Scala analysis: xen09-wilson-marwa-13-10
Marwa permutation 10 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: 16/15 111.731285 minor diatonic semitone 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 36/25 631.282574 classic diminished fifth 5: 8/5 813.686286 minor sixth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 16/15 111.7313 minor diatonic semitone 2: 10/9 182.4037 minor whole tone 3: 9/8 203.9100 major whole tone 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: 9/8 203.9100 major 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 : 111.7 294.1 498.0 631.3 813.7 996.1 1200.0 111.7 : 182.4 386.3 519.6 702.0 884.4 1088.3 1200.0 294.1 : 203.9 337.1 519.6 702.0 905.9 1017.6 1200.0 498.0 : 133.2 315.6 498.0 702.0 813.7 996.1 1200.0 631.3 : 182.4 364.8 568.7 680.4 862.9 1066.8 1200.0 813.7 : 182.4 386.3 498.0 680.4 884.4 1017.6 1200.0 996.1 : 203.9 315.6 498.0 702.0 835.2 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 : 165.45884 cents, oct.: 1158.21190 cents Scale is strictly proper Step pattern alph. order: ABCDBBC Step pattern size order : ACDBCCD 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 : 1 at degree 0 Length of longest subharmonic 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 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.032120 Average absolute harmonicity : 0.232990 Specific harmonicity : 0.194844 Fundamental : 1/675, -9.3987 octaves, 0.3876 Hz. Guide tone : 288, 8.1699 octaves, 75348.163 Hz. Exponens Consonantiae : 1.944000E+05, 17.56867 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 99.5, average 14.21429 Mersenne's string divisions : 761458425 Sum of van Prooijen's expressibility: 6.13573, average 0.87653 Sum of Tenney's harmonic distance : 13.41160, average 1.91594 Vogel's harmonic complexity : 17.00000 Wille's k value : 337 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 86.53374, average 3.09049 Lattice compactness (without 2's) : 57.80932, average 2.06462 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 5 3.00000 21 1 3: -3 .. 2 -0.71429 9 3 5: -2 .. 0 -0.57143 4 3 Average exponent except 2's :-9 / 7 =-1.28571 Average absolute exponent except 2's: 13 / 7 = 1.85714 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: 41.5893 c. M:-59.6973 c. Lebeng 8: 1 1 1 1 1 2 1 P M ME S SD: 40.9670 c. M: 63.6863 c. 9: 1 1 2 1 1 1 2 P M ME S SD: 33.4753 c. M: 62.7567 c. Pseudo Pelog, Pelogic-7, Antiionian 10: 1 1 2 1 2 1 2 P M ME S SD: 29.9955 c. M: 54.1350 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 13.9235 c. M: 31.2826 c. G.Mixolydian, G.Hyperdorian, M.Hypophrygian, M.Locrian, G.M.Hyperaeolian, Rut biscale descending, Pien chih: China, Makam Lami, Yishtabach: Jewish 19: 2 3 3 2 3 3 3 SP M ME S SD: 11.9313 c. M:-21.6545 c. Nineteen-tone Locrian 24: 2 4 4 3 3 4 4 SP D3 S SD: 10.2036 c. M:-18.7174 c. 25: 2 4 4 3 4 4 4 SP T3 SD: 10.7635 c. M: 18.0450 c. 28: 3 4 5 3 4 4 5 SP T3 SD: 10.8479 c. M:-16.8401 c. 29: 3 4 5 3 5 4 5 SP T3 SD: 8.3714 c. M:-13.8999 c. 34: 3 5 6 4 5 5 6 SP SD: 6.2098 c. M: 11.7821 c. 41: 4 6 7 5 6 6 7 SP SD: 5.6697 c. M:-12.6199 c. 46: 4 7 8 5 7 7 8 SP SD: 5.1627 c. M: 7.3835 c. 53: 5 8 9 6 8 8 9 SP SD: 1.2766 c. M:-2.6797 c. 118: 11 18 20 13 18 18 20 SP SD: 0.4751 c. M:-0.7803 c. 171: 16 26 29 19 26 26 29 SP SD: 0.3918 c. M:-0.6018 c. 289: 27 44 49 32 44 44 49 SP SD: 0.3577 c. M:-0.6747 c. 323: 30 49 55 36 49 49 55 SP SD: 0.3377 c. M: 0.6365 c. 388: 36 59 66 43 59 59 66 SP SD: 0.2724 c. M: 0.3911 c. 441: 41 67 75 49 67 67 75 SP SD: 0.1402 c. M: 0.2574 c. 559: 52 85 95 62 85 85 95 SP SD: 0.0805 c. M: 0.1556 c. 612: 57 93 104 68 93 93 104 SP SD: 0.0400 c. M:-0.0900 c. 1171: 109 178 199 130 178 178 199 SP SD: 0.0222 c. M: 0.0319 c. 1783: 166 271 303 198 271 271 303 SP SD: 0.0128 c. M: 0.0239 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: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 29.8275 cents 5 x 6 x 7:8:9:10 S SD: 11.4954 cents 6 x 7:8:9:10:11:12 S SD: 19.4154 cents 7 x 8:9:10:11:12:14 S SD: 19.0435 cents 8 x 9:11:12:13:14:16 SD: 22.0082 cents 9:10:11:12:13:14:16:18 S SD: 14.4559 cents 10:11:12:13:14:16:18:20 S SD: 12.8276 cents 11:12:13:15:16:18:20:22 SD: 11.4122 cents 12:13:14:16:17:19:21:24 SD: 8.2507 cents 15:16:18:20:22:24:27:30 S SD: 6.2827 cents 18:19:21:24:26:29:32:36 SD: 5.0386 cents 27:29:32:36:39:43:48:54 SD: 2.1971 cents 45:48:53:60:65:72:80:90 SD: 1.7278 cents 48:51:57:64:69:77:85:96 SD: 1.6448 cents 59:63:70:79:85:94:105:118 SD: 1.5543 cents 60:64:71:80:86:96:107:120 SD: 1.4360 cents 75:80:89:100:108:120:133:150 SD: 0.6919 cents 120:128:142:160:173:192:213:240 SD: 0.6172 cents 135:144:160:180:194:216:240:270 SD: 0.5094 cents 150:160:178:200:216:240:267:300 SD: 0.4369 cents 180:192:213:240:259:288:320:360 SD: 0.4313 cents 195:208:231:260:281:312:347:390 SD: 0.3188 cents 225:240:267:300:324:360:400:450 SD: 0.3090 cents 243:259:288:324:350:389:432:486 SD: 0.2363 cents 270:288:320:360:389:432:480:540 SD: 0.1272 cents 405:432:480:540:583:648:720:810 SD: 0.0848 cents