Scala analysis: xen09-wilson-marwa-18b-05
Marwa permutation 5 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: 4/3 498.044999 perfect fourth 4: 22/15 663.049228 undecimal diminished fifth 5: 33/20 866.959229 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: 10/9 182.4037 minor whole tone 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 9/8 203.9100 major whole tone 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 10/9 182.4037 minor whole 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: 1 6/5 315.641 cents minor third 2: 2 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 99/80 368.914 cents 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: 1 160/99 831.086 cents 5: 1 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 2 33/20 866.959 cents 5: 1 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 : 165.0 315.6 498.0 663.0 867.0 1017.6 1200.0 165.0 : 150.6 333.0 498.0 702.0 852.6 1035.0 1200.0 315.6 : 182.4 347.4 551.3 702.0 884.4 1049.4 1200.0 498.0 : 165.0 368.9 519.6 702.0 867.0 1017.6 1200.0 663.0 : 203.9 354.5 537.0 702.0 852.6 1035.0 1200.0 867.0 : 150.6 333.0 498.0 648.7 831.1 996.1 1200.0 1017.6: 182.4 347.4 498.0 680.4 845.5 1049.4 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 .. 368.9142 cents 33/32, 53.2729 cents 16/15, 111.7313 cents 3: 498.0450 .. 551.3179 cents 33/32, 53.2729 cents 320/297, 129.1308 cents 4: 648.6821 .. 701.9550 cents 33/32, 53.2729 cents 128/121, 97.3641 cents 5: 831.0858 .. 884.3587 cents 33/32, 53.2729 cents 320/297, 129.1308 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 : 169.87852 cents, oct.: 1189.14963 cents Scale is strictly proper Step pattern alph. order: ABCADBC Step pattern size order : BACBDAC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 97.36412 cents Scale diversity : 1.283021 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.733635 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 Phrygian 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 : 3 at degree 6 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 n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 53.2729 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 33 Scale harmonicity : 0.027336 Average absolute harmonicity : 0.215361 Specific harmonicity : 0.127644 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 396, 8.6294 octaves, 103603.724 Hz. Exponens Consonantiae : 2.376000E+04, 14.53625 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 73.0, average 10.42857 Mersenne's string divisions : 905982 Sum of van Prooijen's expressibility: 5.86633, average 0.83805 Sum of Tenney's harmonic distance : 11.89000, average 1.69857 Vogel's harmonic complexity : 12.28571 Wille's k value : 49 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 67.31675, average 2.40417 Lattice compactness (without 2's) : 46.51413, average 1.66122 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.28571 8 1 3: -1 .. 2 0.28571 6 1 5: -1 .. 0 -0.71429 5 2 11: 0 .. 