sval mapping: {{mapping| 1 0 0 2 -1 | 0 2 0 1 3 | 0 0 1 0 1 }}
+Optimal tunings:
+* WE: ~2 = 1202.7771, ~7/4 = 951.9629, ~5/4 = 381.0131
+* CWE: ~2 = 1200.0000, ~7/4 = 950.6703, ~5/4 = 382.2972
+{{Optimal ET sequence|legend=0| 5, 9, 10, 14cf, 15, 19, 48df, 53d, 67cddf, 72dd }}
+Badness (Sintel): 0.380
 == Selenium ==