Table of 198edo intervals: Difference between revisions
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| 0 | | 0 | ||
| 0.0000 | | 0.0000 | ||
| colspan="4"| '''[[1/1]]''' | | colspan="4" | '''[[1/1]]''' | ||
|- | |- | ||
| 1 | | 1 | ||
Line 99: | Line 99: | ||
| [[25/24]] | | [[25/24]] | ||
| ? | | ? | ||
| | | 126/121 | ||
| ? | | ? | ||
|- | |- | ||
Line 121: | Line 121: | ||
| | | | ||
| ? | | ? | ||
| | | 96/91 | ||
|- | |- | ||
| 16 | | 16 | ||
| 96.9697 | | 96.9697 | ||
| ? | | ? | ||
| | | 200/189 | ||
| [[128/121]] | | [[128/121]] | ||
| ? | | ? | ||
Line 168: | Line 168: | ||
| 133.3333 | | 133.3333 | ||
| [[27/25]] | | [[27/25]] | ||
| | | 175/162 | ||
| ? | | ? | ||
| ? | | ? | ||
Line 182: | Line 182: | ||
| 145.4545 | | 145.4545 | ||
| ? | | ? | ||
| [[49/45]], | | [[49/45]], 160/147 | ||
| ? | | ? | ||
| ? | | ? | ||
Line 239: | Line 239: | ||
| ? | | ? | ||
| [[28/25]] | | [[28/25]] | ||
| | | 121/108 | ||
| ? | | ? | ||
|- | |- | ||
Line 658: | Line 658: | ||
| 557.5758 | | 557.5758 | ||
| ? | | ? | ||
| | | 441/320 | ||
| ? | | ? | ||
| ? | | ? | ||
Line 756: | Line 756: | ||
| 642.4242 | | 642.4242 | ||
| ? | | ? | ||
| | | 640/441 | ||
| ? | | ? | ||
| ? | | ? | ||
Line 770: | Line 770: | ||
| 654.5455 | | 654.5455 | ||
| ? | | ? | ||
| [[ | | [[35/24]] | ||
| ? | | ? | ||
| ? | | ? | ||
Line 784: | Line 784: | ||
| 666.6667 | | 666.6667 | ||
| ? | | ? | ||
| | | [[72/49]] | ||
| ? | | ? | ||
| ? | | ? | ||
Line 825: | Line 825: | ||
| 116 | | 116 | ||
| 703.0303 | | 703.0303 | ||
| [[3/2]] | | '''[[3/2]]''' | ||
| ? | | ? | ||
| ? | | ? | ||
Line 890: | Line 890: | ||
| | | | ||
| | | | ||
| | | [[99/64]] | ||
| ? | | ? | ||
|- | |- | ||
Line 1,051: | Line 1,051: | ||
| ? | | ? | ||
| [[42/25]] | | [[42/25]] | ||
| | | [[121/72]] | ||
| ? | | ? | ||
|- | |- | ||
Line 1,072: | Line 1,072: | ||
| | | | ||
| | | | ||
| | | [[56/33]] | ||
| ? | | ? | ||
|- | |- | ||
Line 1,176: | Line 1,176: | ||
| 1006.0606 | | 1006.0606 | ||
| ? | | ? | ||
| | | [[25/14]] | ||
| | | 216/121 | ||
| ? | | ? | ||
|- | |- | ||
Line 1,204: | Line 1,204: | ||
| 1030.3030 | | 1030.3030 | ||
| ? | | ? | ||
| | | [[49/27]] | ||
| ? | | ? | ||
| ? | | ? | ||
Line 1,218: | Line 1,218: | ||
| 1042.4242 | | 1042.4242 | ||
| ? | | ? | ||
| | | [[64/35]] | ||
| ? | | ? | ||
| ? | | ? | ||
Line 1,232: | Line 1,232: | ||
| 1054.5455 | | 1054.5455 | ||
| ? | | ? | ||
| | | [[90/49]], 147/80 | ||
| ? | | ? | ||
| ? | | ? | ||
Line 1,246: | Line 1,246: | ||
| 1066.6667 | | 1066.6667 | ||
| [[50/27]] | | [[50/27]] | ||
| | | 384/175 | ||
| ? | | ? | ||
| ? | | ? | ||
Line 1,282: | Line 1,282: | ||
| | | | ||
| | | | ||
| | | [[66/35]] | ||
| ? | | ? | ||
|- | |- | ||
Line 1,288: | Line 1,288: | ||
| 1103.0303 | | 1103.0303 | ||
| ? | | ? | ||
| | | 189/100 | ||
| | | [[121/64]] | ||
| ? | | ? | ||
|- | |- | ||
Line 1,297: | Line 1,297: | ||
| | | | ||
| ? | | ? | ||
| | | 91/48 | ||
|- | |- | ||
| 184 | | 184 | ||
Line 1,317: | Line 1,317: | ||
| [[48/25]] | | [[48/25]] | ||
| ? | | ? | ||
| 121/63 | |||
| ? | | ? | ||
|- | |- | ||
| 187 | | 187 | ||
Line 1,324: | Line 1,324: | ||
| | | | ||
| | | | ||
| | | 77/40 | ||
| [[25/13]], [[52/27]] | | [[25/13]], [[52/27]] | ||
|- | |- | ||
Line 1,399: | Line 1,399: | ||
| 198 | | 198 | ||
| 1200.0000 | | 1200.0000 | ||
| colspan="4"| '''[[2/1]]''' | | colspan="4" | '''[[2/1]]''' | ||
|- | |- | ||
|} | |} |
Revision as of 12:38, 9 November 2020
This article is a work in progress.
