Tetracot

Tetracot, in this article, is the rank-2 regular temperament for the 2.3.5.11.13 subgroup defined by tempering out 100/99, 144/143, and 243/242.

It can be seen as implying a rank-2 tuning which is generated by a sub-major second of about 176 cents which represents both 10/9 and 11/10. It is so named because the generator is a quarter of fifth: four generators make a fifth which approximates 3/2, which cannot occur in 12edo. Equal temperaments that support tetracot include 27, 34, and 41.

Tetracot has many extensions for the 7-, 11- and 13-limit. See Tetracot extensions.

See Tetracot family or No-sevens subgroup temperaments #Tetracot for more technical data.

Interval chain

Tetracot is considered as a cluster temperament with seven clusters of notes in an octave. The chroma interval between adjacent notes in each cluster represents 40/39 ~ 45/44 ~ 55/54 ~ 65/64 ~ 66/65 ~ 81/80 ~ 121/120 all tempered together. In the following table, prime harmonics are in bold.

#	Cents*	Approximate Ratios
0	0.00	1/1
1	176.20	11/10, 10/9
2	352.39	11/9, 16/13
3	528.59	15/11
4	704.79	3/2
5	880.98	5/3
6	1057.18	11/6, 24/13
7	33.38	55/54, 45/44, 40/39
8	209.57	9/8
9	385.77	5/4
10	561.96	11/8, 18/13
11	738.16	20/13
12	914.36	22/13
13	1090.55	15/8
14	66.75	33/32, 27/26, 25/24
15	242.95	15/13