Cotoneum: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,170 edits
→Tuning spectrum: improve and standardize tuning spectra tables
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,025 edits
mNo edit summary
Line 5: Line 5:
== Interval chain ==
== Interval chain ==
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
! Number of <br>Fifth <br>generators
! Number of <br>fifth
! Cents <br>value*
! Cents <br>value*
! Approximate Ratios
! Approximate Ratios
Line 574: Line 574:
{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
! ET <br>generator
! [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! fifth<br>(¢)
! fifth<br>(¢)
! comments
! comments
|-
|-
|
| 4/3
| 4/3
| 701.9550
| 701.9550
|  
|  
|-
|-
|
| 9/7
| 9/7
| 702.1928
| 702.1928
|  
|  
|-
|-
|
| 7/6
| 7/6
| 702.2086
| 702.2086
|  
|  
|-
|-
| 79\135
|
| 702.2222
|
|-
|
| 8/7
| 8/7
| 702.2267
| 702.2267
|  
|  
|-
|-
|
| 14/11
| 14/11
| 702.2295
| 702.2295
|  
|  
|-
|-
|
| 11/8
| 11/8
| 702.2312
| 702.2312
|  
|  
|-
|-
|
| 22/21
| 22/21
| 702.2371
| 702.2371
|  
|  
|-
|-
|
| 20/19
| 20/19
| 702.2399
| 702.2399
|  
|  
|-
|-
|
| 12/11
| 12/11
| 702.2438
| 702.2438
|  
|  
|-
|-
|
| 21/16
| 21/16
| 702.2476
| 702.2476
|  
|  
|-
|-
|
| 11/9
| 11/9
| 702.2575
| 702.2575
|  
|  
|-
|-
| 103\176
|
| 702.2727
|
|-
|
| 14/13
| 14/13
| 702.2894
| 702.2894
|  
|  
|-
|-
|
| 11/10
| 11/10
| 702.2917
| 702.2917
| 11 and 13-odd-limit minimax
| 11 and 13-odd-limit minimax
|-
|-
|
| 17/14
| 17/14
| 702.2925
| 702.2925
|  
|  
|-
|-
|
| 26/21
| 26/21
| 702.2939
| 702.2939
|  
|  
|-
|-
|
| 22/19
| 22/19
| 702.2956
| 702.2956
|  
|  
|-
|-
|
| 21/17
| 21/17
| 702.2958
| 702.2958
|  
|  
|-
|-
|
| 15/11
| 15/11
| 702.2965
| 702.2965
| 15, 17, 19, and 21-odd-limit minimax  
| 15, 17, 19, and 21-odd-limit minimax  
|-
|-
|
| 17/13
| 17/13
| 702.3010
| 702.3010
|  
|  
|-
|-
|
| 17/16
| 17/16
| 702.3029
| 702.3029
|  
|  
|-
|-
|
| 16/13
| 16/13
| 702.3037
| 702.3037
|  
|  
|-
|-
| 127\217
|
| 702.3041
|
|-
|
| 10/9
| 10/9
| 702.3058
| 702.3058
| 9-odd-limit minimax
| 9-odd-limit minimax
|-
|-
|
| 24/17
| 24/17
| 702.3068
| 702.3068
|  
|  
|-
|-
|
| 20/17
| 20/17
| 702.3090
| 702.3090
|  
|  
|-
|-
|
| 13/12
| 13/12
| 702.3095
| 702.3095
|  
|  
|-
|-
|
| 18/17
| 18/17
| 702.3109
| 702.3109
|  
|  
|-
|-
|
| 13/10
| 13/10
| 702.3110
| 702.3110
|  
|  
|-
|-
|
| 19/15
| 19/15
| 702.3111
| 702.3111
|  
|  
|-
|-
|
| 17/15
| 17/15
| 702.3116
| 702.3116
|  
|  
|-
|-
|
| 19/17
| 19/17
| 702.3116
| 702.3116
|  
|  
|-
|-
|
| 6/5
| 6/5
| 702.3128
| 702.3128
| 5 and 7-odd-limit minimax
| 5 and 7-odd-limit minimax
|-
|-
|
| 19/18
| 19/18
| 702.3130
| 702.3130
|  
|  
|-
|-
|
| 15/13
| 15/13
| 702.3143
| 702.3143
|  
|  
|-
|-
|
| 26/19
| 26/19
| 702.3144
| 702.3144
|  
|  
|-
|-
|
| 18/13
| 18/13
| 702.3156
| 702.3156
|  
|  
|-
|-
|
| 5/4
| 5/4
| 702.3201
| 702.3201
|  
|  
|-
|-
|
| 24/19
| 24/19
| 702.3209
| 702.3209
|  
|  
|-
|-
| 151\258
|
| 702.2727
|
|-
|
| 16/15
| 16/15
| 702.3277
| 702.3277
|  
|  
|-
|-
|
| 22/17
| 22/17
| 702.3278
| 702.3278
|  
|  
|-
|-
|
| 19/16
| 19/16
| 702.3292
| 702.3292
|  
|  
|-
|-
| 175\299
|
| 702.3411
|
|-
|
| 21/20
| 21/20
| 702.3463
| 702.3463
|  
|  
|-
|-
|
| 13/11
| 13/11
| 702.3476
| 702.3476
|  
|  
|-
|-
|
| 7/5
| 7/5
| 702.3575
| 702.3575
|  
|  
|-
|-
|
| 21/19
| 21/19
| 702.3635
| 702.3635
|  
|  
|-
|-
|
| 15/14
| 15/14
| 702.3693
| 702.3693
|  
|  
|-
|-
|
| 19/14
| 19/14
| 702.3771
| 702.3771
|
|-
| 24\41
|
| 702.4390
|  
|  
|}
|}

Revision as of 04:14, 17 October 2021

Cotoneum temperament is temperament for the 7, 11, 13, 17, and 19 prime limits. It is a member of hemimage temperaments, quince clan, and garischismic clan. 217EDO is an excellent tuning for cotoneum, with a fifth generator of 127\217, and MOS of 12, 17, 29, 41, 53, 94, 135, or 176 notes are available.

