Scala analysis: 15highschool1
First 15-note Highschool scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 3: 9/8 203.910002 major whole tone 4: 6/5 315.641287 minor third 5: 5/4 386.313714 major third 6: 4/3 498.044999 perfect fourth 7: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 8: 36/25 631.282574 classic diminished fifth 9: 3/2 701.955001 perfect fifth 10: 8/5 813.686286 minor sixth 11: 5/3 884.358713 major sixth, BP sixth 12: 7/4 968.825906 harmonic seventh 13: 9/5 1017.596288 just minor seventh, BP seventh 14: 15/8 1088.268715 classic major seventh 15: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 21/20 84.4672 minor semitone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 16/15 111.7313 minor diatonic semitone 5: 25/24 70.6724 classic chromatic semitone, minor chroma 6: 16/15 111.7313 minor diatonic semitone 7: 21/20 84.4672 minor semitone 8: 36/35 48.7704 septimal diesis, 1/4-tone 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 16/15 111.7313 minor diatonic semitone 11: 25/24 70.6724 classic chromatic semitone, minor chroma 12: 21/20 84.4672 minor semitone 13: 36/35 48.7704 septimal diesis, 1/4-tone 14: 25/24 70.6724 classic chromatic semitone, minor chroma 15: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 36/35 48.770 cents septimal diesis, 1/4-tone 1: 5 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 3 21/20 84.467 cents minor semitone 1: 4 16/15 111.731 cents minor diatonic semitone 2: 3 15/14 119.443 cents major diatonic semitone 2: 3 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 1 35/32 155.140 cents septimal neutral second 2: 6 10/9 182.404 cents minor whole tone 2: 2 28/25 196.198 cents middle second 3: 4 9/8 203.910 cents major whole tone 3: 3 8/7 231.174 cents septimal whole tone 3: 2 144/125 244.969 cents classic diminished third 3: 2 125/108 253.076 cents semi-augmented whole tone 3: 3 7/6 266.871 cents septimal minor third 3: 1 32/27 294.135 cents Pythagorean minor third 4: 1 75/64 274.582 cents classic augmented second 4: 2 25/21 301.847 cents BP second, quasi-equal minor third 4: 9 6/5 315.641 cents minor third 4: 1 175/144 337.543 cents 4: 1 100/81 364.807 cents grave major third 4: 1 56/45 378.602 cents septimal narrow major third 5: 1 216/175 364.412 cents 5: 8 5/4 386.314 cents major third 5: 1 63/50 400.108 cents quasi-equal major third 5: 1 80/63 413.578 cents wide major third 5: 3 32/25 427.373 cents classic diminished fourth 5: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 6: 2 9/7 435.084 cents septimal major third, BP third 6: 1 162/125 448.879 cents 6: 1 125/96 456.986 cents classic augmented third 6: 2 21/16 470.781 cents narrow fourth 6: 9 4/3 498.045 cents perfect fourth 7: 1 75/56 505.757 cents marvelous fourth 7: 3 27/20 519.551 cents acute fourth 7: 2 48/35 546.815 cents septimal semi-augmented fourth 7: 4 25/18 568.717 cents classic augmented fourth 7: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 7: 2 64/45 609.776 cents 2nd tritone 8: 2 45/32 590.224 cents diatonic tritone 8: 3 10/7 