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 EDOs.
Tetracot has many extensions for 7, 11 and 13-limit include monkey (34&41), bunya (34d&41), modus (27e&34d) and wollemia (27e&34).
See Tetracot family or No-sevens subgroup temperaments #Tetracot for more technical data.
Intervals
| Generators
|
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
|
45/44
|
| 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
|
- * in 2.3.5.11.13 POTE tuning
Monkey
| Generators
|
Cents*
|
Approximate ratios
|
| 0
|
0.00
|
1/1
|
| 1
|
175.62
|
11/10, 10/9
|
| 2
|
351.24
|
11/9, 16/13
|
| 3
|
526.87
|
15/11
|
| 4
|
702.49
|
3/2
|
| 5
|
878.11
|
5/3
|
| 6
|
1053.73
|
11/6, 24/13
|
| 7
|
29.36
|
|
| 8
|
204.98
|
9/8
|
| 9
|
380.60
|
5/4
|
| 10
|
556.22
|
11/8, 18/13
|
| 11
|
731.85
|
20/13
|
| 12
|
907.47
|
22/13
|
| 13
|
1083.09
|
13/7, 15/8
|
| 14
|
58.71
|
|
| 15
|
234.34
|
8/7, 15/13
|
| 16
|
409.96
|
|
| 17
|
585.58
|
|
| 18
|
761.20
|
|
| 19
|
936.83
|
12/7
|
| 20
|
1112.45
|
|
| 21
|
88.07
|
|
| 22
|
263.69
|
|
| 23
|
439.31
|
9/7
|
| 24
|
614.94
|
10/7
|
| 25
|
790.56
|
11/7
|
| 26
|
966.18
|
|
| 27
|
1141.80
|
|
| 28
|
117.43
|
15/14
|
- * in 13-limit POTE tuning
Bunya
| Generators
|
Cents*
|
Approximate ratios
|
| 0
|
0.00
|
1/1
|
| 1
|
175.89
|
11/10, 10/9
|
| 2
|
351.77
|
11/9, 16/13
|
| 3
|
527.66
|
15/11
|
| 4
|
703.54
|
3/2
|
| 5
|
879.43
|
5/3
|
| 6
|
1055.31
|
11/6, 24/13
|
| 7
|
31.20
|
|
| 8
|
207.09
|
9/8
|
| 9
|
382.97
|
5/4
|
| 10
|
558.86
|
11/8, 18/13
|
| 11
|
734.74
|
20/13
|
| 12
|
910.63
|
22/13
|
| 13
|
1086.52
|
28/15, 15/8
|
| 14
|
62.40
|
|
| 15
|
238.29
|
15/13
|
| 16
|
414.17
|
14/11
|
| 17
|
590.06
|
7/5
|
| 18
|
765.94
|
14/9
|
| 19
|
941.83
|
|
| 20
|
1117.72
|
|
| 21
|
93.60
|
|
| 22
|
269.49
|
7/6
|
| 23
|
445.37
|
|
| 24
|
621.26
|
|
| 25
|
797.15
|
|
| 26
|
973.03
|
7/4
|
| 27
|
1148.92
|
|
| 28
|
124.80
|
14/13
|
- * in 13-limit POTE tuning
Modus
| Generators
|
Cents*
|
Approximate ratios
|
| 0
|
0.00
|
1/1
|
| 1
|
176.95
|
11/10, 10/9
|
| 2
|
353.91
|
11/9, 16/13
|
| 3
|
530.86
|
15/11
|
| 4
|
707.81
|
3/2
|
| 5
|
884.77
|
5/3
|
| 6
|
1061.72
|
11/6, 24/13, 13/7
|
| 7
|
38.67
|
|
| 8
|
215.63
|
9/8, 8/7
|
| 9
|
392.58
|
5/4
|
| 10
|
569.53
|
11/8, 18/13
|
| 11
|
746.49
|
20/13
|
| 12
|
923.44
|
22/13, 12/7
|
| 13
|
1100.39
|
15/8
|
| 14
|
77.35
|
|
| 15
|
254.30
|
15/13
|
| 16
|
431.25
|
9/7
|
| 17
|
608.20
|
10/7
|
| 18
|
785.16
|
11/7
|
| 19
|
962.11
|
|
| 20
|
1139.06
|
|
| 21
|
116.02
|
15/14
|
- * in 13-limit POTE tuning
Wollemia
| Generators
|
Cents*
|
Approximate ratios
|
| 0
|
0.00
|
1/1
|
| 1
|
177.23
|
11/10, 10/9
|
| 2
|
354.46
|
11/9, 16/13
|
| 3
|
531.69
|
15/11
|
| 4
|
708.92
|
3/2
|
| 5
|
886.16
|
5/3
|
| 6
|
1063.39
|
11/6, 24/13, 28/15
|
| 7
|
40.62
|
|
| 8
|
217.85
|
9/8
|
| 9
|
395.08
|
5/4, 14/11
|
| 10
|
572.31
|
11/8, 18/13, 7/5
|
| 11
|
749.54
|
20/13, 14/9
|
| 12
|
926.77
|
22/13
|
| 13
|
1104.01
|
15/8
|
| 14
|
81.24
|
|
| 15
|
258.47
|
15/13, 7/6
|
| 16
|
435.70
|
|
| 17
|
612.93
|
|
| 18
|
790.16
|
|
| 19
|
967.39
|
7/4
|
| 20
|
1144.62
|
|
| 21
|
121.86
|
14/13
|
- * in 13-limit POTE tuning