Scala analysis: bihexany
Hole around [0, 1/2, 1/2, 1/2]
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 35/33 101.866677 2: 7/6 266.870906 septimal minor third 3: 5/4 386.313714 major third 4: 14/11 417.507964 undecimal diminished fourth or major third 5: 15/11 536.950772 undecimal augmented fourth 6: 3/2 701.955001 perfect fifth 7: 35/22 803.821678 8: 5/3 884.358713 major sixth, BP sixth 9: 7/4 968.825906 harmonic seventh 10: 20/11 1034.995772 large minor seventh 11: 21/11 1119.462965 undecimal major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 22/21 80.5370 undecimal minor semitone 1: 35/33 101.8667 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 15/14 119.4428 major diatonic semitone 4: 56/55 31.1943 undecimal diesis, konbini comma 5: 15/14 119.4428 major diatonic semitone 6: 11/10 165.0042 Ptolemy's second, 4/5-tone 7: 35/33 101.8667 8: 22/21 80.5370 undecimal minor semitone 9: 21/20 84.4672 minor semitone 10: 80/77 66.1699 11: 21/20 84.4672 minor semitone 12: 22/21 80.5370 undecimal minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 56/55 31.194 cents undecimal diesis, konbini comma 1: 1 80/77 66.170 cents 1: 2 22/21 80.537 cents undecimal minor semitone 1: 2 21/20 84.467 cents minor semitone 1: 2 35/33 101.867 cents 1: 2 15/14 119.443 cents major diatonic semitone 1: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 4 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 2 10/9 182.404 cents minor whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 2 33/28 284.447 cents undecimal minor third 3: 2 8/7 231.174 cents septimal whole tone 3: 1 63/55 235.104 cents 3: 2 7/6 266.871 cents septimal minor third 3: 1 90/77 270.080 cents 3: 2 6/5 315.641 cents minor third 3: 2 11/9 347.408 cents undecimal neutral third 3: 2 5/4 386.314 cents major third 4: 2 6/5 315.641 cents minor third 4: 2 40/33 333.041 cents 4: 2 14/11 417.508 cents undecimal diminished fourth or major third 4: 2 77/60 431.875 cents 4: 2 9/7 435.084 cents septimal major third, BP third 4: 2 55/42 466.851 cents 5: 1 44/35 396.178 cents 5: 2 14/11 417.508 cents undecimal diminished fourth or major third 5: 4 4/3 498.045 cents perfect fourth 5: 2 15/11 536.951 cents undecimal augmented fourth 5: 2 11/8 551.318 cents undecimal semi-augmented fourth 5: 1 99/70 600.088 cents 2nd quasi-equal tritone 6: 2 4/3 498.045 cents perfect fourth 6: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 4 10/7 617.488 cents Euler's tritone 6: 2 3/2 701.955 cents perfect fifth 7: 1 140/99 599.912 cents quasi-equal tritone 7: 2 16/11 648.682 cents undecimal semi-diminished fifth 7: 2 22/15 663.049 cents undecimal diminished fifth 7: 4 3/2 701.955 cents perfect fifth 7: 2 11/7 782.492 cents undecimal augmented fifth 7: 1 35/22 803.822 cents 8: 2 84/55 733.149 cents 8: 2 14/9 764.916 cents septimal minor sixth 8: 2 120/77 768.125 cents 8: 2 11/7 782.492 cents undecimal augmented fifth 8: 2 33/20 866.959 cents 8: 2 5/3 884.359 cents major sixth, BP sixth 9: 2 8/5 813.686 cents minor sixth 9: 2 18/11 852.592 cents undecimal neutral sixth 9: 2 5/3 884.359 cents major sixth, BP sixth 9: 1 77/45 929.920 cents 9: 2 12/7 933.129 cents septimal major sixth 9: 1 110/63 964.896 cents 9: 2 7/4 968.826 cents harmonic seventh 10: 2 56/33 915.553 cents 10: 