617.488 cents Euler's tritone 8: 4 36/25 631.283 cents classic diminished fifth 8: 2 35/24 653.185 cents septimal semi-diminished fifth 8: 3 40/27 680.449 cents grave fifth 8: 1 112/75 694.243 cents marvelous fifth 9: 9 3/2 701.955 cents perfect fifth 9: 2 32/21 729.219 cents wide fifth 9: 1 192/125 743.014 cents classic diminished sixth 9: 1 125/81 751.121 cents 9: 2 14/9 764.916 cents septimal minor sixth 10: 1 54/35 750.725 cents septimal semi-augmented fifth 10: 3 25/16 772.627 cents classic augmented fifth 10: 1 63/40 786.422 cents narrow minor sixth 10: 1 100/63 799.892 cents quasi-equal minor sixth 10: 8 8/5 813.686 cents minor sixth 10: 1 175/108 835.588 cents 11: 1 45/28 821.398 cents septimale wide minor sixth 11: 1 81/50 835.193 cents acute minor sixth 11: 1 288/175 862.457 cents 11: 9 5/3 884.359 cents major sixth, BP sixth 11: 2 42/25 898.153 cents quasi-equal major sixth 11: 1 128/75 925.418 cents diminished seventh 12: 1 27/16 905.865 cents Pythagorean major sixth 12: 3 12/7 933.129 cents septimal major sixth 12: 2 216/125 946.924 cents semi-augmented sixth 12: 2 125/72 955.031 cents classic augmented sixth 12: 3 7/4 968.826 cents harmonic seventh 12: 4 16/9 996.090 cents Pythagorean minor seventh 13: 2 25/14 1003.802 cents middle minor seventh 13: 6 9/5 1017.596 cents just minor seventh, BP seventh 13: 1 64/35 1044.860 cents septimal neutral seventh 13: 3 50/27 1066.762 cents grave major seventh 13: 3 28/15 1080.557 cents grave major seventh 14: 4 15/8 1088.269 cents classic major seventh 14: 3 40/21 1115.533 cents acute major seventh 14: 5 48/25 1129.328 cents classic diminished octave 14: 3 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.42857 = 38/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 84.5 133.2 203.9 315.6 386.3 498.0 582.5 631.3 702.0 813.7 884.4 968.8 1017.6 1088.3 1200.0 84.5 : 48.8 119.4 231.2 301.8 413.6 498.0 546.8 617.5 729.2 799.9 884.4 933.1 1003.8 1115.5 1200.0 133.2 : 70.7 182.4 253.1 364.8 449.3 498.0 568.7 680.4 751.1 835.6 884.4 955.0 1066.8 1151.2 1200.0 203.9 : 111.7 182.4 294.1 378.6 427.4 498.0 609.8 680.4 764.9 813.7 884.4 996.1 1080.6 1129.3 1200.0 315.6 : 70.7 182.4 266.9 315.6 386.3 498.0 568.7 653.2 702.0 772.6 884.4 968.8 1017.6 1088.3 1200.0 386.3 : 111.7 196.2 245.0 315.6 427.4 498.0 582.5 631.3 702.0 813.7 898.2 946.9 1017.6 1129.3 1200.0 498.0 : 84.5 133.2 203.9 315.6 386.3 470.8 519.6 590.2 702.0 786.4 835.2 905.9 1017.6 1088.3 1200.0 582.5 : 48.8 119.4 231.2 301.8 386.3 435.1 505.8 617.5 702.0 750.7 821.4 933.1 1003.8 1115.5 1200.0 631.3 : 70.7 182.4 253.1 337.5 386.3 457.0 568.7 653.2 702.0 772.6 884.4 955.0 1066.8 1151.2 1200.0 702.0 : 111.7 182.4 266.9 315.6 386.3 498.0 582.5 631.3 702.0 813.7 884.4 996.1 1080.6 1129.3 1200.0 813.7 : 70.7 155.1 203.9 274.6 386.3 470.8 519.6 590.2 702.0 772.6 884.4 968.8 1017.6 1088.3 1200.0 884.4 : 84.5 133.2 203.9 315.6 400.1 448.9 519.6 631.3 702.0 813.7 898.2 946.9 1017.6 1129.3 1200.0 968.8 : 48.8 119.4 231.2 315.6 364.4 435.1 546.8 617.5 729.2 813.7 862.5 933.1 1044.9 1115.5 1200.0 1017.6: 70.7 182.4 266.9 315.6 386.3 498.0 568.7 680.4 764.9 813.7 884.4 996.1 1066.8 1151.2 1200.0 1088.3: 111.7 196.2 245.0 315.6 427.4 498.0 609.8 694.2 743.0 813.7 925.4 996.1 1080.6 1129.