Scala analysis: xen09-wilson-marwa-18b-10
Marwa permutation 10 from Figure 18b, Ptolemy 10/9 11/10 12/11
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: 22/15 663.049228 undecimal 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: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 12/11 150.6371 undecimal neutral second, 3/4-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 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 2 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 40/33 333.041 cents 2: 1 99/80 368.914 cents 2: 2 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 3: 1 15/11 536.951 cents undecimal augmented fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 1 22/15 663.049 cents undecimal diminished fifth 4: 1 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: 1 160/99 831.086 cents 5: 1 33/20 866.959 cents 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: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 20/11 1034.996 cents large minor seventh 6: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 111.7 294.1 498.0 663.0 813.7 996.1 1200.0 111.7 : 182.4 386.3 551.3 702.0 884.4 1088.3 1200.0 294.1 : 203.9 368.9 519.6 702.0 905.9 1017.6 1200.0 498.0 : 165.0 315.6 498.0 702.0 813.7 996.1 1200.0 663.0 : 150.6 333.0 537.0 648.7 831.1 1035.0 1200.0 813.7 : 182.4 386.3 498.0 680.4 884.4 1049.4 1200.0 996.1 : 203.9 315.6 498.0 702.0 867.0 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 .. 551.3179 cents 33/32, 53.2729 cents 16/15, 111.7313 cents 4: 648.6821 .. 701.9550 cents 33/32, 53.2729 cents 128/121, 97.3641 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: 2 Least squares average step : 166.36646 cents, oct.: 1164.56523 cents Scale is strictly proper Step pattern alph. order: ABCDEBC Step pattern size order : ADECBDE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.440363 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.603949 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 121/120, 14.3672 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 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 1 = 14.2857% Scale is 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 Limited inverse transpositions with margin 92.1787 cents: 1 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 27 Scale harmonicity : 0.026609 Average absolute harmonicity : 0.230952 Specific harmonicity : 0.171150 Fundamental : 1/135, -7.0768 octaves, 1.9380 Hz. Guide tone : 352, 8.4594 octaves, 92092.199 Hz. Exponens Consonantiae : 4.752000E+04, 15.53625 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 87.5, average 12.50000 Mersenne's string divisions : 461868225 Sum of van Prooijen's expressibility: 5.91388, average 0.84484 Sum of Tenney's harmonic distance : 12.97587, average 1.85370 Vogel's harmonic complexity : 12.85714 Wille's k value : 67 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 78.43993, average 2.80143 Lattice compactness (without 2's) : 44.76534, average 1.59876 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 5 2.85714 20 1 3: -3 .. 0 -1.14286 8 3 5: -1 .. 0 -0.42857 3 2 11: 0 .. 