Tetracot (temperament): Difference between revisions
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'''Tetracot''' is a 2.3.5 temperament that splits 3/2 into four flattened 10/9's | '''Tetracot''', 2.3.5[27 & 34], is a 2.3.5 temperament that splits 3/2 into four flattened 10/9's, so that: | ||
* 2 generators = a neutral third | |||
* 3 generators = 27/20 | |||
* 4 generators = 3/2 | |||
* 5 generators = 5/3 | |||
* 6 generators = a neutral seveneth | |||
* 7 generators = 81/80 | |||
* 8 generators = 9/8 | |||
* 9 generators = 5/4 | |||
== Extensions == | == Extensions == | ||
Revision as of 21:07, 28 February 2026
Tetracot, 2.3.5[27 & 34], is a 2.3.5 temperament that splits 3/2 into four flattened 10/9's, so that:
- 2 generators = a neutral third
- 3 generators = 27/20
- 4 generators = 3/2
- 5 generators = 5/3
- 6 generators = a neutral seveneth
- 7 generators = 81/80
- 8 generators = 9/8
- 9 generators = 5/4
Extensions
Tetracot has a number of strong extensions, but most of them are problematic in some way. This is because the Tetracot generator is, optimally, approximately 31/28 --- not easily interpretable as LCJI.
- Prime 13 can be added by equating (10/9)^2 (the neutral third) with 16/13.
- Prime 11 is often added by equating (10/9)^2 with 11/9, but this is questionable because it produces either a very sharp 11/8 or a flat 5/4.
- There isn't a canonical way to add prime 7; there are no less than 4 strong extensions to 2.3.5.7: Bunya (34d & 41), Monkey (34 & 41), Modus (27e & 34d), and Wollemia (27e & 34). The weak extension Octacot (27 & 41) splits the Tetracot generator into two semitones representing 21/20, thus equating three Octacot generators with 7/6.
