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Imanuel's 25-tone half third 80 to 160 reflection harmonic tuning – A reflection harmonic tuning
Scala file contents
! Imanuel's 25-tone half third 80 to 160 reflection harmonic tuning.scl ! A reflection harmonic tuning, more info at http://imanuelhab.mooo.com/25-tone-half-third-80-to-160-reflection-harmonic-tuning-imanuel 25 ! 41/40 21/20 40/37 10/9 8/7 47/40 40/33 5/4 32/25 21/16 80/59 7/5 10/7 59/40 121/80 25/16 8/5 33/20 27/16 7/4 143/80 37/20 151/80 80/41 2/1
Prime factors and frequencies
Frequencies (Hz) | |||||||||||||||||||||||||
D♭ | D♭ | E♭ | E♭ | G♭ | G♭ | A♭ | A♭ | B♭ | B♭ | ||||||||||||||||
C | C | C♯ | C♯ | D | D | D♯ | D♯ | E | E | F | F | F♯ | F♯ | G | G | G♯ | G♯ | A | A | A♯ | A♯ | B | B | C | C |
261.6 | 268.2 | 274.7 | 282.8 | 290.7 | 299 | 307.4 | 317.1 | 327 | 334.9 | 343.4 | 354.7 | 366.3 | 373.8 | 385.9 | 395.7 | 408.8 | 418.6 | 431.7 | 441.5 | 457.8 | 467.7 | 484 | 493.8 | 510.5 | 523.3 |
Logarithmic frequency values (cents) | |||||||||||||||||||||||||
D♭ | D♭ | E♭ | E♭ | G♭ | G♭ | A♭ | A♭ | B♭ | B♭ | ||||||||||||||||
C | C | C♯ | C♯ | D | D | D♯ | D♯ | E | E | F | F | F♯ | F♯ | G | G | G♯ | G♯ | A | A | A♯ | A♯ | B | B | C | C |
0 | 89.1 | 176 | 281.2 | 380 | 481.6 | 581.7 | 693.8 | 804.8 | 890.4 | 980.8 | 1098.2 | 1213.6 | 1286.4 | 1401.8 | 1492.3 | 1609.6 | 1695.2 | 1806.2 | 1887.2 | 2018.4 | 2094.9 | 2218.8 | 2291.2 | 2410.9 | 2500 |
0 | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | 900 | 1000 | 1100 | 1200 | 1300 | 1400 | 1500 | 1600 | 1700 | 1800 | 1900 | 2000 | 2100 | 2200 | 2300 | 2400 | 2500 |
0 | -10.9 | -24 | -18.8 | -20 | -18.4 | -18.3 | -6.2 | 4.8 | -9.6 | -19.2 | -1.8 | 13.6 | -13.6 | 1.8 | -7.7 | 9.6 | -4.8 | 6.2 | -12.8 | 18.4 | -5.1 | 18.8 | -8.8 | 10.9 | 0 |
Logarithmic frequency values (cents, for 12-ET with octave equivalence) | |||||||||||||||||||||||||
D♭ | D♭ | E♭ | E♭ | G♭ | G♭ | A♭ | A♭ | B♭ | B♭ | ||||||||||||||||
C | C | C♯ | C♯ | D | D | D♯ | D♯ | E | E | F | F | F♯ | F♯ | G | G | G♯ | G♯ | A | A | A♯ | A♯ | B | B | C | C |
0 | 42.7 | 84.5 | 135 | 182.4 | 231.2 | 279.2 | 333 | 386.3 | 427.4 | 470.8 | 527.1 | 582.5 | 617.5 | 672.9 | 716.3 | 772.6 | 813.7 | 867 | 905.9 | 968.8 | 1005.5 | 1065 | 1099.8 | 1157.3 | 1200 |
