Scala analysis: xen09-wilson-marwa-15b-09
Marwa permutation 9 from Figure 15b, Ptolemy 22/21 12/11 7/6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88/81 143.497939 2nd undecimal neutral second 2: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 14/9 764.915905 septimal minor sixth 5: 44/27 845.452940 neutral 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: 88/81 143.4979 2nd undecimal neutral second 2: 9/8 203.9100 major whole tone 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 7/6 266.8709 septimal minor third 5: 22/21 80.5370 undecimal minor semitone 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 88/81 143.498 cents 2nd undecimal neutral second 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 3 11/9 347.408 cents undecimal neutral third 2: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 9/7 435.084 cents septimal major third, BP third 3: 4 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 63/44 621.418 cents 4: 1 88/63 578.582 cents 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 14/9 764.916 cents septimal minor sixth 5: 1 11/7 782.492 cents undecimal augmented fifth 5: 2 44/27 845.453 cents neutral sixth 5: 3 18/11 852.592 cents undecimal neutral sixth 5: 1 7/4 968.826 cents harmonic seventh 6: 1 12/7 933.129 cents septimal major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 81/44 1056.502 cents 2nd undecimal neutral seventh 6: 1 21/11 1119.463 cents undecimal major seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 143.5 347.4 498.0 764.9 845.5 996.1 1200.0 143.5 : 203.9 354.5 621.4 702.0 852.6 1056.5 1200.0 347.4 : 150.6 417.5 498.0 648.7 852.6 996.1 1200.0 498.0 : 266.9 347.4 498.0 702.0 845.5 1049.4 1200.0 764.9 : 80.5 231.2 435.1 578.6 782.5 933.1 1200.0 845.5 : 150.6 354.5 498.0 702.0 852.6 1119.5 1200.0 996.1 : 203.9 347.4 551.3 702.0 968.8 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 266.8709 cents 49/44, 186.3339 cents 22/21, 80.5370 cents 2: 231.1741 .. 417.5080 cents 49/44, 186.3339 cents 48/49,-35.6968 cents 3: 435.0841 .. 621.4180 cents 49/44, 186.3339 cents 99/98, 17.5761 cents 4: 578.5820 .. 764.9159 cents 49/44, 186.3339 cents 3872/3969,-42.8359 cents 5: 782.4920 .. 968.8259 cents 49/44, 186.3339 cents 99/98, 17.5761 cents 6: 933.1291 .. 1119.4630 cents 49/44, 186.3339 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 2.128568 Largest / Average step : 1.556747 Largest / Smallest step : 3.313642 Median interval of one step : 12/11, 150.6371 cents, amount: 2 Least squares average step : 171.39941 cents, oct.: 1199.79586 cents Scale is not proper Step pattern alph. order: ABCDECB Step pattern size order : BDCEACD Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.559442 Lumma stability : 0.163522 Lumma impropriety factor : 0.095191 Rothenberg efficiency : 0.423129 redundancy: 0.576871 Efficiency x scale size : 2.961905 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 243/242, 7.1391 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 minor thirds form a closed circle 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 class 3 Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 11 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.023183 Average absolute harmonicity : 0.213001 Specific harmonicity : 0.124418 Fundamental : 1/81, -6.3399 