2 12/7 933.129 cents septimal major sixth 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 2 20/11 1034.996 cents large minor seventh 10: 4 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 11: 2 20/11 1034.996 cents large minor seventh 11: 2 28/15 1080.557 cents grave major seventh 11: 2 66/35 1098.133 cents 11: 2 40/21 1115.533 cents acute major seventh 11: 2 21/11 1119.463 cents undecimal major seventh 11: 1 77/40 1133.830 cents 11: 1 55/28 1168.806 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 101.9 266.9 386.3 417.5 537.0 702.0 803.8 884.4 968.8 1035.0 1119.5 1200.0 101.9 : 165.0 284.4 315.6 435.1 600.1 702.0 782.5 867.0 933.1 1017.6 1098.1 1200.0 266.9 : 119.4 150.6 270.1 435.1 537.0 617.5 702.0 768.1 852.6 933.1 1035.0 1200.0 386.3 : 31.2 150.6 315.6 417.5 498.0 582.5 648.7 733.1 813.7 915.6 1080.6 1200.0 417.5 : 119.4 284.4 386.3 466.9 551.3 617.5 702.0 782.5 884.4 1049.4 1168.8 1200.0 537.0 : 165.0 266.9 347.4 431.9 498.0 582.5 663.0 764.9 929.9 1049.4 1080.6 1200.0 702.0 : 101.9 182.4 266.9 333.0 417.5 498.0 599.9 764.9 884.4 915.6 1035.0 1200.0 803.8 : 80.5 165.0 231.2 315.6 396.2 498.0 663.0 782.5 813.7 933.1 1098.1 1200.0 884.4 : 84.5 150.6 235.1 315.6 417.5 582.5 702.0 733.1 852.6 1017.6 1119.5 1200.0 968.8 : 66.2 150.6 231.2 333.0 498.0 617.5 648.7 768.1 933.1 1035.0 1115.5 1200.0 1035.0: 84.5 165.0 266.9 431.9 551.3 582.5 702.0 867.0 968.8 1049.4 1133.8 1200.0 1119.5: 80.5 182.4 347.4 466.9 498.0 617.5 782.5 884.4 964.9 1049.4 1115.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.1943 .. 165.0042 cents 121/112, 133.8100 cents 56/55, 31.1943 cents 2: 150.6371 .. 284.4470 cents 121/112, 133.8100 cents 120/121,-14.3672 cents 3: 231.1741 .. 386.3137 cents 35/32, 155.1396 cents 32/33,-53.2729 cents 4: 315.6413 .. 466.8507 cents 275/252, 151.2095 cents 24/25,-70.6724 cents 5: 396.1783 .. 600.0883 cents 9/8, 203.9100 cents 24/25,-70.6724 cents 6: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 280/297,-102.0433 cents 7: 599.9117 .. 803.8217 cents 9/8, 203.9100 cents 280/297,-102.0433 cents 8: 733.1493 .. 884.3587 cents 275/252, 151.2095 cents 24/25,-70.6724 cents 9: 813.6863 .. 968.8259 cents 35/32, 155.1396 cents 24/25,-70.6724 cents 10: 915.5530 .. 1049.3629 cents 121/112, 133.8100 cents 32/33,-53.2729 cents 11: 1034.9958 .. 1168.8057 cents 121/112, 133.8100 cents 120/121,-14.3672 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 56/55, 31.1943 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 11/10, 165.0042 cents Average / Smallest step : 3.205719 Largest / Average step : 1.650042 Largest / Smallest step : 5.289572 Median interval of one step : 93.16694 cents, amount: 0 Least squares average step : 105.91719 cents, oct.: 1271.00622 cents Scale is not proper Step pattern alph. order: ABCDCBAEFGFE Step pattern size order : EGFAFGECDBDC Scale is not a Constant Structure Scale diversity : 1.510488 Lumma stability : 0.051990 Lumma impropriety factor : 0.518233 Rothenberg efficiency : 0.284271 redundancy: 0.715729 Efficiency x scale size : 3.411255 Number of different interval sizes : 56 = 5.09091 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 6.00000 = 6 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 9801/9800, 0.1766 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 