0 | 0 | 100 | 100 | 200 | 200 | 300 | 300 | 400 | 400 | 500 | 500 | 600 | 600 | 700 | 700 | 800 | 800 | 900 | 900 | 1000 | 1000 | 1100 | 1100 | 1200 | 1200 |
0 | 42.7 | -15.5 | 35 | -17.6 | 31.2 | -20.8 | 33 | -13.7 | 27.4 | -29.2 | 27.1 | -17.5 | 17.5 | -27.1 | 16.3 | -27.4 | 13.7 | -33 | 5.9 | -31.2 | 5.5 | -35 | -0.2 | -42.7 | 0 |
C | C | C♯ | C♯ | D | D | D♯ | D♯ | E | E | F | F | F♯ | F♯ | G | G | G♯ | G♯ | A | A | A♯ | A♯ | B | B | C | C |
D♭ | D♭ | E♭ | E♭ | G♭ | G♭ | A♭ | A♭ | B♭ | B♭ | ||||||||||||||||
Numerators | |||||||||||||||||||||||||
D♭ | D♭ | E♭ | E♭ | G♭ | G♭ | A♭ | A♭ | B♭ | B♭ | ||||||||||||||||
C | C | C♯ | C♯ | D | D | D♯ | D♯ | E | E | F | F | F♯ | F♯ | G | G | G♯ | G♯ | A | A | A♯ | A♯ | B | B | C | C |
1 | 41 | 21 | 40 | 10 | 8 | 47 | 40 | 5 | 32 | 21 | 80 | 7 | 10 | 59 | 121 | 25 | 8 | 33 | 27 | 7 | 143 | 37 | 151 | 80 | 2 |
41 | 7 | 5 | 5 | 2 | 47 | 5 | 5 | 2 | 7 | 5 | 7 | 5 | 59 | 11 | 5 | 2 | 11 | 3 | 7 | 13 | 37 | 151 | 5 | 2 | |
3 | 2 | 2 | 2 | 2 | 2 | 3 | 2 | 2 | 11 | 5 | 2 | 3 | 3 | 11 | 2 | ||||||||||
2 | 2 | 2 | 2 | 2 | 2 | 3 | 2 | ||||||||||||||||||
2 | 2 | 2 | 2 | 2 | |||||||||||||||||||||
2 | 2 | 2 | |||||||||||||||||||||||
Denominators | |||||||||||||||||||||||||
D♭ | D♭ | E♭ | E♭ | G♭ | G♭ | A♭ | A♭ | B♭ | B♭ | ||||||||||||||||
C | C | C♯ | C♯ | D | D | D♯ | D♯ | E | E | F | F | F♯ | F♯ | G | G | G♯ | G♯ | A | A | A♯ | A♯ | B | B | C | C |
1 | 40 | 20 | 37 | 9 | 7 | 40 | 33 | 4 | 25 | 16 | 59 | 5 | 7 | 40 | 80 | 16 | 5 | 20 | 16 | 4 | 80 | 20 | 80 | 41 | 1 |
5 | 5 | 37 | 3 | 7 | 5 | 11 | 2 | 5 | 2 | 59 | 5 | 7 | 5 | 5 | 2 | 5 | 5 | 2 | 2 | 5 | 5 | 5 | 41 | ||
2 | 2 | 3 | 2 | 3 | 2 | 5 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | |||||||||
2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | ||||||||||||||
2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | |||||||||||||||||
2 | 2 | 2 | |||||||||||||||||||||||
Intervals | |||||||||||||||||||||||||
1 | 41 | 21 | 40 | 10 | 8 | 47 | 40 | 5 | 32 | 21 | 80 | 7 | 10 | 59 | 121 | 25 | 8 | 33 | 27 | 7 | 143 | 37 | 151 | 80 | 2 |
1 | 40 | 20 | 37 | 9 | 7 | 40 | 33 | 4 | 25 | 16 | 59 | 5 | 7 | 40 | 80 | 16 | 5 | 20 | 16 | 4 | 80 | 20 | 80 | 41 | 1 |
Shift intervals in table | |||||||||||||||||||||||||
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