Tertiaseptal: Difference between revisions

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<sup>a</sup> in 11-limit POTE tuning
<sup>a</sup> in 11-limit POTE tuning

Revision as of 03:52, 28 January 2019

Tertiaseptal is a temperament for the 7, 11, 13, and 17 limit. EDOs that support tertiaseptal include 31edo, 140edo, and 171edo.

See Breedsmic temperaments for more information.

Interval chain

Tertiaseptal and tertia

generator cents value a
(octave-reduced) 		17-limit ratio
(octave-reduced)
tertiaseptal
(31&171) 		tertia
(31&140)
1 77.2 117/112, 256/245, 68/65 117/112, 256/245, 68/65, 22/21
2 154.4 130/119, 35/32 12/11, 130/119, 35/32
3 231.6 8/7
4 308.8 117/98, 140/117
5 386.0 5/4
6 463.1 17/13
7 540.3 175/128 15/11, 175/128
8 617.5 10/7
9 694.7 112/75
10 771.9 25/16
11 849.1 44/27, 80/49, 49/30, 85/52, 18/11 80/49, 49/30, 85/52
12 926.3 128/75
13 1003.5 25/14
14 1080.7 28/15
15 1157.9 39/20 39/20, 88/45
16 35.1 55/54, 52/51, 51/50, 50/49, 49/48, 45/44 56/55, 52/51, 51/50, 50/49, 49/48
17 112.3 16/15
18 189.4 39/35
19 266.6 7/6
20 343.8 39/32 39/32, 11/9
21 421.0 51/40 14/11, 51/40
22 498.2 4/3
23 575.4 39/28
24 652.6 35/24 16/11, 35/24
25 729.8 32/21
26 807.0 51/32 35/22, 51/32
27 884.2 5/3
28 961.4 68/39
29 1038.6 51/28 20/11, 51/28
30 1115.7 40/21, 21/11 40/21
31 1192.9
32 70.1 26/25, 25/24
33 147.3 49/45, 12/11 49/45
34 224.5 91/80 25/22, 91/80
35 301.7 25/21
36 378.9 56/45, 96/77 56/45
37 456.1 13/10
38 533.3 34/25, 15/11 34/25
39 610.5 64/45
40 687.7 52/35
41 764.8 14/9
42 842.0 13/8
43 919.2 17/10
44 996.4 16/9
45 1073.6 13/7
46 1150.8 68/35, 35/18 64/33, 68/35, 35/18
47 28.0 65/64, 64/63, 56/55 78/77, 65/64, 64/63, 55/54
48 105.2 17/16
49 182.4 10/9
50 259.6 65/56, 64/55 65/56
51 336.8 17/14
52 414.0 80/63, 14/11 80/63
53 491.1 65/49
54 568.3 25/18
55 645.5 16/11
56 722.7 85/56 50/33, 85/56
57 799.9 100/63, 35/22 100/63
58 877.1 128/77
59 954.3 26/15
60 1031.5 136/75, 20/11 136/75
61 1108.7 91/48, 256/135
62 1185.9 208/105 196/99, 208/105
63 63.1 28/27
64 140.3 13/12
65 217.4 17/15, 25/22 17/15
66 294.6 32/27 13/11, 32/27
67 371.8 26/21
68 449.0 35/27
69 526.2 65/48
70 603.4 17/12
71 680.6 40/27
72 757.8 65/42 17/11, 65/42
73 835.0 34/21
74 912.2 56/33
75 989.4 39/22 136/77, 85/48
76 1066.6 50/27
77 1143.7 64/33 85/44
78 20.9 91/90, 85/84, 78/77 100/99, 91/90, 85/84
79 98.1 35/33
80 175.3 195/176
81 252.5 52/45
82 329.7 40/33
83 406.9 91/72
84 484.1 119/90
85 561.3 112/81
86 638.5 13/9
87 715.7 68/45, 50/33 68/45
88 792.8 128/81 52/33, 128/81
89 870.0 119/72
90 947.2 140/81
91 1024.4 65/36
92 1101.6 17/9
93 1178.8 160/81, 196/99, 240/121 65/33, 160/81
94 56.0 91/88 34/33
95 133.2 68/63
96 210.4 112/99
97 287.6 13/11
98 364.8 68/55
99 442.0 128/99
100 519.1 104/77
101 596.3
102 673.5
103 750.7 17/11
104 827.9 160/99
105 905.1
106 982.3 136/77
107 1059.5
108 1136.7 52/27, 85/44 52/27
109 13.9 100/99
110 91.1 128/121, 256/243 104/99, 256/243
111 168.3
112 245.4
113 322.6
114 399.8 34/27
115 477.0
116 554.2
117 631.4
118 708.6
119 785.8 52/33
120 863.0
121 940.2
122 1017.4
123 1094.5
124 1171.7 65/33
125 48.9 34/33

