Tetracot (temperament)
From Xenharmonic Reference
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 seventh
- 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 with 11/10, but this is questionable because it produces either a very sharp 11/8 (as in 27edo and 34edo) or a flat 5/4 (as in 41edo and 48edo).
- 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) is more elegant; it splits the Tetracot generator into two semitones representing 21/20, thus equating three Octacot generators with 7/6.