6 Most common triad is 0.0 701.955 1168.806 cents, amount: 1 Number of recognisable fifths : 6, average 701.9550 cents Length of longest harmonic part : 2 at degree 10 Length of longest subharmonic part : 2 at degree 7 Formal octave complements present : 1 = 8.3333% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Scale is differentially coherent in interval classes 5 and 6 combined Scale is n-1 differentially coherent in interval classes 6 and 7 combined Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 9-10 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 35 Scale harmonicity : 0.022624 Average absolute harmonicity : 0.154169 Specific harmonicity : 0.097776 Fundamental : 1/132, -7.0444 octaves, 1.9820 Hz. Guide tone : 420, 8.7142 octaves, 109882.737 Hz. Exponens Consonantiae : 5.544000E+04, 15.75864 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 144.0, average 12.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.23449, average 0.93621 Sum of Tenney's harmonic distance : 21.68682, average 1.80724 Vogel's harmonic complexity : 16.25000 Wille's k value : 115 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 173.01395, average 2.21813 Lattice compactness (without 2's) : 121.12856, average 1.55293 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.25000 11 1 3: -1 .. 1 0.00000 6 1 5: 0 .. 1 0.50000 6 2 7: 0 .. 1 0.50000 6 2 11: -1 .. 0 -0.50000 6 6 Average exponent except 2's : 6 / 12 = 0.50000 Average absolute exponent except 2's: 24 / 12 = 2.00000 Scale is weakly epimorphic with val: <12 17 25 31 45| Scale is weakly epimorphic with val: <12 17 25 33 39| Scale is weakly epimorphic with val: <12 17 25 33 43| Scale is weakly epimorphic with val: <12 17 25 35 45| Scale is weakly epimorphic with val: <12 17 27 35 43| Scale is weakly epimorphic with val: <12 17 27 37 45| Scale is weakly epimorphic with val: <12 17 31 35 39| Scale is weakly epimorphic with val: <12 17 31 37 45| Scale is weakly epimorphic with val: <12 18 25 32 40| Scale is weakly epimorphic with val: <12 18 25 33 41| Scale is weakly epimorphic with val: <12 18 25 34 44| Scale is weakly epimorphic with val: <12 18 25 35 39| Scale is weakly epimorphic with val: <12 18 25 35 45| Scale is weakly epimorphic with val: <12 18 26 31 40| Scale is weakly epimorphic with val: <12 18 26 33 40| Scale is weakly epimorphic with val: <12 18 26 34 39| Scale is weakly epimorphic with val: <12 18 26 34 41| Scale is weakly epimorphic with val: <12 18 26 34 43| Scale is weakly epimorphic with val: <12 18 26 34 45| Scale is weakly epimorphic with val: <12 18 26 35 40| Scale is weakly epimorphic with val: <12 18 26 37 40| Scale is weakly epimorphic with val: <12 18 27 31 41| Scale is weakly epimorphic with val: <12 18 27 32 40| Scale is weakly epimorphic with val: <12 18 27 34 44| Scale is weakly epimorphic with val: <12 18 27 35 43| Scale is weakly epimorphic with val: <12 18 27 37 41| Scale is weakly epimorphic with val: <12 18 28 31 44| Scale is weakly epimorphic with val: <12 18 28 32 39| Scale is weakly epimorphic with val: <12 18 28 32 41| Scale is weakly epimorphic with val: <12 18 28 32 43| Scale is weakly epimorphic with val: <12 18 28 32 45| Scale is weakly epimorphic with val: <12 18 28 33 44| Scale is weakly epimorphic with val: <12 