This table of 198edo intervals assumes 13-limit patent val ⟨198 314 460 556 685 733].
Intervals highlighted in bold are prime harmonics or subharmonics. Intervals that differ from their assigned steps by more than 50% or intervals with odd limit over 729 are not shown. Note that no 7-limit interval can be represented by odd degrees, so those entries are left blank.
# | Cents | 5 limit | 7 limit | 11 limit | 13 limit |
---|---|---|---|---|---|
0 | 0.0000 | 1/1 | |||
1 | 6.0606 | 385/384, 441/440, 540/539 | 196/195, 325/324, 351/350, 364/363 | ||
2 | 12.1212 | ? | 126/125, 245/243 | 121/120 | 144/143, 169/168 |
3 | 18.1818 | 99/98, 100/99 | ? | ||
4 | 24.2424 | 81/80 | 64/63 | ? | 66/65, 78/77 |
5 | 30.3030 | 55/54, 56/55 | ? | ||
6 | 36.3636 | ? | 49/48, 50/49 | ? | ? |
7 | 42.4242 | ? | 40/39 | ||
8 | 48.4848 | ? | 36/35 | ? | ? |
9 | 54.5455 | 33/32 | 65/63 | ||
10 | 60.6061 | ? | 28/27 | ? | ? |
11 | 66.6667 | 80/77 | 26/25, 27/26 | ||
12 | 72.7273 | 25/24 | ? | 126/121 | ? |
13 | 78.7879 | 22/21 | ? | ||
14 | 84.8485 | ? | 21/20 | ? | ? |
15 | 90.9091 | ? | 96/91 | ||
16 | 96.9697 | ? | 200/189 | 128/121 | ? |
17 | 103.0303 | 35/33 | ? | ||
18 | 109.0909 | 16/15 | ? | ? | ? |
19 | 115.1515 | ? | ? | ||
20 | 121.2121 | ? | 15/14 | ? | ? |
21 | 127.2727 | ? | 14/13 | ||
22 | 133.3333 | 27/25 | 175/162 | ? | ? |
23 | 139.3939 | ? | 13/12 | ||
24 | 145.4545 | ? | 49/45, 160/147 | ? | ? |
25 | 151.5152 | 12/11 | ? | ||
26 | 157.5758 | ? | 35/32 | ? | ? |
27 | 163.6364 | 11/10 | ? | ||
28 | 169.6970 | ? | 54/49 | ? | ? |
29 | 175.7576 | ? | ? | ||
30 | 181.8182 | 10/9 | ? | ? | ? |
31 | 187.8788 | ? | ? | ||
32 | 193.9394 | ? | 28/25 | 121/108 | ? |
33 | 200.0000 | ? | 91/81 | ||
34 | 206.0606 | 9/8 | ? | ? | 44/39 |
35 | 212.1212 | ? | ? | ||
36 | 218.1818 | ? | ? | ? | ? |
37 | 224.2424 | ? | 91/80 | ||
38 | 230.3030 | ? | 8/7 | ? | ? |
39 | 236.3636 | 55/48 | ? | ||
40 | 242.4242 | ? | 280/243 | ? | ? |
41 | 248.4848 | ? | 15/13 | ||
42 | 254.5455 | ? | 81/70 | 140/121 | ? |
43 | 260.6061 | 64/55 | ? | ||
44 | 266.6667 | ? | 7/6 | ? | ? |
45 | 272.7273 | ? | ? | ||
46 | 278.7879 | ? | ? | ? | ? |
47 | 284.8485 | 33/28 | ? | ||
48 | 290.9091 | ? | 189/160 | ? | 13/11 |
49 | 296.9697 | ? | ? | ||
50 | 303.0303 | ? | 25/21 | 144/121 | ? |
51 | 309.0909 | ? | ? | ||
52 | 315.1515 | 6/5 | ? | ? | ? |
53 | 321.2121 | ? | ? | ||
54 | 327.2727 | ? | ? | ? | ? |
55 | 333.3333 | ? | 63/52 | ||
56 | 339.3939 | ? | ? | ? | ? |
