Table of 198edo intervals: Difference between revisions

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Line 43: Line 43:
| [[81/80]]
| [[81/80]]
| [[64/63]]
| [[64/63]]
| ?
| 245/242
| [[66/65]], [[78/77]]
| [[66/65]], [[78/77]]
|-
|-
Line 69: Line 69:
| 8
| 8
| 48.4848
| 48.4848
| ?
| [[250/243]]
| [[36/35]]
| [[36/35]]
| ?
| ?
Line 83: Line 83:
| 10
| 10
| 60.6061
| 60.6061
| ?
| [[648/625]]
| [[28/27]]
| [[28/27]]
| ?
| ?
Line 126: Line 126:
| 96.9697
| 96.9697
| ?
| ?
| 200/189
| 200/189, 343/324
| [[128/121]]
| [[128/121]]
| ?
| ?
Line 210: Line 210:
| 169.6970
| 169.6970
| ?
| ?
| [[54/49]]
| [[54/49]], 441/400
| ?
| ?
| ?
| ?
Line 238: Line 238:
| 193.9394
| 193.9394
| ?
| ?
| [[28/25]]
| [[28/25]], 384/343
| 121/108
| 121/108
| ?
| ?
Line 293: Line 293:
| 40
| 40
| 242.4242
| 242.4242
| ?
| 144/125
| [[280/243]]
| 147/128, 280/243
| ?
| ?
| ?
| ?
Line 307: Line 307:
| 42
| 42
| 254.5455
| 254.5455
| ?
| 125/108
| [[81/70]]
| [[81/70]]
| [[140/121]]
| [[140/121]]
Line 364: Line 364:
| 303.0303
| 303.0303
| ?
| ?
| [[25/21]]
| [[25/21]], 343/288
| [[144/121]]
| [[144/121]]
| ?
| ?
Line 392: Line 392:
| 327.2727
| 327.2727
| ?
| ?
| ?
| [[98/81]]
| ?
| ?
| ?
| ?
Line 405: Line 405:
| 56
| 56
| 339.3939
| 339.3939
| ?
| 243/200
| ?
| ?
| ?
| ?
Line 433: Line 433:
| 60
| 60
| 363.6364
| 363.6364
| ?
| 100/81
| ?
| ?
| ?
| ?
Line 448: Line 448:
| 375.7576
| 375.7576
| ?
| ?
| ?
| [[56/45]]
| ?
| ?
| ?
| ?
Line 476: Line 476:
| 400.0000
| 400.0000
| ?
| ?
| [[63/50]]
| [[63/50]], 432/343
| [[121/96]]
| [[121/96]]
| ?
| ?
Line 517: Line 517:
| 72
| 72
| 436.3636
| 436.3636
| ?
| 625/486
| [[9/7]]
| [[9/7]]
| ?
| ?
Line 531: Line 531:
| 74
| 74
| 448.4848
| 448.4848
| ?
| 162/125
| [[35/27]]
| [[35/27]]
| ?
| ?
Line 546: Line 546:
| 460.6061
| 460.6061
| ?
| ?
| ?
| [[64/49]], 98/75
| ?
| ?
| ?
| ?
Line 602: Line 602:
| 509.0909
| 509.0909
| ?
| ?
| ?
| 343/256
| ?
| ?
| ?
| ?
Line 630: Line 630:
| 533.3333
| 533.3333
| ?
| ?
| [[49/36]]
| [[49/36]], 200/147
| ?
| ?
| ?
| ?
Line 643: Line 643:
| 90
| 90
| 545.4545
| 545.4545
| ?
| 1000/729
| [[48/35]]
| [[48/35]]
| ?
| ?
Line 700: Line 700:
| 593.9394
| 593.9394
| ?
| ?
| ?
| 343/243, 800/567
| ?
| ?
| ?
| ?
Line 714: Line 714:
| 606.0606
| 606.0606
| ?
| ?
| ?
| 486/343, 567/400
| ?
| ?
| ?
| ?
Line 769: Line 769:
| 108
| 108
| 654.5455
| 654.5455
| ?
| 729/500
| [[35/24]]
| [[35/24]]
| ?
| ?
Line 784: Line 784:
| 666.6667
| 666.6667
| ?
| ?
| [[72/49]]
| [[72/49]], 147/100
| ?
| ?
| ?
| ?
Line 812: Line 812:
| 690.9091
| 690.9091
| ?
| ?
| ?
| 512/343
| ?
| ?
| ?
| ?
Line 868: Line 868:
| 739.3939
| 739.3939
| ?
| ?
| ?
| [[49/32]], 75/49
| ?
| ?
| ?
| ?
Line 881: Line 881:
| 124
| 124
| 751.5152
| 751.5152
| ?
| 125/81
| [[54/35]]
| [[54/35]]
| ?
| ?
Line 895: Line 895:
| 126
| 126
| 763.6364
| 763.6364
| ?
| 972/625
| [[14/9]]
| [[14/9]]
| ?
| ?
Line 938: Line 938:
| 800.0000
| 800.0000
| ?
| ?
| [[100/63]]
| [[100/63]], 343/216
| [[192/121]]
| [[192/121]]
| ?
| ?
Line 966: Line 966:
| 824.2424
| 824.2424
| ?
| ?
| ?
| [[45/28]]
| ?
| ?
| ?
| ?
Line 979: Line 979:
| 138
| 138
| 836.3636
| 836.3636
| ?
| 81/50
| ?
| ?
| ?
| ?
Line 1,007: Line 1,007:
| 142
| 142
| 860.6061
| 860.6061
| ?
| 400/243
| ?
| ?
| ?
| ?
