Scala analysis: xen09-wilson-marwa-18b-07
Marwa permutation 7 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: 6/5 315.641287 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: 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: 16/15 111.7313 minor diatonic semitone 2: 9/8 203.9100 major whole tone 3: 10/9 182.4037 minor 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: 9/8 203.9100 major 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 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 11/9 347.408 cents undecimal neutral third 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 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 44/27 845.453 cents neutral sixth 5: 1 18/11 852.592 cents undecimal neutral 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: 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 : 111.7 315.6 498.0 663.0 813.7 1017.6 1200.0 111.7 : 203.9 386.3 551.3 702.0 905.9 1088.3 1200.0 315.6 : 182.4 347.4 498.0 702.0 884.4 996.1 1200.0 498.0 : 165.0 315.6 519.6 702.0 813.7 1017.6 1200.0 663.0 : 150.6 354.5 537.0 648.7 852.6 1035.0 1200.0 813.7 : 203.9 386.3 498.0 702.0 884.4 1049.4 1200.0 1017.6: 182.4 294.1 498.0 680.4 845.5 996.1 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 : 167.59539 cents, oct.: 1173.16775 cents Scale is strictly proper Step pattern alph. order: ABCDEBC Step pattern size order : AEDCBED Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.438286 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 : 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 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 : 4 at degree 1 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 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 classes 5 and 6 combined Limited inverse transpositions with margin 92.1787 cents: 1 -- Rational properties -- Prime limit : 11 Odd number limit : 27 (O: 27 U: 27) Highest odd numerator or denominator: 15 Scale harmonicity : 0.027336 Average absolute harmonicity : 0.231023 Specific harmonicity : 0.177807 Fundamental : 1/15, -3.9069 octaves, 17.4417 Hz. Guide tone : 1584, 10.6294 octaves, 414414.895 Hz. Exponens Consonantiae : 2.376000E+04, 14.53625 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 58.0, average 8.28571 Mersenne's string divisions : 6888882 Sum of van Prooijen's expressibility: 5.18149, average 0.74021 Sum of Tenney's harmonic distance : 11.01133, average 1.57305 Vogel's harmonic complexity : 7.71429 Wille's k value : 13 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 69.50314, average 2.48226 Lattice compactness (without 2's) : 44.63242, average 1.59402 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 4 1.71429 12 1 3: -1 .. 2 0.00000 6 1 5: -1 .. 0 -0.71429 5 4 11: 0 .. 1 0.14286 1 1 Average exponent except 2's :-4 / 7 =-0.57143 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 15 26| Scale is JI-epimorphic with val: <7 11 16 24| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 31.8274 c. M:-59.6973 c. Lebeng 9: 1 1 2 1 1 2 1 P M ME S SD: 30.9809 c. M:-49.0704 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 17.9220 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 15: 1 3 2 2 2 3 2 P D3 SD: 19.1684 c. M: 31.7313 c. 18: 2 3 2 3 2 3 3 SP M ME S SD: 18.0249 c. M: 31.3783 c. 19: 2 3 3 2 3 3 3 SP M ME S SD: 13.9359 c. M: 31.4703 c. Nineteen-tone Locrian 20: 2 3 3 3 3 3 3 SP M ME S SD: 13.8674 c. M:-26.3137 c. 21: 2 4 3 3 2 4 3 SP T3 SD: 16.1796 c. M:-27.2159 c. 22: 2 4 3 3 3 4 3 SP D3 SD: 9.5463 c. M:-18.7673 c. Gandhaara Grama (Somanatha) 24: 2 4 4 3 3 4 4 SP D3 S SD: 12.2668 c. M: 17.5963 c. 27: 3 4 4 4 3 5 4 SP D3 SD: 10.6423 c. M:-21.6020 c. 29: 3 5 4 4 4 5 4 SP D3 SD: 11.1639 c. M:-16.8865 c. 31: 3 5 5 4 4 5 5 SP D3 S SD: 5.7497 c. M: 11.1447 c. 34: 3 6 5 5 4 6 5 SP SD: 4.6197 c. M:-7.5390 c. 53: 5 9 8 7 7 9 8 SP SD: 2.6491 c. M: 6.4455 c. 65: 6 11 10 9 8 11 10 SP SD: 1.3921 c. M: 2.2117 c. 118: 11 20 18 16 15 20 18 SP SD: 0.8281 c. M: 2.0323 c. 152: 14 26 23 21 19 26 23 SP SD: 0.6440 c. M: 1.2050 c. 183: 17 31 28 25 23 31 28 SP SD: 0.6860 c. M: 1.2028 c. 217: 20 37 33 30 27 37 33 SP SD: 0.5988 c. M: 1.1322 c. 224: 21 38 34 31 28 38 34 SP SD: 0.6280 c. M:-1.2365 c. 270: 25 46 41 37 34 46 41 SP SD: 0.4317 c. M: 0.8270 c. 335: 31 57 51 46 42 57 51 SP SD: 0.4105 c. M: 0.6865 c. 342: 32 58 52 47 43 58 52 SP SD: 0.2673 c. M:-0.5494 c. 407: 38 69 62 56 51 69 62 SP SD: 0.2553 c. M: 0.3973 c. 494: 46 84 75 68 62 84 75 SP SD: 0.1148 c. M:-0.2175 c. 677: 63 115 103 93 85 115 103 SP SD: 0.1035 c. M: 0.1665 c. 1019: 95 173 155 140 128 173 155 SP SD: 0.0857 c. M:-0.1431 c. 1053: 98 179 160 145 132 179 160 SP SD: 0.0837 c. M:-0.1986 c. 1106: 103 188 168 152 139 188 168 SP SD: 0.0786 c. M:-0.1252 c. 1171: 109 199 178 161 147 199 178 SP SD: 0.0189 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: 23.5675 cents 5 x 6 x 7:8:9:10 S SD: 16.1074 cents 6 x 7:8:9:10:11:12 S SD: 16.5797 cents 7 x 8:9:10:11:13:14 SD: 21.7786 cents 8:9:10:11:12:13:14:16 S SD: 20.6734 cents 9:10:11:12:13:14:16:18 S SD: 13.9558 cents 10:11:12:13:15:16:18:20 SD: 11.3145 cents 11:12:13:15:16:18:20:22 SD: 10.8315 cents 13:14:16:17:19:21:23:26 SD: 9.6129 cents 14:15:17:19:21:22:25:28 SD: 9.1420 cents 15:16:18:20:22:24:27:30 S SD: 0.0000 cents