57 | 345.4545 | 11/9 | 39/32 | ||
58 | 351.5152 | ? | 49/40, 60/49 | ? | ? |
59 | 357.5757 | 27/22 | 16/13 | ||
60 | 363.6364 | ? | ? | ? | ? |
61 | 369.6970 | ? | 26/21 | ||
62 | 375.7576 | ? | ? | ? | ? |
63 | 381.8182 | ? | ? | ||
64 | 387.8788 | 5/4 | ? | ? | ? |
65 | 393.9394 | ? | ? | ||
66 | 400.0000 | ? | 63/50 | 121/96 | ? |
67 | 406.0606 | ? | ? | ||
68 | 412.1212 | ? | 80/63 | ? | 33/26 |
69 | 418.1818 | 14/11 | ? | ||
70 | 424.2424 | ? | ? | ? | ? |
71 | 430.3030 | ? | ? | ||
72 | 436.3636 | ? | 9/7 | ? | ? |
73 | 442.4242 | 128/99 | ? | ||
74 | 448.4848 | ? | 35/27 | ? | ? |
75 | 454.5455 | ? | 13/10 | ||
76 | 460.6061 | ? | ? | ? | ? |
77 | 466.6667 | ? | ? | ||
78 | 472.7273 | ? | 21/16 | ? | ? |
79 | 478.7879 | ? | ? | ||
80 | 484.8485 | ? | ? | ? | ? |
81 | 490.9091 | ? | ? | ||
82 | 496.9697 | 4/3 | ? | ? | ? |
83 | 503.0303 | ? | ? | ||
84 | 509.0909 | ? | ? | ? | ? |
85 | 515.1515 | ? | ? | ||
86 | 521.2121 | 27/20 | ? | ? | ? |
87 | 527.2727 | ? | ? | ||
88 | 533.3333 | ? | 49/36 | ? | ? |
89 | 539.3939 | 15/11 | ? | ||
90 | 545.4545 | ? | 48/35 | ? | ? |
91 | 551.5152 | 11/8 | ? | ||
92 | 557.5758 | ? | 441/320 | ? | ? |
93 | 563.6364 | ? | 18/13 | ||
94 | 569.6970 | 25/18 | ? | ? | ? |
95 | 575.7576 | ? | ? | ||
96 | 581.8182 | ? | 7/5 | ? | ? |
97 | 587.8788 | ? | ? | ||
98 | 593.9394 | ? | ? | ? | ? |
99 | 600.0000 | 99/70, 140/99 | ? | ||
100 | 606.0606 | ? | ? | ? | ? |
101 | 612.1212 | ? | ? | ||
102 | 618.1818 | ? | 10/7 | ? | ? |
103 | 624.2424 | ? | ? | ||
104 | 630.3030 | 36/25 | ? | ? | ? |
105 | 636.3636 | ? | 13/9 | ||
106 | 642.4242 | ? | 640/441 | ? | ? |
107 | 648.4848 | 16/11 | ? | ||
108 | 654.5455 | ? | 35/24 | ? | ? |
109 | 660.6061 | 22/15 | ? | ||
110 | 666.6667 | ? | 72/49 | ? | ? |
111 | 672.7273 | ? | ? | ||
112 | 678.7879 | 40/27 | ? | ? | ? |
113 | 684.8485 | ? | ? | ||
114 | 690.9091 | ? | ? | ? | ? |
115 | 696.9697 | ? | ? | ||
116 | 703.0303 | 3/2 | ? | ? | ? |
117 | 709.0909 | ? | ? | ||
118 | 715.1515 | ? | ? | ? | ? |
119 | 721.2121 | ? | ? | ||
120 | 727.2727 | 32/21 | ? | ? | |
121 | 733.3333 | ? | ? | ||
122 | 739.3939 | ? | ? | ? | ? |
123 | 745.4545 | ? | 20/13 | ||
124 | 751.5152 | ? | 54/35 | ? | ? |
125 | 757.5758 | 99/64 | ? | ||
126 | 763.6364 | ? | 14/9 | ? | ? |
127 | 769.6970 | ? | ? | ||
128 | 775.7576 | ? | ? | ? | ? |
129 | 781.8182 | 11/7 | ? | ||
130 | 787.8788 | ? | 63/40 | ? | 52/33 |
131 | 793.9394 | ? | ? | ||
