Scala analysis: xen09-wilson-marwa-18a-06
Marwa permutation 6 from Figure 18a, Ptolemy 12/11 11/10 10/9
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: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 22/15 663.049228 undecimal diminished fifth 5: 44/27 845.452940 neutral sixth 6: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 10/9 182.4037 minor whole tone 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 10/9 182.4037 minor whole tone 6: 9/8 203.9100 major whole tone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 2 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 2: 2 6/5 315.641 cents minor third 2: 1 40/33 333.041 cents 2: 2 11/9 347.408 cents undecimal neutral third 2: 1 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: 1 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 1 33/20 866.959 cents 5: 2 5/3 884.359 cents major sixth, BP sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 20/11 1034.996 cents large minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 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 : 165.0 347.4 498.0 663.0 845.5 1049.4 1200.0 165.0 : 182.4 333.0 498.0 680.4 884.4 1035.0 1200.0 347.4 : 150.6 315.6 498.0 702.0 852.6 1017.6 1200.0 498.0 : 165.0 347.4 551.3 702.0 867.0 1049.4 1200.0 663.0 : 182.4 386.3 537.0 702.0 884.4 1035.0 1200.0 845.5 : 203.9 354.5 519.6 702.0 852.6 1017.6 1200.0 1049.4: 150.6 315.6 498.0 648.7 813.7 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 203.9100 cents 33/32, 53.2729 cents 12/11, 150.6371 cents 2: 315.6413 .. 386.3137 cents 25/24, 70.6724 cents 16/15, 111.7313 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 .. 884.3587 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 6: 996.0900 .. 1049.3629 cents 33/32, 53.2729 cents 16/15, 111.7313 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.138024 Largest / Average step : 1.189475 Largest / Smallest step : 1.353651 Median interval of one step : 11/10, 165.0042 cents, amount: 2 Least squares average step : 170.92567 cents, oct.: 1196.47972 cents Scale is strictly proper Step pattern alph. order: ABCABDC Step pattern size order : BCABCDA Scale is a Constant Structure, by a margin of 97.36412 cents Scale diversity : 1.313255 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.704636 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 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 Number of recognisable fifths : 4, average 701.9550 cents Scale is Lydian octave species of abstract tetrachord 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 : 1 at degree 0 Length of longest subharmonic part : 4 at degree 2 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 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 53.2729 cents: 3 -- Rational properties -- Prime limit : 11 Odd number limit : 33 (O: 33 U: 33) Highest odd numerator or denominator: 27 Scale harmonicity : 0.028104 Average absolute harmonicity : 0.201793 Specific harmonicity : 0.133279 Fundamental : 1/270, -8.0768 octaves, 0.9690 Hz. Guide tone : 44, 5.4594 octaves, 11511.525 Hz. Exponens Consonantiae : 1.188000E+04, 13.53625 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 88.0, average 12.57143 Mersenne's string divisions : 18756780 Sum of van Prooijen's expressibility: 6.20875, average 0.88696 Sum of Tenney's harmonic distance : 12.83011, average 1.83287 Vogel's harmonic complexity : 18.57143 Wille's k value : 247 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 65.66535, average 2.34519 Lattice compactness (without 2's) : 46.17703, average 1.64918 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 8 1 3: -3 .. 