Imanuel's website

nl-NLen-US

Imanuel's 53-tone JI 1 – A new just tuning

Description

These "just" scales are based on equal temperament. All intervals are aimed to be within a schisma (32805/32768, ~1.95 cents) of the approximated interval from equal temperament.

I wrote a program that evaluates fractional approximations to the intervals by repeatedly incrementing the numerator of the fraction. The denominator is increased accordingly. These approximations are assigned a "distance" (or, inverse score) by dividing the larger of the two intervals (either the approximated equal temperament interval, or the approximation itself) by the smaller one. The program for a specific interval will stop when a sufficiently good approximation is found (I chose a distance below a schisma to be "sufficiently good").

One other factor however is also introduced, which often times makes these distances larger than that schisma in the end: the interval encompassing both the harmonics and the subharmonics (the product of the numerator and denominator) should be smaller than 8 octaves (2^8 = 256).

For getting the prime-limit scales, I could simply skip the approximations where either the numerator or the denominator had prime factors above the designated value. For example a 19-limit by definition has no prime factors above 19 in the numerator or denominator.

Try it now / Get Scala file

Scala file (.scl) Try it online

Scala file contents

! Imanuel's 53-tone JI 1.scl
!
A new just tuning, more info at http://imanuelhab.mooo.com/new-53-tone-just-tuning-imanuel
 53
!
 57/56
 33/32
 24/23
 19/18
 15/14
 13/12
 11/10
 10/9
 9/8
 8/7
 15/13
 7/6
 13/11
 6/5
 11/9
 16/13
 5/4
 19/15
 9/7
 13/10
 21/16
 4/3
 19/14
 11/8
 18/13
 7/5
 10/7
 13/9
 16/11
 28/19
 3/2
 29/19
 17/11
 14/9
 19/12
 8/5
 13/8
 18/11
 5/3
 22/13
 12/7
 19/11
 7/4
 16/9
 9/5
 11/6
 13/7
 15/8
 19/10
 23/12
 33/17
 57/29
 2/1

Prime factors and frequencies

Frequencies (Hz)

D♭ D♭ D♭ D♭ E♭ E♭ E♭ E♭ G♭ G♭ G♭ G♭ A♭ A♭ A♭ A♭ B♭ B♭ B♭ B♭ B♭
C C C C♯ C♯ C♯ C♯ D D D D D D♯ D♯ D♯ D♯ E E E E F F F F F F♯ F♯ F♯ F♯ G G G G G G♯ G♯ G♯ G♯ A A A A A♯ A♯ A♯ A♯ A♯ B B B B C C C
261.6 266.3 269.8 273 276.2 280.3 283.4 287.8 290.7 294.3 299 301.9 305.2 309.2 314 319.8 322 327 331.4 336.4 340.1 343.4 348.8 355.1 359.7 362.3 366.3 373.8 377.9 380.5 385.6 392.4 399.3 404.3 407 414.2 418.6 425.1 428.1 436 442.8 448.5 451.9 457.8 465.1 470.9 479.6 485.9 490.5 497.1 501.4 507.9 514.2 523.3

Logarithmic frequency values (cents)

