Table of 198edo intervals
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 | |||