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 111.7313 cents 28/27, 62.9609 cents 36/35, 48.7704 cents 2: 119.4428 .. 196.1985 cents 392/375, 76.7557 cents 225/224, 7.7115 cents 3: 203.9100 .. 294.1350 cents 256/243, 90.2250 cents 225/224, 7.7115 cents 4: 274.5824 .. 378.6022 cents 3584/3375, 104.0198 cents 2025/2048,-19.5526 cents 5: 364.4117 .. 449.2746 cents 6125/5832, 84.8629 cents 243/245,-14.1905 cents 6: 435.0841 .. 498.0450 cents 28/27, 62.9609 cents 243/245,-14.1905 cents 7: 505.7565 .. 609.7763 cents 3584/3375, 104.0198 cents 225/224, 7.7115 cents 8: 590.2237 .. 694.2435 cents 3584/3375, 104.0198 cents 2025/2048,-19.5526 cents 9: 701.9550 .. 764.9159 cents 28/27, 62.9609 cents 225/224, 7.7115 cents 10: 750.7254 .. 835.5883 cents 6125/5832, 84.8629 cents 243/245,-14.1905 cents 11: 821.3978 .. 925.4176 cents 3584/3375, 104.0198 cents 243/245,-14.1905 cents 12: 905.8650 .. 996.0900 cents 256/243, 90.2250 cents 2025/2048,-19.5526 cents 13: 1003.8015 .. 1080.5572 cents 392/375, 76.7557 cents 225/224, 7.7115 cents 14: 1088.2687 .. 1151.2296 cents 28/27, 62.9609 cents 225/224, 7.7115 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 80.0000 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 1.640340 Largest / Average step : 1.396641 Largest / Smallest step : 2.290966 Median interval of one step : 25/24, 70.6724 cents, amount: 5 Most common interval of one step : 25/24, 70.6724 cents, amount: 5 Least squares average step : 79.47238 cents, oct.: 1192.08569 cents Scale is not proper Step pattern alph. order: ABCDCDABCDCABCD Step pattern size order : CABDBDCABDBCABD Scale is a Constant Structure, by a margin of 0.39576 cents Scale diversity : 1.494901 Lumma stability : 0.119842 Lumma impropriety factor : 0.096183 Number of different interval sizes : 76 = 5.42857 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 5.42857 = 38/7 Median interval variety : 4.5 Lowest interval variety : 4 Smallest interval difference : 4375/4374, 0.3958 cents Most common triad is 0.0 498.045 884.359 cents, amount: 7 Number of recognisable fifths : 10, average 701.1838 cents Scale contains a complete diamond : 1 3 5 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 46.6667% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined -- Rational properties -- Prime limit : 7 Odd number limit : 175 (O: 175 U: 175) Highest odd numerator or denominator: 27 Scale harmonicity : 0.021667 Average absolute harmonicity : 0.166405 Specific harmonicity : 0.134845 Fundamental : 1/600, -9.2288 octaves, 0.4360 Hz. Guide tone : 7560, 12.8842 octaves, 1977889.274 Hz. Exponens Consonantiae : 4.536000E+06, 22.11299 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 143.5, average 9.56667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.67642, average 0.84509 Sum of Tenney's harmonic distance : 24.70241, average 1.64683 Vogel's harmonic complexity : 17.33333 Wille's k value : 562 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 374.21955, average 3.11850 Lattice compactness (without 2's) : 237.87947, average 1.98233 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 -0.26667 22 1 3: -1 .. 