Scala analysis: 10highschool1
First 10-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: 9/8 203.910002 major whole tone 3: 5/4 386.313714 major third 4: 4/3 498.044999 perfect fourth 5: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 6: 3/2 701.955001 perfect fifth 7: 5/3 884.358713 major sixth, BP sixth 8: 7/4 968.825906 harmonic seventh 9: 15/8 1088.268715 classic major seventh 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 21/20 84.4672 minor semitone 2: 15/14 119.4428 major diatonic semitone 3: 10/9 182.4037 minor whole tone 4: 16/15 111.7313 minor diatonic semitone 5: 21/20 84.4672 minor semitone 6: 15/14 119.4428 major diatonic semitone 7: 10/9 182.4037 minor whole tone 8: 21/20 84.4672 minor semitone 9: 15/14 119.4428 major diatonic semitone 10: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 3 15/14 119.443 cents major diatonic semitone 1: 2 10/9 182.404 cents minor whole tone 2: 2 28/25 196.198 cents middle second 2: 3 9/8 203.910 cents major whole tone 2: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 25/21 301.847 cents BP second, quasi-equal minor third 3: 4 6/5 315.641 cents minor third 3: 1 56/45 378.602 cents septimal narrow major third 3: 4 5/4 386.314 cents major third 3: 1 80/63 413.578 cents wide major third 4: 1 63/50 400.108 cents quasi-equal major third 4: 1 9/7 435.084 cents septimal major third, BP third 4: 1 21/16 470.781 cents narrow fourth 4: 6 4/3 498.045 cents perfect fourth 4: 1 75/56 505.757 cents marvelous fourth 5: 1 27/20 519.551 cents acute fourth 5: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 1 45/32 590.224 cents diatonic tritone 5: 1 64/45 609.776 cents 2nd tritone 5: 3 10/7 617.488 cents Euler's tritone 5: 1 40/27 680.449 cents grave fifth 6: 1 112/75 694.243 cents marvelous fifth 6: 6 3/2 701.955 cents perfect fifth 6: 1 32/21 729.219 cents wide fifth 6: 1 14/9 764.916 cents septimal minor sixth 6: 1 100/63 799.892 cents quasi-equal minor sixth 7: 1 63/40 786.422 cents narrow minor sixth 7: 4 8/5 813.686 cents minor sixth 7: 1 45/28 821.398 cents septimale wide minor sixth 7: 4 5/3 884.359 cents major sixth, BP sixth 8: 2 42/25 898.153 cents quasi-equal major sixth 8: 1 27/16 905.865 cents Pythagorean major sixth 8: 1 12/7 933.129 cents septimal major sixth 8: 1 7/4 968.826 cents harmonic seventh 8: 3 16/9 996.090 cents Pythagorean minor seventh 8: 2 25/14 1003.802 cents middle minor seventh 9: 2 9/5 1017.596 cents just minor seventh, BP seventh 9: 3 28/15 1080.557 cents grave major seventh 9: 2 15/8 1088.269 cents classic major seventh 9: 3 40/21 1115.533 cents acute major seventh Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.88889 = 44/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 84.5 203.9 386.3 498.0 582.5 702.0 884.4 968.8 1088.3 1200.0 84.5 : 119.4 301.8 413.6 498.0 617.5 799.9 884.4 1003.8 1115.5 1200.0 203.9 : 182.4 294.1 378.6 498.0 680.4 764.9 884.4 996.1 1080.6 1200.0 386.3 : 111.7 196.2 315.6 498.0 582.5 702.0 813.7 898.2 1017.6 1200.0 498.0 : 84.5 203.9 386.3 470.8 590.2 702.0 786.4 905.9 1088.3 1200.0 582.5 : 119.4 301.8 386.3 505.8 617.5 702.0 821.4 1003.8 1115.5 1200.0 702.0 : 182.4 266.9 386.3 498.0 582.5 702.0 884.4 996.1 1080.6 1200.0 884.4 : 84.5 203.9 315.6 400.1 519.6 702.0 813.7 898.2 1017.6 1200.0 968.8 : 119.4 231.2 315.6 435.1 617.5 729.2 813.7 933.1 1115.5 1200.0 1088.3: 111.7 196.2 315.6 498.0 609.8 694.2 813.7 996.1 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 182.4037 cents 200/189, 97.9365 cents 21/20, 84.4672 cents 2: 196.1985 .. 