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26-ED2/1 (Farey deg. 38) – Benyamind's 26-tone Harmonic Seventh JI

Description

Music created with this tuning

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Scala file (.scl) Try it online

Scala file contents

! 26-ED2/1 (Farey deg. 38).scl
!
Benyamind's 26-tone Harmonic Seventh JI, more info at http://imanuelhab.mooo.com/seventus-just-tuning-benyamind
 26
!
 38/37
 19/18
 13/12
 10/9
 8/7
 27/23
 41/34
 26/21
 14/11
 47/36
 4/3
 11/8
 41/29
 16/11
 3/2
 23/15
 11/7
 21/13
 5/3
 46/27
 7/4
 9/5
 24/13
 55/29
 37/19
 2/1

Prime factors and frequencies

Frequencies (Hz)

D♭ D♭ E♭ E♭ G♭ G♭ G♭ A♭ A♭ B♭ B♭
C C C♯ C♯ D D D♯ D♯ E E F F F♯ F♯ F♯ G G G♯ G♯ A A A♯ A♯ B B C C
261.6 268.7 276.2 283.4 290.7 299 307.1 315.5 323.9 333 341.6 348.8 359.7 369.9 380.5 392.4 401.2 411.1 422.6 436 445.7 457.8 470.9 483 496.2 509.5 523.3

Logarithmic frequency values (cents)

D♭ D♭ E♭ E♭ G♭ G♭ G♭ A♭ A♭ B♭ B♭
C C C♯ C♯ D D D♯ D♯ E E F F F♯ F♯ F♯ G G G♯ G♯ A A A♯ A♯ B B C C
0 100 202.8 300.2 395.2 500.9 601.4 702.2 801.1 904.6 1000.1 1079.1 1194.5 1298.9 1405.5 1520.9 1603.3 1695.4 1798.9 1916.1 1998.6 2099.1 2204.8 2299.8 2400.8 2500 2600
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
0 0 2.8 0.2 -4.8 0.9 1.4 2.2 1.1 4.6 0.1 -20.9 -5.5 -1.1 5.5 20.9 3.3 -4.6 -1.1 16.1 -1.4 -0.9 4.8 -0.2 0.8 0 0

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

D♭ D♭ E♭ E♭ G♭ G♭ G♭ A♭ A♭ B♭ B♭
C C C♯ C♯ D D D♯ D♯ E E F F F♯ F♯ F♯ G G G♯ G♯ A A A♯ A♯ B B C C
0 46.2 93.6 138.6 182.4 231.2 277.6 324.1 369.7 417.5 461.6 498 551.3 599.5 648.7 702 740 782.5 830.3 884.4 922.4 968.8 1017.6 1061.4 1108.1 1153.8 1200
0 0 100 100 200 200 300 300 400 400 500 500 600 600 600 700 700 800 800 900 900 1000 1000 1100 1100 1200 1200
0 46.2 -6.4 38.6 -17.6 31.2 -22.4 24.1 -30.3 17.5 -38.4 -2 -48.7 -0.5 48.7 2 40 -17.5 30.3 -15.6 22.4 -31.2 17.6 -38.6 8.1 -46.2 0
C C C♯ C♯ D D D♯ D♯ E E F F F♯ F♯ F♯ G G G♯ G♯ A A A♯ A♯ B B C C
D♭ D♭ E♭ E♭ G♭ G♭ G♭ A♭ A♭ B♭ B♭

Numerators

D♭ D♭ E♭ E♭ G♭ G♭ G♭ A♭ A♭ B♭ B♭
C C C♯ C♯ D D D♯ D♯ E E F F F♯ F♯ F♯ G G G♯ G♯ A A A♯ A♯ B B C C
1 38 19 13 10 8 27 41 26 14 47 4 11 41 16 3 23 11 21 5 46 7 9 24 55 37 2
19 19 13 5 2 3 41 13 7 47 2 11 41 2 3 23 11 7 5 23 7 3 3 11 37 2
2 2 2 3 2 2 2 2 3 2 3 2 5
2 3 2 2
2 2

Denominators

D♭ D♭ E♭ E♭ G♭ G♭ G♭ A♭ A♭ B♭ B♭
C C C♯ C♯ D D D♯ D♯ E E F F F♯ F♯ F♯ G G G♯ G♯ A A A♯ A♯ B B C C
1 37 18 12 9 7 23 34 21 11 36 3 8 29 11 2 15 7 13 3 27 4 5 13 29 19 1
37 3 3 3 7 23 17 7 11 3 3 2 29 11 2 5 7 13 3 3 2 5 13 29 19
3 2 3 2 3 3 2 3 3 2
2 2 2 2 3
2

