Table of 198edo intervals
This article is a work in progress.
11-limit is done.
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. Note that no 7-limit interval can be represented by odd degrees, so those entries are left blank. 7-limit intervals that differ from their assigned steps by more than 50%, but no more than 100%, are shown in italic, for they are consistent under the criterion of 99edo. Intervals otherwise that differ by more than 50%, with odd limit over 729, or with two more simpler mapped to the same degree, are not shown.
| # | Cents | 5 limit | 7 limit | 11 limit | 13 limit |
|---|---|---|---|---|---|
| 0 | 0.00 | 1/1 | |||
| 1 | 6.06 | 385/384, 441/440 | 196/195, 325/324 | ||
| 2 | 12.12 | ? | 126/125, 225/224 | 121/120 | 144/143, 169/168 |
| 3 | 18.18 | 99/98, 100/99 | 91/90, 105/104 | ||
| 4 | 24.24 | 81/80 | 64/63 | 245/242 | 66/65, 78/77 |
| 5 | 30.30 | 55/54, 56/55 | 637/625, 648/637 | ||
| 6 | 36.36 | 128/125 | 49/48, 50/49 | ? | 143/140, 729/715 |
| 7 | 42.42 | 352/343 | 40/39, 169/165 | ||
| 8 | 48.48 | 250/243 | 36/35 | ? | 147/143 |
| 9 | 54.54 | 33/32, 567/550 | 65/63, 375/364 | ||
| 10 | 60.60 | 648/625 | 28/27 | 363/350 | 91/88, 175/169 |
| 11 | 66.66 | 80/77, 343/330 | 26/25, 27/26 | ||
| 12 | 72.72 | 25/24 | 729/700 | 126/121 | 169/162, 448/429 |
| 13 | 78.78 | 22/21, 288/275 | 245/234 | ||
| 14 | 84.84 | 256/243 | 21/20, 360/343 | 605/576 | 104/99, 150/143 |
| 15 | 90.90 | 539/512, 625/594 | 96/91, 343/325 | ||
| 16 | 96.96 | 135/128 | 200/189, 343/324 | 128/121, 363/343 | 55/52, 143/135 |
| 17 | 103.03 | 35/33, 297/280 | 52/49, 441/416 | ||
| 18 | 109.09 | 16/15 | ? | ? | 117/110, 180/169 |
| 19 | 115.15 | 77/72, 294/275 | 125/117, 260/243 | ||
| 20 | 121.21 | ? | 15/14, 343/320 | 648/605 | 338/315, 363/338 |
| 21 | 127.27 | 264/245, 320/297 | 14/13 | ||
| 22 | 133.33 | 27/25 | 175/162 | 121/112, 392/363 | 416/385, 676/625 |
| 23 | 139.39 | 250/231, 693/640 | 13/12, 550/507 | ||
| 24 | 145.45 | 625/576 | 49/45, 160/147 | ? | 99/91, 572/525 |
| 25 | 151.51 | 12/11, 275/252 | 273/250, 567/520 | ||
| 26 | 157.57 | 800/729 | 35/32, 192/175 | ? | 325/297, 385/351 |
| 27 | 163.63 | 11/10 | 100/91, 169/154 | ||
| 28 | 169.69 | ? | 54/49, 441/400 | 400/363 | 182/165, 315/286 |
| 29 | 175.75 | 256/231 | 72/65, 325/294 | ||
| 30 | 181.81 | 10/9 | 567/512 | 672/605 | 231/208, 375/338 |
| 31 | 187.87 | 49/44, 600/539 | 39/35 | ||
