Scala analysis: 09highschool
Nine note Highschool scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 6/5 315.641287 minor third 3: 5/4 386.313714 major third 4: 4/3 498.044999 perfect fourth 5: 3/2 701.955001 perfect fifth 6: 8/5 813.686286 minor sixth 7: 5/3 884.358713 major sixth, BP sixth 8: 15/8 1088.268715 classic major seventh 9: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 9/8 203.9100 major whole tone 2: 16/15 111.7313 minor diatonic semitone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 16/15 111.7313 minor diatonic semitone 5: 9/8 203.9100 major whole tone 6: 16/15 111.7313 minor diatonic semitone 7: 25/24 70.6724 classic chromatic semitone, minor chroma 8: 9/8 203.9100 major whole tone 9: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 4 16/15 111.731 cents minor diatonic semitone 1: 3 9/8 203.910 cents major whole tone 2: 3 10/9 182.404 cents minor whole tone 2: 1 75/64 274.582 cents classic augmented second 2: 5 6/5 315.641 cents minor third 3: 1 32/27 294.135 cents Pythagorean minor third 3: 5 5/4 386.314 cents major third 3: 2 32/25 427.373 cents classic diminished fourth 3: 1 27/20 519.551 cents acute fourth 4: 6 4/3 498.045 cents perfect fourth 4: 2 45/32 590.224 cents diatonic tritone 4: 1 36/25 631.283 cents classic diminished fifth 5: 1 25/18 568.717 cents classic augmented fourth 5: 2 64/45 609.776 cents 2nd tritone 5: 6 3/2 701.955 cents perfect fifth 6: 1 40/27 680.449 cents grave fifth 6: 2 25/16 772.627 cents classic augmented fifth 6: 5 8/5 813.686 cents minor sixth 6: 1 27/16 905.865 cents Pythagorean major sixth 7: 5 5/3 884.359 cents major sixth, BP sixth 7: 1 128/75 925.418 cents diminished seventh 7: 3 9/5 1017.596 cents just minor seventh, BP seventh 8: 3 16/9 996.090 cents Pythagorean minor seventh 8: 4 15/8 1088.269 cents classic major seventh 8: 2 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.25000 = 13/4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 203.9 315.6 386.3 498.0 702.0 813.7 884.4 1088.3 1200.0 203.9 : 111.7 182.4 294.1 498.0 609.8 680.4 884.4 996.1 1200.0 315.6 : 70.7 182.4 386.3 498.0 568.7 772.6 884.4 1088.3 1200.0 386.3 : 111.7 315.6 427.4 498.0 702.0 813.7 1017.6 1129.3 1200.0 498.0 : 203.9 315.6 386.3 590.2 702.0 905.9 1017.6 1088.3 1200.0 702.0 : 111.7 182.4 386.3 498.0 702.0 813.7 884.4 996.1 1200.0 813.7 : 70.7 274.6 386.3 590.2 702.0 772.6 884.4 1088.3 1200.0 884.4 : 203.9 315.6 519.6 631.3 702.0 813.7 1017.6 1129.3 1200.0 1088.3: 111.7 315.6 427.4 498.0 609.8 813.7 925.4 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 203.9100 cents 27/25, 133.2376 cents 25/24, 70.6724 cents 2: 182.4037 .. 315.6413 cents 27/25, 133.2376 cents 80/81,-21.5063 cents 3: 294.1350 .. 519.5513 cents 729/640, 225.4163 cents 80/81,-21.5063 cents 4: 498.0450 .. 631.2826 cents 27/25, 133.2376 cents 80/81,-21.5063 cents 5: 568.7174 .. 701.9550 cents 27/25, 133.2376 cents 625/648,-62.5651 cents 6: 680.4487 .. 905.8650 cents 729/640, 225.4163 cents 80/81,-21.5063 cents 7: 884.3587 .. 1017.5963 cents 27/25, 133.2376 cents 80/81,-21.5063 cents 8: 996.0900 .. 1129.3276 cents 27/25, 133.2376 cents 80/81,-21.5063 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.886639 Largest / Average step : 1.529325 Largest / Smallest step : 2.885284 Median interval of one step : 16/15, 111.7313 cents, amount: 4 Most common interval of one step : 16/15, 111.7313 cents, amount: 4 Least squares average step : 133.59603 cents, oct.: 1202.36423 cents Scale is not proper Step pattern alph. order: ABCBABCAB Step pattern size order : LMSMLMSLM Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.400466 Lumma stability : 0.117787 Lumma impropriety factor : 0.159669 Rothenberg efficiency : 0.445767 redundancy: 0.554233 Efficiency x scale size : 4.011905 Number of different interval sizes : 26 = 3.25000 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.25000 = 13/4 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 6 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 6, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic 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 = 77.7778% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 75 (O: 75 U: 75) Highest odd numerator or denominator: 15 Scale harmonicity : 0.037313 Average absolute harmonicity : 0.236105 Specific harmonicity : 0.209438 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 360, 8.4919 octaves, 94185.204 Hz. Exponens Consonantiae : 4.320000E+04, 15.39874 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 48.0, average 5.33333 Mersenne's string divisions : 140900760 Sum of van Prooijen's expressibility: 5.88046, average 0.65338 Sum of Tenney's harmonic distance : 11.65118, average 1.29458 Vogel's harmonic complexity : 12.33333 Wille's k value : 112 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 136.83711, average 3.04082 Lattice compactness (without 2's) : 70.84981, average 1.57444 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 -0.22222 16 1 3: -1 .. 2 0.33333 7 3 5: -1 .. 1 0.11111 5 5 Average exponent except 2's : 4 / 9 = 0.44444 Average absolute exponent except 2's: 12 / 9 = 1.33333 Scale is JI-epimorphic with val: <9 14 21| = patent
FIT/MODE
9: 2 0 1 1 1 1 1 1 1 N T3 SD: 36.6170 c. M:-62.7567 c. 10: 2 1 0 1 2 1 0 2 1 N SD: 28.5624 c. M:-44.3587 c. 12: 2 1 1 1 2 1 1 2 1 P D3 SD: 10.6692 c. M: 15.6413 c. 19: 3 2 1 2 3 2 1 3 2 N SD: 8.3924 c. M: 14.5845 c. 22: 4 2 1 2 4 2 1 4 2 N SD: 8.3233 c. M:-14.2718 c. 31: 5 3 2 3 5 3 2 5 3 N SD: 5.2993 c. M: 10.3616 c. 34: 6 3 2 3 6 3 2 6 3 N SD: 3.9747 c. M:-7.8547 c. 41: 7 4 2 4 7 4 2 7 4 N SD: 4.4404 c. M:-6.3099 c. 46: 8 4 3 4 8 4 3 8 4 N SD: 4.1120 c. M:-7.3835 c. 53: 9 5 3 5 9 5 3 9 5 N SD: 1.0415 c. M: 1.4763 c. 118: 20 11 7 11 20 11 7 20 11 N SD: 0.2897 c. M: 0.5202 c. 289: 49 27 17 27 49 27 17 49 27 N SD: 0.2369 c. M: 0.4498 c. 323: 55 30 19 30 55 30 19 55 30 N SD: 0.2104 c. M:-0.4244 c. 376: 64 35 22 35 64 35 22 64 35 N SD: 0.2162 c. M:-0.3453 c. 441: 75 41 26 41 75 41 26 75 41 N SD: 0.0972 c. M:-0.1716 c. 494: 84 46 29 46 84 46 29 84 46 N SD: 0.0973 c. M: 0.1482 c. 559: 95 52 33 52 95 52 33 95 52 N SD: 0.0668 c. M:-0.1034 c. 612: 104 57 36 57 104 57 36 104 57 N SD: 0.0306 c. M:-0.0450 c. 1171: 199 109 69 109 199 109 69 199 109 N SD: 0.0180 c. M:-0.0319 c. 1783: 303 166 105 166 303 166 105 303 166 N SD: 0.0079 c. M:-0.0160 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x 4 S SD: 0.0000 cents 3 x x x 4 x x 5 x 6 S SD: 0.0000 cents 4 x x 5 x 6 x 7 x 8 S SD: 21.1168 cents 5 x 6 x 7 x 8 x 9:10 S SD: 22.0266 cents 6 x 7 x 8:9 x 10:11:12 S SD: 10.3979 cents 7:8 x 9 x x 11:12:13:14 SD: 13.6910 cents 8:9 x 10:11:12:13 x 15:16 SD: 8.5218 cents 9:10:11 x 12 x 14:15:17:18 SD: 9.0502 cents 10:11:12 x 13:15:16:17:19:20 SD: 8.9582 cents 11:12:13:14:15:17 x 18:21:22 SD: 12.9160 cents 12 x 14:15:16:18:19:20:23:24 SD: 8.0574 cents 13:15 x 16:17:20:21:22:24:26 SD: 10.7431 cents 14:16:17:18:19:21:22:23:26:28 SD: 8.8532 cents 15:17:18:19:20:23:24:25:28:30 SD: 5.2073 cents 24:27:29:30:32:36:38:40:45:48 SD: 2.4144 cents 40:45:48:50:53:60:64:67:75:80 SD: 1.5411 cents 48:54:58:60:64:72:77:80:90:96 SD: 1.4221 cents 64:72:77:80:85:96:102:107:120:128 SD: 1.3207 cents 72:81:86:90:96:108:115:120:135:144 SD: 0.9531 cents 80:90:96:100:107:120:128:133:150:160 SD: 0.7695 cents 96:108:115:120:128:144:154:160:180:192 SD: 0.6017 cents 120:135:144:150:160:180:192:200:225:240 S SD: 0.0000 cents