Scala analysis: semipor1
First 16/15&250/243 = 648/625&250/243 scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 6/5 315.641287 minor third 3: 5/4 386.313714 major third 4: 27/20 519.551289 acute fourth 5: 3/2 701.955001 perfect fifth 6: 5/3 884.358713 major sixth, BP sixth 7: 9/5 1017.596288 just minor seventh, BP seventh 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 10/9 182.4037 minor whole tone 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 5: 10/9 182.4037 minor whole tone 6: 10/9 182.4037 minor whole tone 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 8: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 3 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 4 10/9 182.404 cents minor whole tone 2: 2 9/8 203.910 cents major whole tone 2: 4 6/5 315.641 cents minor third 2: 2 100/81 364.807 cents grave major third 3: 1 243/200 337.148 cents acute minor third 3: 2 5/4 386.314 cents major third 3: 5 4/3 498.045 cents perfect fourth 4: 2 27/20 519.551 cents acute fourth 4: 2 25/18 568.717 cents classic augmented fourth 4: 2 36/25 631.283 cents classic diminished fifth 4: 2 40/27 680.449 cents grave fifth 5: 5 3/2 701.955 cents perfect fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 400/243 862.852 cents grave major sixth 6: 2 81/50 835.193 cents acute minor sixth 6: 4 5/3 884.359 cents major sixth, BP sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 7: 4 9/5 1017.596 cents just minor seventh, BP seventh 7: 3 50/27 1066.762 cents grave major seventh 7: 1 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: 3.14286 = 22/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 182.4 315.6 386.3 519.6 702.0 884.4 1017.6 1200.0 182.4 : 133.2 203.9 337.1 519.6 702.0 835.2 1017.6 1200.0 315.6 : 70.7 203.9 386.3 568.7 702.0 884.4 1066.8 1200.0 386.3 : 133.2 315.6 498.0 631.3 813.7 996.1 1129.3 1200.0 519.6 : 182.4 364.8 498.0 680.4 862.9 996.1 1066.8 1200.0 702.0 : 182.4 315.6 498.0 680.4 813.7 884.4 1017.6 1200.0 884.4 : 133.2 315.6 498.0 631.3 702.0 835.2 1017.6 1200.0 1017.6: 182.4 364.8 498.0 568.7 702.0 884.4 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 182.4037 cents 16/15, 111.7313 cents 25/24, 70.6724 cents 2: 203.9100 .. 364.8074 cents 800/729, 160.8974 cents 81/80, 21.5063 cents 3: 337.1476 .. 498.0450 cents 800/729, 160.8974 cents 19683/20000,-27.6598 cents 4: 519.5513 .. 680.4487 cents 800/729, 160.8974 cents 81/80, 21.5063 cents 5: 701.9550 .. 862.8524 cents 800/729, 160.8974 cents 81/80, 21.5063 cents 6: 835.1926 .. 996.0900 cents 800/729, 160.8974 cents 19683/20000,-27.6598 cents 7: 1017.5963 .. 1129.3276 cents 16/15, 111.7313 cents 81/80, 21.5063 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 2.122469 Largest / Average step : 1.216025 Largest / Smallest step : 2.580974 Median interval of one step : 157.82064 cents, amount: 0 Most common interval of one step : 10/9, 182.4037 cents, amount: 4 Least squares average step : 145.04870 cents, oct.: 1160.38956 cents Scale is not proper Step pattern alph. order: ABCBAABA Step pattern size order : LMSMLLML Scale is a Constant Structure, by a margin of 21.50629 cents Scale diversity : 1.352034 Lumma stability : 0.189475 Lumma impropriety factor : 0.046100 Rothenberg efficiency : 0.466964 redundancy: 0.533036 Efficiency x scale size : 3.735714 Number of different interval sizes : 22 = 3.14286 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.14286 = 22/7 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 81/80, 21.5063 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 5, average 701.9550 cents Scale contains a complete diamond : 3 5 