| 32 | 193.93 | ? | 28/25, 384/343 | 121/108 | 143/128, 160/143 |
| 33 | 200.00 | 55/49, 432/385 | 91/81, 175/156 | ||
| 34 | 206.06 | 9/8 | 640/567 | ? | 44/39, 169/150 |
| 35 | 212.12 | 112/99, 198/175 | 147/140, 325/288 | ||
| 36 | 218.18 | 256/225 | 245/216, 500/441 | 363/320, 686/605 | 162/143, 143/126 |
| 37 | 224.24 | 25/22 | 91/80, 338/297 | ||
| 38 | 230.30 | 729/640 | 8/7, 343/300 | ? | 143/125, 297/260 |
| 39 | 236.36 | 55/48, 63/55 | 416/363, 625/546 | ||
| 40 | 242.42 | 144/125 | 147/128, 280/243 | ? | 169/147, 455/396 |
| 41 | 248.48 | 231/200, 343/297 | 15/13, 52/45 | ||
| 42 | 254.54 | 125/108 | 81/70 | 140/121 | 196/169, 624/539 |
| 43 | 260.60 | 64/55, 220/189 | 65/56, 121/104 | ||
| 44 | 266.66 | ? | 7/6, 400/343 | ? | 286/245, 500/429 |
| 45 | 272.72 | 90/77 | 117/100, 198/169 | ||
| 46 | 278.78 | 75/64 | 147/125, 288/245 | ? | 168/143, 169/144 |
| 47 | 284.84 | 33/28, 324/275 | 245/208, 520/441 | ||
| 48 | 290.90 | 32/27 | 189/160 | 605/512 | 13/11, 77/65 |
| 49 | 296.96 | 196/165, 297/250 | 108/91, 208/175 | ||
| 50 | 303.03 | ? | 25/21, 343/288 | 144/121 | 143/120, 495/416 |
| 51 | 309.09 | 176/147 | 117/98, 140/117 | ||
| 52 | 315.15 | 6/5 | ? | 605/504 | 343/286, 405/338 |
| 53 | 321.21 | 77/64, 648/539 | 65/54, 125/104 | ||
| 54 | 327.27 | ? | 98/81, 135/112 | 121/100 | 110/91, 169/140 |
| 55 | 333.33 | 40/33, 297/245 | 63/52, 91/75 | ||
| 56 | 339.39 | 243/200 | 175/144 | 147/121 | 396/325, 468/385 |
| 57 | 345.45 | 11/9, 336/275 | 39/32 | ||
| 58 | 351.51 | 768/625 | 49/40, 60/49 | ? | 175/143, 364/297 |
| 59 | 357.57 | 27/22, 275/224 | 16/13, 338/275 | ||
| 60 | 363.63 | 100/81 | 216/175 | 121/98, 448/363 | 385/312, 625/507 |
| 61 | 369.69 | 99/80, 245/198 | 26/21, 225/182 | ||
| 62 | 375.75 | ? | 56/45, 243/196 | ? | 210/169, 273/220 |
| 63 | 381.81 | 96/77, 343/275 | 81/65, 156/125 | ||
| 64 | 387.87 | 5/4 | ? | 756/605 | 169/135, 429/343 |
| 65 | 393.93 | 44/35 | 49/39, 351/280 | ||
| 66 | 400.00 | 512/405 | 63/50, 432/343 | 121/96 | 180/143, 208/165 |
| 67 | 406.06 | 125/99, 486/385 | 91/72, 576/455 | ||
| 68 | 412.12 | 81/64 | 80/63, 343/270 | 768/605 | 33/26, 507/400 |
| 69 | 418.18 | 14/11, 275/216 | 312/245, 637/500 | ||
| 70 | 424.24 | 32/25 | 125/98, 245/192 | ? | 143/112, 351/275 |
| 71 | 430.30 | 77/60, 440/343 | 50/39, 104/81 | ||
| 72 | 436.36 | 625/486 | 9/7 | ? | 637/495, 676/525 |
| 73 | 442.42 | 128/99, 165/128 | 84/65, 156/121 | ||
| 74 | 448.48 | 162/125 | 35/27 | 363/280, 784/605 | 539/416, 572/441 |