0 -1.14286 8 1 5: -1 .. 0 -0.28571 2 11: 0 .. 1 0.71429 5 5 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is weakly epimorphic with val: <7 10 18 26| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 11 17 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 14.1844 c. M:-22.6651 c. Lebeng 17: 2 3 2 2 3 3 2 SP D3 S SD: 14.5221 c. M: 27.7551 c. Dastgah-e Sehgah 22: 3 3 3 3 3 4 3 SP M ME S SD: 14.3588 c. M: 27.2711 c. 23: 3 4 3 3 3 4 3 SP M ME I SD: 13.7862 c. M:-23.6941 c. Armodue-7, Antidorian 24: 3 4 3 3 4 4 3 SP D3 S SD: 7.8105 c. M: 15.0042 c. Dastgah-e Sehgah, Neutral Diatonic Lydian 31: 4 5 4 4 5 5 4 SP D3 S SD: 5.4978 c. M: 10.1655 c. Neutral Diatonic Lydian 38: 5 6 5 5 6 6 5 SP D3 S SD: 5.4362 c. M: 7.2577 c. 41: 6 6 5 6 6 7 5 SP T3 SD: 6.0852 c. M:-10.6055 c. 51: 7 8 6 7 8 9 6 SP SD: 4.7218 c. M:-9.4606 c. 58: 8 9 7 8 9 10 7 SP SD: 3.0190 c. M:-5.8095 c. 65: 9 10 8 9 10 11 8 SP SD: 2.3357 c. M:-3.7778 c. 87: 12 13 11 12 13 15 11 SP SD: 1.9960 c. M: 4.0736 c. 94: 13 14 12 13 14 16 12 SP SD: 1.8485 c. M: 2.8997 c. 111: 15 17 14 15 17 19 14 SP SD: 2.0373 c. M: 3.5898 c. 118: 16 18 15 16 18 20 15 SP SD: 1.5905 c. M: 2.2924 c. 125: 17 19 16 17 19 21 16 SP SD: 1.5805 c. M: 2.9629 c. 145: 20 22 18 20 22 25 18 SP SD: 1.0696 c. M:-1.6715 c. 152: 21 23 19 21 23 26 19 SP SD: 0.5354 c. M:-0.7852 c. 183: 25 28 23 25 28 31 23 SP SD: 0.5432 c. M: 1.0698 c. 270: 37 41 34 37 41 46 34 SP SD: 0.6392 c. M: 1.0085 c. 277: 38 42 35 38 42 47 35 SP SD: 0.5823 c. M: 0.9875 c. 311: 43 47 39 43 47 53 39 SP SD: 0.4682 c. M:-0.9122 c. 335: 46 51 42 46 51 57 42 SP SD: 0.1878 c. M: 0.3627 c. 342: 47 52 43 47 52 58 43 SP SD: 0.1443 c. M: 0.2401 c. 494: 68 75 62 68 75 84 62 SP SD: 0.0945 c. M:-0.1780 c. 677: 93 103 85 93 103 115 85 SP SD: 0.0799 c. M: 0.1593 c. 829: 114 126 104 114 126 141 104 SP SD: 0.0700 c. M: 0.0971 c. 836: 115 127 105 115 127 142 105 SP SD: 0.0611 c. M:-0.1087 c. 1171: 161 178 147 161 178 199 147 SP SD: 0.0156 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: 12.9686 cents 4 x 5 x 6 x 7:8 S SD: 24.3843 cents 5 x 6 x 7:8:9:10 S SD: 19.5075 cents 6 x 7:8:9:10:11:12 S SD: 16.2562 cents 7:8 x 9:10:11:13:14 SD: 20.3316 cents 8:9:10:11:12:13:15:16 SD: 13.4899 cents 9:10:11:12:13:15:17:18 SD: 10.2878 cents 13:14:16:17:19:21:24:26 SD: 7.8719 cents 17:19:21:23:25:28:31:34 SD: 6.6761 cents 18:20:22:24:26:29:33:36 SD: 5.3315 cents 19:21:23:25:28:31:35:38 SD: 4.5447 cents 27:30:33:36:40:44:50:54 SD: 4.3053 cents 28:31:34:37:41:46:51:56 SD: 4.1029 cents 30:33:37:40:44:49:55:60 SD: 2.3075 cents 41:45:50:55:60:67:75:82 SD: 1.9836 cents 49:54:60:65:72:80:90:98 SD: 1.6282 cents 60:66:73:80:88:98:110:120 SD: 1.2589 cents 81:89:99:108:119:132:149:162 SD: 0.9702 cents 90:99:110:120:132:147:165:180 SD: 0.5615 cents 162:178:198:216:238:264:297:324 SD: 0.5002 cents 180:198:220:240:264:293:330:360 SD: 0.2812 cents 270:297:330:360:396:440:495:540 S SD: 0.0000 cents