Scala analysis: xen09-wilson-marwa-04-08
Marwa permutation 8 from Figure 4, Didymus 16/15 10/9 9/8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect 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: 9/8 203.9100 major whole tone 2: 16/15 111.7313 minor diatonic semitone 3: 10/9 182.4037 minor whole tone 4: 9/8 203.9100 major whole tone 5: 16/15 111.7313 minor diatonic semitone 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: 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 : 203.9 315.6 498.0 702.0 813.7 1017.6 1200.0 203.9 : 111.7 294.1 498.0 609.8 813.7 996.1 1200.0 315.6 : 182.4 386.3 498.0 702.0 884.4 1088.3 1200.0 498.0 : 203.9 315.6 519.6 702.0 905.9 1017.6 1200.0 702.0 : 111.7 315.6 498.0 702.0 813.7 996.1 1200.0 813.7 : 203.9 386.3 590.2 702.0 884.4 1088.3 1200.0 1017.6: 182.4 386.3 498.0 680.4 884.4 996.1 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 : 169.36541 cents, oct.: 1185.55784 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : LSMLSLM 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 0.0 315.641 701.955 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 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 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 5 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 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 92.1787 cents: 6 -- 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 : 0.271137 Specific harmonicity : 0.255659 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 72, 6.1699 octaves, 18837.041 Hz. Exponens Consonantiae : 8.640000E+03, 13.07682 octaves Euler's gradus suavitatis : 17 Sum of Mann's harmonic distance : 35.0, average 5.00000 Mersenne's string divisions : 510510 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 : 11.42857 Wille's k value : 67 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: -3 .. 3 0.42857 11 1 3: -1 .. 2 0.71429 7 3 5: -1 .. 0 -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 1 2 2 1 2 2 P M ME S SD: 10.4507 c. M: 17.5963 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 19: 3 2 3 3 2 3 3 SP M ME S SD: 7.7171 c. M: 14.4363 c. Nineteen-tone Natural Minor, Aeolian 31: 5 3 5 5 3 5 5 SP M DE S SD: 6.7763 c. M: 11.1447 c. Thirty-one tone Natural Minor, Intense Diatonic Hypodorian, Aeolian 34: 6 3 5 6 3 6 5 P T3 SD: 4.3991 c. M:-7.8547 c. Thirty-four tone Natural Minor 41: 7 4 6 7 4 7 6 SP T3 SD: 4.1631 c. M:-6.7940 c. Forty-one tone "Just" Minor 46: 8 4 7 8 4 8 7 P T3 SD: 3.0718 c. M: 4.9906 c. Forty-six tone Natural Minor 53: 9 5 8 9 5 9 8 SP T3 SD: 0.8802 c. M:-1.4081 c. Fifty-three tone "Just" Minor 118: 20 11 18 20 11 20 18 SP T3 SD: 0.3762 c. M: 0.6471 c. 171: 29 16 26 29 16 29 26 SP T3 SD: 0.2354 c. M: 0.4012 c. 289: 49 27 44 49 27 49 44 SP T3 SD: 0.2448 c. M: 0.4498 c. 323: 55 30 49 55 30 55 49 SP T3 SD: 0.2467 c. M:-0.4244 c. 376: 64 35 57 64 35 64 57 SP T3 SD: 0.2773 c. M:-0.4888 c. 388: 66 36 59 66 36 66 59 SP T3 SD: 0.1629 c. M: 0.2842 c. 441: 75 41 67 75 41 75 67 SP T3 SD: 0.0918 c. M:-0.1716 c. 559: 95 52 85 95 52 95 85 SP T3 SD: 0.0527 c. M: 0.0906 c. 612: 104 57 93 104 57 104 93 SP T3 SD: 0.0301 c. M:-0.0508 c. 1171: 199 109 178 199 109 199 178 SP T3 SD: 0.0132 c. M: 0.0228 c. 1783: 303 166 271 303 166 303 271 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: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 21.4668 cents 5 x 6:7 x 8:9:10 S SD: 16.8934 cents 6 x 7:8:9:10:11:12 S SD: 15.2591 cents 7:8 x 9 x 11:13:14 SD: 18.5557 cents 8:9:10:11:12:13:14:16 S SD: 14.9363 cents 9:10:11:12 x 14:16:18 S SD: 10.9452 cents 10:11:12:13:15:16:18:20 SD: 8.3725 cents 12 x 14:16:18:19:22:24 SD: 10.1603 cents 14:16:17:19:21:22:25:28 SD: 8.1634 cents 15:17:18:20:23:24:27:30 SD: 5.7341 cents 24:27:29:32:36:38:43:48 SD: 3.3096 cents 30:34:36:40:45:48:54:60 SD: 1.8252 cents 40:45:48:53:60:64:72:80 SD: 1.5506 cents 66:74:79:88:99:106:119:132 SD: 1.4609 cents 70:79:84:93:105:112:126:140 SD: 1.1821 cents 80:90:96:107:120:128:144:160 SD: 0.7717 cents 90:101:108:120:135:144:162:180 SD: 0.6114 cents 120:135:144:160:180:192:216:240 S SD: 0.0000 cents