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Gert Kramer's Divine 9 – A new tuning

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Scala file contents

! Gert Kramer's Divine 9.scl
!
A new tuning, more info at http://imanuelhab.mooo.com/divine-9-tuning
 12
!
 16/15
 4375/3888
 32/27
 512/405
 4/3
 64/45
 15625/10368
 8/5
 2048/1215
 16/9
 256/135
 2/1

Prime factors and frequencies

Frequencies (Hz)

D♭ E♭ G♭ A♭ B♭
C C♯ D D♯ E F F♯ G G♯ A A♯ B C
213.6 227.8 240.3 253.1 270 284.8 303.8 321.9 341.7 360 379.7 405 427.1

Logarithmic frequency values (cents)

D♭ E♭ G♭ A♭ B♭
C C♯ D D♯ E F F♯ G G♯ A A♯ B C
0 111.7 204.3 294.1 405.9 498 609.8 710.1 813.7 903.9 996.1 1107.8 1200
0 100 200 300 400 500 600 700 800 900 1000 1100 1200
0 11.7 4.3 -5.9 5.9 -2 9.8 10.1 13.7 3.9 -3.9 7.8 0

Numerators

D♭ E♭ G♭ A♭ B♭
C C♯ D D♯ E F F♯ G G♯ A A♯ B C
1 16 4375 32 512 4 64 15625 8 2048 16 256 2
2 7 2 2 2 2 5 2 2 2 2 2
2 5 2 2 2 2 5 2 2 2 2
2 5 2 2 2 5 2 2 2 2
2 5 2 2 2 5 2 2 2
5 2 2 2 5 2 2
2 2 5 2 2
2 2 2
2 2 2
2 2
2
2

Denominators

D♭ E♭ G♭ A♭ B♭
C C♯ D D♯ E F F♯ G G♯ A A♯ B C
1 15 3888 27 405 3 45 10368 5 1215 9 135 1
5 3 3 5 3 5 3 5 5 3 5
3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3
3 3 3 3 3
3 3 2 3
2 2 3
2 2
2 2
2 2
2
2

Intervals

1 16 4375 32 512 4 64 15625 8 2048 16 256 2
1 15 3888 27 405 3 45 10368 5 1215 9 135 1
15625 120 7962624 432 103680 6 1440 90720000 320 1244160 72 17280 31250
10368 80 5315625 288 69120 4 960 60750000 216 829440 48 11520 20736
1 40 243 144 34560 2 480 810000 8 414720 24 5760 2
15625 3 32768 3 3 3 3 112 40 3 3 3 15625
10368 2 21875 2 2 2 2 75 27 2 2 2 10368
15625 3 32768 3 3 3 3 112 40 3 3 3 15625
10368 2 21875 2 2 2 2 75 27 2 2 2 10368
512 60 248832 421875 3240 6144 720 2654208 10 38880 78750 8640 1024
405 48 196875 331776 2560 4860 576 2109375 8 30720 62208 6912 810
1 12 9 27 40 12 144 27 2 480 18 1728 2
512 5 27648 15625 81 512 5 98304 5 81 4375 5 512
405 4 21875 12288 64 405 4 78125 4 64 3456 4 405
512 5 27648 15625 81 512 5 98304 5 81 4375 5 512
405 4 21875 12288 64 405 4 78125 4 64 3456 4 405
16 65625 124416 13824 1620 192 703125 82944 10240 19440 2304 270 32
15 62208 118125 12960 1536 180 663552 78125 9720 18432 2160 256 30
1 3 27 864 12 12 9 1 40 144 144 2 2
16 21875 4608 16 135 16 78125 82944 256 135 16 135 16
15 20736 4375 15 128 15 73728 78125 243 128 15 128 15
16 21875 4608 16 135 16 78125 82944 256 135 16 135 16
15 20736 4375 15 128 15 73728 78125 243 128 15 128 15

Shift intervals in table

Numerators (circle of fifths)

G♭ D♭ A♭ E♭ B♭
C G D A E B F♯ C♯ G♯ D♯ A♯ F C
1 15625 4375 4096 2048 1024 512 256 128 1024 512 256 128
5 7 2 2 2 2 2 2 2 2 2 2
5 5 2 2 2 2 2 2 2 2 2 2
5 5 2 2 2 2 2 2 2 2 2 2
5 5 2 2 2 2 2 2 2 2 2 2
5 5 2 2 2 2 2 2 2 2 2 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
2 2 2 2
2 2
2

Denominators (circle of fifths)

G♭ D♭ A♭ E♭ B♭
C G D A E B F♯ C♯ G♯ D♯ A♯ F C
1 10368 1944 1215 405 135 45 15 5 27 9 3 1
3 3 5 5 5 5 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
2 3 3 3
2 2 3
2 2
2 2
2
2
2

Intervals

1 15625 4375 4096 2048 1024 512 256 128 1024 512 256 128
1 10368 1944 1215 405 135 45 15 5 27 9 3 1
15625 45360000 7962624 2488320 414720 69120 11520 1920 5120 13824 2304 384 2000000
10368 30375000 5315625 1658880 276480 46080 7680 1280 3456 9216 1536 256 1327104
1 405000 243 829440 138240 23040 3840 640 128 4608 768 128 128
15625 112 32768 3 3 3 3 3 40 3 3 3 15625
10368 75 21875 2 2 2 2 2 27 2 2 2 10368
15625 112 32768 3 3 3 3 3 40 3 3 3 15625
10368 75 21875 2 2 2 2 2 27 2 2 2 10368

Shift intervals in table by fifths

Numerators (circle of fourths)

B♭ E♭ A♭ D♭ G♭
C F A♯ D♯ G♯ C♯ F♯ B E A D G C
1 4 16 64 16 64 256 1024 4096 16384 4375 15625 32
2 2 2 2 2 2 2 2 2 7 5 2
2 2 2 2 2 2 2 2 2 5 5 2
2 2 2 2 2 2 2 2 5 5 2
2 2 2 2 2 2 2 2 5 5 2
2 2 2 2 2 2 5 5 2
2 2 2 2 2 2 5
2 2 2 2
2 2 2 2
2 2 2
2 2 2
2 2
2 2
2
2

Denominators (circle of fourths)

B♭ E♭ A♭ D♭ G♭
C F A♯ D♯ G♯ C♯ F♯ B E A D G C
1 3 9 27 5 15 45 135 405 1215 243 648 1
3 3 3 5 5 5 5 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 2
3 2
2

Intervals

1 4 16 64 16 64 256 1024 4096 16384 4375 15625 32
1 3 9 27 5 15 45 135 405 1215 243 648 1
4 48 576 432 320 3840 46080 552960 6635520 5315625 3796875 20736 128
3 36 432 320 240 2880 34560 414720 4976640 3981312 2835000 15625 96
1 12 144 16 80 960 11520 138240 1658880 243 50625 1 32
4 4 4 27 4 4 4 4 4 21875 75 20736 4
3 3 3 20 3 3 3 3 3 16384 56 15625 3
4 4 4 27 4 4 4 4 4 21875 75 20736 4
3 3 3 20 3 3 3 3 3 16384 56 15625 3

Shift intervals in table by fourths

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