D♭ D♭ D♭ D♭ E♭ E♭ E♭ E♭ G♭ G♭ G♭ G♭ A♭ A♭ A♭ A♭ B♭ B♭ B♭ B♭ B♭
C C C C♯ C♯ C♯ C♯ D D D D D D♯ D♯ D♯ D♯ E E E E F F F F F F♯ F♯ F♯ F♯ G G G G G G♯ G♯ G♯ G♯ A A A A A♯ A♯ A♯ A♯ A♯ B B B B C C C
0 135.3 235.3 325.4 413.4 527.5 612 728.8 805.6 900.6 1021 1094.2 1178.7 1277.3 1394.1 1534.4 1587.7 1706.2 1807.5 1921.6 2006.1 2079.3 2199.7 2335 2435 2488.3 2572.8 2727.2 2811.7 2865 2965 3100.3 3233.3 3328.6 3378.4 3513.7 3593.8 3712.3 3765.6 3905.9 4022.7 4121.3 4179 4279 4399.4 4494.4 4634.7 4733.3 4806.5 4907.8 4974.6 5071.7 5167 5300
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 2600 2700 2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 4000 4100 4200 4300 4400 4500 4600 4700 4800 4900 5000 5100 5200 5300
0 35.3 35.3 25.4 13.4 27.5 12 28.8 5.6 0.6 21 -5.8 -21.3 -22.7 -5.9 34.4 -12.3 6.2 7.5 21.6 6.1 -20.7 -0.3 35 35 -11.7 -27.2 27.2 11.7 -35 -35 0.3 33.3 28.6 -21.6 13.7 -6.2 12.3 -34.4 5.9 22.7 21.3 -21 -21 -0.6 -5.6 34.7 33.3 6.5 7.8 -25.4 -28.3 -33 0

Logarithmic frequency values (cents, for 12-ET with octave equivalence)

D♭ D♭ D♭ D♭ E♭ E♭ E♭ E♭ G♭ G♭ G♭ G♭ A♭ A♭ A♭ A♭ B♭ B♭ B♭ B♭ B♭
C C C C♯ C♯ C♯ C♯ D D D D D D♯ D♯ D♯ D♯ E E E E F F F F F F♯ F♯ F♯ F♯ G G G G G G♯ G♯ G♯ G♯ A A A A A♯ A♯ A♯ A♯ A♯ B B B B C C C
0 30.6 53.3 73.7 93.6 119.4 138.6 165 182.4 203.9 231.2 247.7 266.9 289.2 315.6 347.4 359.5 386.3 409.2 435.1 454.2 470.8 498 528.7 551.3 563.4 582.5 617.5 636.6 648.7 671.3 702 732.1 753.6 764.9 795.6 813.7 840.5 852.6 884.4 910.8 933.1 946.2 968.8 996.1 1017.6 1049.4 1071.7 1088.3 1111.2 1126.3 1148.3 1169.9 1200
0 0 100 100 100 100 100 200 200 200 200 200 300 300 300 300 400 400 400 400 500 500 500 500 600 600 600 600 600 600 700 700 700 800 800 800 800 800 900 900 900 900 900 1000 1000 1000 1000 1100 1100 1100 1100 1100 1200 1200
0 30.6 -46.7 -26.3 -6.4 19.4 38.6 -35 -17.6 3.9 31.2 47.7 -33.1 -10.8 15.6 47.4 -40.5 -13.7 9.2 35.1 -45.8 -29.2 -2 28.7 -48.7 -36.6 -17.5 17.5 36.6 48.7 -28.7 2 32.1 -46.4 -35.1 -4.4 13.7 40.5 -47.4 -15.6 10.8 33.1 46.2 -31.2 -3.9 17.6 49.4 -28.3 -11.7 11.2 26.3 48.3 -30.1 0
C C C♯ C♯ C♯ C♯ C♯ D D D D D D♯ D♯ D♯ D♯ E E E E F F F F F♯ F♯ F♯ F♯ F♯ F♯ G G G G♯ G♯ G♯ G♯ G♯ A A A A A A♯ A♯ A♯ A♯ B B B B B C C
D♭ D♭ D♭ D♭ D♭ E♭ E♭ E♭ E♭ G♭ G♭ G♭ G♭ G♭ G♭ A♭ A♭ A♭ A♭ A♭ B♭ B♭ B♭ B♭

