Tetracot: Difference between revisions

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#REDIRECT [[Tetracot family #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 [[Generator|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 {{EDOs|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 ==
{| class="wikitable right-1"
|-
! Generators
! Cents<sup>*</sup>
! 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
|}
: <sup>*</sup> in 2.3.5.11.13 POTE tuning
 
=== Monkey ===
{| class="wikitable right-1"
|-
! Generators
! Cents<sup>*</sup>
! 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
|}
: <sup>*</sup> in 13-limit POTE tuning
 
=== Bunya ===
{| class="wikitable right-1"
|-
! Generators
! Cents<sup>*</sup>
! 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
|}
: <sup>*</sup> in 13-limit POTE tuning
 
=== Modus ===
{| class="wikitable right-1"
|-
! Generators
! Cents<sup>*</sup>
! 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
|}
: <sup>*</sup> in 13-limit POTE tuning
 
=== Wollemia ===
{| class="wikitable right-1"
|-
! Generators
! Cents<sup>*</sup>
! 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
|}
: <sup>*</sup> in 13-limit POTE tuning


[[Category:Temperaments]]
[[Category:Temperaments]]
[[Category:Tetracot family]]
[[Category:Tetracot family]]
[[Category:Index of temperaments]]

Revision as of 12:40, 12 March 2022

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
Retrieved from "https://en.xen.wiki/index.php?title=Tetracot&oldid=89392"