| 75 | 454.54 | 100/77, 343/264 | 13/10, 135/104 | ||
| 76 | 460.60 | 125/96 | 64/49, 98/75 | ? | 441/338, 560/429 |
| 77 | 466.66 | 55/42, 72/55 | 637/486 | ||
| 78 | 472.72 | 320/243 | 21/16, 450/343 | ? | 130/99, 154/117 |
| 79 | 478.78 | 33/25, 392/297 | 120/91, 343/260 | ||
| 80 | 484.84 | ? | 250/189, 324/245 | 160/121 | 143/108, 189/143 |
| 81 | 490.90 | 175/132, 297/224 | 65/49, 121/91 | ||
| 82 | 496.96 | 4/3 | ? | ? | 225/169, 693/520 |
| 83 | 503.03 | 147/110, 385/288 | 234/175, 243/182 | ||
| 84 | 509.09 | ? | 75/56, 168/125 | ? | 169/126, 192/143 |
| 85 | 515.15 | 66/49, 400/297 | 35/26, 182/135 | ||
| 86 | 521.21 | 27/20 | 256/189 | 490/343, 605/448 | 104/77, 169/125 |
| 87 | 527.27 | 110/81, 224/165 | 65/48, 441/325 | ||
| 88 | 533.33 | 512/375 | 49/36, 200/147 | ? | 143/105, 495/364 |
| 89 | 539.39 | 15/11 | 160/117, 231/169 | ||
| 90 | 545.45 | 1000/729 | 48/35, 343/250 | ? | 196/143 |
| 91 | 551.51 | 11/8, 378/275 | 125/91, 260/189 | ||
| 92 | 557.57 | 864/625 | 112/81, 441/320 | ? | 91/66, 338/245 |
| 93 | 563.63 | 320/231, 686/495 | 18/13, 104/75 | ||
| 94 | 569.69 | 25/18 | 243/175 | 168/121 | 338/243 |
| 95 | 575.75 | 88/63, 384/275 | 39/28, 363/260 | ||
| 96 | 581.81 | ? | 7/5, 480/343 | 605/432 | 200/143, 416/297 |
| 97 | 587.87 | 108/77, 275/196 | 128/91, 351/250 | ||
| 98 | 593.93 | 45/32 | 343/243, 800/567 | 484/343, 512/363 | 55/39, 169/120 |
| 99 | 600.00 | 99/70, 140/99 | 147/104, 208/147 | ||
| 100 | 606.06 | 64/45 | 486/343, 567/400 | 343/242, 363/256 | 78/55, 240/169 |
| 101 | 612.12 | 77/54, 392/275 | 91/64, 500/351 | ||
| 102 | 618.18 | ? | 10/7, 343/240 | 864/605 | 143/100, 297/208 |
| 103 | 624.24 | 63/44, 275/192 | 56/39, 351/245 | ||
| 104 | 630.30 | 36/25 | 350/243 | 121/84 | 243/169 |
| 105 | 636.36 | 231/160, 495/343 | 13/9, 75/52 | ||
| 106 | 642.42 | 625/432 | 81/56, 640/441 | ? | 132/91, 245/169 |
| 107 | 648.48 | 16/11, 275/189 | 182/125, 189/130 | ||
| 108 | 654.54 | 729/500 | 35/24, 500/343 | ? | 143/98 |
| 109 | 660.60 | 22/15 | 117/80, 338/231 | ||
| 110 | 666.66 | 375/256 | 72/49, 147/100 | ? | 210/143, 715/486 |
| 111 | 672.72 | 81/55, 165/112 | 96/65, 637/432 | ||
| 112 | 678.78 | 40/27 | 189/128 | 363/245, 896/605 | 77/52, 250/169 |
| 113 | 684.84 | 49/33, 297/200 | 52/35, 135/91 | ||
| 114 | 690.90 | ? | 112/75, 125/84 | ? | 143/96, 252/169 |
| 115 | 696.96 | 220/147, 539/360 | 175/117, 364/243 | ||