1 0.14286 1 1 Average exponent except 2's :-10 / 7 =-1.42857 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 12 18 24|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 37.1457 c. M:-59.6973 c. Lebeng 9: 1 1 2 1 1 1 2 P M ME S SD: 30.7181 c. M: 62.7567 c. Pseudo Pelog, Pelogic-7, Antiionian 11: 1 2 2 1 1 2 2 P D3 S SD: 29.6015 c. M: 50.0499 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 15.7834 c. M:-36.9508 c. G.Dorian, M.Phrygian, G.M.Hypoaeolian, Bhairavi That, Mela Hanumatodi, Raga Asavari (Asaveri), Bilashkhani Todi, Ghanta, Makam Kurd, Gregorian nr.3, In, Zokuso: Japan, Ousak: Greece, Major inverse 13: 1 2 2 2 2 2 2 SP M ME S SD: 20.5490 c. M: 36.5065 c. Zo-Kalarian 16: 2 2 3 2 2 2 3 SP M ME S SD: 20.4976 c. M:-38.2687 c. Pseudo Pelog, Pelogic-7, Antiionian 17: 1 3 3 2 2 3 3 SP D3 S SD: 24.0952 c. M: 41.1430 c. 18: 1 3 3 3 2 3 3 P T3 SD: 23.8616 c. M: 45.0646 c. 19: 2 3 3 3 2 3 3 SP M ME S SD: 16.9052 c. M:-31.6876 c. Nineteen-tone Phrygian 20: 2 3 3 3 3 3 3 SP M ME S SD: 15.5921 c. M:-26.3137 c. 21: 2 3 4 3 2 3 4 SP T3 SD: 15.3548 c. M: 24.6614 c. 22: 2 3 4 3 3 3 4 SP D3 SD: 10.7729 c. M: 21.4077 c. 24: 2 4 4 3 3 4 4 SP D3 S SD: 8.8538 c. M: 13.6863 c. 29: 3 4 5 4 4 4 5 SP D3 SD: 7.3612 c. M:-13.8999 c. 31: 3 5 5 4 4 5 5 SP D3 S SD: 7.7512 c. M:-15.5424 c. 34: 3 5 6 5 4 5 6 SP SD: 6.6620 c. M: 11.7821 c. 40: 4 6 7 5 5 6 7 SP SD: 6.6081 c. M:-11.9550 c. 41: 4 6 7 6 5 6 7 SP SD: 4.9019 c. M:-10.1215 c. 52: 5 8 9 7 6 8 9 SP SD: 5.7229 c. M:-9.6473 c. 53: 5 8 9 7 7 8 9 SP SD: 2.5571 c. M: 6.4455 c. 65: 6 10 11 9 8 10 11 SP SD: 1.0494 c. M:-1.5662 c. 118: 11 18 20 16 15 18 20 SP SD: 0.8545 c. M: 2.0323 c. 159: 15 24 27 22 20 24 27 SP SD: 0.8816 c. M:-1.4763 c. 183: 17 28 31 25 23 28 31 SP SD: 0.5801 c. M:-0.9470 c. 224: 21 34 38 31 28 34 38 SP SD: 0.6415 c. M:-1.2365 c. 248: 23 38 42 34 31 38 42 SP SD: 0.5937 c. M:-1.0263 c. 270: 25 41 46 37 34 41 46 SP SD: 0.5597 c. M: 0.8270 c. 277: 26 42 47 38 35 42 47 SP SD: 0.5008 c. M:-0.9041 c. 335: 31 51 57 46 42 51 57 SP SD: 0.4072 c. M: 0.6865 c. 342: 32 52 58 47 43 52 58 SP SD: 0.3777 c. M:-0.6018 c. 407: 38 62 69 56 51 62 69 SP SD: 0.3762 c. M:-0.7053 c. 429: 40 65 73 59 54 65 73 SP SD: 0.2429 c. M: 0.4287 c. 494: 46 75 84 68 62 75 84 SP SD: 0.1104 c. M: 0.2079 c. 677: 63 103 115 93 85 103 115 SP SD: 0.0808 c. M: 0.1246 c. 1106: 103 168 188 152 139 168 188 SP SD: 0.0701 c. M: 0.1198 c. 1171: 109 178 199 161 147 178 199 SP SD: 0.0220 c. M: 0.0319 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: 19.4529 cents 3 x x 4 x 5 x 6 S SD: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 25.9253 cents 5 x 6 x 7:8:9:10 S SD: 17.2177 cents 6 x 7:8:9:10:11:12 S SD: 16.7412 cents 7 x 8:9:10:11:12:14 S SD: 20.3723 cents 8 x 9:11:12:13:14:16 SD: 19.6893 cents 9:10:11:12:13:14:16:18 S SD: 14.9214 cents 10:11:12:13:15:16:18:20 SD: 12.1200 cents 11:12:13:15:16:18:20:22 SD: 11.3257 cents 12:13:14:16:18:19:21:24 SD: 9.0907 cents 13:14:15:17:19:21:23:26 SD: 8.9646 cents 15:16:18:20:22:24:27:30 S SD: 4.3449 cents 27:29:32:36:40:43:48:54 SD: 3.2288 cents 32:34:38:43:47:51:57:64 SD: 2.4834 cents 43:46:51:57:63:69:76:86 SD: 2.3002 cents 45:48:53:60:66:72:80:90 SD: 1.5506 cents 60:64:71:80:88:96:107:120 SD: 0.8632 cents 75:80:89:100:110:120:133:150 SD: 0.6919 cents 120:128:142:160:176:192:213:240 SD: 0.5469 cents 135:144:160:180:198:216:240:270 S SD: 0.0000 cents