Intervals

1 38 19 13 10 8 27 41 26 14 47 4 11 41 16 3 23 11 21 5 46 7 9 24 55 37 2
1 37 18 12 9 7 23 34 21 11 36 3 8 29 11 2 15 7 13 3 27 4 5 13 29 19 1
3 851 198 252 45 322 161 306 504 605 1332 6 608 1102 286 40 240 378 1066 156 756 376 40 286 2378 608 6
2 570 133 169 30 216 108 205 338 406 893 4 407 738 192 27 161 253 714 105 506 252 27 192 1595 407 4
1 1 1 1 15 2 1 1 2 1 1 2 1 2 2 1 1 1 2 3 2 4 1 2 29 1 2
3 851 198 252 3 161 161 306 252 605 1332 3 608 551 143 40 240 378 533 52 378 94 40 143 82 608 3
2 570 133 169 2 108 108 205 169 406 893 2 407 369 96 27 161 253 357 35 253 63 27 96 55 407 2
3 851 198 252 3 161 161 306 252 605 1332 3 608 551 143 40 240 378 533 52 378 94 40 143 82 608 3
2 570 133 169 2 108 108 205 169 406 893 2 407 369 96 27 161 253 357 35 253 63 27 96 55 407 2
14 1739 72 132 369 112 69 782 231 231 180 138 56 261 264 110 555 14 988 114 702 80 80 702 2378 988 28
11 1368 57 104 290 88 54 615 182 182 141 108 44 205 208 87 437 11 777 90 552 63 63 552 1870 777 22
1 1 3 4 1 8 3 1 7 7 3 6 4 1 8 1 1 1 1 6 6 1 1 6 2 1 2
14 1739 24 33 369 14 23 782 33 33 60 23 14 261 33 110 555 14 988 19 117 80 80 117 1189 988 14
11 1368 19 26 290 11 18 615 26 26 47 18 11 205 26 87 437 11 777 15 92 63 63 92 935 777 11
14 1739 24 33 369 14 23 782 33 33 60 23 14 261 33 110 555 14 988 19 117 80 80 117 1189 988 14
11 1368 19 26 290 11 18 615 26 26 47 18 11 205 26 87 437 11 777 15 92 63 63 92 935 777 11
38 703 234 120 72 189 943 884 294 517 144 33 328 464 33 46 165 147 65 138 189 36 120 715 1073 38 76
37 684 228 117 70 184 918 861 286 504 141 32 319 451 32 45 161 143 63 135 184 35 117 696 1045 37 74
1 19 6 3 2 1 1 1 2 1 3 1 1 1 1 1 1 1 1 3 1 1 3 1 1 1 2
38 37 39 40 36 189 943 884 147 517 48 33 328 464 33 46 165 147 65 46 189 36 40 715 1073 38 38
37 36 38 39 35 184 918 861 143 504 47 32 319 451 32 45 161 143 63 45 184 35 39 696 1045 37 37
38 37 39 40 36 189 943 884 147 517 48 33 328 464 33 46 165 147 65 46 189 36 40 715 1073 38 38
37 36 38 39 35 184 918 861 143 504 47 32 319 451 32 45 161 143 63 45 184 35 39 696 1045 37 37

Shift intervals in table

Numerators (circle of fifths)

G♭ G♭ D♭ A♭ E♭ B♭ G♭ D♭ A♭ E♭ B♭
C G D A E B F♯ C G D A E B F♯ C♯ G♯ D♯ A♯ F C F♯ C♯ G♯ D♯ A♯ F C
1 3 20 10 104 96 11 608 368 256 1472 896 3520 5248 2432 2816 13824 896 12032 37888 32768 13312 86016 167936 73728 65536 32768
3 5 5 13 3 11 19 23 2 23 7 11 41 19 11 3 7 47 37 2 13 7 41 3 2 2
2 2 2 2 2 2 2 2 2 5 2 2 2 3 2 2 2 2 2 3 2 3 2 2
2 2 2 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 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 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♭ G♭ D♭ A♭ E♭ B♭ G♭ D♭ A♭ E♭ B♭
C G D A E B F♯ C G D A E B F♯ C♯ G♯ D♯ A♯ F C F♯ C♯ G♯ D♯ A♯ F C
1 2 9 3 21 13 1 37 15 7 27 11 29 29 9 7 23 1 9 19 11 3 13 17 5 3 1
2 3 3 7 13 37 5 7 3 11 29 29 3 7 23 3 19 11 3 13 17 5 3
3 3 3 3 3 3
3