Line 1,022: Line 1,022:
| 872.7273
| 872.7273
| ?
| ?
| ?
| [[81/49]]
| ?
| ?
| ?
| ?
Line 1,050: Line 1,050:
| 896.9697
| 896.9697
| ?
| ?
| [[42/25]]
| [[42/25]], 576/343
| [[121/72]]
| [[121/72]]
| ?
| ?
Line 1,105: Line 1,105:
| 156
| 156
| 945.4545
| 945.4545
| ?
| 216/125
| [[140/81]]
| [[140/81]]
| [[121/70]]
| [[121/70]]
Line 1,119: Line 1,119:
| 158
| 158
| 957.5758
| 957.5758
| ?
| 125/72
| [[243/140]]
| 243/140, 256/147
| ?
| ?
| ?
| ?
Line 1,176: Line 1,176:
| 1006.0606
| 1006.0606
| ?
| ?
| [[25/14]]
| [[25/14]], 343/192
| 216/121
| 216/121
| ?
| ?
Line 1,204: Line 1,204:
| 1030.3030
| 1030.3030
| ?
| ?
| [[49/27]]
| [[49/27]], 800/441
| ?
| ?
| ?
| ?
Line 1,288: Line 1,288:
| 1103.0303
| 1103.0303
| ?
| ?
| 189/100
| 189/100, 648/343
| [[121/64]]
| [[121/64]]
| ?
| ?
Line 1,329: Line 1,329:
| 188
| 188
| 1139.3939
| 1139.3939
| ?
| 625/324
| [[27/14]]
| [[27/14]]
| ?
| ?
Line 1,343: Line 1,343:
| 190
| 190
| 1151.5152
| 1151.5152
| ?
| 243/125
| [[35/18]]
| [[35/18]]
| ?
| ?
Line 1,373: Line 1,373:
| 160/81
| 160/81
| 63/32
| 63/32
| ?
| 484/245
| 65/33, 77/39
| 65/33, 77/39
|-
|-

Revision as of 13:47, 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 64/63 245/242 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 250/243 36/35 ? ?
9 54.5455 33/32 65/63
10 60.6061 648/625 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, 343/324 128/121 ?
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, 441/400 ? ?
29 175.7576 ? ?
30 181.8182 10/9 ? ? ?
31 187.8788 ? ?
32 193.9394 ? 28/25, 384/343 121/108 ?
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 144/125 147/128, 280/243 ? ?
41 248.4848 ? 15/13
42 254.5455 125/108 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, 343/288 144/121 ?
51 309.0909 ? ?
52 315.1515 6/5 ? ? ?
53 321.2121 ? ?
54 327.2727 ? 98/81 ? ?
55 333.3333 ? 63/52
56 339.3939 243/200 ? ? ?
57 345.4545 11/9 39/32
58 351.5152 ? 49/40, 60/49 ? ?
59 357.5757 27/22 16/13
60 363.6364 100/81 ? ? ?
61 369.6970 ? 26/21
62 375.7576 ? 56/45 ? ?
63 381.8182 ? ?
64 387.8788 5/4 ? ? ?
65 393.9394 ? ?
66 400.0000 ? 63/50, 432/343 121/96 ?
67 406.0606 ? ?
68 412.1212 ? 80/63 ? 33/26
69 418.1818 14/11 ?
70 424.2424 ? ? ? ?
71 430.3030 ? ?
72 436.3636 625/486 9/7 ? ?
73 442.4242 128/99 ?
74 448.4848 162/125 35/27 ? ?
75 454.5455 ? 13/10
76 460.6061 ? 64/49, 98/75 ? ?
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 ? 343/256 ? ?
85 515.1515 ? ?
86 521.2121 27/20 ? ? ?
87 527.2727 ? ?
88 533.3333 ? 49/36, 200/147 ? ?
89 539.3939 15/11 ?
90 545.4545 1000/729 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 ? 343/243, 800/567 ? ?
99 600.0000 99/70, 140/99 ?
100 606.0606 ? 486/343, 567/400 ? ?
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 729/500 35/24 ? ?
109 660.6061 22/15 ?
110 666.6667 ? 72/49, 147/100 ? ?
111 672.7273 ? ?
112 678.7879 40/27 ? ? ?
113 684.8485 ? ?
114 690.9091 ? 512/343 ? ?
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 ? 49/32, 75/49 ? ?
123 745.4545 ? 20/13
124 751.5152 125/81 54/35 ? ?
125 757.5758 99/64 ?
126 763.6364 972/625 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, 343/216 192/121 ?
133 806.0606 ? ?
134 812.1212 8/5 ? ? ?
135 818.1818 ? ?
136 824.2424 ? 45/28 ? ?
137 830.3030 ? 21/13
138 836.3636 81/50 ? ? ?
139 842.4242 44/27 13/8
140 848.4848 ? 49/30, 80/49 ? ?
141 854.5455 18/11 64/39
142 860.6061 400/243 ? ? ?
143 866.6667 ? 104/63
144 872.7273 ? 81/49 ? ?
145 878.7879 ? ?
146 884.8485 5/3 ? ? ?
147 890.9091 ? ?
148 896.9697 ? 42/25, 576/343 121/72 ?
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 216/125 140/81 121/70 ?
157 951.5152 ? 26/15
158 957.5758 125/72 243/140, 256/147 ? ?
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, 343/192 216/121 ?
167 1012.1212 ? ?
168 1018.1818 9/5 ? ? ?
169 1024.2424 ? ?
170 1030.3030 ? 49/27, 800/441 ? ?
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, 648/343 121/64 ?
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 625/324 27/14 ? ?
189 1145.4545 64/33 126/65
190 1151.5152 243/125 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 63/32 484/245 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
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