18 28 35 44| Scale is weakly epimorphic with val: <12 18 28 37 44| Scale is weakly epimorphic with val: <12 18 29 31 39| Scale is weakly epimorphic with val: <12 18 29 31 45| Scale is weakly epimorphic with val: <12 18 29 32 40| Scale is weakly epimorphic with val: <12 18 29 33 43| Scale is weakly epimorphic with val: <12 18 29 34 44| Scale is weakly epimorphic with val: <12 18 29 37 39| Scale is weakly epimorphic with val: <12 18 29 37 45| Scale is weakly epimorphic with val: <12 18 31 32 40| Scale is weakly epimorphic with val: <12 18 31 33 41| Scale is weakly epimorphic with val: <12 18 31 34 44| Scale is weakly epimorphic with val: <12 18 31 35 39| Scale is weakly epimorphic with val: <12 18 31 35 45| Scale is weakly epimorphic with val: <12 19 25 33 41| Scale is weakly epimorphic with val: <12 19 25 35 39| Scale is weakly epimorphic with val: <12 19 27 35 41| Scale is weakly epimorphic with val: <12 19 27 35 45| Scale is weakly epimorphic with val: <12 19 29 35 39| Scale is weakly epimorphic with val: <12 19 29 37 45| Scale is weakly epimorphic with val: <12 21 25 31 41| Scale is weakly epimorphic with val: <12 21 25 35 41| Scale is weakly epimorphic with val: <12 21 26 31 44| Scale is weakly epimorphic with val: <12 21 26 32 43| Scale is weakly epimorphic with val: <12 21 27 34 44| Scale is weakly epimorphic with val: <12 21 27 35 43| Scale is weakly epimorphic with val: <12 21 27 37 41| Scale is weakly epimorphic with val: <12 21 29 37 39| Scale is weakly epimorphic with val: <12 21 29 37 43| Scale is weakly epimorphic with val: <12 21 31 35 39| Scale is weakly epimorphic with val: <12 21 31 37 41|
FIT/MODE
12: 1 2 1 0 1 2 1 1 1 0 1 1 N T3 SD: 21.9823 c. M: 36.9508 c. 14: 1 2 1 1 1 2 1 1 1 1 1 1 N D3 SD: 21.7492 c. M: 43.4566 c. 15: 1 2 2 0 2 2 1 1 1 1 1 1 N SD: 14.9660 c. M: 26.8709 c. 22: 2 3 2 1 2 3 2 1 2 1 2 1 N SD: 12.1559 c. M:-25.9916 c. 24: 2 3 3 0 3 3 2 2 1 2 1 2 N SD: 13.4588 c. M: 19.4630 c. 27: 2 4 3 0 3 4 2 2 2 1 2 2 N SD: 9.6065 c. M: 17.5080 c. 31: 3 4 3 1 3 4 3 2 2 2 2 2 N SD: 6.9140 c. M:-14.2624 c. 41: 3 6 4 1 4 6 3 3 3 2 3 3 N SD: 8.1889 c. M: 14.0618 c. 42: 4 5 5 1 4 6 3 3 3 2 3 3 N SD: 8.3507 c. M:-13.6863 c. 43: 4 6 4 1 4 6 4 3 3 2 3 3 N SD: 6.5311 c. M:-12.1989 c. 45: 4 6 4 2 4 6 4 3 3 3 3 3 N SD: 6.4531 c. M: 12.9804 c. 46: 4 6 5 1 5 6 4 3 3 3 3 3 N SD: 5.0970 c. M:-10.8753 c. 49: 4 7 5 1 5 7 4 3 4 2 4 3 N SD: 5.4642 c. M:-10.7659 c. 51: 4 7 5 2 5 7 4 4 3 3 4 3 N SD: 6.5645 c. M:-9.9488 c. 57: 5 8 5 2 5 8 5 4 4 3 4 4 N SD: 5.2436 c. M: 10.6350 c. 58: 5 8 6 1 6 8 5 4 4 3 4 4 N SD: 3.2347 c. M:-6.7897 c. 72: 6 10 7 2 7 10 6 5 5 4 5 5 N SD: 2.2533 c. M: 3.8217 c. 94: 8 13 9 3 9 13 8 6 7 5 7 6 N SD: 2.2054 c. M:-3.9413 c. 103: 9 14 10 3 10 14 9 7 7 6 7 7 N SD: 1.7312 c. M:-2.9877 c. 118: 10 16 12 3 12 16 10 8 8 7 8 8 N SD: 1.4233 c. M: 2.7242 c. 130: 11 18 13 3 13 18 11 9 9 7 9 9 N SD: 1.3395 c. M: 2.5399 c. 152: 13 21 15 4 15 21 13 10 11 8 11 10 N SD: 1.1095 c. M:-2.2267 c. 212: 18 29 21 6 21 29 18 14 15 12 15 14 N SD: 0.9199 c. M: 1.4081 c. 224: 19 31 22 6 22 31 19 15 16 12 16 15 N SD: 0.6522 c. M: 1.2365 c. 270: 23 37 27 7 27 37 23 18 19 15 19 18 N SD: 0.4205 c. M:-0.8270 c. 342: 29 47 34 9 34 47 29 23 24 19 24 23 N SD: 0.2138 c. M: 0.4049 c. 612: 52 84 61 16 61 84 52 41 43 34 43 41 N SD: 