Schisma: Difference between revisions

Line 20:

As the schisma is expressible as [[361/360|S19]]/([[1216/1215|S16/S18]])<sup>2</sup> and ([[513/512|S15/S20]])/([[1216/1215|S16/S18]]), we can derive the 12&53 temperament:

Subgroup: 2.3.5.19

[[Subgroup]]: 2.3.5.19

Patent EDO tunings: 12, 17, 24, 29, 36, 41, 53, 65, 77, 82, 89, 94, 101, 106, 118, 130, 135, 142, 147, 154, 159, 171, 183, 195, 207, 219, 248, 260, 272

CTE generator: 701.684{{cent}}

[[CTE]] generator: 701.684{{cent}}

===[[Garibaldi]]===

As the schisma is also equal to [[225/224|S15]]/([[5120/5103|S8/S9]]), we can derive the 41&53 temperament:

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

Patent EDO tunings: 12, 29, 41, 53, 82, 94, 106, 135, 147

CTE generator: 702.059{{cent}}

[[CTE]] generator: 702.059{{cent}}

==== 2.3.5.7.19[53&147] (garibaldi nestoria) ====

Line 49:

As the schisma also equals [[57375/57344|S15/S16]] * [[1701/1700|S18/S20]], we can derive the extremely accurate 12&41 temperament:

Subgroup: 2.3.5.7.17

[[Subgroup]]: 2.3.5.7.17

Patent EDO tunings < 300 (largest is 2548): 12, 29, 41, 53, 118, 130, 142, 159, 171, 183, 212, 224, 236, 289

CTE generators: (2/1,) 3/2 = 701.72{{cent}}, 7/4 = 968.831{{cent}}

[[CTE]] generators: (2/1,) 3/2 = 701.72{{cent}}, 7/4 = 968.831{{cent}}

==== 2.3.5.7.17.19[12&130&171] (unnamed Nestoria) ====

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

[[Subgroup]]: 2.3.5.7.17.19

Patent EDO tunings: 12, 29, 41, 53, 118, 130, 142, 159, 171, 183

CTE generators: (2/1,) 3/2 = 701.705{{cent}}, 7/4 = 968.928{{cent}}

[[CTE]] generators: (2/1,) 3/2 = 701.705{{cent}}, 7/4 = 968.928{{cent}}

== Trivia ==

@@ Line 20: / Line 20: @@
 As the schisma is expressible as [[361/360|S19]]/([[1216/1215|S16/S18]])<sup>2</sup> and ([[513/512|S15/S20]])/([[1216/1215|S16/S18]]), we can derive the 12&53 temperament:
-Subgroup: 2.3.5.19
+[[Subgroup]]: 2.3.5.19
 Patent EDO tunings: 12, 17, 24, 29, 36, 41, 53, 65, 77, 82, 89, 94, 101, 106, 118, 130, 135, 142, 147, 154, 159, 171, 183, 195, 207, 219, 248, 260, 272
-CTE generator: 701.684{{cent}}
+[[CTE]] generator: 701.684{{cent}}
 ===[[Garibaldi]]===
 As the schisma is also equal to [[225/224|S15]]/([[5120/5103|S8/S9]]), we can derive the 41&53 temperament:
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 Patent EDO tunings: 12, 29, 41, 53, 82, 94, 106, 135, 147
-CTE generator: 702.059{{cent}}
+[[CTE]] generator: 702.059{{cent}}
 ==== 2.3.5.7.19[53&147] (garibaldi nestoria) ====
@@ Line 49: / Line 49: @@
 As the schisma also equals [[57375/57344|S15/S16]] * [[1701/1700|S18/S20]], we can derive the extremely accurate 12&41 temperament:
-Subgroup: 2.3.5.7.17
+[[Subgroup]]: 2.3.5.7.17
 Patent EDO tunings < 300 (largest is 2548): 12, 29, 41, 53, 118, 130, 142, 159, 171, 183, 212, 224, 236, 289
-CTE generators: (2/1,) 3/2 = 701.72{{cent}}, 7/4 = 968.831{{cent}}
+[[CTE]] generators: (2/1,) 3/2 = 701.72{{cent}}, 7/4 = 968.831{{cent}}
 ==== 2.3.5.7.17.19[12&130&171] (unnamed Nestoria) ====
 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
+[[Subgroup]]: 2.3.5.7.17.19
 Patent EDO tunings: 12, 29, 41, 53, 118, 130, 142, 159, 171, 183
-CTE generators: (2/1,) 3/2 = 701.705{{cent}}, 7/4 = 968.928{{cent}}
+[[CTE]] generators: (2/1,) 3/2 = 701.705{{cent}}, 7/4 = 968.928{{cent}}
 == Trivia ==