Scala analysis: diab17ascl
[25, 125, 175, 2401, 12005] breed diamond
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 2560/2401 111.010088 2: 343/320 120.164006 3: 8/7 231.174094 septimal whole tone 4: 400/343 266.149708 5: 2401/2000 316.362484 6: 5/4 386.313714 major third 7: 3200/2401 497.323802 8: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 9: 10/7 617.487807 Euler's tritone 10: 2401/1600 702.676198 two (larger approximation to neutral third) 11: 8/5 813.686286 minor sixth 12: 4000/2401 883.637516 13: 343/200 933.850292 14: 7/4 968.825906 harmonic seventh 15: 640/343 1079.835994 16: 2401/1280 1088.989912 17: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 2560/2401 111.0101 1: 2560/2401 111.0101 2: 823543/819200 9.1539 quince 3: 2560/2401 111.0101 4: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 5: 823543/800000 50.2128 6: 2500/2401 69.9512 two (Erlich's decatonic comma, tritonic diesis) 7: 2560/2401 111.0101 8: 16807/16000 85.1884 9: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 10: 16807/16000 85.1884 11: 2560/2401 111.0101 12: 2500/2401 69.9512 two (Erlich's decatonic comma, tritonic diesis) 13: 823543/800000 50.2128 14: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 15: 2560/2401 111.0101 16: 823543/819200 9.1539 quince 17: 2560/2401 111.0101
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 823543/819200 9.154 cents quince 1: 3 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 2 823543/800000 50.213 cents 1: 2 2500/2401 69.951 cents two (Erlich's decatonic comma, tritonic diesis) 1: 2 16807/16000 85.188 cents 1: 6 2560/2401 111.010 cents 2: 2 16807/16000 85.188 cents 2: 8 343/320 120.164 cents 2: 2 128000/117649 145.986 cents 2: 2 6400000/5764801 180.961 cents 2: 2 28/25 196.198 cents middle second 2: 1 6553600/5764801 222.020 cents 3: 4 35/32 155.140 cents septimal neutral second 3: 2 28/25 196.198 cents middle second 3: 1 5764801/5120000 205.352 cents 3: 8 8/7 231.174 cents septimal whole tone 3: 2 400/343 266.150 cents 4: 2 5764801/5120000 205.352 cents 4: 1 117649/102400 240.328 cents 4: 6 400/343 266.150 cents 4: 2 20000/16807 301.125 cents 4: 4 2401/2000 316.362 cents 4: 2 20480/16807 342.184 cents 5: 2 2401/2048 275.304 cents 5: 2 2401/2000 316.362 cents 5: 6 49/40 351.338 cents larger approximation to neutral third 5: 4 1024000/823543 377.160 cents 5: 2 5/4 386.314 cents major third 5: 1 32/25 427.373 cents classic diminished fourth 6: 8 5/4 386.314 cents major third 6: 2 32/25 427.373 cents classic diminished fourth 6: 2 823543/640000 436.526 cents 6: 3 64/49 462.348 cents 2 septatones or septatonic major third 6: 2 3200/2401 497.324 cents 7: 2 823543/640000 436.526 cents 7: 4 16807/12800 471.502 cents 7: 8 3200/2401 497.324 cents 7: 