Schisma: Difference between revisions

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Garibaldi tempers out [[225/224]] (S15) and [[5120/5103]] ([[64/63|S8]]/[[81/80|S9]]), and can be described as the 41 & 53 temperament in the 7-limit that equates the two aforementioned commas (S8 = (8/7)/(9/8) = 64/63 and S9 = (9/8)/(10/9) = 81/80) into a general purpose comma reached at 12 fifths via (9/8)<sup>6 / (2/1). This is derived ~~since~~ the schisma is also equal to [[225/224|S15]]/([[5120/5103|S8/S9]]).

Garibaldi tempers out [[225/224]] (S15) and [[5120/5103]] ([[64/63|S8]]/[[81/80|S9]]), and can be described as the 41 & 53 temperament in the 7-limit that equates the two aforementioned commas (S8 = (8/7)/(9/8) = 64/63 and S9 = (9/8)/(10/9) = 81/80) into a general purpose comma reached at 12 fifths via (9/8)<sup>6</sup> / (2/1). This is derived as the schisma is also equal to [[225/224|S15]]/([[5120/5103|S8/S9]]).

==== 2.3.5.7.19 subgroup ====

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==== 2.3.5.7.17.19 12 & 118 & 171 (unnamed) ====

By tempering [[1216/1215|S16/S18]] we equate [[225/224|S15]] with [[400/399|S20]] (tempering the other comma of Nestoria) because of S15~S16~S18~S20 ~~(meaning the [[superparticular interval]]s in 14:15:16:17:18:19:20:21 are mapped equidistantly, so requiring a large edo tuning)~~, leading to:

By tempering [[1216/1215|S16/S18]] we equate [[225/224|S15]] with [[400/399|S20]] (tempering the other comma of Nestoria) because of S15~S16~S18~S20, leading to:

[[Subgroup]]: 2.3.5.7.17.19

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[[Category:Schismic]]

[[Category:Commas named for their regular temperament properties]]

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 {{Main| Garibaldi }}
-Garibaldi tempers out [[225/224]] (S15) and [[5120/5103]] ([[64/63|S8]]/[[81/80|S9]]), and can be described as the 41 & 53 temperament in the 7-limit that equates the two aforementioned commas (S8 = (8/7)/(9/8) = 64/63 and S9 = (9/8)/(10/9) = 81/80) into a general purpose comma reached at 12 fifths via (9/8)<sup>6 / (2/1). This is derived since the schisma is also equal to [[225/224|S15]]/([[5120/5103|S8/S9]]).
+Garibaldi tempers out [[225/224]] (S15) and [[5120/5103]] ([[64/63|S8]]/[[81/80|S9]]), and can be described as the 41 & 53 temperament in the 7-limit that equates the two aforementioned commas (S8 = (8/7)/(9/8) = 64/63 and S9 = (9/8)/(10/9) = 81/80) into a general purpose comma reached at 12 fifths via (9/8)<sup>6</sup> / (2/1). This is derived as the schisma is also equal to [[225/224|S15]]/([[5120/5103|S8/S9]]).
 ==== 2.3.5.7.19 subgroup ====
@@ Line 53: / Line 53: @@
 ==== 2.3.5.7.17.19 12 & 118 & 171 (unnamed) ====
-By tempering [[1216/1215|S16/S18]] we equate [[225/224|S15]] with [[400/399|S20]] (tempering the other comma of Nestoria) because of S15~S16~S18~S20 (meaning the [[superparticular interval]]s in 14:15:16:17:18:19:20:21 are mapped equidistantly, so requiring a large edo tuning), leading to:
+By tempering [[1216/1215|S16/S18]] we equate [[225/224|S15]] with [[400/399|S20]] (tempering the other comma of Nestoria) because of S15~S16~S18~S20, leading to:
 [[Subgroup]]: 2.3.5.7.17.19
@@ Line 83: / Line 83: @@
 [[Category:Schismic]]
+[[Category:Commas named for their regular temperament properties]]