Scala analysis: xen09-wilson-marwa-18b-03
Marwa permutation 3 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: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 6/5 315.641287 minor third 3: 27/20 519.551289 acute 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: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 9/8 203.9100 major whole tone 4: 88/81 143.4979 2nd undecimal neutral second 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 88/81 143.498 cents 2nd undecimal neutral second 1: 2 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: 1 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: 1 6/5 315.641 cents minor third 2: 2 11/9 347.408 cents undecimal neutral third 2: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 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: 1 8/5 813.686 cents minor sixth 5: 2 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 1 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: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 20/11 1034.996 cents large 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 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 : 165.0 315.6 519.6 663.0 813.7 1017.6 1200.0 165.0 : 150.6 354.5 498.0 648.7 852.6 1035.0 1200.0 315.6 : 203.9 347.4 498.0 702.0 884.4 1049.4 1200.0 519.6 : 143.5 294.1 498.0 680.4 845.5 996.1 1200.0 663.0 : 150.6 354.5 537.0 702.0 852.6 1056.5 1200.0 813.7 : 203.9 386.3 551.3 702.0 905.9 1049.4 1200.0 1017.6: 182.4 347.4 498.0 702.0 845.5 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 143.4979 .. 203.9100 cents 729/704, 60.4121 cents 88/81, 143.4979 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 .. 1056.5021 cents 729/704, 60.4121 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 88/81, 143.4979 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.194641 Largest / Average step : 1.189475 Largest / Smallest step : 1.420996 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 168.43676 cents, oct.: 1179.05734 cents Scale is strictly proper Step pattern alph. order: ABCDBCE Step pattern size order : CBEABED Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.365754 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.656894 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 Length of longest harmonic part : 4 at degree 5 Length of longest subharmonic part : 1 at degree 0 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 Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions with margin 92.1787 cents: 5 -- Rational properties -- Prime limit : 11 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.024846 Average absolute harmonicity : 0.203773 Specific harmonicity : 0.141182 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 2376, 11.2143 octaves, 621622.343 Hz. Exponens Consonantiae : 1.425600E+05, 17.12121 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 73.0, average 10.42857 Mersenne's string divisions : 10444434 Sum of van Prooijen's expressibility: 6.00103, average 0.85729 Sum of Tenney's harmonic distance : 12.32572, average 1.76082 Vogel's harmonic complexity : 11.42857 Wille's k value : 40 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 76.84870, average 2.74460 Lattice compactness (without 2's) : 51.66587, average 1.84521 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.42857 9 1 3: -1 .. 3 0.71429 7 5: -1 .. 0 -0.85714 6 4 11: 0 .. 