Intervals

1 3 20 10 104 96 11 608 368 256 1472 896 3520 5248 2432 2816 13824 896 12032 37888 32768 13312 86016 167936 73728 65536 32768
1 2 9 3 21 13 1 37 15 7 27 11 29 29 9 7 23 1 9 19 11 3 13 17 5 3 1
3 40 90 312 2016 143 608 13616 3840 10304 24192 38720 152192 70528 25344 96768 20608 12032 340992 622592 146432 258048 2183168 1253376 327680 98304 98304
2 27 60 210 1352 96 407 9120 2576 6912 16192 25984 102080 47232 17024 64768 13824 8064 228608 416768 98304 173056 1462272 839680 221184 65536 65536
1 1 30 6 8 1 1 16 16 64 64 64 1856 128 128 256 128 128 256 1024 1024 1024 4096 4096 8192 32768 32768
3 40 3 52 252 143 608 851 240 161 378 605 82 551 198 378 161 94 1332 608 143 252 533 306 40 3 3
2 27 2 35 169 96 407 570 161 108 253 406 55 369 133 253 108 63 893 407 96 169 357 205 27 2 2
3 40 3 52 252 143 608 851 240 161 378 605 82 551 198 378 161 94 1332 608 143 252 533 306 40 3 3
2 27 2 35 169 96 407 570 161 108 253 406 55 369 133 253 108 63 893 407 96 169 357 205 27 2 2

Shift intervals in table by fifths

Numerators (circle of fourths)

B♭ E♭ A♭ D♭ G♭ B♭ E♭ A♭ D♭ G♭ G♭
C F A♯ D♯ G♯ C♯ F♯ C F A♯ D♯ G♯ C♯ F♯ B E A D G C F♯ B E A D G C
1 4 9 41 42 13 64 148 94 14 432 176 304 1312 1760 896 2944 1024 2944 9728 352 6144 13312 2560 10240 1536 2048
2 3 41 7 13 2 37 47 7 3 11 19 41 11 7 23 2 23 19 11 3 13 5 5 3 2
2 3 3 2 2 2 2 3 2 2 2 5 2 2 2 2 2 2 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 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 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♭ G♭
C F A♯ D♯ G♯ C♯ F♯ C F A♯ D♯ G♯ C♯ F♯ B E A D G C F♯ B E A D G C
1 3 5 17 13 3 11 19 9 1 23 7 9 29 29 11 27 7 15 37 1 13 21 3 9 1 1
3 5 17 13 3 11 19 3 23 7 3 29 29 11 3 7 5 37 13 7 3 3
3 3 3 3 3 3
3

Intervals

1 4 9 41 42 13 64 148 94 14 432 176 304 1312 1760 896 2944 1024 2944 9728 352 6144 13312 2560 10240 1536 2048
1 3 5 17 13 3 11 19 9 1 23 7 9 29 29 11 27 7 15 37 1 13 21 3 9 1 1
4 27 205 714 169 192 1628 1786 126 432 4048 2128 11808 51040 25984 32384 27648 20608 145920 13024 6144 173056 53760 30720 13824 2048 8192
3 20 153 533 126 143 1216 1332 94 322 3024 1584 8816 38048 19360 24192 20608 15360 108928 9728 4576 129024 39936 23040 10240 1536 6144
1 1 1 1 1 1 4 2 2 2 16 16 16 928 32 128 128 128 128 32 32 1024 1536 7680 512 512 2048
4 27 205 714 169 192 407 893 63 216 253 133 738 55 812 253 216 161 1140 407 192 169 35 4 27 4 4
3 20 153 533 126 143 304 666 47 161 189 99 551 41 605 189 161 120 851 304 143 126 26 3 20 3 3
4 27 205 714 169 192 407 893 63 216 253 133 738 55 812 253 216 161 1140 407 192 169 35 4 27 4 4
3 20 153 533 126 143 304 666 47 161 189 99 551 41 605 189 161 120 851 304 143 126 26 3 20 3 3

Shift intervals in table by fourths

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