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Imanuel's Bohlen-Pierce JI 1 – A new just tuning
Scala file contents
! Imanuel's Bohlen-Pierce JI 1.scl ! A new just tuning, more info at http://imanuelhab.mooo.com/bp-new-just-tuning-imanuel 13 ! 25/23 13/11 9/7 7/5 29/19 5/3 9/5 49/25 15/7 7/3 33/13 69/25 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 | 284.4 | 309.2 | 336.4 | 366.3 | 399.3 | 436 | 470.9 | 512.8 | 560.6 | 610.5 | 664.1 | 722.1 | 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 | 98.7 | 197.7 | 297.4 | 398.2 | 500.4 | 604.5 | 695.5 | 796.3 | 901.8 | 1002.6 | 1102.3 | 1201.3 | 1300 |
| 0 | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | 900 | 1000 | 1100 | 1200 | 1300 |
| 0 | -1.3 | -2.3 | -2.6 | -1.8 | 0.4 | 4.5 | -4.5 | -3.7 | 1.8 | 2.6 | 2.3 | 1.3 | 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 | 144.4 | 289.2 | 435.1 | 582.5 | 732.1 | 884.4 | 1017.6 | 1165 | 1319.4 | 1466.9 | 1612.7 | 1757.6 | 1902 |
| 0 | 100 | 300 | 400 | 600 | 700 | 900 | 1000 | 1200 | 1300 | 1500 | 1600 | 1800 | 1900 |
| 0 | 44.4 | -10.8 | 35.1 | -17.5 | 32.1 | -15.6 | 17.6 | -35 | 19.4 | -33.1 | 12.7 | -42.4 | 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 | 25 | 13 | 9 | 7 | 29 | 5 | 9 | 49 | 15 | 7 | 33 | 69 | 3 |
| 5 | 13 | 3 | 7 | 29 | 5 | 3 | 7 | 5 | 7 | 11 | 23 | 3 | |
| 5 | 3 | 3 | 7 | 3 | 3 | 3 | |||||||
Denominators | |||||||||||||
| D♭ | G♭ | J♭ | B♭ | ||||||||||
| C | C♯ | D | E | F | F♯ | G | H | H♯ | J | A | A♯ | B | C |
| 1 | 23 | 11 | 7 | 5 | 19 | 3 | 5 | 25 | 7 | 3 | 13 | 25 | 1 |
| 23 | 11 | 7 | 5 | 19 | 3 | 5 | 5 | 7 | 3 | 13 | 5 | ||
| 5 | 5 | ||||||||||||
Intervals | |||||||||||||
| 1 | 25 | 13 | 9 | 7 | 29 | 5 | 9 | 49 | 15 | 7 | 33 | 69 | 3 |
| 1 | 23 | 11 | 7 | 5 | 19 | 3 | 5 | 25 | 7 | 3 | 13 | 25 | 1 |
| 9 | 1127 | 165 | 49 | 165 | 1311 | 9 | 375 | 975 | 189 | 63 | 1131 | 375 | 27 |
| 5 | 625 | 91 | 27 | 91 | 725 | 5 | 207 | 539 | 105 | 35 | 627 | 207 | 15 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 1 | 21 | 7 | 3 | 3 | 3 |
| 9 | 1127 | 165 | 49 | 165 | 1311 | 9 | 125 | 975 | 9 | 9 | 377 | 125 | 9 |
| 5 | 625 | 91 | 27 | 91 | 725 | 5 | 69 | 539 | 5 | 5 | 209 | 69 | 5 |
| 9 | 1127 | 165 | 49 | 165 | 1311 | 9 | 125 | 975 | 9 | 9 | 377 | 125 | 9 |
| 5 | 625 | 91 | 27 | 91 | 725 | 5 | 69 | 539 | 5 | 5 | 209 | 69 | 5 |
| 7 | 667 | 55 | 63 | 245 | 285 | 21 | 165 | 1725 | 21 | 225 | 507 | 675 | 21 |
| 5 | 475 | 39 | 45 | 175 | 203 | 15 | 117 | 1225 | 15 | 161 | 363 | 483 | 15 |
| 1 | 1 | 1 | 9 | 35 | 1 | 3 | 3 | 25 | 3 | 1 | 3 | 3 | 3 |
| 7 | 667 | 55 | 7 | 7 | 285 | 7 | 55 | 69 | 7 | 225 | 169 | 225 | 7 |
| 5 | 475 | 39 | 5 | 5 | 203 | 5 | 39 | 49 | 5 | 161 | 121 | 161 | 5 |
| 7 | 667 | 55 | 7 | 7 | 285 | 7 | 55 | 69 | 7 | 225 | 169 | 225 | 7 |
| 5 | 475 | 39 | 5 | 5 | 203 | 5 | 39 | 49 | 5 | 161 | 121 | 161 | 5 |
| 25 | 299 | 99 | 49 | 145 | 95 | 27 | 245 | 375 | 49 | 99 | 897 | 75 | 75 |
| 23 | 275 | 91 | 45 | 133 | 87 | 25 | 225 | 343 | 45 | 91 | 825 | 69 | 69 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 5 | 1 | 1 | 1 | 3 | 3 | 3 |
