Schisma: Difference between revisions

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Nestoria tempers out [[361/360]] and [[513/512]], and can be described as the 12 & 53 temperament in the 2.3.5.19 subgroup. This is derived since the schisma is expressible as [[361/360|S19]]/([[1216/1215|S16/S18]])<sup>2</sup> and ([[513/512|S15/S20]])/([[1216/1215|S16/S18]]).

Nestoria tempers out [[361/360]] (S19) and [[513/512]] (S15/S20), and can be described as the 12 & 53 temperament in the 2.3.5.19 subgroup. This is derived since the schisma is expressible as [[361/360|S19]]/([[1216/1215|S16/S18]])<sup>2</sup> and ([[513/512|S15/S20]])/([[1216/1215|S16/S18]]).

=== Garibaldi ===

Garibaldi tempers out [[225/224]] and [[5120/5103]], and can be described as the 41 & 53 temperament in the 7-limit. 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]] (S8/S9), and can be described as the 41 & 53 temperament in the 7-limit. This is derived since the schisma is also equal to [[225/224|S15]]/([[5120/5103|S8/S9]]).

==== 2.3.5.7.19 subgroup ====

Adding nestoria to garibaldi (tempering [[400/399~~|S20~~]]) results in an extremely elegant temperament which has all of the same patent tunings that garibaldi has but which includes a mapping for 19 through nestoria.

Adding nestoria to garibaldi (tempering [[400/399]] (S20)) results in an extremely elegant temperament which has all of the same patent tunings that garibaldi has but which includes a mapping for 19 through nestoria.

=== 2.3.5.7.17 12 & 118 & 171 (unnamed) ===

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 {{See also| No-sevens subgroup temperaments #Nestoria }}
-Nestoria tempers out [[361/360]] and [[513/512]], and can be described as the 12 & 53 temperament in the 2.3.5.19 subgroup. This is derived since the schisma is expressible as [[361/360|S19]]/([[1216/1215|S16/S18]])<sup>2</sup> and ([[513/512|S15/S20]])/([[1216/1215|S16/S18]]).
+Nestoria tempers out [[361/360]] (S19) and [[513/512]] (S15/S20), and can be described as the 12 & 53 temperament in the 2.3.5.19 subgroup. This is derived since the schisma is expressible as [[361/360|S19]]/([[1216/1215|S16/S18]])<sup>2</sup> and ([[513/512|S15/S20]])/([[1216/1215|S16/S18]]).
 === Garibaldi ===
 {{Main| Garibaldi }}
-Garibaldi tempers out [[225/224]] and [[5120/5103]], and can be described as the 41 & 53 temperament in the 7-limit. 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]] (S8/S9), and can be described as the 41 & 53 temperament in the 7-limit. This is derived since the schisma is also equal to [[225/224|S15]]/([[5120/5103|S8/S9]]).
 ==== 2.3.5.7.19 subgroup ====
 {{Main| Garibaldi }}
-Adding nestoria to garibaldi (tempering [[400/399|S20]]) results in an extremely elegant temperament which has all of the same patent tunings that garibaldi has but which includes a mapping for 19 through nestoria.
+Adding nestoria to garibaldi (tempering [[400/399]] (S20)) results in an extremely elegant temperament which has all of the same patent tunings that garibaldi has but which includes a mapping for 19 through nestoria.
 === 2.3.5.7.17 12 & 118 & 171 (unnamed) ===