Tertiaseptal

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

See Breedsmic temperaments #Tertiaseptal 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 spectra

Tertiaseptal

Gencom: [2 68/65; 243/242 375/374 441/440 625/624 3584/3575]

Gencom mapping: [1 3 2 3 7 1 1], 0 -22 5 -3 -55 42 48]]

eigenmonzo
(unchanged interval
)
generator
(¢)
comments
8/7 77.0580
13/10 77.1409
14/13 77.1489
16/13 77.1554
15/13 77.1569
16/15 77.1607
13/12 77.1652
18/13 77.1700
20/17 77.1777
17/14 77.1790
17/15 77.1798
15/14 77.1827
4/3 77.1839
18/17 77.1853
24/17 77.1857
7/5 77.1860 7 and 9-odd-limit minimax
17/16 77.1866
10/9 77.1919
9/7 77.1931
6/5 77.1985 5-odd-limit minimax
7/6 77.2037
13/11 77.2083 13, 15 and 17-odd-limit minimax
22/17 77.2198
11/8 77.2488
11/10 77.2499 11-odd-limit minimax
14/11 77.2598
5/4 77.2627
15/11 77.2882
12/11 77.2920
17/13 77.4046
11/9 77.5084

Tertia

Gencom: [2 22/21; 352/351 385/384 561/560 625/624 715/714]

Gencom mapping: [1 3 2 3 5 1 1], 0 -22 5 -3 -24 42 48]]

eigenmonzo
(unchanged interval)
generator
(¢)
comments
12/11 75.3185
15/11 76.7073
14/11 77.0242
11/8 77.0284
8/7 77.0580
11/10 77.0688
13/11 77.1092
22/17 77.1339
13/10 77.1409
14/13 77.1489
16/13 77.1554
15/13 77.1569
16/15 77.1607
13/12 77.1652
18/13 77.1700 13, 15 and 17-odd-limit minimax
20/17 77.1777
17/14 77.1790
17/15 77.1798
15/14 77.1827
4/3 77.1839 11-odd-limit minimax
18/17 77.1853
24/17 77.1857
7/5 77.1860 7 and 9-odd-limit minimax
17/16 77.1866
10/9 77.1919
9/7 77.1931
6/5 77.1985 5-odd-limit minimax
7/6 77.2037
5/4 77.2627
11/9 77.3704
17/13 77.4046

Hemitert

Gencom: [2 45/44; 2401/2400 3025/3024 65625/65536]

Gencom mapping: [1 3 2 3 6], 0 -44 10 -6 -79]]

eigenmonzo
(unchanged interval)
generator
(¢)
comments
8/7 38.5290
16/15 38.5803
12/11 38.5896
11/8 38.5909
15/14 38.5913
4/3 38.5919
7/5 38.5930 7, 9 and 11-odd-limit minimax
11/10 38.5955
10/9 38.59596
14/11 38.59600
9/7 38.5965
15/11 38.5989
6/5 38.5992 5-odd-limit minimax
11/9 38.6009
7/6 38.6019
5/4 38.6314