Scala analysis: 10highschool2
Second 10-note Highschool scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 9/8 203.910002 major whole tone 3: 5/4 386.313714 major third 4: 4/3 498.044999 perfect fourth 5: 10/7 617.487807 Euler's tritone 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: 15/14 119.4428 major diatonic semitone 2: 21/20 84.4672 minor semitone 3: 10/9 182.4037 minor whole tone 4: 16/15 111.7313 minor diatonic semitone 5: 15/14 119.4428 major diatonic semitone 6: 21/20 84.4672 minor 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: 3 9/8 203.910 cents major whole tone 2: 3 8/7 231.174 cents septimal whole tone 2: 3 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 3: 3 6/5 315.641 cents minor third 3: 1 60/49 350.617 cents smaller approximation to neutral third 3: 1 49/40 351.338 cents larger approximation to neutral third 3: 1 56/45 378.602 cents septimal narrow major third 3: 3 5/4 386.314 cents major third 3: 1 80/63 413.578 cents wide major third 4: 2 9/7 435.084 cents septimal major third, BP third 4: 2 21/16 470.781 cents narrow fourth 4: 6 4/3 498.045 cents perfect 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: 6 3/2 701.955 cents perfect fifth 6: 2 32/21 729.219 cents wide fifth 6: 2 14/9 764.916 cents septimal minor sixth 7: 1 63/40 786.422 cents narrow minor sixth 7: 3 8/5 813.686 cents minor sixth 7: 1 45/28 821.398 cents septimale wide minor sixth 7: 1 80/49 848.662 cents smaller approximation to neutral sixth 7: 1 49/30 849.383 cents larger approximation to neutral sixth 7: 3 5/3 884.359 cents major sixth, BP sixth 8: 1 27/16 905.865 cents Pythagorean major sixth 8: 3 12/7 933.129 cents septimal major sixth 8: 3 7/4 968.826 cents harmonic seventh 8: 3 16/9 996.090 cents Pythagorean 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: 4.44444 = 40/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 119.4 203.9 386.3 498.0 617.5 702.0 884.4 968.8 1088.3 1200.0 119.4 : 84.5 266.9 378.6 498.0 582.5 764.9 849.4 968.8 1080.6 1200.0 203.9 : 182.4 294.1 413.6 498.0 680.4 764.9 884.4 996.1 1115.5 1200.0 386.3 : 111.7 231.2 315.6 498.0 582.5 702.0 813.7 933.1 1017.6 1200.0 498.0 : 119.4 203.9 386.3 470.8 590.2 702.0 821.4 905.9 1088.3 1200.0 617.5 : 84.5 266.9 351.3 470.8 582.5 702.0 786.4 968.8 1080.6 1200.0 702.0 : 182.4 266.9 386.3 498.0 617.5 702.0 884.4 996.1 1115.5 1200.0 884.4 : 84.5 203.9 315.6 435.1 519.6 702.0 813.7 933.1 1017.6 1200.0 968.8 : 119.4 231.2 350.6 435.1 617.5 729.2 848.7 933.1 1115.5 1200.0 1088.3: 111.7 231.2 315.6 498.0 609.8 729.2 813.7 996.1 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: 203.9100 .. 294.1350 cents 256/243, 90.2250 cents 81/80, 21.5063 cents 3: 315.6413 .. 413.5778 cents 200/189, 97.9365 cents 81/80, 21.5063 cents 4: 435.0841 .. 498.0450 cents 28/27, 62.9609 cents 81/80, 21.5063 cents 5: 519.5513 .. 680.4487 cents 800/729, 160.8974 cents 81/80, 21.5063 cents 6: 701.9550 .. 764.9159 cents 28/27, 62.9609 cents 81/80, 21.5063 cents 7: 786.4222 .. 884.3587 cents 200/189, 97.9365 cents 81/80, 21.5063 cents 8: 905.8650 .. 996.0900 cents 256/243, 90.2250 cents 81/80, 21.5063 cents 9: 1017.5963 .. 1115.5328 cents 200/189, 97.9365 cents 81/80, 21.5063 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 : 121.33270 cents, oct.: 1213.32700 cents Scale is strictly proper Step pattern alph. order: ABCDABCBAD Step pattern size order : CADBCADACB Scale is a Constant Structure, by a margin of 21.50629 cents Scale diversity : 1.450540 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.284154 Rothenberg efficiency : 0.346111 redundancy: 0.653889 Efficiency x scale size : 3.461111 Number of different interval sizes : 40 = 4.44444 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.44444 = 40/9 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2401/2400, 0.7212 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 