1 0.42857 3 3 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 14 / 7 = 2.00000 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: 15.9296 c. M:-27.2159 c. Lebeng 15: 2 2 2 2 3 2 2 SP M ME S SD: 14.9901 c. M: 23.0492 c. 20: 3 2 3 3 3 3 3 SP M ME S SD: 14.8180 c. M: 26.9592 c. Minor quasi-equal Heptatonic 22: 3 3 3 3 4 3 3 SP M ME S SD: 9.6057 c. M:-18.7673 c. 24: 3 3 4 3 4 3 4 SP M ME S SD: 13.3155 c. M: 17.5963 c. Neutral Phrygian, Iced Locrian 26: 4 3 4 3 5 3 4 SP D3 SD: 11.4803 c. M:-19.6112 c. 27: 4 3 4 4 5 3 4 SP T3 SD: 10.5757 c. M:-21.9297 c. 29: 4 4 4 4 5 4 4 SP M ME S SD: 8.6980 c. M:-16.8865 c. 31: 4 4 5 4 5 4 5 SP M ME S SD: 8.8665 c. M: 15.3463 c. Neutral Phrygian 34: 5 4 5 5 6 4 5 SP T3 SD: 8.2802 c. M:-15.3937 c. 37: 5 5 5 5 7 4 6 SP SD: 9.6291 c. M: 14.4006 c. 38: 5 5 6 5 6 5 6 SP M ME S SD: 7.1509 c. M: 14.3277 c. 41: 6 5 6 6 7 5 6 SP T3 SD: 7.7838 c. M:-11.0896 c. 43: 6 5 7 6 7 5 7 SP T3 SD: 6.7130 c. M: 12.9451 c. 46: 6 6 7 6 8 6 7 SP T3 S SD: 5.8533 c. M: 10.8753 c. 50: 7 6 8 7 8 6 8 SP T3 SD: 5.8390 c. M: 9.5963 c. 51: 7 6 8 7 9 6 8 SP SD: 5.0112 c. M: 9.7589 c. 53: 7 7 8 7 9 7 8 SP T3 S SD: 4.3212 c. M: 6.5819 c. 58: 8 7 9 8 10 7 9 SP SD: 2.6725 c. M: 5.2965 c. 65: 9 8 10 9 11 8 10 SP SD: 1.3416 c. M: 2.2117 c. 118: 16 15 18 16 20 15 18 SP SD: 1.5370 c. M: 2.5524 c. 125: 17 16 19 17 21 16 19 SP SD: 1.4692 c. M: 2.9592 c. 137: 19 17 21 19 23 17 21 SP SD: 1.3631 c. M:-2.6442 c. 145: 20 18 22 20 25 18 22 SP SD: 1.1297 c. M:-2.0063 c. 152: 21 19 23 21 26 19 23 SP SD: 0.7488 c. M:-1.4618 c. 159: 22 20 24 22 27 20 24 SP SD: 0.9733 c. M:-1.3398 c. 183: 25 23 28 25 31 23 28 SP SD: 0.9232 c. M: 1.3855 c. 190: 26 24 29 26 32 24 29 SP SD: 0.8387 c. M: 1.6961 c. 217: 30 27 33 30 37 27 33 SP SD: 0.6504 c. M:-1.2435 c. 224: 31 28 34 31 38 28 34 SP SD: 0.7325 c. M:-1.2365 c. 255: 35 32 39 35 43 32 39 SP SD: 0.7044 c. M: 1.1257 c. 270: 37 34 41 37 46 34 41 SP SD: 0.4131 c. M: 0.8270 c. 277: 38 35 42 38 47 35 42 SP SD: 0.3927 c. M:-0.6042 c. 335: 46 42 51 46 57 42 51 SP SD: 0.2576 c. M: 0.4174 c. 342: 47 43 52 47 58 43 52 SP SD: 0.1562 c. M: 0.2926 c. 494: 68 62 75 68 84 62 75 SP SD: 0.1598 c. M:-0.2472 c. 677: 93 85 103 93 115 85 103 SP SD: 0.1335 c. M: 0.1941 c. 829: 114 104 126 114 141 104 126 SP SD: 0.0704 c. M:-0.1095 c. 1171: 161 147 178 161 199 147 178 SP SD: 0.0138 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: 5.7998 cents 4 x 5 x 6 x 7:8 S SD: 23.5675 cents 5 x 6 x 7:8:9:10 S SD: 19.3124 cents 6 x 7:8:9:10:11:12 S SD: 12.0232 cents 7:8 x 9:10:12:13:14 S SD: 22.1887 cents 8:9:10:11:12:13:14:16 S SD: 16.8651 cents 9:10:11:12:13:15:16:18 SD: 7.5265 cents 19:21:23:25:28:31:34:38 SD: 5.2913 cents 20:22:24:27:29:33:36:40 SD: 4.1747 cents 21:23:25:28:31:35:38:42 SD: 3.9343 cents 30:33:36:40:44:50:54:60 SD: 2.4856 cents 39:43:47:52:57:64:70:78 SD: 2.1241 cents 40:44:48:53:59:66:72:80 SD: 2.0899 cents 49:54:59:65:72:81:88:98 SD: 1.8031 cents 51:56:61:68:75:84:92:102 SD: 1.3306 cents 60:66:72:80:88:99:108:120 S SD: 0.0000 cents