301.8465 cents 625/588, 105.6480 cents 126/125, 13.7948 cents 3: 315.6413 .. 413.5778 cents 200/189, 97.9365 cents 126/125, 13.7948 cents 4: 400.1085 .. 505.7565 cents 625/588, 105.6480 cents 3969/4000,-13.4693 cents 5: 519.5513 .. 680.4487 cents 800/729, 160.8974 cents 126/125, 13.7948 cents 6: 694.2435 .. 799.8915 cents 625/588, 105.6480 cents 126/125, 13.7948 cents 7: 786.4222 .. 884.3587 cents 200/189, 97.9365 cents 3969/4000,-13.4693 cents 8: 898.1535 .. 1003.8015 cents 625/588, 105.6480 cents 126/125, 13.7948 cents 9: 1017.5963 .. 1115.5328 cents 200/189, 97.9365 cents 126/125, 13.7948 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 1.420670 Largest / Average step : 1.520031 Largest / Smallest step : 2.159462 Median interval of one step : 115.58705 cents, amount: 0 Least squares average step : 120.78763 cents, oct.: 1207.87626 cents Scale is not proper Step pattern alph. order: ABCDABCABD Step pattern size order : ACDBACDACB Scale is a Constant Structure, by a margin of 13.46933 cents Scale diversity : 1.434056 Lumma stability : 0.209752 Lumma impropriety factor : 0.022449 Rothenberg efficiency : 0.332698 redundancy: 0.667302 Efficiency x scale size : 3.326984 Number of different interval sizes : 44 = 4.88889 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.88889 = 44/9 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 225/224, 7.7115 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 : 7, average 700.8534 cents Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 8 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 30.0000% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 6 and 7 combined -- Rational properties -- Prime limit : 7 Odd number limit : 75 (O: 75 U: 75) Highest odd numerator or denominator: 21 Scale harmonicity : 0.027712 Average absolute harmonicity : 0.210738 Specific harmonicity : 0.156941 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 1260, 10.2992 octaves, 329648.212 Hz. Exponens Consonantiae : 1.512000E+05, 17.20610 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 68.0, average 6.80000 Mersenne's string divisions : 444379320 Sum of van Prooijen's expressibility: 7.49493, average 0.74949 Sum of Tenney's harmonic distance : 14.18647, average 1.41865 Vogel's harmonic complexity : 13.50000 Wille's k value : 112 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 147.79984, average 2.68727 Lattice compactness (without 2's) : 89.74948, average 1.63181 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -1.00000 16 1 3: -1 .. 2 0.30000 7 3 5: -1 .. 1 0.10000 5 3 7: 0 .. 1 0.30000 3 3 Average exponent except 2's : 7 / 10 = 0.70000 Average absolute exponent except 2's: 15 / 10 = 1.50000 Scale is JI-epimorphic with val: <10 16 23 28| = patent