| 25 | 299 | 99 | 49 | 145 | 95 | 27 | 49 | 375 | 49 | 99 | 299 | 25 | 25 |
| 23 | 275 | 91 | 45 | 133 | 87 | 25 | 45 | 343 | 45 | 91 | 275 | 23 | 23 |
| 25 | 299 | 99 | 49 | 145 | 95 | 27 | 49 | 375 | 49 | 99 | 299 | 25 | 25 |
| 23 | 275 | 91 | 45 | 133 | 87 | 25 | 45 | 343 | 45 | 91 | 275 | 23 | 23 |
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 | 75 | 147 | 117 | 135 | 243 | 63 | 567 | 2673 | 7047 | 16767 | 1215 | 2187 |
| 3 | 5 | 7 | 13 | 5 | 3 | 7 | 7 | 11 | 29 | 23 | 5 | 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 | 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 | 23 | 25 | 11 | 7 | 7 | 1 | 5 | 13 | 19 | 25 | 1 | 1 |
| 5 | 23 | 5 | 11 | 7 | 7 | 5 | 13 | 19 | 5 | ||||
| 5 | 5 | ||||||||||||
Intervals | |||||||||||||
| 1 | 9 | 75 | 147 | 117 | 135 | 243 | 63 | 567 | 2673 | 7047 | 16767 | 1215 | 2187 |
| 1 | 5 | 23 | 25 | 11 | 7 | 7 | 1 | 5 | 13 | 19 | 25 | 1 | 1 |
| 9 | 375 | 3381 | 2925 | 1485 | 1701 | 441 | 567 | 13365 | 91611 | 318573 | 30375 | 2187 | 19683 |
| 5 | 207 | 1875 | 1617 | 819 | 945 | 243 | 315 | 7371 | 50787 | 176175 | 16767 | 1215 | 10935 |
| 1 | 3 | 3 | 3 | 9 | 189 | 9 | 63 | 81 | 243 | 243 | 243 | 243 | 2187 |
| 9 | 125 | 1127 | 975 | 165 | 9 | 49 | 9 | 165 | 377 | 1311 | 125 | 9 | 9 |
| 5 | 69 | 625 | 539 | 91 | 5 | 27 | 5 | 91 | 209 | 725 | 69 | 5 | 5 |
| 9 | 125 | 1127 | 975 | 165 | 9 | 49 | 9 | 165 | 377 | 1311 | 125 | 9 | 9 |
| 5 | 69 | 625 | 539 | 91 | 5 | 27 | 5 | 91 | 209 | 725 | 69 | 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 | 69 | 87 | 99 | 63 | 21 | 243 | 405 | 1053 | 3969 | 6075 | 2187 | 729 |
| 5 | 23 | 29 | 11 | 7 | 7 | 3 | 5 | 13 | 7 | 5 | 3 | 3 | |
| 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 7 | 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 | ||||||||||||
Denominators (circle of fourths) | |||||||||||||
| G♭ | B♭ | J♭ | D♭ | ||||||||||
| C | G | B | F♯ | A♯ | F | A | E | J | D | H♯ | C♯ | H | C |
| 1 | 3 | 25 | 19 | 13 | 5 | 1 | 7 | 7 | 11 | 25 | 23 | 5 | 1 |
| 3 | 5 | 19 | 13 | 5 | 7 | 7 | 11 | 5 | 23 | 5 | |||
| 5 | 5 | ||||||||||||
Intervals | |||||||||||||
| 1 | 5 | 69 | 87 | 99 | 63 | 21 | 243 | 405 | 1053 | 3969 | 6075 | 2187 | 729 |
| 1 | 3 | 25 | 19 | 13 | 5 | 1 | 7 | 7 | 11 | 25 | 23 | 5 | 1 |
| 5 | 207 | 2175 | 1881 | 819 | 105 | 243 | 2835 | 7371 | 43659 | 151875 | 50301 | 3645 | 3645 |
| 3 | 125 | 1311 | 1131 | 495 | 63 | 147 | 1701 | 4455 | 26325 | 91287 | 30375 | 2187 | 2187 |
| 1 | 1 | 3 | 3 | 9 | 21 | 3 | 567 | 81 | 81 | 81 | 243 | 729 | 729 |
| 5 | 207 | 725 | 627 | 91 | 5 | 81 | 5 | 91 | 539 | 1875 | 207 | 5 | 5 |
| 3 | 125 | 437 | 377 | 55 | 3 | 49 | 3 | 55 | 325 | 1127 | 125 | 3 | 3 |
| 5 | 207 | 725 | 627 | 91 | 5 | 81 | 5 | 91 | 539 | 1875 | 207 | 5 | 5 |
| 3 | 125 | 437 | 377 | 55 | 3 | 49 | 3 | 55 | 325 | 1127 | 125 | 3 | 3 |
Shift intervals in table by fourths | |||||||||||||
Other tunings
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