Numerators

D♭ D♭ D♭ D♭ E♭ E♭ E♭ E♭ G♭ G♭ G♭ G♭ A♭ A♭ A♭ A♭ B♭ B♭ B♭ B♭ B♭
C C C C♯ C♯ C♯ C♯ D D D D D D♯ D♯ D♯ D♯ E E E E F F F F F F♯ F♯ F♯ F♯ G G G G G G♯ G♯ G♯ G♯ A A A A A♯ A♯ A♯ A♯ A♯ B B B B C C C
1 57 33 24 19 15 13 11 10 9 8 15 7 13 6 11 16 5 19 9 13 21 4 19 11 18 7 10 13 16 28 3 29 17 14 19 8 13 18 5 22 12 19 7 16 9 11 13 15 19 23 33 57 2
19 11 3 19 5 13 11 5 3 2 5 7 13 3 11 2 5 19 3 13 7 2 19 11 3 7 5 13 2 7 3 29 17 7 19 2 13 3 5 11 3 19 7 2 3 11 13 5 19 23 11 19 2
3 3 2 3 2 3 2 3 2 2 3 3 2 3 2 2 2 2 2 3 2 2 2 3 3 3 3
2 2 2 2 2 2 2 2 2 2
2 2 2 2

Denominators

D♭ D♭ D♭ D♭ E♭ E♭ E♭ E♭ G♭ G♭ G♭ G♭ A♭ A♭ A♭ A♭ B♭ B♭ B♭ B♭ B♭
C C C C♯ C♯ C♯ C♯ D D D D D D♯ D♯ D♯ D♯ E E E E F F F F F F♯ F♯ F♯ F♯ G G G G G G♯ G♯ G♯ G♯ A A A A A♯ A♯ A♯ A♯ A♯ B B B B C C C
1 56 32 23 18 14 12 10 9 8 7 13 6 11 5 9 13 4 15 7 10 16 3 14 8 13 5 7 9 11 19 2 19 11 9 12 5 8 11 3 13 7 11 4 9 5 6 7 8 10 12 17 29 1
7 2 23 3 7 3 5 3 2 7 13 3 11 5 3 13 2 5 7 5 2 3 7 2 13 5 7 3 11 19 2 19 11 3 3 5 2 11 3 13 7 11 2 3 5 3 7 2 5 3 17 29
2 2 3 2 2 2 3 2 2 3 2 3 2 2 2 2 3 3 2 2 2 3 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2
2 2 2
2

