Scala analysis: xen09-wilson-marwa-18b-09
Marwa permutation 9 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: 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: 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: 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: 3 6/5 315.641 cents minor third 2: 1 40/33 333.041 cents 2: 1 11/9 347.408 cents undecimal neutral third 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 18/11 852.592 cents undecimal neutral sixth 5: 1 33/20 866.959 cents 5: 3 5/3 884.359 cents major sixth, BP 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 111.7 315.6 498.0 663.0 813.7 996.1 1200.0 111.7 : 203.9 386.3 551.3 702.0 884.4 1088.3 1200.0 315.6 : 182.4 347.4 498.0 680.4 884.4 996.1 1200.0 498.0 : 165.0 315.6 498.0 702.0 813.7 1017.6 1200.0 663.0 : 150.6 333.0 537.0 648.7 852.6 1035.0 1200.0 813.7 : 182.4 386.3 498.0 702.0 884.4 1049.4 1200.0 996.1 : 203.9 315.6 519.6 702.0 867.0 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: 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 .. 1088.2687 cents 135/128, 92.1787 cents 16/15, 111.7313 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 : 166.67369 cents, oct.: 1166.71586 cents Scale is strictly proper Step pattern alph. order: ABCDECB Step pattern size order : AEDCBDE Scale is a Constant Structure, by a margin of 97.36412 cents Scale diversity : 1.395193 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.639793 Rothenberg efficiency : 0.423129 redundancy: 0.576871 Efficiency x scale size : 2.961905 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 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 : 4 at degree 1 Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval class 3 Scale is 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 : 33 (O: 33 U: 33) Highest odd numerator or denominator: 15 Scale harmonicity : 0.027336 Average absolute harmonicity : 0.234154 Specific harmonicity : 0.177939 Fundamental : 1/45, -5.4919 octaves, 5.8139 Hz. Guide tone : 528, 9.0444 octaves, 138138.298 Hz. Exponens Consonantiae : 2.376000E+04, 14.53625 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 63.5, average 9.07143 Mersenne's string divisions : 86111025 Sum of van Prooijen's expressibility: 5.18149, average 0.74021 Sum of Tenney's harmonic distance : 11.51648, average 1.64521 Vogel's harmonic complexity : 10.28571 Wille's k value : 22 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 69.73999, average 2.49071 Lattice compactness (without 2's) : 41.38034, average 1.47787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 4 2.28571 16 1 3: -2 .. 1 -0.57143 6 2 5: -1 .. 0 -0.57143 4 3 11: 0 .. 1 0.14286 1 1 Average exponent except 2's :-7 / 7 =-1.00000 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is weakly epimorphic with val: <7 10 15 23| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 12 18 22|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 33.8599 c. M:-59.6973 c. Lebeng 10: 1 2 1 2 1 1 2 P M ME S SD: 32.9501 c. M:-56.9508 c. 11: 1 2 2 1 1 2 2 P D3 S SD: 27.1791 c. M: 50.0499 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 16.7078 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 2 3 SP D3 S SD: 21.9498 c. M: 36.0900 c. 16: 1 3 3 2 2 2 3 P T3 SD: 20.8259 c. M: 36.7313 c. 17: 2 2 3 2 3 2 3 SP M ME S SD: 23.7135 c. M:-33.3725 c. Safi al-Din's maqam Higazi 18: 2 3 2 3 2 3 3 SP M ME S SD: 16.8181 c. M: 31.3783 c. 19: 2 3 3 3 2 3 3 SP M ME S SD: 14.7919 c. M:-31.6876 c. Nineteen-tone Phrygian 20: 2 3 3 3 3 3 3 SP M ME S SD: 16.5272 c. M:-26.3137 c. 22: 2 4 3 3 3 3 4 SP D3 S SD: 8.3614 c. M: 14.2718 c. 29: 3 5 4 4 4 4 5 SP D3 S SD: 9.2288 c. M:-15.3932 c. 31: 3 5 5 4 4 5 5 SP D3 S SD: 5.5365 c. M:-10.3616 c. 34: 3 6 5 5 4 5 6 SP SD: 5.0126 c. M: 7.8547 c. 41: 4 7 6 6 5 6 7 SP SD: 5.4236 c. M:-10.1215 c. 46: 4 8 7 6 6 7 8 SP S SD: 5.7703 c. M: 10.8753 c. 53: 5 9 8 7 7 8 9 SP S SD: 2.6056 c. M: 6.4455 c. 65: 6 11 10 9 8 10 11 SP SD: 1.1569 c. M: 1.7951 c. 118: 11 20 18 16 15 18 20 SP SD: 0.8152 c. M: 2.0323 c. 152: 14 26 23 21 19 23 26 SP SD: 0.7610 c. M: 1.3532 c. 183: 17 31 28 25 23 28 31 SP SD: 0.5665 c. M: 0.8872 c. 217: 20 37 33 30 27 33 37 SP SD: 0.6536 c. M: 1.1322 c. 224: 21 38 34 31 28 34 38 SP SD: 0.6333 c. M:-1.2365 c. 248: 23 42 38 34 31 38 42 SP SD: 0.6188 c. M: 1.1252 c. 270: 25 46 41 37 34 41 46 SP SD: 0.4717 c. M: 0.8270 c. 311: 29 53 47 43 39 47 53 SP SD: 0.4828 c. M:-0.7574 c. 335: 31 57 51 46 42 51 57 SP SD: 0.4092 c. M: 0.6865 c. 342: 32 58 52 47 43 52 58 SP SD: 0.3067 c. M:-0.5494 c. 407: 38 69 62 56 51 62 69 SP SD: 0.2724 c. M:-0.4702 c. 429: 40 73 65 59 54 65 73 SP SD: 0.2464 c. M:-0.4426 c. 460: 43 78 70 63 58 70 78 SP SD: 0.3104 c. M:-0.4426 c. 494: 46 84 75 68 62 75 84 SP SD: 0.0957 c. M:-0.1482 c. 677: 63 115 103 93 85 103 115 SP SD: 0.0863 c. M: 0.1317 c. 1053: 98 179 160 145 132 160 179 SP SD: 0.0851 c. M:-0.1986 c. 1106: 103 188 168 152 139 168 188 SP SD: 0.0679 c. M: 0.1198 c. 1171: 109 199 178 161 147 178 199 SP SD: 0.0201 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: 21.2891 cents 5 x 6 x 7:8:9:10 S SD: 16.6718 cents 6 x 7:8:9:10:11:12 S SD: 18.0469 cents 7 x 8:9:10:11:12:14 S SD: 22.4300 cents 8:9:10:11:12:13:14:16 S SD: 19.8499 cents 9:10:11:12:13:14:16:18 S SD: 13.6134 cents 10:11:12:13:15:16:18:20 SD: 11.7242 cents 12:13:14:16:18:19:21:24 SD: 10.7709 cents 13:14:16:17:19:21:23:26 SD: 8.6974 cents 15:16:18:20:22:24:27:30 S SD: 3.0723 cents 30:32:36:40:44:48:53:60 SD: 1.5506 cents 45:48:54:60:66:72:80:90 S SD: 0.0000 cents