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 25.1565 c. M: 44.3587 c. 12: 1 1 2 1 1 1 2 1 1 1 P D3 SD: 14.5308 c. M:-31.1741 c. 19: 1 2 3 2 1 2 3 1 2 2 N SD: 13.0103 c. M: 21.4575 c. 22: 2 2 3 2 2 2 3 2 2 2 SP D3 SD: 12.4457 c. M:-24.6237 c. Standard Pentachordal Major 24: 2 2 4 2 2 2 4 1 3 2 P SD: 12.2230 c. M: 18.8259 c. 27: 2 3 4 2 2 3 4 2 3 2 P SD: 11.6392 c. M:-22.8424 c. 29: 2 3 4 3 2 3 4 2 3 3 P SD: 9.5032 c. M: 17.1018 c. 31: 2 3 5 3 2 3 5 2 3 3 N SD: 5.2048 c. M: 10.3616 c. 41: 3 4 6 4 3 4 6 3 4 4 P SD: 3.6306 c. M: 6.3099 c. 53: 4 5 8 5 4 5 8 4 5 5 P SD: 3.2228 c. M:-6.1671 c. 72: 5 7 11 7 5 7 11 5 7 7 N SD: 2.5268 c. M: 4.9354 c. 84: 6 8 13 8 6 8 13 6 8 8 N SD: 2.2414 c. M: 3.9100 c. 87: 6 9 13 8 6 9 13 6 9 8 N SD: 2.0492 c. M: 3.3087 c. 99: 7 10 15 9 7 10 15 7 10 9 N SD: 1.3411 c. M:-2.6404 c. 130: 9 13 20 12 9 13 20 9 13 12 N SD: 1.0067 c. M:-1.7951 c. 140: 10 14 21 13 10 14 21 10 14 13 N SD: 0.9658 c. M:-1.8043 c. 171: 12 17 26 16 12 17 26 12 17 16 N SD: 0.3033 c. M: 0.5494 c. 441: 31 44 67 41 31 44 67 31 44 41 N SD: 0.1205 c. M: 0.1993 c. 612: 43 61 93 57 43 61 93 43 61 57 N SD: 0.0965 c. M: 0.1985 c. 966: 68 96 147 90 68 96 147 68 96 90 N SD: 0.0959 c. M: 0.1833 c. 1053: 74 105 160 98 74 105 160 74 105 98 N SD: 0.0947 c. M: 0.1760 c. 1106: 78 110 168 103 78 110 168 78 110 103 N SD: 0.0817 c. M:-0.1621 c. 1236: 87 123 188 115 87 123 188 87 123 115 N SD: 0.0627 c. M:-0.1073 c. 1277: 90 127 194 119 90 127 194 90 127 119 N SD: 0.0705 c. M:-0.1060 c. 1407: 99 140 214 131 99 140 214 99 140 131 N SD: 0.0427 c. M:-0.0763 c. 1718: 121 171 261 160 121 171 261 121 171 160 N SD: 0.0401 c. M: 0.0747 c. 1848: 130 184 281 172 130 184 281 130 184 172 N SD: 0.0354 c. M:-0.0569 c. 2019: 142 201 307 188 142 201 307 142 201 188 N SD: 0.0359 c. M: 0.0690 c.
FIT/HARMONIC
1 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 4 S SD: 0.0000 cents 3 x x x 4 x x 5 x x 6 S SD: 0.0000 cents 4 x x 5 x x 6 x 7 x 8 S SD: 0.0000 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 22.2421 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 12.3353 cents 7 x 8:9 x 10:11 x 12:13:14 S SD: 15.8951 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 6.7248 cents 9 x 10:11:12:13:14:15:16:17:18 S SD: 10.9850 cents 10 x 11 x 13:14:15:17:18:19:20 SD: 10.8358 cents 11 x 12:14:15 x 17:18:19:21:22 SD: 12.8027 cents 12:13:14:15:16:17:18:20:21:23:24 SD: 9.3590 cents 14:15:16:18:19:20:21:23:25:26:28 SD: 9.2875 cents 15:16:17:19:20:21:23:25:26:28:30 SD: 5.6694 cents 16:17:18:20:21:22:24:27:28:30:32 S SD: 5.0977 cents 23:24:26:29:31:32:35:38:40:43:46 SD: 4.3221 cents 24:25:27:30:32:34:36:40:42:45:48 SD: 2.4699 cents 39:41:44:49:52:55:59:65:68:73:78 SD: 2.3088 cents 40:42:45:50:53:56:60:67:70:75:80 SD: 1.3870 cents 63:66:71:79:84:88:95:105:110:118:126 SD: 1.3137 cents 64:67:72:80:85:90:96:107:112:120:128 SD: 1.2696 cents 72:76:81:90:96:101:108:120:126:135:144 SD: 0.9759 cents 80:84:90:100:107:112:120:133:140:150:160 SD: 0.6925 cents 96:101:108:120:128:134:144:160:168:180:192 SD: 0.6197 cents 120:126:135:150:160:168:180:200:210:225:240 S SD: 0.0000 cents