2 343/250 547.537 cents 7: 1 8000000/5764801 567.275 cents 8: 4 343/256 506.478 cents 8: 1 160000/117649 532.299 cents 8: 2 343/250 547.537 cents 8: 6 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 8: 2 8192000/5764801 608.334 cents 8: 2 10/7 617.488 cents Euler's tritone 9: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 9: 2 5764801/4096000 591.666 cents 9: 6 10/7 617.488 cents Euler's tritone 9: 2 500/343 652.463 cents 9: 1 117649/80000 667.701 cents 9: 4 512/343 693.522 cents 3 septatones or septatonic fifth 10: 1 5764801/4000000 632.725 cents 10: 2 500/343 652.463 cents 10: 8 2401/1600 702.676 cents two (larger approximation to neutral third) 10: 4 25600/16807 728.498 cents 10: 2 1280000/823543 763.474 cents 11: 2 2401/1600 702.676 cents two (larger approximation to neutral third) 11: 3 49/32 737.652 cents 11: 2 1280000/823543 763.474 cents 11: 2 25/16 772.627 cents classic augmented fifth 11: 8 8/5 813.686 cents minor sixth 12: 1 25/16 772.627 cents classic augmented fifth 12: 2 8/5 813.686 cents minor sixth 12: 4 823543/512000 822.840 cents 12: 6 80/49 848.662 cents smaller approximation to neutral sixth 12: 2 4000/2401 883.638 cents 12: 2 4096/2401 924.696 cents 4 septatones or septatonic major sixth 13: 2 16807/10240 857.816 cents 13: 4 4000/2401 883.638 cents 13: 2 16807/10000 898.875 cents 13: 6 343/200 933.850 cents 13: 1 204800/117649 959.672 cents 13: 2 10240000/5764801 994.648 cents 14: 2 343/200 933.850 cents 14: 8 7/4 968.826 cents harmonic seventh 14: 1 10240000/5764801 994.648 cents 14: 2 25/14 1003.802 cents middle minor seventh 14: 4 64/35 1044.860 cents septimal neutral seventh 15: 1 5764801/3276800 977.980 cents 15: 2 25/14 1003.802 cents middle minor seventh 15: 2 5764801/3200000 1019.039 cents 15: 2 117649/64000 1054.014 cents 15: 8 640/343 1079.836 cents 15: 2 32000/16807 1114.812 cents 16: 6 2401/1280 1088.990 cents 16: 2 32000/16807 1114.812 cents 16: 2 2401/1250 1130.049 cents 16: 2 1600000/823543 1149.787 cents 16: 3 49/25 1165.024 cents BP eighth 16: 2 1638400/823543 1190.846 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.62500 = 45/8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 111.0 120.2 231.2 266.1 316.4 386.3 497.3 582.5 617.5 702.7 813.7 883.6 933.9 968.8 1079.8 1089.0 1200.0 111.0 : 9.2 120.2 155.1 205.4 275.3 386.3 471.5 506.5 591.7 702.7 772.6 822.8 857.8 968.8 978.0 1089.0 1200.0 120.2 : 111.0 146.0 196.2 266.1 377.2 462.3 497.3 582.5 693.5 763.5 813.7 848.7 959.7 968.8 1079.8 1190.8 1200.0 231.2 : 35.0 85.2 155.1 266.1 351.3 386.3 471.5 582.5 652.5 702.7 737.7 848.7 857.8 968.8 1079.8 1089.0 1200.0 266.1 : 50.2 120.2 231.2 316.4 351.3 436.5 547.5 617.5 667.7 702.7 813.7 822.8 933.9 1044.9 1054.0 1165.0 1200.0 316.4 : 70.0 181.0 