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 62.5000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval class 5 Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 6-7 -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.034325 Average absolute harmonicity : 0.228268 Specific harmonicity : 0.179574 Fundamental : 1/180, -7.4919 octaves, 1.4535 Hz. Guide tone : 270, 8.0768 octaves, 70638.903 Hz. Exponens Consonantiae : 4.860000E+04, 15.56867 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 58.0, average 7.25000 Mersenne's string divisions : 24753960 Sum of van Prooijen's expressibility: 5.91388, average 0.73924 Sum of Tenney's harmonic distance : 11.37327, average 1.42166 Vogel's harmonic complexity : 14.25000 Wille's k value : 121 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 99.33368, average 2.75927 Lattice compactness (without 2's) : 77.42753, average 2.15076 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.25000 8 1 3: -2 .. 3 0.50000 10 1 5: -1 .. 1 0.00000 6 6 Average exponent except 2's : 4 / 8 = 0.50000 Average absolute exponent except 2's: 16 / 8 = 2.00000 Scale is JI-epimorphic with val: <8 13 19| = patent Scale is weakly epimorphic with val: <8 13 20|
FIT/MODE
8: 1 1 1 0 2 1 1 1 N T3 SD: 41.5195 c. M: 69.5513 c. 10: 1 1 1 1 2 1 1 2 P D3 S SD: 46.7483 c. M: 75.6413 c. 12: 2 1 1 1 2 2 1 2 N D3 SD: 14.4998 c. M: 19.5513 c. Minor Bebop, Dorian Bebop, Raga Khokhar, Zilla, Mixolydian/Dorian mixed 19: 3 2 1 2 3 3 2 3 N G SD: 7.1635 c. M: 14.2881 c. 27: 4 3 2 3 4 4 3 4 P SD: 8.2533 c. M:-13.7820 c. 33: 5 4 2 3 5 5 4 5 N SD: 9.2872 c. M:-13.6863 c. 34: 5 4 2 4 5 5 4 5 P SD: 4.9345 c. M:-9.8605 c. 41: 6 5 2 5 6 6 5 6 P SD: 5.6909 c. M:-7.2780 c. 46: 7 5 3 5 7 7 5 7 N SD: 2.4749 c. M:-4.9906 c. 53: 8 6 3 6 8 8 6 8 N SD: 1.1325 c. M: 1.4081 c. 99: 15 11 6 11 15 15 11 15 N SD: 0.9702 c. M:-1.6608 c. 118: 18 13 7 13 18 18 13 18 N SD: 0.5055 c. M: 0.9072 c. 171: 26 19 10 19 26 26 19 26 N SD: 0.1855 c. M: 0.3488 c. 388: 59 43 23 43 59 59 43 59 N SD: 0.1442 c. M:-0.2842 c. 441: 67 49 26 49 67 67 49 67 N SD: 0.0878 c. M:-0.1766 c. 559: 85 62 33 62 85 85 62 85 N SD: 0.0629 c. M:-0.0906 c. 612: 93 68 36 68 93 93 68 93 N SD: 0.0418 c. M:-0.0566 c. 1000: 152 111 59 111 152 152 111 152 N SD: 0.0437 c. M:-0.0863 c. 1171: 178 130 69 130 178 178 130 178 N SD: 0.0114 c. M:-0.0228 c. 1783: 271 198 105 198 271 271 198 271 N SD: 0.0116 c. M:-0.0225 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x 4 S SD: 0.0000 cents 3 x x x 4 x 5 x 6 S SD: 7.1688 cents 4 x x 5 x 6 x 7:8 S SD: 12.1926 cents 5 x 6 x 7 x 8:9:10 S SD: 18.9300 cents 6 x 7 x 8:9:10:11:12 S SD: 10.3417 cents 7:8 x 9 x 11:12:13:14 SD: 21.4407 cents 8:9 x 10:11:12:13:14:16 S SD: 10.8528 cents 9:10:11 x 12:14:15:16:18 S SD: 10.9714 cents 10:11:12 x 14:15:17:18:20 SD: 10.5387 cents 11:12:13:14:15:17:18:20:22 SD: 10.4332 cents 12:13:14:15:16:18:20:22:24 S SD: 9.4962 cents 13:14 x 16:18:20:22:23:26 SD: 13.6126 cents 14:16:17:18:19:21:23:25:28 SD: 9.7397 cents 15:17:18:19:20:23:25:27:30 SD: 7.5120 cents 16:18:19:20:22:24:27:29:32 SD: 6.1318 cents 20:22:24:25:27:30:33:36:40 SD: 3.0758 cents 35:39:42:44:47:53:58:63:70 SD: 2.9942 cents 36:40:43:45:49:54:60:65:72 SD: 2.1447 cents 44:49:53:55:59:66:73:79:88 SD: 2.0785 cents 45:50:54:56:61:68:75:81:90 SD: 2.0663 cents 54:60:65:68:73:81:90:97:108 SD: 1.8117 cents 56:62:67:70:76:84:93:101:112 SD: 1.7616 cents 60:67:72:75:81:90:100:108:120 SD: 1.0793 cents 80:89:96:100:108:120:133:144:160 SD: 0.6054 cents 100:111:120:125:135:150:167:180:200 SD: 0.4836 cents 160:178:192:200:216:240:267:288:320 SD: 0.3823 cents 180:200:216:225:243:270:300:324:360 SD: 0.0000 cents