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Bohlen-Pierce JI – A scale with tritave equivalence
Scala file contents
! Bohlen-Pierce JI.scl ! A scale with tritave equivalence, more info at http://imanuelhab.mooo.com/bp-just-tuning 13 ! 27/25 25/21 9/7 7/5 75/49 5/3 9/5 49/25 15/7 7/3 63/25 25/9 3/1
Prime factors and frequencies
Frequencies (Hz) | |||||||||||||
| D♭ | G♭ | J♭ | B♭ | ||||||||||
| C | C♯ | D | E | F | F♯ | G | H | H♯ | J | A | A♯ | B | C |
| 261.6 | 282.6 | 311.5 | 336.4 | 366.3 | 400.4 | 436 | 470.9 | 512.8 | 560.6 | 610.5 | 659.3 | 726.7 | 784.9 |
Logarithmic frequency values (cents) | |||||||||||||
| D♭ | G♭ | J♭ | B♭ | ||||||||||
| C | C♯ | D | E | F | F♯ | G | H | H♯ | J | A | A♯ | B | C |
| 0 | 91.1 | 206.3 | 297.4 | 398.2 | 503.7 | 604.5 | 695.5 | 796.3 | 901.8 | 1002.6 | 1093.7 | 1208.9 | 1300 |
| 0 | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | 900 | 1000 | 1100 | 1200 | 1300 |
| 0 | -8.9 | 6.3 | -2.6 | -1.8 | 3.7 | 4.5 | -4.5 | -3.7 | 1.8 | 2.6 | -6.3 | 8.9 | 0 |
Logarithmic frequency values (cents, for 12-ET with octave equivalence) | |||||||||||||
| D♭ | G♭ | J♭ | B♭ | ||||||||||
| C | C♯ | D | E | F | F♯ | G | H | H♯ | J | A | A♯ | B | C |
| 0 | 133.2 | 301.8 | 435.1 | 582.5 | 736.9 | 884.4 | 1017.6 | 1165 | 1319.4 | 1466.9 | 1600.1 | 1768.7 | 1902 |
| 0 | 100 | 300 | 400 | 600 | 700 | 900 | 1000 | 1200 | 1300 | 1500 | 1600 | 1800 | 1900 |
| 0 | 33.2 | 1.8 | 35.1 | -17.5 | 36.9 | -15.6 | 17.6 | -35 | 19.4 | -33.1 | 0.1 | -31.3 | 2 |
| C | C♯ | D♯ | E | F♯ | G | A | A♯ | C | C♯ | D♯ | E | F♯ | G |
| D♭ | E♭ | G♭ | B♭ | D♭ | E♭ | G♭ | |||||||
Numerators | |||||||||||||
| D♭ | G♭ | J♭ | B♭ | ||||||||||
| C | C♯ | D | E | F | F♯ | G | H | H♯ | J | A | A♯ | B | C |
| 1 | 27 | 25 | 9 | 7 | 75 | 5 | 9 | 49 | 15 | 7 | 63 | 25 | 3 |
| 3 | 5 | 3 | 7 | 5 | 5 | 3 | 7 | 5 | 7 | 7 | 5 | 3 | |
| 3 | 5 | 3 | 5 | 3 | 7 | 3 | 3 | 5 | |||||
| 3 | 3 | 3 | |||||||||||
Denominators | |||||||||||||
| D♭ | G♭ | J♭ | B♭ | ||||||||||
| C | C♯ | D | E | F | F♯ | G | H | H♯ | J | A | A♯ | B | C |
| 1 | 25 | 21 | 7 | 5 | 49 | 3 | 5 | 25 | 7 | 3 | 25 | 9 | 1 |
| 5 | 7 | 7 | 5 | 7 | 3 | 5 | 5 | 7 | 3 | 5 | 3 | ||
| 5 | 3 | 7 | 5 | 5 | 3 | ||||||||
Intervals | |||||||||||||
| 1 | 27 | 25 | 9 | 7 | 75 | 5 | 9 | 49 | 15 | 7 | 63 | 25 | 3 |
| 1 | 25 | 21 | 7 | 5 | 49 | 3 | 5 | 25 | 7 | 3 | 25 | 9 | 1 |
| 9 | 1225 | 315 | 49 | 315 | 1225 | 9 | 405 | 1875 | 189 | 63 | 5625 | 135 | 27 |