266.1 301.1 386.3 497.3 567.3 617.5 652.5 763.5 772.6 883.6 994.6 1003.8 1114.8 1149.8 1200.0 386.3 : 111.0 196.2 231.2 316.4 427.4 497.3 547.5 582.5 693.5 702.7 813.7 924.7 933.9 1044.9 1079.8 1130.0 1200.0 497.3 : 85.2 120.2 205.4 316.4 386.3 436.5 471.5 582.5 591.7 702.7 813.7 822.8 933.9 968.8 1019.0 1089.0 1200.0 582.5 : 35.0 120.2 231.2 301.1 351.3 386.3 497.3 506.5 617.5 728.5 737.7 848.7 883.6 933.9 1003.8 1114.8 1200.0 617.5 : 85.2 196.2 266.1 316.4 351.3 462.3 471.5 582.5 693.5 702.7 813.7 848.7 898.9 968.8 1079.8 1165.0 1200.0 702.7 : 111.0 181.0 231.2 266.1 377.2 386.3 497.3 608.3 617.5 728.5 763.5 813.7 883.6 994.6 1079.8 1114.8 1200.0 813.7 : 70.0 120.2 155.1 266.1 275.3 386.3 497.3 506.5 617.5 652.5 702.7 772.6 883.6 968.8 1003.8 1089.0 1200.0 883.6 : 50.2 85.2 196.2 205.4 316.4 427.4 436.5 547.5 582.5 632.7 702.7 813.7 898.9 933.9 1019.0 1130.0 1200.0 933.9 : 35.0 146.0 155.1 266.1 377.2 386.3 497.3 532.3 582.5 652.5 763.5 848.7 883.6 968.8 1079.8 1149.8 1200.0 968.8 : 111.0 120.2 231.2 342.2 351.3 462.3 497.3 547.5 617.5 728.5 813.7 848.7 933.9 1044.9 1114.8 1165.0 1200.0 1079.8: 9.2 120.2 231.2 240.3 351.3 386.3 436.5 506.5 617.5 702.7 737.7 822.8 933.9 1003.8 1054.0 1089.0 1200.0 1089.0: 111.0 222.0 231.2 342.2 377.2 427.4 497.3 608.3 693.5 728.5 813.7 924.7 994.6 1044.9 1079.8 1190.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 9.1539 .. 111.0101 cents 2097152000/1977326743, 101.8562 ce 823543/819200, 9.1539 cents 2: 85.1884 .. 222.0202 cents 136.83179 cents 40353607/40960000,-25.8217 cents 3: 155.1396 .. 266.1497 cents 2560/2401, 111.0101 cents 40353607/41943040,-66.8806 cents 4: 205.3524 .. 342.1842 cents 136.83179 cents 1977326743/2048000000,-60.7973 cents 5: 275.3036 .. 427.3726 cents 65536/60025, 152.0689 cents 40353607/41943040,-66.8806 cents 6: 386.3137 .. 497.3238 cents 2560/2401, 111.0101 cents 125/128,-41.0589 cents 7: 436.5265 .. 567.2750 cents 130.74854 cents 1977326743/2048000000,-60.7973 cents 8: 506.4777 .. 617.4878 cents 2560/2401, 111.0101 cents 1977326743/2048000000,-60.7973 cents 9: 582.5122 .. 693.5223 cents 2560/2401, 111.0101 cents 49/50,-34.9756 cents 10: 632.7250 .. 763.4735 cents 130.74854 cents 1977326743/2048000000,-60.7973 cents 11: 702.6762 .. 813.6863 cents 2560/2401, 111.0101 cents 1977326743/2048000000,-60.7973 cents 12: 772.6274 .. 924.6964 cents 65536/60025, 152.0689 cents 125/128,-41.0589 cents 13: 857.8158 .. 994.6476 cents 136.83179 cents 40353607/41943040,-66.8806 cents 14: 933.8503 .. 1044.8604 cents 2560/2401, 111.0101 cents 1977326743/2048000000,-60.7973 cents 15: 977.9798 .. 1114.8116 cents 136.83179 cents 40353607/41943040,-66.8806 cents 16: 1088.9899 .. 