a in 7-limit POTE tuning

Hemitert

generator cents value a
(octave-reduced) 		11-limit ratio
(octave-reduced)
1 38.6 45/44
2 77.2 256/245
3 115.8
4 154.4 35/32
5 193.0
6 231.6 8/7
7 270.2
8 308.8
9 347.4 11/9
10 386.0 5/4
11 424.6
12 463.1 64/49
13 501.7
14 540.3
15 578.9
16 617.5 10/7
17 656.1
18 694.7
19 733.3
20 771.9 25/16
21 810.5
22 849.1
23 887.7
24 926.3
25 964.9
26 1003.5 25/14
27 1042.1
28 1080.7 28/15
29 1119.3 21/11
30 1157.9
31 1196.5
32 35.1 50/49, 49/48
33 73.7
34 112.2 16/15
35 150.8 12/11
36 189.4
37 228.0
38 266.6 7/6
39 305.2
40 343.8
41 382.4
42 421.0
43 459.6
44 498.2 4/3
45 536.8 15/11
46 575.4
47 614.0
48 652.6
49 691.2
50 729.8 32/21
51 768.4
52 807.0
53 845.6
54 884.2 5/3
55 922.8
56 961.4
57 999.9
58 1038.5
59 1077.1
60 1115.7 40/21
61 1154.3
62 1192.9
63 31.5
64 70.1 25/24
65 108.7
66 147.3
67 185.9
68 224.5
69 263.1
70 301.7
71 340.3
72 378.9
73 417.5 14/11
74 456.1
75 494.7
76 533.3
77 571.9
78 610.5
79 649.1 16/11
80 687.6
81 726.2
82 764.8 14/9
83 803.4
84 842.0
85 880.6
86 919.2
87 957.8
88 996.4 16/9
89 1035.0 20/11
90 1073.6
91 1112.2
92 1150.8
93 1189.4
94 28.0 64/63
95 66.6
96 105.2
97 143.8
98 182.4 10/9

a in 11-limit POTE tuning

Tuning spectrum by Eigenmonzos

Tertiaseptal

Eigenmonzo Septimal
whole tone 		Major third Perfect fifth
4/3 231.5516 385.9193 701.9550
5/4 231.7882 386.3137 700.2197
6/5 231.5954 385.9924 701.6336
7/5 231.5579 385.9299 701.9085
7/6 231.6112 386.0187 701.5179
8/7 231.1741 385.2902 704.7233
9/7 231.5792 385.9654 701.7524
10/9 231.5757 385.9596 701.7779
11/8 231.7463 386.2438 700.5272
11/9 232.5251 387.5418 694.8159
11/10 231.7498 386.2496 700.5016
12/11 231.8761 386.4602 699.5753
14/11 231.7793 386.2988 700.2851
13/10 231.4228 385.7046 702.8998
13/11 231.6250 386.0417 701.4164
13/12 231.4956 385.8260 702.3656
14/13 231.4468 385.7446 702.7236
16/13 231.4663 385.7771 702.5807
18/13 231.5099 385.8499 702.2606
15/11 231.8645 386.4409 699.6601
15/13 231.4708 385.7847 702.5475
15/14 231.5480 385.9133 701.9816
16/15 231.4820 385.8033 702.4654
17/13 232.2139 387.0231 697.0983
17/14 231.5370 385.8950 702.0618
17/15 231.5394 385.8990 702.0445
17/16 231.5597 385.9329 701.8954
18/17 231.5558 385.9264 701.9239
20/17 231.5331 385.8886 702.0903
22/17 231.6593 386.0989 701.1648
24/17 231.5572 385.9286 701.9142

Tertia

Eigenmonzo Septimal
whole tone 		Major third Perfect fifth
4/3 231.5516 385.9193 701.9550
5/4 231.7882 386.3137 700.2197
6/5 231.5954 385.9924 701.6336
7/5 231.5579 385.9299 701.9085
7/6 231.6112 386.0187 701.5179
8/7 231.1741 385.2902 704.7233
9/7 231.5792 385.9654 701.7524
10/9 231.5757 385.9596 701.7779
11/8 231.0853 385.1421 705.3748
11/9 232.1112 386.8520 697.8513
11/10 231.2065 385.3441 704.4860
12/11 225.9556 376.5926 742.9924
14/11 231.0726 385.1209 705.4678
13/10 231.4228 385.7046 702.8998
13/11 231.3277 385.5462 703.5968
13/12 231.4956 385.8260 702.3656
14/13 231.4468 385.7446 702.7236
16/13 231.4663 385.7771 702.5807
18/13 231.5099 385.8499 702.2606
15/11 230.1218 383.5363 712.4404
15/13 231.4708 385.7847 702.5475
15/14 231.5480 385.9133 701.9816
16/15 231.4820 385.8033 702.4654
17/13 232.2139 387.0231 697.0983
17/14 231.5370 385.8950 702.0618
17/15 231.5394 385.8990 702.0445
17/16 231.5597 385.9329 701.8954
18/17 231.5558 385.9264 701.9239
20/17 231.5331 385.8886 702.0903
22/17 231.4016 385.6693 703.0552
24/17 231.5572 385.9286 701.9142

Hemitert

Eigenmonzo Septimal
whole tone 		Major third Perfect fifth
4/3 231.5516 385.9193 701.9550
5/4 231.7882 386.3137 700.2197
6/5 231.5954 385.9924 701.6336
7/5 231.5579 385.9299 701.9085
7/6 231.6112 386.0187 701.5179
8/7 231.1741 385.2902 704.7233
9/7 231.5792 385.9654 701.7524
10/9 231.5757 385.9596 701.7779
11/8 231.5455 385.9091 701.9999
11/9 231.6053 386.0088 701.5612
11/10 231.5727 385.9546 701.7998
12/11 231.5378 385.8963 702.0563
14/11 231.5760 385.9600 701.7760
15/11 231.5934 385.9891 701.6481
15/14 231.5480 385.9133 701.9816
16/15 231.4820 385.8033 702.4654
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