3 0.73333 15 3 5: -2 .. 1 -0.40000 12 8 7: 0 .. 1 0.20000 3 3 Average exponent except 2's : 8 / 15 = 0.53333 Average absolute exponent except 2's: 30 / 15 = 2.00000 Scale is JI-epimorphic with val: <15 24 35 42| = patent
FIT/MODE
15: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.7475 c. M:-36.0900 c. 19: 1 1 1 2 1 2 1 1 1 2 1 1 1 1 2 N D3 S SD: 11.0904 c. M: 21.4575 c. 24: 2 1 1 2 2 2 2 1 1 2 2 1 1 2 2 N D3 SD: 13.8250 c. M: 18.8259 c. 25: 2 1 1 3 1 2 2 1 2 2 1 2 1 2 2 N D3 SD: 12.6346 c. M:-20.3587 c. 26: 2 1 1 3 1 3 2 1 1 3 1 2 1 2 2 N SD: 12.2494 c. M:-19.4236 c. 27: 2 1 2 2 2 2 2 1 2 2 2 2 1 1 3 N SD: 10.3632 c. M: 21.6020 c. 28: 2 1 2 2 2 3 2 1 1 3 2 2 1 1 3 N SD: 12.3223 c. M:-17.4878 c. 31: 2 1 2 3 2 3 2 1 2 3 2 2 1 2 3 N SD: 7.5994 c. M: 17.1085 c. 35: 2 2 2 3 2 4 2 1 2 4 2 2 2 2 3 N SD: 10.1457 c. M:-16.2407 c. 38: 3 1 2 4 2 4 2 2 2 4 2 3 1 2 4 N SD: 8.7115 c. M: 14.5845 c. 41: 3 2 2 4 2 4 3 2 2 4 2 3 2 2 4 N SD: 6.2327 c. M:-13.1039 c. 43: 3 2 2 4 3 4 3 2 2 4 3 3 1 3 4 N SD: 6.7991 c. M: 12.9451 c. 46: 3 2 3 4 3 4 3 2 3 4 3 3 2 3 4 P SD: 4.5648 c. M: 8.5991 c. 53: 4 2 3 5 3 5 4 2 3 5 3 4 2 3 5 N SD: 2.8666 c. M:-6.1671 c. 72: 5 3 4 7 4 7 5 3 4 7 4 5 3 4 7 N SD: 2.2929 c. M: 4.9354 c. 84: 6 3 5 8 5 8 6 3 5 8 5 6 3 5 8 N SD: 2.4835 c. M: 4.6661 c. 87: 6 4 5 8 5 8 6 4 5 8 5 6 4 5 8 N SD: 2.4000 c. M:-4.6935 c. 99: 7 4 6 9 6 9 7 4 6 9 6 7 4 6 9 N SD: 1.2107 c. M:-2.6404 c. 118: 8 5 7 11 7 11 8 5 7 11 7 8 5 7 11 N SD: 1.3681 c. M: 3.1113 c. 152: 11 6 9 14 9 14 11 6 9 14 9 11 6 9 14 N SD: 1.1547 c. M:-2.3749 c. 171: 12 7 10 16 10 16 12 7 10 16 10 12 7 10 16 N SD: 0.2785 c. M: 0.5494 c. 441: 31 18 26 41 26 41 31 18 26 41 26 31 18 26 41 N SD: 0.1062 c. M: 0.1993 c. 612: 43 25 36 57 36 57 43 25 36 57 36 43 25 36 57 N SD: 0.0882 c. M: 0.1985 c. 1053: 74 43 62 98 62 98 74 43 62 98 62 74 43 62 98 N SD: 0.0846 c. M: 0.1760 c. 1376: 97 56 81 128 81 128 97 56 81 128 81 97 56 81 128 N SD: 0.0992 c. M:-0.1927 c. 1407: 99 57 83 131 83 131 99 57 83 131 83 99 57 83 131 N SD: 0.0804 c. M: 0.1885 c. 1547: 109 63 91 144 91 144 109 63 91 144 91 109 63 91 144 N SD: 0.0806 c. M:-0.1819 c. 1578: 111 64 93 147 93 147 111 64 93 147 93 111 64 93 147 N SD: 0.0712 c. M: 0.1577 c. 1677: 118 68 99 156 99 156 118 68 99 156 99 118 68 99 156 N SD: 0.0792 c. M: 0.1556 c. 1718: 121 70 101 160 101 160 121 70 101 160 101 121 70 101 160 N SD: 0.0758 c. M:-0.1734 c. 1749: 123 71 103 163 103 163 123 71 103 163 103 123 71 103 163 N SD: 0.0745 c. M: 0.1364 c. 1848: 130 75 109 172 109 172 130 75 109 172 109 130 75 109 172 N SD: 0.0576 c. M: 0.1207 c. 2019: 142 82 119 188 119 188 142 82 119 188 119 142 82 119 188 N SD: 0.0485 c. M: 0.1024 c. 2190: 154 89 129 204 129 204 154 89 129 204 129 154 89 129 204 N SD: 0.0508 c. M: 0.0869 c. 2243: 158 91 132 209 