Intervals

1 57 33 24 19 15 13 11 10 9 8 15 7 13 6 11 16 5 19 9 13 21 4 19 11 18 7 10 13 16 28 3 29 17 14 19 8 13 18 5 22 12 19 7 16 9 11 13 15 19 23 33 57 2
1 56 32 23 18 14 12 10 9 8 7 13 6 11 5 9 13 4 15 7 10 16 3 14 8 13 5 7 9 11 19 2 19 11 9 12 5 8 11 3 13 7 11 4 9 5 6 7 8 10 12 17 29 1
3 1624 544 322 342 112 156 180 45 176 84 247 42 176 45 99 169 60 285 161 330 912 6 1596 528 624 190 210 234 242 380 36 304 330 126 312 60 176 352 30 494 126 286 168 72 190 132 252 112 200 312 544 1624 6
2 1083 363 216 228 75 104 121 30 117 56 165 28 117 30 66 112 40 190 108 221 609 4 1064 352 414 126 140 156 160 252 24 203 221 84 209 40 117 234 20 330 84 190 112 48 126 88 169 75 133 207 363 1083 4
1 1 1 2 114 1 52 1 15 1 28 1 14 1 15 33 1 20 95 1 1 3 2 532 176 6 2 70 78 2 4 12 1 1 42 1 20 1 2 10 2 42 2 56 24 2 44 1 1 1 3 1 1 2
3 1624 544 161 3 112 3 180 3 176 3 247 3 176 3 3 169 3 3 161 330 304 3 3 3 104 95 3 3 121 95 3 304 330 3 312 3 176 176 3 247 3 143 3 3 95 3 252 112 200 104 544 1624 3
2 1083 363 108 2 75 2 121 2 117 2 165 2 117 2 2 112 2 2 108 221 203 2 2 2 69 63 2 2 80 63 2 203 221 2 209 2 117 117 2 165 2 95 2 2 63 2 169 75 133 69 363 1083 2
3 1624 544 161 3 112 3 180 3 176 3 247 3 176 3 3 169 3 3 161 330 304 3 3 3 104 95 3 3 121 95 3 304 330 3 312 3 176 176 3 247 3 143 3 3 95 3 252 112 200 104 544 1624 3
2 1083 363 108 2 75 2 121 2 117 2 165 2 117 2 2 112 2 2 108 221 203 2 2 2 69 63 2 2 80 63 2 203 221 2 209 2 117 117 2 165 2 95 2 2 63 2 169 75 133 69 363 1083 2
19 504 416 483 72 266 132 180 63 80 91 208 168 33 145 153 182 76 120 91 180 80 66 168 152 91 80 63 99 143 285 38 437 363 513 24 570 528 528 114 390 182 242 80 162 80 180 98 208 120 264 544 290 38
15 399 330 384 57 210 104 143 50 63 72 165 133 26 114 121 144 60 95 72 143 63 52 133 121 72 63 50 78 112 224 30 348 289 406 19 448 416 414 90 308 144 190 63 128 63 143 78 165 95 207 429 228 30
1 21 2 3 3 14 4 1 1 1 1 1 7 1 1 1 2 4 5 1 1 1 2 7 1 1 1 1 3 1 1 2 1 1 1 1 2 16 6 6 2 2 2 1 2 1 1 2 1 5 3 1 2 2
19 24 208 161 24 19 33 180 63 80 91 208 24 33 145 153 91 19 24 91 180 80 33 24 152 91 80 63 33 143 285 19 437 363 513 24 285 33 88 19 195 91 121 80 81 80 180 49 208 24 88 544 145 19
15 19 165 128 19 15 26 143 50 63 72 165 19 26 114 121 72 15 19 72 143 63 26 19 121 72 63 50 26 112 224 15 348 289 406 19 224 26 69 15 154 72 95 63 64 63 143 39 165 19 69 429 114 15
19 24 208 161 24 19 33 180 63 80 91 208 24 33 145 153 91 19 24 91 180 80 33 24 152 91 80 63 33 143 285 19 437 363 513 24 285 33 88 19 195 91 121 80 81 80 180 49 208 24 88 544 145 19
15 19 165 128 19 15 26 143 50 63 72 165 19 26 114 121 72 15 19 72 143 63 26 19 121 72 63 50 26 112 224 15 348 289 406 19 224 26 69 15 154 72 95 63 64 63 143 39 165 19 69 429 114 15
57 1848 768 437 270 182 132 100 81 64 105 91 78 66 55 144 65 76 135 91 210 64 57 154 144 91 50 91 144 308 57 58 323 154 171 96 65 144 55 66 156 133 77 64 81 55 78 105 152 230 396 969 58 114
56 1824 759 432 266 180 130 99 80 63 104 90 77 65 54 143 64 75 133 90 208 63 56 152 143 90 49 90 143 304 56 57 319 153 168 95 64 143 54 65 154 132 76 63 80 54 77 104 150 228 391 957 57 112
1 24 3 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 4 1 1 1 1 3 1 1 1 1 1 2 1 1 1 1 1 1 1 2 2 1 3 1 2
57 77 256 437 135 91 66 100 81 64 105 91 78 66 55 144 65 76 135 91 105 64 57 77 144 91 50 91 144 77 57 58 323 154 57 96 65 144 55 66 78 133 77 64 81 55 78 105 76 115 396 323 58 57
56 76 253 432 133 90 65 99 80 63 104 90 77 65 54 143 64 75 133 90 104 63 56 76 143 90 49 90 143 76 56 57 319 153 56 95 64 143 54 65 77 132 76 63 80 54 77 104 75 114 391 319 57 56
57 77 256 437 135 91 66 100 81 64 105 91 78 66 55 144 65 76 135 91 105 64 57 77 144 91 50 91 144 77 57 58 323 154 57 96 65 144 55 66 78 133 77 64 81 55 78 105 76 115 396 323 58 57
56 76 253 432 133 90 65 99 80 63 104 90 77 65 54 143 64 75 133 90 104 63 56 76 143 90 49 90 143 76 56 57 319 153 56 95 64 143 54 65 77 132 76 63 80 54 77 104 75 114 391 319 57 56

