Scala analysis: xen09-wilson-marwa-13-01
Marwa permutation 1 from Figure 13, Al-Farabi 10/9 10/9 27/25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 2: 243/200 337.147577 acute minor third 3: 27/20 519.551289 acute fourth 4: 36/25 631.282574 classic diminished fifth 5: 81/50 835.192576 acute minor sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 2: 9/8 203.9100 major whole tone 3: 10/9 182.4037 minor whole tone 4: 16/15 111.7313 minor diatonic semitone 5: 9/8 203.9100 major whole tone 6: 10/9 182.4037 minor whole tone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 3 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 1 243/200 337.148 cents acute minor third 2: 1 100/81 364.807 cents grave major third 2: 2 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 2 27/20 519.551 cents acute fourth 3: 1 25/18 568.717 cents classic augmented fourth 4: 1 36/25 631.283 cents classic diminished fifth 4: 2 40/27 680.449 cents grave fifth 4: 4 3/2 701.955 cents perfect fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 81/50 835.193 cents acute minor sixth 5: 1 400/243 862.852 cents grave major sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 3 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 50/27 1066.762 cents grave major seventh 6: 1 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 133.2 337.1 519.6 631.3 835.2 1017.6 1200.0 133.2 : 203.9 386.3 498.0 702.0 884.4 1066.8 1200.0 337.1 : 182.4 294.1 498.0 680.4 862.9 996.1 1200.0 519.6 : 111.7 315.6 498.0 680.4 813.7 1017.6 1200.0 631.3 : 203.9 386.3 568.7 702.0 905.9 1088.3 1200.0 835.2 : 182.4 364.8 498.0 702.0 884.4 996.1 1200.0 1017.6: 182.4 315.6 519.6 702.0 813.7 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 203.9100 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 2: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 256/243, 90.2250 cents 3: 498.0450 .. 568.7174 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 4: 631.2826 .. 701.9550 cents 25/24, 70.6724 cents 648/625, 62.5651 cents 5: 813.6863 .. 905.8650 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 6: 996.0900 .. 1088.2687 cents 135/128, 92.1787 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.534293 Largest / Average step : 1.189475 Largest / Smallest step : 1.825004 Median interval of one step : 10/9, 182.4037 cents, amount: 3 Most common interval of one step : 10/9, 182.4037 cents, amount: 3 Least squares average step : 168.37755 cents, oct.: 1178.64287 cents Scale is strictly proper Step pattern alph. order: ABCDBCC Step pattern size order : BDCADCC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 62.56515 cents Scale diversity : 1.442956 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.574950 Rothenberg efficiency : 0.436735 redundancy: 0.563265 Efficiency x scale size : 3.057143 Number of different interval sizes : 24 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.00000 = 4 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: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Length of longest harmonic part : 2 at degree 1 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 243 Scale harmonicity : 0.032120 Average absolute harmonicity : 0.188449 Specific harmonicity : 0.164299 Fundamental : 1/200, -7.6439 octaves, 1.3081 Hz. Guide tone : 972, 9.9248 octaves, 254300.049 Hz. Exponens Consonantiae : 1.944000E+05, 17.56867 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 375.5, average 53.