octaves, 3.2299 Hz. Guide tone : 1232, 10.2668 octaves, 322322.696 Hz. Exponens Consonantiae : 9.979200E+04, 16.60664 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 159.0, average 22.71429 Mersenne's string divisions : 579551700 Sum of van Prooijen's expressibility: 6.76685, average 0.96669 Sum of Tenney's harmonic distance : 14.56236, average 2.08034 Vogel's harmonic complexity : 13.57143 Wille's k value : 49 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 77.14379, average 2.75514 Lattice compactness (without 2's) : 53.98785, average 1.92814 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 4 1.85714 13 1 3: -4 .. 0 -2.00000 14 2 7: 0 .. 1 0.14286 1 1 11: 0 .. 1 0.42857 3 3 Average exponent except 2's :-10 / 7 =-1.42857 Average absolute exponent except 2's: 18 / 7 = 2.57143 Scale is weakly epimorphic with val: <7 10 18 22| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 34.9064 c. M: 79.2016 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 39.1011 c. M:-54.5471 c. 10: 1 2 1 2 1 1 2 P M ME S SD: 25.0314 c. M: 44.9159 c. 14: 2 2 2 3 1 2 2 P T3 SD: 18.1214 c. M:-32.4814 c. 16: 2 3 2 3 1 2 3 P T3 SD: 19.3308 c. M:-27.5921 c. 17: 2 3 2 4 1 2 3 N SD: 5.9668 c. M:-11.5547 c. 31: 4 5 4 7 2 4 5 N SD: 7.4431 c. M:-11.3408 c. 41: 5 7 5 9 3 5 7 N SD: 2.6828 c. M: 3.9403 c. 58: 7 10 7 13 4 7 10 N SD: 2.3868 c. M:-4.3162 c. 94: 11 16 12 21 6 12 16 N SD: 1.9464 c. M: 3.0724 c. 111: 13 19 14 25 7 14 19 N SD: 1.9121 c. M: 2.9574 c. 118: 14 20 15 26 8 15 20 N SD: 1.2585 c. M: 2.2040 c. 135: 16 23 17 30 9 17 23 N SD: 0.7342 c. M: 1.2757 c. 176: 21 30 22 39 12 22 30 N SD: 0.5787 c. M: 1.2795 c. 193: 23 33 24 43 13 24 33 N SD: 0.6450 c. M: 1.2713 c. 224: 27 38 28 50 15 28 38 N SD: 0.7921 c. M:-1.1555 c. 284: 34 48 36 63 19 36 48 N SD: 0.6031 c. M:-1.0931 c. 301: 36 51 38 67 20 38 51 N SD: 0.3977 c. M:-0.5877 c. 342: 41 58 43 76 23 43 58 N SD: 0.2267 c. M:-0.4012 c. 477: 57 81 60 106 32 60 81 N SD: 0.1402 c. M: 0.2381 c. 670: 80 114 84 149 45 84 114 N SD: 0.1537 c. M: 0.2691 c. 819: 98 139 103 182 55 103 139 N SD: 0.1289 c. M:-0.2470 c. 836: 100 142 105 186 56 105 142 N SD: 0.0719 c. M:-0.1559 c. 971: 116 165 122 216 65 122 165 N SD: 0.0945 c. M: 0.1406 c. 1012: 121 172 127 225 68 127 172 N SD: 0.0414 c. M: 0.0938 c. 1354: 162 230 170 301 91 170 230 N SD: 0.0518 c. M:-0.0767 c. 1371: 164 233 172 305 92 172 233 N SD: 0.0508 c. M:-0.0756 c. 1506: 180 256 189 335 101 189 256 N SD: 0.0444 c. M: 0.0741 c. 1848: 221 314 232 411 124 232 314 N SD: 0.0101 c. M:-0.0192 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: 31.4805 cents 3 x x 4 x 5 x 6 S SD: 12.9686 cents 4 x 5 x 6 x 7:8 S SD: 19.7184 cents 5 x 6:7 x 8:9:10 S SD: 19.6117 cents 6 x 7:8:9:10:11:12 S SD: 20.2772 cents 7:8 x 9:11 x 12:14 SD: 25.2382 cents 8:9:10:11:12:13:14:16 S SD: 16.1201 cents 9:10:11:12:14:15:16:18 S SD: 7.8602 cents 10:11:12:13 x 16:18:20 SD: 11.6243 cents 12:13:15:16:19:20:21:24 SD: 9.8290 cents 13:14:16:17:20:21:23:26 SD: 6.6598 cents 18:20:22:24:28:29:32:36 SD: 6.2354 cents 21:23:26:28:33:34:37:42 SD: 5.2917 cents 22:24:27:29:34:36:39:44 SD: 3.7684 cents 27:29:33:36:42:44:48:54 SD: 2.8265 cents 36:39:44:48:56:59:64:72 SD: 1.5680 cents 45:49:55:60:70:73:80:90 SD: 1.2589 cents 72:78:88:96:112:117:128:144 SD: 0.9951 cents 81:88:99:108:126:132:144:162 SD: 0.0000 cents