Shift intervals in table

Numerators (circle of fifths)

G♭ D♭ A♭ E♭ B♭ G♭ D♭ A♭ E♭ B♭ B♭ G♭ D♭ A♭ E♭ B♭ G♭ D♭ A♭ E♭ B♭
C G D A E B F♯ C♯ G♯ D♯ A♯ F C G D A E B F♯ C♯ G♯ D♯ A♯ F C G D A♯ F C G D A E B F♯ C♯ G♯ D♯ A♯ F C G D A E B F♯ C♯ G♯ D♯ A♯ F C
1 3 9 44 76 38 80 120 128 192 288 608 912 3712 2048 3072 4608 2944 13312 6656 3328 45056 22528 11264 16896 278528 491520 622592 425984 2162688 2097152 1441792 4718592 8388608 6815744 18874368 50331648 29360128 14680064 7340032 11010048 478150656 469762048 335544320 167772160 83886080 125829120 939524096 2550136832 1275068416 6979321856 8589934592 4294967296 2147483648
3 3 11 19 19 5 5 2 3 3 19 19 29 2 3 3 23 13 13 13 11 11 11 11 17 5 19 13 11 2 11 3 2 13 3 3 7 7 7 7 19 7 5 5 5 5 7 19 19 13 2 2 2
3 2 2 2 2 3 2 2 3 2 3 2 2 2 3 2 2 2 2 2 2 2 3 2 3 2 2 3 2 2 3 2 2 3 2 2 2 2 3 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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
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 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 2
2

Denominators (circle of fifths)

G♭ D♭ A♭ E♭ B♭ G♭ D♭ A♭ E♭ B♭ B♭ G♭ D♭ A♭ E♭ B♭ G♭ D♭ A♭ E♭ B♭
C G D A E B F♯ C♯ G♯ D♯ A♯ F C G D A E B F♯ C♯ G♯ D♯ A♯ F C G D A♯ F C G D A E B F♯ C♯ G♯ D♯ A♯ F C G D A E B F♯ C♯ G♯ D♯ A♯ F C
1 2 4 13 15 5 7 7 5 5 5 7 7 19 7 7 7 3 9 3 1 9 3 1 1 11 13 11 5 17 11 5 11 13 7 13 23 9 3 1 1 29 19 9 3 1 1 5 9 3 11 9 3 1
2 2 13 5 5 7 7 5 5 5 7 7 19 7 7 7 3 3 3 3 3 11 13 11 5 17 11 5 11 13 7 13 23 3 3 29 19 3 3 5 3 3 11 3 3
2 3 3 3 3 3 3 3