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.50900, average 1.35843 Sum of Tenney's harmonic distance : 18.76427, average 2.68061 Vogel's harmonic complexity : 13.57143 Wille's k value : 121 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 92.23499, average 3.29411 Lattice compactness (without 2's) : 68.25630, average 2.43773 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.42857 9 1 3: 0 .. 5 2.71429 19 5: -2 .. 0 -1.42857 10 6 Average exponent except 2's : 9 / 7 = 1.28571 Average absolute exponent except 2's: 29 / 7 = 4.14286 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 26.9496 c. M:-54.4317 c. Lebeng 11: 1 2 2 1 2 1 2 P M ME S SD: 25.5836 c. M:-37.5347 c. Orgone-7 12: 1 2 2 1 2 2 2 P M ME S SD: 27.7583 c. M: 37.1476 c. G.Mixolydian, G.Hyperdorian, M.Hypophrygian, M.Locrian, G.M.Hyperaeolian, Rut biscale descending, Pien chih: China, Makam Lami, Yishtabach: Jewish 13: 1 3 2 1 2 2 2 P D3 SD: 24.2791 c. M: 40.9299 c. 14: 2 2 2 1 3 2 2 P T3 SD: 21.0433 c. M:-38.1910 c. 17: 2 3 2 2 3 2 3 SP M ME S SD: 16.8111 c. M: 29.3610 c. 19: 2 3 3 2 3 3 3 SP M ME S SD: 11.7001 c. M: 21.3581 c. Nineteen-tone Locrian 25: 3 4 4 2 4 4 4 SP T3 SD: 10.0143 c. M: 19.1926 c. 26: 3 4 4 3 4 4 4 SP M ME S SD: 9.3467 c. M:-14.8713 c. 32: 4 5 5 3 5 5 5 SP T3 SD: 8.2748 c. M:-16.7624 c. 33: 4 5 5 3 6 5 5 SP SD: 8.6975 c. M: 13.1008 c. 34: 4 6 5 3 6 5 5 SP SD: 9.2720 c. M:-15.7936 c. 35: 4 6 5 3 6 6 5 SP SD: 8.8489 c. M: 14.1397 c. 36: 4 6 6 3 6 6 5 SP SD: 8.1048 c. M:-15.7370 c. 39: 4 7 6 4 6 6 6 SP SD: 7.2013 c. M:-14.8713 c. 40: 4 7 6 4 7 6 6 SP SD: 7.0517 c. M: 13.2376 c. 42: 5 7 6 4 7 7 6 SP SD: 6.8087 c. M:-10.9751 c. 46: 5 8 7 4 8 7 7 SP SD: 2.5008 c. M: 5.1956 c. 53: 6 9 8 5 9 8 8 SP SD: 2.0584 c. M:-2.6797 c. 99: 11 17 15 9 17 15 15 SP SD: 1.2240 c. M:-2.2464 c. 118: 13 20 18 11 20 18 18 SP SD: 1.0001 c. M: 1.5544 c. 171: 19 29 26 16 29 26 26 SP SD: 0.1957 c. M: 0.3055 c. 388: 43 66 59 36 66 59 59 SP SD: 0.1751 c. M: 0.3547 c. 441: 49 75 67 41 75 67 67 SP SD: 0.1479 c. M:-0.2674 c. 559: 62 95 85 52 95 85 85 SP SD: 0.1083 c. M: 0.1556 c. 612: 68 104 93 57 104 93 93 SP SD: 0.0801 c. M:-0.1073 c. 783: 87 133 119 73 133 119 119 SP SD: 0.0674 c. M:-0.1351 c. 1000: 111 170 152 93 170 152 152 SP SD: 0.0438 c. M: 0.0826 c. 1171: 130 199 178 109 199 178 178 SP SD: 0.0130 c. M: 0.0272 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 35.3362 cents 3 x x 4 x 5 x 6 S SD: 17.8880 cents 4 x 5 x 6 x 7:8 S SD: 24.7367 cents 5 x 6 x 7:8:9:10 S SD: 11.4954 cents 6 x 7:8:9:10:11:12 S SD: 19.5948 cents 7:8 x 9:10:11:13:14 SD: 25.0673 cents 8:9:10:11:12:13:14:16 S SD: 17.9697 cents 9:10:11:12:13:15:16:18 SD: 10.9669 cents 10:11:12 x 14:16:18:20 S SD: 10.9452 cents 11:12:13:15:16:18:20:22 SD: 8.8199 cents 14:15:17:19:20:23:25:28 SD: 5.0381 cents 23:25:28:31:33:37:41:46 SD: 3.5338 cents 34:37:41:46:49:55:61:68 SD: 2.8487 cents 37:40:45:50:53:60:67:74 SD: 2.0338 cents 52:56:63:70:75:84:94:104 SD: 1.8058 cents 60:65:73:81:86:97:108:120 SD: 1.5075 cents 61:66:74:82:88:99:110:122 SD: 1.4378 cents 66:71:80:89:95:107:119:132 SD: 1.2598 cents 74:80:90:100:107:120:133:148 SD: 1.1923 cents 89:96:108:120:128:144:160:178 SD: 0.7568 cents 111:120:135:150:160:180:200:222 SD: 0.6061 cents 163:176:198:220:235:264:293:326 SD: 0.4620 cents 177:191:215:239:255:287:319:354 SD: 0.4579 cents 186:201:226:251:268:301:335:372 SD: 0.3799 cents 200:216:243:270:288:324:360:400 SD: 0.0000 cents