| 5 | 675 | 175 | 27 | 175 | 675 | 5 | 225 | 1029 | 105 | 35 | 3087 | 75 | 15 |
| 1 | 25 | 35 | 1 | 35 | 25 | 1 | 45 | 3 | 21 | 7 | 9 | 15 | 3 |
| 9 | 49 | 9 | 49 | 9 | 49 | 9 | 9 | 625 | 9 | 9 | 625 | 9 | 9 |
| 5 | 27 | 5 | 27 | 5 | 27 | 5 | 5 | 343 | 5 | 5 | 343 | 5 | 5 |
| 9 | 49 | 9 | 49 | 9 | 49 | 9 | 9 | 625 | 9 | 9 | 625 | 9 | 9 |
| 5 | 27 | 5 | 27 | 5 | 27 | 5 | 5 | 343 | 5 | 5 | 343 | 5 | 5 |
| 7 | 1875 | 105 | 63 | 245 | 735 | 21 | 315 | 625 | 21 | 243 | 1875 | 243 | 21 |
| 5 | 1323 | 75 | 45 | 175 | 525 | 15 | 225 | 441 | 15 | 175 | 1323 | 175 | 15 |
| 1 | 3 | 15 | 9 | 35 | 105 | 3 | 45 | 1 | 3 | 1 | 3 | 1 | 3 |
| 7 | 625 | 7 | 7 | 7 | 7 | 7 | 7 | 625 | 7 | 243 | 625 | 243 | 7 |
| 5 | 441 | 5 | 5 | 5 | 5 | 5 | 5 | 441 | 5 | 175 | 441 | 175 | 5 |
| 7 | 625 | 7 | 7 | 7 | 7 | 7 | 7 | 625 | 7 | 243 | 625 | 243 | 7 |
| 5 | 441 | 5 | 5 | 5 | 5 | 5 | 5 | 441 | 5 | 175 | 441 | 175 | 5 |
| 27 | 625 | 189 | 49 | 375 | 245 | 27 | 245 | 375 | 49 | 189 | 625 | 27 | 81 |
| 25 | 567 | 175 | 45 | 343 | 225 | 25 | 225 | 343 | 45 | 175 | 567 | 25 | 75 |
| 1 | 1 | 7 | 1 | 1 | 5 | 1 | 5 | 1 | 1 | 7 | 1 | 1 | 3 |
| 27 | 625 | 27 | 49 | 375 | 49 | 27 | 49 | 375 | 49 | 27 | 625 | 27 | 27 |
| 25 | 567 | 25 | 45 | 343 | 45 | 25 | 45 | 343 | 45 | 25 | 567 | 25 | 25 |
| 27 | 625 | 27 | 49 | 375 | 49 | 27 | 49 | 375 | 49 | 27 | 625 | 27 | 27 |
| 25 | 567 | 25 | 45 | 343 | 45 | 25 | 45 | 343 | 45 | 25 | 567 | 25 | 25 |
Shift intervals in table | |||||||||||||
Numerators (circle of fifths) | |||||||||||||
| D♭ | J♭ | B♭ | G♭ | ||||||||||
| C | H | C♯ | H♯ | D | J | E | A | F | A♯ | F♯ | B | G | C |
| 1 | 9 | 81 | 147 | 75 | 135 | 243 | 63 | 567 | 5103 | 18225 | 675 | 1215 | 2187 |
| 3 | 3 | 7 | 5 | 5 | 3 | 7 | 7 | 7 | 5 | 5 | 5 | 3 | |
| 3 | 3 | 7 | 5 | 3 | 3 | 3 | 3 | 3 | 5 | 5 | 3 | 3 | |
| 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | ||
| 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | |||||
| 3 | 3 | 3 | 3 | 3 | 3 | 3 | |||||||
| 3 | 3 | 3 | 3 | ||||||||||
| 3 | 3 | 3 | |||||||||||
| 3 | |||||||||||||
Denominators (circle of fifths) | |||||||||||||
| D♭ | J♭ | B♭ | G♭ | ||||||||||
| C | H | C♯ | H♯ | D | J | E | A | F | A♯ | F♯ | B | G | C |
| 1 | 5 | 25 | 25 | 7 | 7 | 7 | 1 | 5 | 25 | 49 | 1 | 1 | 1 |
| 5 | 5 | 5 | 7 | 7 | 7 | 5 | 5 | 7 | |||||
| 5 | 5 | 5 | 7 | ||||||||||
Intervals | |||||||||||||