Intervals

1 3 9 44 76 38 80 120 128 192 288 608 912 3712 2048 3072 4608 2944 13312 6656 3328 45056 22528 11264 16896 278528 491520 622592 425984 2162688 2097152 1441792 4718592 8388608 6815744 18874368 50331648 29360128 14680064 7340032 11010048 478150656 469762048 335544320 167772160 83886080 125829120 939524096 2550136832 1275068416 6979321856 8589934592 4294967296 2147483648
1 2 4 13 15 5 7 7 5 5 5 7 7 19 7 7 7 3 9 3 1 9 3 1 1 11 13 11 5 17 11 5 11 13 7 13 23 9 3 1 1 29 19 9 3 1 1 5 9 3 11 9 3 1
3 18 176 988 570 400 840 896 960 1440 3040 6384 25984 38912 21504 32256 20608 39936 59904 9984 45056 202752 33792 16896 278528 5406720 8093696 4685824 10813440 35651584 15859712 23592960 92274688 88604672 132120576 654311424 675282944 132120576 22020096 11010048 478150656 13623099392 6375342080 1509949440 251658240 125829120 939524096 12750684160 11475615744 20937965568 94489280512 38654705664 6442450944 6442450944
2 12 117 660 380 266 560 600 640 960 2016 4256 17328 25984 14336 21504 13824 26496 39936 6656 29952 135168 22528 11264 185856 3620864 5406720 3112960 7241728 23789568 10485760 15859712 61341696 58720256 88604672 434110464 452984832 88080384 14680064 7340032 319291392 9084862464 4227858432 1006632960 167772160 83886080 629145600 8455716864 7650410496 14025752576 62813896704 25769803776 4294967296 4294967296
1 6 1 4 190 2 280 8 320 480 32 2128 16 128 7168 10752 128 384 19968 3328 256 67584 11264 5632 512 16384 32768 32768 32768 65536 131072 131072 524288 524288 524288 6291456 4194304 44040192 7340032 3670016 1572864 8388608 67108864 503316480 83886080 41943040 8388608 134217728 3825205248 67108864 536870912 12884901888 2147483648 2147483648
3 3 176 247 3 200 3 112 3 3 95 3 1624 304 3 3 161 104 3 3 176 3 3 3 544 330 247 143 330 544 121 180 176 169 252 104 161 3 3 3 304 1624 95 3 3 3 112 95 3 312 176 3 3 3
2 2 117 165 2 133 2 75 2 2 63 2 1083 203 2 2 108 69 2 2 117 2 2 2 363 221 165 95 221 363 80 121 117 112 169 69 108 2 2 2 203 1083 63 2 2 2 75 63 2 209 117 2 2 2
3 3 176 247 3 200 3 112 3 3 95 3 1624 304 3 3 161 104 3 3 176 3 3 3 544 330 247 143 330 544 121 180 176 169 252 104 161 3 3 3 304 1624 95 3 3 3 112 95 3 312 176 3 3 3
2 2 117 165 2 133 2 75 2 2 63 2 1083 203 2 2 108 69 2 2 117 2 2 2 363 221 165 95 221 363 80 121 117 112 169 69 108 2 2 2 203 1083 63 2 2 2 75 63 2 209 117 2 2 2

Shift intervals in table by fifths

Numerators (circle of fourths)

B♭ E♭ A♭ D♭ G♭ B♭ E♭ A♭ D♭ G♭ B♭ B♭ E♭ A♭ D♭ G♭ B♭ E♭ A♭ D♭ G♭
C F A♯ D♯ G♯ C♯ F♯ B E A D G C F A♯ D♯ G♯ C♯ F♯ B E A D G C F A♯ D G C F A♯ D♯ G♯ C♯ F♯ B E A D G C F A♯ D♯ G♯ C♯ F♯ B E A D G C
1 4 16 26 19 38 28 15 10 40 160 448 912 42 56 224 896 3072 2304 1664 4096 4608 2816 8192 16896 6656 19456 30720 34816 4224 5632 22528 90112 13312 53248 212992 94208 294912 393216 524288 1900544 933888 1245184 1179648 1572864 2097152 3932160 5242880 4980736 19922944 23068672 2359296 3145728 4194304
2 2 13 19 19 7 5 5 5 5 7 19 7 7 7 7 3 3 13 2 3 11 2 11 13 19 5 17 11 11 11 11 13 13 13 23 3 3 2 29 19 19 3 3 2 5 5 19 19 11 3 3 2
2 2 2 2 2 3 2 2 2 2 3 3 2 2 2 2 3 2 2 3 2 2 3 2 2 3 2 3 2 2 2 2 2 2 2 3 2 2 2 3 2 3 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 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 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 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 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 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 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 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 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 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 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 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 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 fourths)

