Scala analysis: xen09-wilson-marwa-03-12
Marwa permutation 12 from Figure 3, Ptolemy 16/15 9/8 10/9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP 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: 10/9 182.4037 minor whole tone 2: 9/8 203.9100 major whole tone 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 16/15 111.7313 minor diatonic semitone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 10/9 182.404 cents minor whole tone 1: 3 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 6/5 315.641 cents minor third 2: 3 5/4 386.314 cents major third 3: 5 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 3: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 40/27 680.449 cents grave fifth 4: 5 3/2 701.955 cents perfect fifth 5: 3 8/5 813.686 cents minor sixth 5: 3 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 182.4 386.3 498.0 702.0 884.4 996.1 1200.0 182.4 : 203.9 315.6 519.6 702.0 813.7 1017.6 1200.0 386.3 : 111.7 315.6 498.0 609.8 813.7 996.1 1200.0 498.0 : 203.9 386.3 498.0 702.0 884.4 1088.3 1200.0 702.0 : 182.4 294.1 498.0 680.4 884.4 996.1 1200.0 884.4 : 111.7 315.6 498.0 702.0 813.7 1017.6 1200.0 996.1 : 203.9 386.3 590.2 702.0 905.9 1088.3 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 .. 590.2237 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 4: 609.7763 .. 701.9550 cents 135/128, 92.1787 cents 2048/2025, 19.5526 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 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 171.82371 cents, oct.: 1202.76598 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCBACB Step pattern size order : MLSLMSL Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.374079 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.539106 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 386.314 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Hypophrygian 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 Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval class 5 Limited inverse transpositions with margin 92.1787 cents: 1 -- Rational properties -- Prime limit : 5 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 9 Scale harmonicity : 0.049020 Average absolute harmonicity : 0.271718 Specific harmonicity : 0.255659 Fundamental : 1/36, -5.1699 octaves, 7.2674 Hz. Guide tone : 240, 7.9069 octaves, 62790.136 Hz. Exponens Consonantiae : 8.640000E+03, 13.07682 octaves Euler's gradus suavitatis : 17 Sum of Mann's harmonic distance : 38.0, average 5.42857 Mersenne's string divisions : 239400 Sum of van Prooijen's expressibility: 4.26067, average 0.60867 Sum of Tenney's harmonic distance : 8.74809, average 1.24973 Vogel's harmonic complexity : 8.71429 Wille's k value : 22 Wilson's harmonic complexity : 14 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 78.47882, average 2.80282 Lattice compactness (without 2's) : 42.59183, average 1.52114 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 0.71429 11 1 3: -2 .. 1 -0.71429 7 3 5: 0 .. 1 0.42857 3 3 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 24.8774 c. M: 43.4566 c. Lebeng 12: 2 2 1 2 2 1 2 P M ME S SD: 10.4507 c. M:-17.5963 c. G.Hypophrygian, G.Ionian (Iastian), M.Mixolydian, G.M.Hypoionian, Hypermixolydian, Mischung 3, Khamaj That, Mela Harikambhoji, Raga Balahamsa, Bhim, Devamanohari, Harini, Janjhuti, Kaamaai, Khambhavati, Surati, Gregorian nr.7, Enharmonic Byzantine Liturgical, Rast descending: Greece, Ching, Shang: China 19: 3 3 2 3 3 2 3 SP M ME S SD: 7.7171 c. M:-14.4363 c. Nineteen-tone Mixolydian 31: 5 5 3 5 5 3 5 SP M DE S SD: 6.7763 c. M:-11.1447 c. Intense Diatonic Hypophrygian, M.Mixolydian 34: 5 6 3 6 5 3 6 P T3 SD: 4.3991 c. M: 7.8547 c. 41: 6 7 4 7 6 4 7 SP T3 SD: 4.1631 c. M: 6.7940 c. 46: 7 8 4 8 7 4 8 P T3 SD: 3.0718 c. M:-4.9906 c. 53: 8 9 5 9 8 5 9 SP T3 SD: 0.8802 c. M: 1.4081 c. 118: 18 20 11 20 18 11 20 SP T3 SD: 0.3762 c. M:-0.6471 c. 171: 26 29 16 29 26 16 29 SP T3 SD: 0.2354 c. M:-0.4012 c. 289: 44 49 27 49 44 27 49 SP T3 SD: 0.2448 c. M:-0.4498 c. 323: 49 55 30 55 49 30 55 SP T3 SD: 0.2467 c. M: 0.4244 c. 376: 57 64 35 64 57 35 64 SP T3 SD: 0.2773 c. M: 0.4888 c. 388: 59 66 36 66 59 36 66 SP T3 SD: 0.1629 c. M:-0.2842 c. 441: 67 75 41 75 67 41 75 SP T3 SD: 0.0918 c. M: 0.1716 c. 559: 85 95 52 95 85 52 95 SP T3 SD: 0.0527 c. M:-0.0906 c. 612: 93 104 57 104 93 57 104 SP T3 SD: 0.0301 c. M: 0.0508 c. 1171: 178 199 109 199 178 109 199 SP T3 SD: 0.0132 c. M:-0.0228 c. 1783: 271 303 166 303 271 166 303 SP T3 SD: 0.0095 c. M: 0.0160 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 6.8160 cents 5 x 6:7 x 8:9:10 S SD: 26.5228 cents 6:7 x 8:9:10:11:12 S SD: 16.6439 cents 7:8:9 x 11:12 x 14 SD: 23.3425 cents 8:9:10:11:12:13:14:16 S SD: 11.0334 cents 9:10:11:12:14:15:16:18 S SD: 10.5731 cents 10:11 x 13:15:17:18:20 SD: 10.3572 cents 12:13:15:16:18:20:21:24 SD: 7.3741 cents 16:18:20:21:24:27:28:32 S SD: 7.0156 cents 18:20:23:24:27:30:32:36 SD: 5.4358 cents 24:27:30:32:36:40:43:48 SD: 3.6254 cents 27:30:34:36:41:45:48:54 SD: 3.5413 cents 28:31:35:37:42:47:50:56 SD: 3.1647 cents 36:40:45:48:54:60:64:72 S SD: 0.0000 cents