1 0.28571 2 2 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is weakly epimorphic with val: <7 10 18 22| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 12 16 25|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 21.8185 c. M:-43.4566 c. Lebeng 12: 2 1 2 2 1 2 2 P M ME S SD: 23.0339 c. M:-36.9508 c. G.M.Hypodorian, G.M.Aeolian, G.Hyperphrygian, Natural Minor, Melodic Minor descending, Asavari That, Mela Natabhairavi, Raga Jaunpuri, Adana, Darbari, Dhanyasi, Jingla, Gregorian nr.2, Makam Buselik, Nihavend, Peruvian Minor, Se, Chiao: China, Geez, Ezel: Ethiopia, Kiourdi descending: Greece, Cushak: Armenia 13: 2 1 3 1 2 2 2 P D3 S SD: 22.8098 c. M: 38.7182 c. 15: 2 2 2 2 2 3 2 SP M ME S SD: 20.1028 c. M: 39.5513 c. 16: 2 2 3 2 2 3 2 SP M ME S SD: 16.1258 c. M:-32.4037 c. Antimixolydian 18: 2 3 3 2 2 3 3 SP D3 S SD: 16.9707 c. M: 31.6709 c. 20: 3 2 4 2 3 3 3 SP D3 S SD: 15.0957 c. M:-26.3137 c. 22: 3 3 4 2 3 4 3 SP D3 SD: 13.3784 c. M:-25.9033 c. 23: 3 3 4 3 3 4 3 SP M ME S SD: 14.2919 c. M:-25.8820 c. 24: 3 3 4 3 3 4 4 SP D3 S SD: 14.7322 c. M: 19.5513 c. Maqam Ouchairan-Hussaini, Bayatan, Neutral Diatonic Mixolydian 25: 3 4 4 3 3 4 4 SP D3 S SD: 12.5618 c. M: 21.0042 c. 27: 4 3 5 3 3 5 4 SP SD: 9.2229 c. M:-13.7820 c. 31: 4 4 5 4 4 5 5 SP D3 S SD: 8.9050 c. M: 16.3255 c. Neutral Diatonic Mixolydian 34: 5 4 6 4 4 6 5 SP SD: 6.8500 c. M:-11.4664 c. 41: 6 5 7 5 5 7 6 SP SD: 7.4432 c. M:-10.6055 c. 44: 6 6 7 5 6 7 7 SP SD: 6.5890 c. M:-11.6314 c. 46: 6 6 8 5 6 8 7 SP SD: 5.6910 c. M: 10.8753 c. 50: 7 6 9 6 6 8 8 SP SD: 6.2241 c. M: 9.5963 c. 53: 7 7 9 6 7 9 8 SP SD: 3.6019 c. M: 6.5137 c. 58: 8 7 10 7 7 10 9 SP SD: 3.6874 c. M: 6.7897 c. 60: 8 8 10 7 8 10 9 SP SD: 3.7641 c. M:-6.3137 c. 65: 9 8 11 8 8 11 10 SP SD: 1.7195 c. M: 2.6282 c. 118: 16 15 20 14 15 20 18 SP SD: 1.2417 c. M: 2.2924 c. 152: 21 19 26 18 19 26 23 SP SD: 0.7430 c. M:-1.5013 c. 159: 22 20 27 19 20 27 24 SP SD: 1.1417 c. M:-1.4081 c. 183: 25 23 31 22 23 31 28 SP SD: 0.9695 c. M: 1.5185 c. 190: 26 24 32 23 24 32 29 SP SD: 0.8519 c. M: 1.6566 c. 212: 29 27 36 25 27 36 32 SP SD: 1.0815 c. M:-1.4081 c. 217: 30 27 37 26 27 37 33 SP SD: 0.5313 c. M:-0.8944 c. 270: 37 34 46 32 34 46 41 SP SD: 0.4413 c. M: 0.8270 c. 277: 38 35 47 33 35 47 42 SP SD: 0.4526 c. M:-0.7541 c. 335: 46 42 57 40 42 57 51 SP SD: 0.3305 c. M: 0.5520 c. 342: 47 43 58 41 43 58 52 SP SD: 0.1815 c. M:-0.3488 c. 494: 68 62 84 59 62 84 75 SP SD: 0.1695 c. M:-0.2868 c. 559: 77 70 95 67 70 95 85 SP SD: 0.1618 c. M:-0.2909 c. 677: 93 85 115 81 85 115 103 SP SD: 0.1393 c. M: 0.2012 c. 829: 114 104 141 99 104 141 126 SP SD: 0.0901 c. M: 0.1760 c. 1106: 152 139 188 132 139 188 168 SP SD: 0.1030 c. M:-0.1594 c. 1171: 161 147 199 140 147 199 178 SP SD: 0.0157 c. M: 0.0262 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: 24.6241 cents 4 x 5 x 6 x 7:8 S SD: 23.5675 cents 5 x 6:7 x 8:9:10 S SD: 12.5922 cents 6 x 7:8:9:10:11:12 S SD: 16.9627 cents 7:8 x 9:10:11:13:14 SD: 22.0413 cents 8:9:10:11:12:13:14:16 S SD: 15.7338 cents 9:10:11:12:13:14:16:18 S SD: 10.4140 cents 11:12:13:15:16:18:20:22 SD: 8.1198 cents 15:17:18:20:22:24:27:30 SD: 7.9969 cents 17:19:20:23:25:27:31:34 SD: 7.3385 cents 19:21:23:26:28:30:34:38 SD: 5.6145 cents 20:22:24:27:29:32:36:40 SD: 2.8265 cents 39:43:47:53:57:62:70:78 SD: 2.8119 cents 40:44:48:54:59:64:72:80 SD: 1.4012 cents 60:66:72:81:88:96:108:120 SD: 0.0000 cents