132 | 800.0000 | ? | 100/63 | 192/121 | ? |
133 | 806.0606 | ? | ? | ||
134 | 812.1212 | 8/5 | ? | ? | ? |
135 | 818.1818 | ? | ? | ||
136 | 824.2424 | ? | ? | ? | ? |
137 | 830.3030 | ? | 21/13 | ||
138 | 836.3636 | ? | ? | ? | ? |
139 | 842.4242 | 44/27 | 13/8 | ||
140 | 848.4848 | ? | 49/30, 80/49 | ? | ? |
141 | 854.5455 | 18/11 | 64/39 | ||
142 | 860.6061 | ? | ? | ? | ? |
143 | 866.6667 | ? | 104/63 | ||
144 | 872.7273 | ? | ? | ? | ? |
145 | 878.7879 | ? | ? | ||
146 | 884.8485 | 5/3 | ? | ? | ? |
147 | 890.9091 | ? | ? | ||
148 | 896.9697 | ? | 42/25 | 121/72 | ? |
149 | 903.0303 | ? | ? | ||
150 | 909.0909 | ? | 320/189 | ? | 22/13 |
151 | 915.1515 | 56/33 | ? | ||
152 | 921.2121 | ? | ? | ? | ? |
153 | 927.2727 | ? | ? | ||
154 | 933.3333 | ? | 12/7 | ? | ? |
155 | 939.3939 | 55/32 | ? | ||
156 | 945.4545 | ? | 140/81 | 121/70 | ? |
157 | 951.5152 | ? | 26/15 | ||
158 | 957.5758 | ? | 243/140 | ? | ? |
159 | 963.6364 | 96/55 | ? | ||
160 | 969.6970 | ? | 7/4 | ? | ? |
161 | 975.7576 | ? | 160/91 | ||
162 | 981.8182 | ? | ? | ? | ? |
163 | 987.8788 | ? | ? | ||
164 | 993.9394 | 16/9 | ? | ? | 39/22 |
165 | 1000.0000 | ? | 162/91 | ||
166 | 1006.0606 | ? | 25/14 | 216/121 | ? |
167 | 1012.1212 | ? | ? | ||
168 | 1018.1818 | 9/5 | ? | ? | ? |
169 | 1024.2424 | ? | ? | ||
170 | 1030.3030 | ? | 49/27 | ? | ? |
171 | 1036.3636 | 20/11 | ? | ||
172 | 1042.4242 | ? | 64/35 | ? | ? |
173 | 1048.4848 | 11/6 | ? | ||
174 | 1054.5455 | ? | 90/49, 147/80 | ? | ? |
175 | 1060.6061 | ? | 24/13 | ||
176 | 1066.6667 | 50/27 | 384/175 | ? | ? |
177 | 1072.7273 | ? | 13/7 | ||
178 | 1078.7879 | ? | 28/15 | ? | ? |
179 | 1084.8485 | ? | ? | ||
180 | 1090.9091 | 15/8 | ? | ? | ? |
181 | 1096.9697 | 66/35 | ? | ||
182 | 1103.0303 | ? | 189/100 | 121/64 | ? |
183 | 1109.0909 | ? | 91/48 | ||
184 | 1115.1515 | ? | 40/21 | ? | ? |
185 | 1121.2121 | 21/11 | ? | ||
186 | 1127.2727 | 48/25 | ? | 121/63 | ? |
187 | 1133.3333 | 77/40 | 25/13, 52/27 | ||
188 | 1139.3939 | ? | 27/14 | ? | ? |
189 | 1145.4545 | 64/33 | 126/65 | ||
190 | 1151.5152 | ? | 35/18 | ? | ? |
191 | 1157.5758 | ? | 39/20 | ||
192 | 1163.6364 | ? | 96/49, 49/25 | ? | ? |
193 | 1169.6970 | 108/55, 55/27 | ? | ||
194 | 1175.7576 | 160/81 | 63/32 | ? | 65/33, 77/39 |
195 | 1181.8182 | 196/99, 99/50 | ? | ||
196 | 1187.8788 | ? | 125/63, 486/245 | 240/121 | 143/72, 336/169 |
197 | 1193.9394 | 768/385, 880/441, 539/270 | 195/98, 648/325, 700/351, 363/182 | ||
198 | 1200.0000 | 2/1 |