SN scale: Difference between revisions

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The simplest 4-SN scale is generated by iterating a) 4 times, leading to the scale abacabad. If we map the intervals introduced with a) as 2/1, 3/2, 7/6, and 15/14, we get the scale 15/14 7/6 5/4 3/2 45/28 7/4 15/8 2/1, with step signature (1,2,4,1), mapped to (6/5, 7/6, 15/14, 16/15).

== ~~Notation~~ ==

== Denoting SN scales ==

Where the [[Meantone]] tempered diatonic scale can be ~~labelled as~~ Meantone[7], we may instead describe it through its derivation as an SN scale through ~~labeling~~ it (2/1, 3/2: 81/80)[7], which specifies that a) introduces the intervals 2/1 and 3/2, and then b) is applied until a 7-note scale is reached, and that 81/80 is tempered out in the scale.

Where the [[Meantone]] tempered diatonic scale can be denoted Meantone[7], we may instead describe it through its derivation as an SN scale through denoting it (2/1, 3/2: 81/80)[7], which specifies that a) introduces the intervals 2/1 and 3/2, and then b) is applied until a 7-note scale is reached, and that 81/80 is tempered out in the scale.

The scale SNS (2/1, 3/2, 5/4: 225/224)[7] describes a [[Marvel]] tempered double harmonic scale, with step signatures (2,1,4) mapped to (~7/6, ~9/8, 16/15~15/14).

MET-24, as a (2.3.7.11.13) Parapyth tempered scale can be ~~labelled~~ ((2/1, 3/2)[12], 28/27~33/32: 352/351, 364/363))[24] (the simplest basis set for commas tempered out is chosen to specify the temperament), with step signatures (5, 12, 7) mapped to (~27/26, 28/27~33/32, ~64/63).

MET-24, as a (2.3.7.11.13) Parapyth tempered scale can be denoted ((2/1, 3/2)[12], 28/27~33/32: 352/351, 364/363))[24] (the simplest basis set for commas tempered out is chosen to specify the temperament), with step signatures (5, 12, 7) mapped to (~27/26, 28/27~33/32, ~64/63).

== Algorithm ==

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 The simplest 4-SN scale is generated by iterating a) 4 times, leading to the scale abacabad. If we map the intervals introduced with a) as 2/1, 3/2, 7/6, and 15/14, we get the scale 15/14 7/6 5/4 3/2 45/28 7/4 15/8 2/1, with step signature (1,2,4,1), mapped to (6/5, 7/6, 15/14, 16/15).
-== Notation ==
+== Denoting SN scales ==
-Where the [[Meantone]] tempered diatonic scale can be labelled as Meantone[7], we may instead describe it through its derivation as an SN scale through labeling it (2/1, 3/2: 81/80)[7], which specifies that a) introduces the intervals 2/1 and 3/2, and then b) is applied until a 7-note scale is reached, and that 81/80 is tempered out in the scale.
+Where the [[Meantone]] tempered diatonic scale can be denoted Meantone[7], we may instead describe it through its derivation as an SN scale through denoting it (2/1, 3/2: 81/80)[7], which specifies that a) introduces the intervals 2/1 and 3/2, and then b) is applied until a 7-note scale is reached, and that 81/80 is tempered out in the scale.
 The scale SNS (2/1, 3/2, 5/4: 225/224)[7] describes a [[Marvel]] tempered double harmonic scale, with step signatures (2,1,4) mapped to (~7/6, ~9/8, 16/15~15/14).
-MET-24, as a (2.3.7.11.13) Parapyth tempered scale can be labelled ((2/1, 3/2)[12], 28/27~33/32: 352/351, 364/363))[24] (the simplest basis set for commas tempered out is chosen to specify the temperament), with step signatures (5, 12, 7) mapped to (~27/26, 28/27~33/32, ~64/63).
+MET-24, as a (2.3.7.11.13) Parapyth tempered scale can be denoted ((2/1, 3/2)[12], 28/27~33/32: 352/351, 364/363))[24] (the simplest basis set for commas tempered out is chosen to specify the temperament), with step signatures (5, 12, 7) mapped to (~27/26, 28/27~33/32, ~64/63).
 == Algorithm ==

SN scale: Difference between revisions

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