B♭ E♭ A♭ D♭ G♭ B♭ E♭ A♭ D♭ G♭ B♭ B♭ E♭ A♭ D♭ G♭ B♭ E♭ A♭ D♭ G♭
C F A♯ D♯ G♯ C♯ F♯ B E A D G C F A♯ D♯ G♯ C♯ F♯ B E A D G C F A♯ D G C F A♯ D♯ G♯ C♯ F♯ B E A D G C F A♯ D♯ G♯ C♯ F♯ B E A D G C
1 3 9 11 6 9 5 2 1 3 9 19 29 1 1 3 9 23 13 7 13 11 5 11 17 5 11 13 11 1 1 3 9 1 3 9 3 7 7 7 19 7 7 5 5 5 7 7 5 15 13 1 1 1
3 3 11 3 3 5 2 3 3 19 29 3 3 23 13 7 13 11 5 11 17 5 11 13 11 3 3 3 3 3 7 7 7 19 7 7 5 5 5 7 7 5 5 13
3 2 3 3 3 3 3 3

Intervals

1 4 16 26 19 38 28 15 10 40 160 448 912 42 56 224 896 3072 2304 1664 4096 4608 2816 8192 16896 6656 19456 30720 34816 4224 5632 22528 90112 13312 53248 212992 94208 294912 393216 524288 1900544 933888 1245184 1179648 1572864 2097152 3932160 5242880 4980736 19922944 23068672 2359296 3145728 4194304
1 3 9 11 6 9 5 2 1 3 9 19 29 1 1 3 9 23 13 7 13 11 5 11 17 5 11 13 11 1 1 3 9 1 3 9 3 7 7 7 19 7 7 5 5 5 7 7 5 15 13 1 1 1
4 48 234 209 228 252 75 20 40 480 4032 17328 1218 56 224 2688 27648 52992 21632 28672 59904 30976 40960 185856 113152 97280 337920 452608 46464 5632 22528 270336 119808 53248 638976 847872 884736 2752512 3670016 13303808 17743872 8716288 8257536 7864320 10485760 19660800 36700160 34865152 99614720 346030080 30670848 3145728 4194304 16777216
3 36 176 156 171 190 56 15 30 360 3040 12992 912 42 168 2016 20608 39936 16128 21632 45056 23040 30976 139264 84480 73216 252928 337920 34816 4224 16896 202752 90112 39936 479232 638976 659456 2064384 2752512 9961472 13303808 6537216 6225920 5898240 7864320 14680064 27525120 26214400 74711040 258998272 23068672 2359296 3145728 12582912
1 12 2 1 57 2 1 5 10 120 32 16 6 14 56 672 128 768 128 128 512 256 256 512 512 512 1024 2048 128 1408 5632 67584 1024 13312 159744 12288 4096 688128 917504 65536 16384 2179072 65536 1966080 2621440 262144 9175040 262144 24903680 1048576 262144 786432 1048576 4194304
4 4 117 209 4 126 75 4 4 4 126 1083 203 4 4 4 216 69 169 224 117 121 160 363 221 190 330 221 363 4 4 4 117 4 4 69 216 4 4 203 1083 4 126 4 4 75 4 133 4 330 117 4 4 4
3 3 88 156 3 95 56 3 3 3 95 812 152 3 3 3 161 52 126 169 88 90 121 272 165 143 247 165 272 3 3 3 88 3 3 52 161 3 3 152 812 3 95 3 3 56 3 100 3 247 88 3 3 3
4 4 117 209 4 126 75 4 4 4 126 1083 203 4 4 4 216 69 169 224 117 121 160 363 221 190 330 221 363 4 4 4 117 4 4 69 216 4 4 203 1083 4 126 4 4 75 4 133 4 330 117 4 4 4
3 3 88 156 3 95 56 3 3 3 95 812 152 3 3 3 161 52 126 169 88 90 121 272 165 143 247 165 272 3 3 3 88 3 3 52 161 3 3 152 812 3 95 3 3 56 3 100 3 247 88 3 3 3

Shift intervals in table by fourths

Copyright © 2020 Imanuel Habekotté

Page rendered on 07-06-2020 at 13:43:26, it took 25.353773 seconds