| 1 | 9 | 81 | 147 | 75 | 135 | 243 | 63 | 567 | 5103 | 18225 | 675 | 1215 | 2187 |
| 1 | 5 | 25 | 25 | 7 | 7 | 7 | 1 | 5 | 25 | 49 | 1 | 1 | 1 |
| 9 | 405 | 3675 | 1875 | 945 | 1701 | 441 | 567 | 25515 | 455625 | 33075 | 1215 | 2187 | 19683 |
| 5 | 225 | 2025 | 1029 | 525 | 945 | 243 | 315 | 14175 | 250047 | 18225 | 675 | 1215 | 10935 |
| 1 | 45 | 75 | 3 | 105 | 189 | 9 | 63 | 2835 | 729 | 675 | 135 | 243 | 2187 |
| 9 | 9 | 49 | 625 | 9 | 9 | 49 | 9 | 9 | 625 | 49 | 9 | 9 | 9 |
| 5 | 5 | 27 | 343 | 5 | 5 | 27 | 5 | 5 | 343 | 27 | 5 | 5 | 5 |
| 9 | 9 | 49 | 625 | 9 | 9 | 49 | 9 | 9 | 625 | 49 | 9 | 9 | 9 |
| 5 | 5 | 27 | 343 | 5 | 5 | 27 | 5 | 5 | 343 | 27 | 5 | 5 | 5 |
Shift intervals in table by fifths | |||||||||||||
Numerators (circle of fourths) | |||||||||||||
| G♭ | B♭ | J♭ | D♭ | ||||||||||
| C | G | B | F♯ | A♯ | F | A | E | J | D | H♯ | C♯ | H | C |
| 1 | 5 | 25 | 225 | 189 | 63 | 21 | 243 | 405 | 675 | 3969 | 6561 | 2187 | 729 |
| 5 | 5 | 5 | 7 | 7 | 7 | 3 | 5 | 5 | 7 | 3 | 3 | 3 | |
| 5 | 5 | 3 | 3 | 3 | 3 | 3 | 5 | 7 | 3 | 3 | 3 | ||
| 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | ||||
| 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | |||||
| 3 | 3 | 3 | 3 | 3 | 3 | 3 | |||||||
| 3 | 3 | 3 | 3 | ||||||||||
| 3 | 3 | ||||||||||||
| 3 | |||||||||||||
Denominators (circle of fourths) | |||||||||||||
| G♭ | B♭ | J♭ | D♭ | ||||||||||
| C | G | B | F♯ | A♯ | F | A | E | J | D | H♯ | C♯ | H | C |
| 1 | 3 | 9 | 49 | 25 | 5 | 1 | 7 | 7 | 7 | 25 | 25 | 5 | 1 |
| 3 | 3 | 7 | 5 | 5 | 7 | 7 | 7 | 5 | 5 | 5 | |||
| 3 | 7 | 5 | 5 | 5 | |||||||||
Intervals | |||||||||||||
| 1 | 5 | 25 | 225 | 189 | 63 | 21 | 243 | 405 | 675 | 3969 | 6561 | 2187 | 729 |
| 1 | 3 | 9 | 49 | 25 | 5 | 1 | 7 | 7 | 7 | 25 | 25 | 5 | 1 |
| 5 | 75 | 2025 | 9261 | 1575 | 105 | 243 | 2835 | 4725 | 27783 | 164025 | 54675 | 3645 | 3645 |
| 3 | 45 | 1225 | 5625 | 945 | 63 | 147 | 1701 | 2835 | 16875 | 99225 | 32805 | 2187 | 2187 |
| 1 | 15 | 25 | 9 | 315 | 21 | 3 | 567 | 945 | 27 | 2025 | 10935 | 729 | 729 |
| 5 | 5 | 81 | 1029 | 5 | 5 | 81 | 5 | 5 | 1029 | 81 | 5 | 5 | 5 |
| 3 | 3 | 49 | 625 | 3 | 3 | 49 | 3 | 3 | 625 | 49 | 3 | 3 | 3 |
| 5 | 5 | 81 | 1029 | 5 | 5 | 81 | 5 | 5 | 1029 | 81 | 5 | 5 | 5 |
| 3 | 3 | 49 | 625 | 3 | 3 | 49 | 3 | 3 | 625 | 49 | 3 | 3 | 3 |
Shift intervals in table by fourths | |||||||||||||
Other tunings
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