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Imanuel's 25-tone half third 80 to 160 reflection harmonic tuning ⋄ A reflection harmonic tuning ⋄

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! Imanuel's 25-tone half third 80 to 160 reflection harmonic tuning.scl
!
A reflection harmonic tuning, more info at http://imanuelhab.mooo.com/functional-web-language/fwd-to-html.php?q=the_strangest_scales%2F25-tone-half-third-80-to-160-reflection-harmonic-tuning-imanuel.fwd
 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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