132 209 158 91 132 209 132 158 91 132 209 N SD: 0.0506 c. M:-0.1004 c. 2342: 165 95 138 218 138 218 165 95 138 218 138 165 95 138 218 N SD: 0.0385 c. M:-0.0896 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x x 3 x x x x x 4 S SD: 0.0000 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 0.0000 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 0.0000 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 0.0000 cents 6 x x x 7 x 8 x x 9 x 10 x 11 x 12 S SD: 9.7006 cents 7 x x 8 x 9 x x 10 x 11 x 12 x 13:14 S SD: 10.9115 cents 8 x x 9 x 10 x 11 x 12:13 x 14 x 15:16 S SD: 5.1441 cents 9 x x 10:11 x 12 x 13 x 14:15 x 16:17:18 S SD: 7.4572 cents 10 x 11 x 12 x 13:14 x 15:16:17 x 18:19:20 S SD: 6.8055 cents 11 x 12 x 13:14:15 x 16:17 x 18:19:20:21:22 S SD: 8.7476 cents 12 x 13 x 14:15:16:17 x 18:19:20:21:22:23:24 S SD: 6.2430 cents 13 x 14:15 x 16:17:18:19:20:21:22:23 x 24:26 S SD: 7.8153 cents 14 x 15:16:17:18:19 x 20:21:22:23 x 25:26:28 SD: 6.9320 cents 15 x 16:17:18:19:20:21:22:23:24:25:26:27:28:30 S SD: 4.4849 cents 16:17 x 18:19:20:21:22:23:24:26:27:28:29:30:32 S SD: 4.4034 cents 17:18 x 19:20:21:23:24 x 26:27:28:30:31:32:34 SD: 5.5773 cents 18:19 x 20:22:23:24:25:26:27:29:30 x 32:34:36 SD: 4.8596 cents 19:20 x 21:23:24:25 x 27:29:30:32:33:34:36:38 SD: 5.4011 cents 20:21:22:23:24:25:27:28:29:30:32:33:35:36:38:40 SD: 4.1588 cents 23:24:25:26:28:29:31:32:33:35:37:38:40:41:43:46 SD: 3.6649 cents 24:25:26:27:29:30:32:34:35:36:38:40:42:43:45:48 SD: 2.7121 cents 30 x 32:34:36:38:40:42:43:45:48:50:53:54:56:60 SD: 2.8075 cents 31:33 x 35:37:39:41:43:45:47:50:52:54:56:58:62 SD: 3.3788 cents 32:34:35:36:38:40:43:45:46:48:51:53:56:58:60:64 SD: 2.8169 cents 35:37:38:39:42:44:47:49:50:53:56:58:61:63:66:70 SD: 2.5388 cents 36:38:39:41:43:45:48:50:52:54:58:60:63:65:68:72 SD: 2.2917 cents 39:41:42:44:47:49:52:55:56:59:62:65:68:70:73:78 SD: 1.8675 cents 40:42:43:45:48:50:53:56:58:60:64:67:70:72:75:80 SD: 1.3341 cents 60:63:65:68:72:75:80:84:86:90:96:100:105:108:113:120 SD: 1.1836 cents 64:67:69:72:77:80:85:90:92:96:102:107:112:115:120:128 SD: 1.0636 cents 72:76:78:81:86:90:96:101:104:108:115:120:126:130:135:144 SD: 1.0629 cents 75:79:81:84:90:94:100:105:108:113:120:125:131:135:141:150 SD: 0.9473 cents 80:84:86:90:96:100:107:112:115:120:128:133:140:144:150:160 SD: 0.7350 cents 96:101:104:108:115:120:128:134:138:144:154:160:168:173:180:192 SD: 0.6968 cents 105:110:113:118:126:131:140:147:151:158:168:175:184:189:197:210 SD: 0.6968 cents 120:126:130:135:144:150:160:168:173:180:192:200:210:216:225:240 SD: 0.3799 cents 160:168:173:180:192:200:213:224:230:240:256:267:280:288:300:320 SD: 0.3338 cents 200:210:216:225:240:250:267:280:288:300:320:333:350:360:375:400 SD: 0.1847 cents 240:252:259:270:288:300:320:336:346:360:384:400:420:432:450:480 SD: 0.1605 cents 360:378:389:405:432:450:480:504:518:540:576:600:630:648:675:720 SD: 0.1071 cents 400:420:432:450:480:500:533:560:576:600:640:667:700:720:750:800 SD: 0.0924 cents 600:630:648:675:720:750:800:840:864:900:960:1000:1050:1080:1125:1200 S SD: 0.0000 cents