0.1647 c. M:-0.3041 c. 742: 63 102 74 19 74 102 63 50 52 41 52 50 N SD: 0.1612 c. M: 0.3255 c. 836: 71 115 83 22 83 115 71 56 59 46 59 56 N SD: 0.1150 c. M:-0.1954 c. 1084: 92 149 108 28 108 149 92 73 76 60 76 73 N SD: 0.1302 c. M: 0.2748 c. 1106: 94 152 110 29 110 152 94 74 78 61 78 74 N SD: 0.1249 c. M:-0.2477 c. 1178: 100 162 117 31 117 162 100 79 83 65 83 79 N SD: 0.1063 c. M: 0.2356 c. 1236: 105 170 123 32 123 170 105 83 87 68 87 83 N SD: 0.0730 c. M:-0.1194 c. 1578: 134 217 157 41 157 217 134 106 111 87 111 106 N SD: 0.0408 c. M: 0.0713 c. 1848: 157 254 184 48 184 254 157 124 130 102 130 124 N SD: 0.0480 c. M:-0.0814 c. 2190: 186 301 218 57 218 301 186 147 154 121 154 147 N SD: 0.0368 c. M:-0.0727 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x x x 4 S SD: 0.0000 cents 3 x x x x 4 x x 5 x x x 6 S SD: 12.9686 cents 4 x x 5 x x 6 x x 7 x x 8 S SD: 0.0000 cents 5 x 6 x x 7 x 8 x x 9 x 10 S SD: 13.9348 cents 6 x 7 x x 8:9 x 10 x 11 x 12 S SD: 6.9123 cents 7 x 8 x 9:10 x 11 x 12:13 x 14 S SD: 15.0820 cents 8 x 9:10 x 11:12:13 x 14 x 15:16 S SD: 10.0708 cents 9:10 x 11 x 12 x 14:15:16 x 17:18 S SD: 13.7555 cents 10:11:12 x 13:14:15:16:17 x 18:19:20 S SD: 10.6919 cents 11:12:13 x 14:15 x x 18:19:20:21:22 S SD: 7.3693 cents 12:13:14:15 x 16:18:19:20:21:22:23:24 S SD: 5.1287 cents 14:15:16 x 18:19:21:22:23 x 25:27:28 SD: 6.5710 cents 15:16:18 x 19:20:23:24:25:26:27:29:30 SD: 7.4175 cents 16:17:19:20 x 22:24:25:27:28:29:31:32 SD: 5.2016 cents 18:19:21 x 23:25:27:29:30:32:33:34:36 SD: 4.8877 cents 19:20:22 x 24:26:29:30:32:33:35:36:38 SD: 4.8177 cents 20:21:23:25 x 27:30:32:33:35:36:38:40 SD: 4.0626 cents 22:23:26 x 28:30:33:35:37:39:40:42:44 SD: 3.9250 cents 23:24:27:29 x 31:35:37:38:40:42:44:46 SD: 4.9350 cents 24:25:28:30:31:33:36:38:40:42:44:46:48 SD: 3.8686 cents 26:28:30 x 33:35:39:41:43:46:47:50:52 SD: 4.6504 cents 27:29:32:34 x 37:41:43:45:47:49:52:54 SD: 4.2995 cents 28:30:33:35:36:38:42:45:47:49:51:53:56 SD: 3.4196 cents 29:31:34:36:37:40:44:46:48:51:53:55:58 SD: 3.3890 cents 30:32:35 x 38:41:45:48:50:53:55:57:60 SD: 2.6059 cents 31:33:36:39 x 42:47:49:52:54:56:59:62 SD: 3.1020 cents 32:34:37:40:41:44:48:51:53:56:58:61:64 SD: 2.2881 cents 34:36:40 x 43:46:51:54:57:60:62:65:68 SD: 2.6925 cents 36:38:42:45:46:49:54:57:60:63:65:69:72 SD: 1.6382 cents 38:40:44 x 48:52:57:60:63:67:69:73:76 SD: 3.0061 cents 39:41:46:49:50:53:59:62:65:68:71:74:78 SD: 2.9360 cents 40:42:47:50:51:55:60:64:67:70:73:76:80 SD: 2.5721 cents 42:45:49 x 53:57:63:67:70:74:76:80:84 SD: 2.6339 cents 43:46:50:54:55:59:65:68:72:75:78:82:86 SD: 2.5170 cents 44:47:51:55:56:60:66:70:73:77:80:84:88 SD: 1.5394 cents 48:51:56:60:61:65:72:76:80:84:87:92:96 SD: 1.4587 cents 60:64:70:75:76:82:90:95:100:105:109:115:120 SD: 1.4379 cents 64:68:75:80:81:87:96:102:107:112:116:122:128 SD: 1.3616 cents 66:70:77:83:84:90:99:105:110:116:120:126:132 SD: 1.0716 cents 80:85:93:100:102:109:120:127:133:140:145:153:160 SD: 0.9538 cents 84:89:98:105:107:115:126:134:140:147:153:160:168 SD: 0.8309 cents 88:93:103:110:112:120:132:140:147:154:160:168:176 SD: 0.7697 cents 96:102:112:120:122:131:144:153:160:168:175:183:192 SD: 0.6129 cents 120:127:140:150:153:164:180:191:200:210:218:229:240 SD: 0.5358 cents 132:140:154:165:168:180:198:210:220:231:240:252:264 SD: 0.0000 cents