| 116 | 703.03 | 3/2 | ? | ? | 338/225, 1140/693 |
| 117 | 709.09 | 264/175, 385/256 | 98/65, 182/121 | ||
| 118 | 715.15 | ? | 189/125, 245/162 | 121/80 | 169/112, 216/143 |
| 119 | 721.21 | 50/33, 297/196 | 91/60, 315/208 | ||
| 120 | 727.27 | 243/160 | 32/21, 343/225 | ? | 99/65, 117/77 |
| 121 | 733.33 | 55/36, 84/55 | 972/637 | ||
| 122 | 739.39 | 192/125 | 49/32, 75/49 | ? | 429/280, 455/297 |
| 123 | 745.45 | 77/50, 528/343 | 20/13, 169/110 | ||
| 124 | 751.51 | 125/81 | 54/35 | 560/363, 605/392 | 441/286, 832/539 |
| 125 | 757.57 | 99/64, 256/165 | 65/42, 121/78 | ||
| 126 | 763.63 | 972/625 | 14/9 | ? | 525/338, 990/637 |
| 127 | 769.69 | 120/77, 343/220 | 39/25, 81/52 | ||
| 128 | 775.75 | 25/16 | 196/125, 384/245 | ? | 224/143, 550/351 |
| 129 | 781.81 | 11/7, 432/275 | 245/156, 637/405 | ||
| 130 | 787.87 | 128/81 | 63/40, 540/343 | 605/384 | 52/33, 800/507 |
| 131 | 793.93 | 198/125, 385/243 | 144/91, 455/288 | ||
| 132 | 800.00 | 405/256 | 100/63, 343/216 | 192/121 | 143/90, 165/104 |
| 133 | 806.06 | 35/22 | 78/49, 539/338 | ||
| 134 | 812.12 | 8/5 | ? | 605/378 | 270/169, 686/429 |
| 135 | 818.18 | 77/48, 441/275 | 125/78, 130/81 | ||
| 136 | 824.24 | ? | 45/28, 392/243 | ? | 169/105, 440/273 |
| 137 | 830.30 | 160/99, 396/245 | 21/13, 364/225 | ||
| 138 | 836.36 | 81/50 | 175/108 | 196/121, 363/224 | 624/385, 715/441 |
| 139 | 842.42 | 44/27, 448/275 | 13/8, 275/169 | ||
| 140 | 848.48 | 625/384 | 49/30, 80/49 | ? | 286/175, 297/182 |
| 141 | 854.54 | 18/11, 275/168 | 64/39 | ||
| 142 | 860.60 | 400/243 | 288/175 | 242/147 | 325/198, 385/234 |
| 143 | 866.66 | 33/20, 490/297 | 104/63, 150/91 | ||
| 144 | 872.72 | ? | 81/49, 224/135 | 200/121 | 91/55, 280/169 |
| 145 | 878.78 | 128/77, 539/324 | 108/65, 208/125 | ||
| 146 | 884.84 | 5/3 | ? | 1008/605 | 572/343, 676/405 |
| 147 | 890.90 | 147/88 | 117/70, 196/117 | ||
| 148 | 896.96 | ? | 42/25, 576/343 | 121/72 | 240/143, 567/338 |
| 149 | 903.03 | 165/98, 500/297 | 91/54, 175/104 | ||
| 150 | 909.09 | 27/16 | 320/189 | 1024/605 | 22/13, 130/77 |
| 151 | 915.15 | 56/33, 275/162 | 416/245, 441/260 | ||
| 152 | 921.21 | 128/75 | 245/144, 250/147 | ? | 143/84, 288/169 |
| 153 | 927.27 | 77/45 | 169/99, 200/117 | ||
| 154 | 933.33 | ? | 12/7, 343/200 | ? | 245/143, 429/250 |
| 155 | 939.39 | 55/32, 189/110 | 112/65, 208/121 | ||
| 156 | 945.45 | 216/125 | 140/81 | 121/70 | 169/98, 539/312 |
| 157 | 951.51 | 343/198, 400/231 | 26/15, 45/26 | ||
