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Music & Audio
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Equally tempered intervals versus just intervals
Primes lower than 7, factors less than 512, ratios within 30 cents
| minor second (1.059) |
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| ratio | decimal | diff |
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| 15:14 | 1.071 | 19.4 |
| 16:15 | 1.067 | 11.7 |
| 21:20 | 1.05 | -15.5 |
| 25:24 | 1.042 | -29.3 |
| 135:128 | 1.055 | -7.8 |
| 200:189 | 1.058 | -2.1 |
| 256:243 | 1.054 | -9.8 |
| 256:245 | 1.045 | -24 |
| 343:320 | 1.072 | 20.2 |
| 343:324 | 1.059 | -1.3 |
| 360:343 | 1.05 | -16.3 |
| 392:375 | 1.045 | -23.2 |
| | major second (1.122) |
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| ratio | decimal | diff |
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| 9:8 | 1.125 | 3.9 |
| 10:9 | 1.111 | -17.6 |
| 28:25 | 1.12 | -3.8 |
| 125:112 | 1.116 | -9.9 |
| 245:216 | 1.134 | 18.1 |
| 256:225 | 1.138 | 23.5 |
| 384:343 | 1.12 | -4.5 |
| 448:405 | 1.106 | -25.3 |
| 500:441 | 1.134 | 17.4 |
| | minor third (1.189) |
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| ratio | decimal | diff |
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| 6:5 | 1.2 | 15.6 |
| 25:21 | 1.19 | 1.8 |
| 32:27 | 1.185 | -5.9 |
| 75:64 | 1.172 | -25.4 |
| 98:81 | 1.21 | 29.8 |
| 135:112 | 1.205 | 23.4 |
| 147:125 | 1.176 | -19.3 |
| 189:160 | 1.181 | -11.6 |
| 288:245 | 1.176 | -20.1 |
| 343:288 | 1.191 | 2.6 |
| 405:343 | 1.181 | -12.3 |
| 448:375 | 1.195 | 7.9 |
| | major third (1.26) |
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| ratio | decimal | diff |
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| 5:4 | 1.25 | -13.7 |
| 32:25 | 1.28 | 27.4 |
| 56:45 | 1.244 | -21.4 |
| 63:50 | 1.26 | 0.1 |
| 80:63 | 1.27 | 13.6 |
| 81:64 | 1.266 | 7.8 |
| 125:98 | 1.276 | 21.3 |
| 245:192 | 1.276 | 22 |
| 243:196 | 1.24 | -27.9 |
| 343:270 | 1.27 | 14.3 |
| 432:343 | 1.259 | -0.6 |
| 512:405 | 1.264 | 5.9 |
| | perfect fourth (1.335) |
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| ratio | decimal | diff |
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| 4:3 | 1.333 | -2 |
| 21:16 | 1.313 | -29.2 |
| 27:20 | 1.35 | 19.6 |
| 75:56 | 1.339 | 5.8 |
| 168:125 | 1.344 | 11.8 |
| 250:189 | 1.323 | -15.7 |
| 256:189 | 1.355 | 25.3 |
| 320:243 | 1.317 | -23.5 |
| 324:245 | 1.322 | -16.1 |
| 343:256 | 1.34 | 6.5 |
| 450:343 | 1.312 | -29.9 |
| | tritone [1:√2] (1.414) |
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| ratio | decimal | diff |
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| 7:5 | 1.4 | -17.5 |
| 10:7 | 1.429 | 17.5 |
| 45:32 | 1.406 | -9.8 |
| 64:45 | 1.422 | 9.8 |
| 343:240 | 1.429 | 18.2 |
| 343:243 | 1.412 | -3.3 |
| 480:343 | 1.399 | -18.2 |
| 486:343 | 1.417 | 3.3 |
| | perfect fifth (1.498) |
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| ratio | decimal | diff |
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| 3:2 | 1.5 | 2 |
| 32:21 | 1.524 | 29.2 |
| 40:27 | 1.481 | -19.6 |
| 112:75 | 1.493 | -5.8 |
| 125:84 | 1.488 | -11.8 |
| 189:125 | 1.512 | 15.7 |
| 189:128 | 1.477 | -25.3 |
| 243:160 | 1.519 | 23.5 |
| 245:162 | 1.512 | 16.1 |
| 343:225 | 1.524 | 29.9 |
| 512:343 | 1.493 | -6.5 |
| | minor sixth (1.587) |
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| ratio | decimal | diff |
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| 8:5 | 1.6 | 13.7 |
| 25:16 | 1.563 | -27.4 |
| 45:28 | 1.607 | 21.4 |
| 63:40 | 1.575 | -13.6 |
| 100:63 | 1.587 | -0.1 |
| 128:81 | 1.58 | -7.8 |
| 196:125 | 1.568 | -21.3 |
| 343:216 | 1.588 | 0.6 |
| 392:243 | 1.613 | 27.9 |
| 384:245 | 1.567 | -22 |
| 405:256 | 1.582 | -5.9 |
| | major sixth (1.682) |
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| ratio | decimal | diff |
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| 5:3 | 1.667 | -15.6 |
| 27:16 | 1.688 | 5.9 |
| 42:25 | 1.68 | -1.8 |
| 81:49 | 1.653 | -29.8 |
| 128:75 | 1.707 | 25.4 |
| 224:135 | 1.659 | -23.4 |
| 245:144 | 1.701 | 20.1 |
| 250:147 | 1.701 | 19.3 |
| 320:189 | 1.693 | 11.6 |
| 375:224 | 1.674 | -7.9 |
| | minor seventh (1.782) |
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| ratio | decimal | diff |
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| 9:5 | 1.8 | 17.6 |
| 16:9 | 1.778 | -3.9 |
| 25:14 | 1.786 | 3.8 |
| 224:125 | 1.792 | 9.9 |
| 225:128 | 1.758 | -23.5 |
| 343:192 | 1.786 | 4.5 |
| 405:224 | 1.808 | 25.3 |
| 432:245 | 1.763 | -18.1 |
| 441:250 | 1.764 | -17.4 |
| | major seventh (1.888) |
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| ratio | decimal | diff |
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| 15:8 | 1.875 | -11.7 |
| 28:15 | 1.867 | -19.4 |
| 40:21 | 1.905 | 15.5 |
| 48:25 | 1.92 | 29.3 |
| 189:100 | 1.89 | 2.1 |
| 243:128 | 1.898 | 9.8 |
| 245:128 | 1.914 | 24 |
| 256:135 | 1.896 | 7.8 |
| 343:180 | 1.906 | 16.3 |
| 375:196 | 1.913 | 23.2 |
| | unison/octave (2) |
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| ratio | decimal | diff |
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| 4:2 | 2 | -0 |
| 63:32 | 1.969 | -27.3 |
| 125:63 | 1.984 | -13.8 |
| 160:81 | 1.975 | -21.5 |
| 448:225 | 1.991 | -7.7 |
| 486:245 | 1.984 | -14.2 |
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Website by Joachim Michaelis
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