1190.8461 cents 2097152000/1977326743, 101.8562 ce 40353607/40960000,-25.8217 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 823543/819200, 9.1539 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 2560/2401, 111.0101 cents Average / Smallest step : 7.711260 Largest / Average step : 1.572643 Largest / Smallest step : 12.127058 Median interval of one step : 2500/2401, 69.9512 cents, amount: 2 Most common interval of one step : 2560/2401, 111.0101 cents, amount: 6 Least squares average step : 70.59600 cents, oct.: 1200.13204 cents Scale is not proper Step pattern alph. order: ABACDEAFCFAEDCABA Step pattern size order : FAFBCDFEBEFDCBFAF Scale is not a Constant Structure Scale diversity : 1.425155 Lumma stability : 0.015257 Lumma impropriety factor : 0.639756 Number of different interval sizes : 68 = 4.25000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 5.62500 = 45/8 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 823543/819200, 9.1539 cents Number of recognisable fifths : 14, average 700.0608 cents Scale contains a complete diamond : 5 25 343 2401 Formal octave complements present : 17 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 8-9 -- Rational properties -- Prime limit : 7 Odd number limit : 5764801 (O: 5764801 U: 5764801) Highest odd numerator or denominator: 2401 Scale harmonicity : 0.007263 Average absolute harmonicity : 0.099195 Specific harmonicity : 0.041314 Fundamental : 1/76832000, -26.1952 octaves, 0.0000 Hz. Guide tone : 153664000, 27.1952 octaves, 40202430866.413 Hz. Exponens Consonantiae : 1.180631E+16, 53.39041 octaves Euler's gradus suavitatis : 90 Sum of Mann's harmonic distance : 16029.0, average 942.88235 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 35.20186, average 2.07070 Sum of Tenney's harmonic distance : 70.55439, average 4.15026 Vogel's harmonic complexity : 51.52941 Wille's k value : 72060012 Wilson's harmonic complexity : 86 Rectangular lattice diameter : 14 Triangular lattice diameter : 8 Lattice compactness : 1088.54215, average 7.11465 Lattice compactness (without 2's) : 597.59080, average 3.90582 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -8 .. 9 0.52941 71 1 5: -3 .. 3 0.00000 22 2 7: -4 .. 4 0.00000 40 14 Average exponent except 2's : 0 / 17 = 0.00000 Average absolute exponent except 2's: 62 / 17 = 3.64706
FIT/MODE
17: 1 0 2 0 1 1 2 1 0 1 2 1 1 0 2 0 2 N T3 SD: 37.8126 c. M: 67.3821 c. 18: 2 0 1 1 1 1 1 2 0 2 1 1 1 1 1 0 2 N I SD: 19.8964 c. M:-31.1741 c. 19: 2 0 2 0 1 1 2 1 1 1 2 1 1 0 2 0 2 N I SD: 12.0365 c. M:-21.4575 c. 22: 2 0 2 1 1 1 2 2 0 2 2 1 1 1 2 0 2 N I SD: 9.8493 c. M:-17.4878 c. 31: 3 0 3 1 1 2 3 2 1 2 3 2 1 1 3 0 3 N I SD: 4.2078 c. M:-6.6851 c. 41: 4 0 4 1 2 2 4 3 1 3 4 2 2 1 4 0 4 N I SD: 4.0001 c. M:-6.0631 c. 68: 6 1 6 2 3 4 6 5 2 5 6 4 3 2 6 1 6 N I SD: 2.6225 c. M: 