| 158 | 957.57 | 125/72 | 243/140, 256/147 | ? | 294/169, 792/455 |
| 159 | 963.63 | 96/55, 110/63 | 363/208, 1092/625 | ||
| 160 | 969.69 | 1280/729 | 7/4, 600/343 | ? | 250/143, 429/245 |
| 161 | 975.75 | 44/25 | 160/91, 297/169 | ||
| 162 | 981.81 | 225/128 | 432/245, 441/250 | 605/343, 640/363 | 143/81, 169/96 |
| 163 | 987.87 | 99/56, 175/99 | 260/147, 576/325 | ||
| 164 | 993.93 | 16/9 | 567/320 | ? | 39/22, 231/130 |
| 165 | 1000.00 | 98/55, 385/216 | 162/91, 312/175 | ||
| 166 | 1006.06 | ? | 25/14, 343/192 | 216/121 | 143/80, 256/143 |
| 167 | 1012.12 | 88/49, 539/300 | 70/39 | ||
| 168 | 1018.18 | 9/5 | 1024/567 | 605/336 | 416/231, 676/375 |
| 169 | 1024.24 | 231/128 | 65/36, 1092/605 | ||
| 170 | 1030.30 | ? | 49/27, 800/441 | 363/200 | 165/91, 507/280 |
| 171 | 1036.36 | 20/11 | 91/50, 189/104 | ||
| 172 | 1042.42 | 729/400 | 64/35, 175/96 | ? | 594/325, 702/385 |
| 173 | 1048.48 | 11/6, 504/275 | 500/273, 1040/567 | ||
| 174 | 1054.54 | 1152/625 | 90/49, 147/80 | ? | 182/99, 525/286 |
| 175 | 1060.60 | 231/125, 1280/693 | 24/13, 507/275 | ||
| 176 | 1066.66 | 50/27 | 324/175 | 224/121, 363/196 | 385/208, 625/338 |
| 177 | 1072.72 | 245/132, 297/160 | 13/7 | ||
| 178 | 1078.78 | ? | 28/15, 640/343 | 605/324 | 315/169, 676/363 |
| 179 | 1084.84 | 144/77, 275/147 | 234/125, 243/130 | ||
| 180 | 1090.90 | 15/8 | ? | ? | 169/90, 220/117 |
| 181 | 1096.96 | 66/35, 560/297 | 49/26, 832/441 | ||
| 182 | 1103.03 | 256/135 | 189/100, 648/343 | 121/64, 686/363 | 104/55, 270/143 |
| 183 | 1109.09 | 1024/539, 1188/625 | 91/48, 650/343 | ||
| 184 | 1115.15 | 243/128 | 40/21, 343/180 | 1152/605 | 99/52, 143/75 |
| 185 | 1121.21 | 21/11, 275/144 | 468/245 | ||
| 186 | 1127.27 | 48/25 | 1400/729 | 121/63 | 324/169, 429/224 |
| 187 | 1133.33 | 77/40, 660/343 | 25/13, 52/27 | ||
| 188 | 1139.39 | 625/324 | 27/14 | 700/363 | 176/91, 338/175 |
| 189 | 1145.45 | 64/33, 1100/567 | 126/65, 605/312 | ||
| 190 | 1151.51 | 243/125 | 35/18 | ? | 286/147 |
| 191 | 1157.57 | 343/176 | 39/20, 330/169 | ||
| 192 | 1163.63 | 125/64 | 49/25, 96/49 | ? | 280/143, 1430/729 |
| 193 | 1169.69 | 108/55, 55/27 | 637/324, 1250/637 | ||
| 194 | 1175.75 | 160/81 | 63/32 | 484/245 | 65/33, 77/39 |
| 195 | 1181.81 | 196/99, 99/50 | 180/91, 208/105 | ||
| 196 | 1187.87 | ? | 125/63, 448/225 | 240/121 | 143/72, 336/169 |
| 197 | 1193.93 | 539/270, 768/385 | 195/98, 363/182 | ||
| 198 | 1200.00 | 2/1 | |||