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Imanuel's Tonemenot JI ⋄ Imanuel Tonemenot JI, palindromic 14/5 period scale, 7-limit ⋄

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Scala file contents

! Imanuel's Tonemenot JI.scl
!
Imanuel Tonemenot JI, palindromic 14/5 period scale, 7-limit, more info at http://imanuelhab.mooo.com/functional-web-language/fwd-to-html.php?q=the_strangest_scales%2Ftonemenot-just-tuning.fwd
 12
!
 21/20
 9/8
 32/27
 56/45
 4/3
 7/5
 3/2
 63/40
 224/135
 16/9
 28/15
 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
261.6 274.7 294.3 310.1 325.6 348.8 366.3 392.4 412.1 434.1 465.1 488.4 523.3

Logarithmic frequency values (cents)

D♭ E♭ G♭ A♭ B♭
C C♯ D D♯ E F F♯ G G♯ A A♯ B C
0 84.5 203.9 294.1 378.6 498 582.5 702 786.4 876.6 996.1 1080.6 1200
0 100 200 300 400 500 600 700 800 900 1000 1100 1200
0 -15.5 3.9 -5.9 -21.4 -2 -17.5 2 -13.6 -23.4 -3.9 -19.4 0

Numerators

D♭ E♭ G♭ A♭ B♭
C C♯ D D♯ E F F♯ G G♯ A A♯ B C
1 21 9 32 56 4 7 3 63 224 16 28 2
7 3 2 7 2 7 3 7 7 2 7 2
3 3 2 2 2 3 2 2 2
2 2 3 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 20 8 27 45 3 5 2 40 135 9 15 1
5 2 3 5 3 5 2 5 5 3 5
2 2 3 3 2 3 3 3
2 2 3 3 2 3
2 3

Intervals

1 21 9 32 56 4 7 3 63 224 16 28 2
1 20 8 27 45 3 5 2 40 135 9 15 1
3 3 1792 3 3 3 3 3 2560 3 3 3 3
2 2 1215 2 2 2 2 2 1701 2 2 2 2

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 3 9 448 224 112 56 84 126 1024 512 256 128
3 3 7 7 7 7 7 7 2 2 2 2
3 2 2 2 2 3 3 2 2 2 2
2 2 2 2 2 3 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 2 4 135 45 15 5 5 5 27 9 3 1
2 2 5 5 5 5 5 5 3 3 3
2 3 3 3 3 3
3 3 3
3

Intervals

1 3 9 448 224 112 56 84 126 1024 512 256 128
1 2 4 135 45 15 5 5 5 27 9 3 1
3 3 1792 3 3 3 3 3 2560 3 3 3 3
2 2 1215 2 2 2 2 2 1701 2 2 2 128

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 63 21 28 112 448 1792 18 24 32
2 2 2 7 7 7 7 7 7 3 3 2
2 2 2 3 3 2 2 2 2 3 2 2
2 2 3 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 fourths)

B♭ E♭ A♭ D♭ G♭
C F A♯ D♯ G♯ C♯ F♯ B E A D G C
1 3 9 27 20 5 5 15 45 135 1 1 1
3 3 3 5 5 5 5 5 5
3 3 2 3 3 3
3 2 3 3
3

Intervals

1 4 16 64 63 21 28 112 448 1792 18 24 32
1 3 9 27 20 5 5 15 45 135 1 1 1
4 4 4 1701 4 4 4 4 4 1215 4 4 4
3 3 3 1280 3 3 3 3 3 896 3 3 3

Shift intervals in table by fourths

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