5.1277 c. 87: 8 1 8 2 4 5 8 6 3 6 8 5 4 2 8 1 8 N I SD: 2.5545 c. M: 4.0807 c. 99: 9 1 9 3 4 6 9 7 3 7 9 6 4 3 9 1 9 N I SD: 1.1024 c. M:-1.9192 c. 140: 13 1 13 4 6 8 13 10 4 10 13 8 6 4 13 1 13 N I SD: 0.4307 c. M:-0.7804 c. 239: 22 2 22 7 10 14 22 17 7 17 22 14 10 7 22 2 22 N I SD: 0.2711 c. M: 0.5498 c. 379: 35 3 35 11 16 22 35 27 11 27 35 22 16 11 35 3 35 N I SD: 0.1616 c. M:-0.2602 c. 550: 51 4 51 16 23 32 51 39 16 39 51 32 23 16 51 4 51 N I SD: 0.1294 c. M: 0.2626 c. 649: 60 5 60 19 27 38 60 46 19 46 60 38 27 19 60 5 60 N I SD: 0.0959 c. M:-0.1837 c. 789: 73 6 73 23 33 46 73 56 23 56 73 46 33 23 73 6 73 N I SD: 0.0104 c. M: 0.0165 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.3606 cents 3 .. 6 match: 3 H SD: 0.3400 cents 4 .. 8 match: 4 H SD: 0.1803 cents 5 .. 10 match: 5 H SD: 9.7551 cents 6 .. 12 match: 6 H SD: 5.0845 cents 7 .. 14 match: 7 H SD: 8.3523 cents 8 .. 16 match: 8 H SD: 6.1719 cents 9 .. 18 match: 9 H SD: 9.2807 cents 10 .. 20 match: 10 H SD: 8.3506 cents 11 .. 22 match: 10 SD: 9.8075 cents 12 .. 24 match: 12 H SD: 4.7152 cents 13 .. 26 match: 12 S SD: 7.1835 cents 14 .. 28 match: 13 S SD: 6.2503 cents 15 .. 30 match: 12 SD: 4.0878 cents 16 .. 32 match: 13 S SD: 4.9523 cents 17 .. 34 match: 13 SD: 5.5155 cents 18 .. 36 match: 14 SD: 4.7154 cents 19 .. 38 match: 13 SD: 5.1430 cents 20 .. 40 match: 15 SD: 3.7726 cents 21 .. 42 match: 15 SD: 4.5702 cents 22 .. 44 match: 14 SD: 5.1516 cents 23 .. 46 match: 15 SD: 4.1251 cents 24 .. 48 match: 14 S SD: 3.0267 cents 25 .. 50 match: 14 SD: 2.9964 cents 26 .. 52 match: 14 SD: 3.9119 cents 27 .. 54 match: 15 SD: 3.1280 cents 28 .. 56 match: 16 SD: 2.4738 cents 29 .. 58 match: 14 SD: 3.0342 cents 30 .. 60 match: 15 SD: 2.3787 cents 31 .. 62 match: 15 SD: 3.0201 cents 32 .. 64 match: 14 SD: 2.4248 cents 33 .. 66 match: 14 SD: 2.5408 cents 34 .. 68 match: 16 SD: 2.9531 cents 35 .. 70 match: 17 SD: 2.3323 cents 36 .. 72 match: 17 SD: 2.2923 cents 37 .. 74 match: 16 SD: 2.7151 cents 38 .. 76 match: 15 SD: 2.7344 cents 39 .. 78 match: 14 SD: 2.3535 cents 40 .. 80 match: 15 SD: 1.6650 cents 41 .. 82 match: 15 SD: 2.2017 cents 42 .. 84 match: 16 SD: 1.7354 cents 43 .. 86 match: 16 SD: 1.9410 cents 44 .. 88 match: 16 SD: 1.8383 cents 45 .. 90 match: 15 SD: 1.8540 cents 46 .. 92 match: 15 SD: 2.2531 cents 47 .. 94 match: 15 SD: 1.8931 cents 48 .. 96 match: 15 SD: 1.3250 cents 53 .. 106 match: 15 SD: 1.7418 cents 54 .. 108 match: 15 SD: 1.5987 cents 55 .. 110 match: 15 SD: 1.3655 cents 56 .. 112 match: 16 SD: 1.2624 cents 57 .. 114 match: 16 SD: 1.5413 cents 58 .. 116 match: 16 SD: 1.6318 cents 59 .. 118 match: 16 SD: 1.5200 cents 60 .. 120 match: 16 SD: 0.8935 cents 61 .. 122 match: 15 SD: 1.4464 cents 62 .. 124 match: 15 SD: 1.6210 cents 63 .. 