See Hemimage temperaments #Cotoneum for more technical data.

Interval chain

Number of
fifth 		Cents
value* 		Approximate Ratios
0 0.000 1/1
1 702.308 3/2
2 204.615 9/8
3 906.923 27/16
4 409.231 19/15
5 1111.539 19/10
6 613.846 57/40
7 116.154 77/72
8 818.462 77/48
9 320.770 77/64
10 1023.077 65/36
11 525.385 65/48
12 27.693 56/55, 64/63,
65/64, 66/65
13 730.001 32/21
14 232.308 8/7
15 934.616 12/7
16 436.924 9/7
17 1139.232 27/14
18 641.539 81/56
19 143.847
20 846.155 44/27
21 348.463 11/9
22 1050.770 11/6
23 553.078 11/8
24 55.386 33/32, 65/63
25 757.694 65/42
26 260.001 64/55, 65/56
27 962.309 68/39, 96/55
28 464.617 17/13
29 1166.925 51/26, 96/49,
108/55, 112/57
30 669.232 28/19
31 171.540 21/19
32 873.848 63/38
33 376.156 56/45
34 1078.463 28/15
35 580.771 7/5
36 83.079 21/20, 22/21
37 785.387 11/7
38 287.694 13/11
39 990.002 39/22
40 492.310
41 1194.618
42 696.925
43 199.233 64/57
44 901.541 32/19
45 403.849 24/19
46 1106.156 36/19
47 608.464 27/19, 64/45
48 110.772 16/15
49 813.080 8/5
50 315.387 6/5
51 1017.695 9/5
52 520.003 27/20
53 22.310 76/75, 77/76,
78/77, 81/80,
99/98
54 724.618 38/25
55 226.926
56 929.234
57 431.541
58 1133.849 52/27
59 636.157 13/9
60 138.465 13/12
61 840.772 13/8
62 343.080 39/32
63 1045.388 64/35
64 547.696 48/35
65 50.003 34/33, 36/35
66 752.311 17/11
67 254.619 22/19
68 956.927 33/19
69 459.234 98/75, 99/76
70 1161.542 88/45, 49/25
71 663.850 22/15
72 166.158 11/10
73 868.465 33/20
74 370.773 26/21
75 1073.081 13/7
76 575.389 39/28
77 77.696
78 780.004
79 282.312
80 984.620
81 486.927
82 1189.235
83 691.543 112/75
84 193.851 28/25
85 896.158 42/25
86 398.466 34/27
87 1100.774 17/9
88 603.082 17/12
89 105.389 17/16
90 807.697 51/32
91 310.005
92 1012.313
93 514.620
94 16.928 121/120
95 719.236
96 221.544
97 923.851
98 426.159 32/25
99 1128.467 48/25
100 630.775 36/25
101 133.082 27/25
102 835.390 34/21
103 337.698 17/14
104 1040.005 51/28
105 542.313 26/19
106 44.621 39/38
107 746.929
108 249.236 52/45
109 951.544 26/15
110 453.852 13/10
111 1156.160 39/20
112 658.467
113 160.775
114 863.083
115 365.391
116 1067.698
117 570.006
118 72.314
119 774.622
120 276.929
121 979.237 44/25
122 481.545 33/25
123 1183.853 99/50
124 686.160 52/35
125 188.468 39/35
126 890.776
127 393.084
128 1095.391
129 597.699
130 100.007
131 802.315
132 304.622
133 1006.930 34/19
134 509.238
135 11.546 126/125
136 713.853
137 216.161 17/15
138 918.469 17/10

* in 19-limit POTE tuning

Tuning spectrum

Gencom: [2 4/3; 343/342 364/363 441/440 595/594 1216/1215 1729/1728]

Gencom map: [⟨1 2 -18 -3 13 29 41 -14], ⟨0 -1 49 14 -23 -61 -89 44]]

ET
generator 		eigenmonzo
(unchanged interval) 		fifth
(¢) 		comments
4/3 701.9550
9/7 702.1928
7/6 702.2086
79\135 702.2222
8/7 702.2267
14/11 702.2295
11/8 702.2312
22/21 702.2371
20/19 702.2399
12/11 702.2438
21/16 702.2476
11/9 702.2575
103\176 702.2727
14/13 702.2894
11/10 702.2917 11 and 13-odd-limit minimax
17/14 702.2925
26/21 702.2939
22/19 702.2956
21/17 702.2958
15/11 702.2965 15, 17, 19, and 21-odd-limit minimax
17/13 702.3010
17/16 702.3029
16/13 702.3037
127\217 702.3041
10/9 702.3058 9-odd-limit minimax
24/17 702.3068
20/17 702.3090
13/12 702.3095
18/17 702.3109
13/10 702.3110
19/15 702.3111
17/15 702.3116
19/17 702.3116
6/5 702.3128 5 and 7-odd-limit minimax
19/18 702.3130
15/13 702.3143
26/19 702.3144
18/13 702.3156
5/4 702.3201
24/19 702.3209
151\258 702.2727
16/15 702.3277
22/17 702.3278
19/16 702.3292
175\299 702.3411
21/20 702.3463
13/11 702.3476
7/5 702.3575
21/19 702.3635
15/14 702.3693
19/14 702.3771
24\41 702.4390

Scales

Template:IoT

Retrieved from "https://en.xen.wiki/index.php?title=Cotoneum&oldid=79644"