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 : 2 at degree 3 Formal octave complements present : 3 = 30.0000% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 63 (O: 63 U: 63) Highest odd numerator or denominator: 15 Scale harmonicity : 0.025018 Average absolute harmonicity : 0.210630 Specific harmonicity : 0.163661 Fundamental : 1/168, -7.3923 octaves, 1.5573 Hz. Guide tone : 1260, 10.2992 octaves, 329648.212 Hz. Exponens Consonantiae : 2.116800E+05, 17.69153 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 64.5, average 6.45000 Mersenne's string divisions : 314317080 Sum of van Prooijen's expressibility: 7.34880, average 0.73488 Sum of Tenney's harmonic distance : 14.18647, average 1.41865 Vogel's harmonic complexity : 14.90000 Wille's k value : 157 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 147.12835, average 2.67506 Lattice compactness (without 2's) : 85.67893, average 1.55780 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.80000 16 1 3: -1 .. 2 0.30000 7 3 5: 0 .. 1 0.50000 5 3 7: -1 .. 1 -0.10000 3 3 Average exponent except 2's : 7 / 10 = 0.70000 Average absolute exponent except 2's: 15 / 10 = 1.50000 Scale is weakly epimorphic with val: <10 16 21 28| Scale is JI-epimorphic with val: <10 16 23 28| = patent Scale is weakly epimorphic with val: <10 16 25 28|
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 22.5083 c. M: 44.3587 c. 12: 1 1 2 1 1 1 2 1 1 1 P D3 SD: 14.9940 c. M:-31.1741 c. 19: 2 1 3 2 2 1 3 1 2 2 P SD: 11.3394 c. M: 21.4575 c. 22: 2 2 3 2 2 2 3 2 2 2 SP D3 SD: 10.2459 c. M: 17.4878 c. Standard Pentachordal Major 29: 3 2 4 3 3 2 4 2 3 3 SP SD: 9.6033 c. M: 17.1018 c. 31: 3 2 5 3 3 2 5 2 3 3 P SD: 4.8188 c. M: 10.3616 c. 41: 4 3 6 4 4 3 6 3 4 4 SP SD: 3.5537 c. M: 6.3099 c. 53: 5 4 8 5 5 4 8 4 5 5 SP SD: 3.2488 c. M: 6.2353 c. 72: 7 5 11 7 7 5 11 5 7 7 SP SD: 2.6508 c. M: 4.9354 c. 87: 9 6 13 8 9 6 13 6 9 8 SP SD: 2.4722 c. M:-4.6951 c. 99: 10 7 15 9 10 7 15 7 10 9 SP SD: 1.4481 c. M:-2.6404 c. 130: 13 9 20 12 13 9 20 9 13 12 SP SD: 0.9226 c. M:-1.7951 c. 140: 14 10 21 13 14 10 21 10 14 13 SP SD: 0.8991 c. M:-1.8043 c. 171: 17 12 26 16 17 12 26 12 17 16 SP SD: 0.2958 c. M: 0.5494 c. 441: 44 31 67 41 44 31 67 31 44 41 SP SD: 0.1461 c. M:-0.2851 c. 612: 61 43 93 57 61 43 93 43 61 57 SP SD: 0.0984 c. M: 0.1985 c. 935: 93 66 142 87 93 66 142 66 93 87 SP SD: 0.1029 c. M: 0.1616 c. 1065: 106 75 162 99 106 75 162 75 106 99 SP SD: 0.1096 c. M:-0.1882 c. 1106: 110 78 168 103 110 78 168 78 110 103 SP SD: 0.0702 c. M: 0.1280 c. 1236: 123 87 188 115 123 87 188 87 123 115 SP SD: 0.0632 c. M:-0.1073 c. 1277: 127 90 194 119 127 90 194 90 127 119 SP SD: 0.0697 c. M: 0.1033 c. 1407: 140 99 214 131 140 99 214 99 140 131 SP SD: 0.0433 c. M:-0.0763 c. 1718: 171 121 261 160 171 121 261 121 171 160 SP SD: 0.0369 c. M: 0.0747 c. 1848: 184 130 281 172 184 130 281 130 184 172 SP SD: 0.0336 c. M:-0.0569 c. 2019: 201 142 307 188 201 142 307 142 201 188 SP SD: 0.0293 c. M: 0.0467 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: 23.3161 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: 15.0894 cents 8 x 9:10:11 x 12:13:14:15:16 S SD: 8.6233 cents 9 x 10:11:12:13:14:15:16:17:18 S SD: 9.4365 cents 10 x 11 x 13:14:15:17:18:19:20 SD: 11.6845 cents 11:12 x 14:15:16:17:18:19:21:22 SD: 10.8857 cents 12:13:14:15:16:17:18:20:21:23:24 SD: 7.7381 cents 15:16:17:19:20:21:23:25:26:28:30 SD: 6.1267 cents 16:17:18:20:21:23:24:27:28:30:32 SD: 3.9142 cents 24:26:27:30:32:34:36:40:42:45:48 S SD: 2.3997 cents 39:42:44:49:52:56:59:65:68:73:78 SD: 2.2929 cents 40:43:45:50:53:57:60:67:70:75:80 SD: 1.5631 cents 56:60:63:70:75:80:84:93:98:105:112 SD: 0.9891 cents 72:77:81:90:96:103:108:120:126:135:144 SD: 0.4009 cents 96:103:108:120:128:137:144:160:168:180:192 SD: 0.3005 cents 168:180:189:210:224:240:252:280:294:315:336 S SD: 0.0000 cents