126 match: 16 SD: 1.4123 cents 64 .. 128 match: 17 SD: 1.3574 cents 65 .. 130 match: 17 SD: 1.2527 cents 68 .. 136 match: 16 SD: 1.1202 cents 69 .. 138 match: 15 SD: 1.3399 cents 70 .. 140 match: 15 SD: 1.1308 cents 71 .. 142 match: 16 SD: 1.2576 cents 72 .. 144 match: 16 SD: 0.9327 cents 73 .. 146 match: 16 SD: 1.1724 cents 74 .. 148 match: 16 SD: 1.2912 cents 75 .. 150 match: 16 SD: 0.9819 cents 76 .. 152 match: 16 SD: 1.1007 cents 77 .. 154 match: 16 SD: 1.1647 cents 78 .. 156 match: 16 SD: 1.1446 cents 79 .. 158 match: 17 SD: 1.1333 cents 80 .. 160 match: 17 SD: 0.9214 cents 84 .. 168 match: 16 SD: 0.6341 cents 85 .. 170 match: 15 SD: 0.9032 cents 86 .. 172 match: 16 SD: 1.1755 cents 87 .. 174 match: 16 SD: 1.0890 cents 88 .. 176 match: 16 SD: 0.9128 cents 89 .. 178 match: 16 SD: 0.9253 cents 90 .. 180 match: 16 SD: 0.7667 cents 93 .. 186 match: 16 SD: 1.0056 cents 95 .. 190 match: 17 SD: 0.8328 cents 96 .. 192 match: 17 SD: 0.7014 cents 99 .. 198 match: 16 SD: 0.8741 cents 100 .. 200 match: 16 SD: 0.7645 cents 101 .. 202 match: 16 SD: 0.9883 cents 102 .. 204 match: 16 SD: 0.9006 cents 103 .. 206 match: 16 SD: 0.7732 cents 104 .. 208 match: 16 SD: 0.7312 cents 105 .. 210 match: 17 SD: 0.6739 cents 108 .. 216 match: 17 SD: 0.6735 cents 114 .. 228 match: 16 SD: 0.7511 cents 115 .. 230 match: 16 SD: 0.7224 cents 116 .. 232 match: 16 SD: 0.7999 cents 117 .. 234 match: 16 SD: 0.7908 cents 118 .. 236 match: 16 SD: 0.8195 cents 119 .. 238 match: 17 SD: 0.6899 cents 120 .. 240 match: 17 SD: 0.4340 cents 129 .. 258 match: 16 SD: 0.7178 cents 130 .. 260 match: 16 SD: 0.7489 cents 131 .. 262 match: 16 SD: 0.7208 cents 132 .. 264 match: 16 SD: 0.5695 cents 135 .. 270 match: 17 SD: 0.5506 cents 140 .. 280 match: 17 SD: 0.4004 cents 144 .. 288 match: 16 SD: 0.5254 cents 145 .. 290 match: 16 SD: 0.5550 cents 146 .. 292 match: 16 SD: 0.7097 cents 147 .. 294 match: 17 SD: 0.5964 cents 148 .. 296 match: 17 SD: 0.5557 cents 150 .. 300 match: 17 SD: 0.5038 cents 152 .. 304 match: 17 SD: 0.4861 cents 155 .. 310 match: 17 SD: 0.4752 cents 159 .. 318 match: 16 SD: 0.5854 cents 160 .. 320 match: 17 SD: 0.5772 cents 161 .. 322 match: 17 SD: 0.5672 cents 162 .. 324 match: 17 SD: 0.5527 cents 163 .. 326 match: 17 SD: 0.4923 cents 164 .. 328 match: 17 SD: 0.4905 cents 165 .. 330 match: 17 SD: 0.4583 cents 168 .. 336 match: 17 SD: 0.2822 cents 180 .. 360 match: 17 SD: 0.2416 cents 240 .. 480 match: 17 SD: 0.2169 cents 315 .. 630 match: 17 SD: 0.2070 cents 320 .. 640 match: 17 SD: 0.1845 cents 348 .. 696 match: 17 SD: 0.1567 cents 420 .. 840 match: 17 SD: 0.1292 cents 499 .. 998 match: 17 SD: 0.1246 cents 553 .. 1106 match: 17 SD: 0.1199 cents 560 .. 1120 match: 17 SD: 0.1086 cents 572 .. 1144 match: 17 SD: 0.1060 cents