Scala analysis: xen09-wilson-marwa-04-03
Marwa permutation 3 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: 27/20 519.551289 acute fourth 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major 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: 9/8 203.9100 major whole tone 4: 10/9 182.4037 minor whole tone 5: 9/8 203.9100 major whole tone 6: 16/15 111.7313 minor diatonic semitone 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 : 203.9 315.6 519.6 702.0 905.9 1017.6 1200.0 203.9 : 111.7 315.6 498.0 702.0 813.7 996.1 1200.0 315.6 : 203.9 386.3 590.2 702.0 884.4 1088.3 1200.0 519.6 : 182.4 386.3 498.0 680.4 884.4 996.1 1200.0 702.0 : 203.9 315.6 498.0 702.0 813.7 1017.6 1200.0 905.9 : 111.7 294.1 498.0 609.8 813.7 996.1 1200.0 1017.6: 182.4 386.3 498.0 702.0 884.4 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 : 173.11835 cents, oct.: 1211.82846 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACABC Step pattern size order : LSLMLSM 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 Hypolydian 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 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 2 at degree 3 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 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 27 Scale harmonicity : 0.051546 Average absolute harmonicity : 0.245943 Specific harmonicity : 0.241813 Fundamental : 1/80, -6.3219 octaves, 3.2703 Hz. Guide tone : 54, 5.7549 octaves, 14127.781 Hz. Exponens Consonantiae : 4.320000E+03, 12.07682 octaves Euler's gradus suavitatis : 16 Sum of Mann's harmonic distance : 70.0, average 10.00000 Mersenne's string divisions : 79364670 Sum of van Prooijen's expressibility: 5.94730, average 0.84961 Sum of Tenney's harmonic distance : 11.43473, average 1.63353 Vogel's harmonic complexity : 10.85714 Wille's k value : 67 Wilson's harmonic complexity : 14 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 81.51348, average 2.91120 Lattice compactness (without 2's) : 46.75411, average 1.66979 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.14286 12 1 3: 0 .. 3 1.71429 12 3 5: -1 .. 0 -0.42857 3 3 Average exponent except 2's : 9 / 7 = 1.28571 Average absolute exponent except 2's: 15 / 7 = 2.14286 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: 25.5833 c. M: 48.7221 c. Lebeng 11: 2 1 2 1 2 1 2 P M ME I SD: 28.3745 c. M: 47.4095 c. Superkleismic-7 12: 2 1 2 2 2 1 2 P M ME I SD: 11.8926 c. M: 19.5513 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 19: 3 2 3 3 3 2 3 SP M ME I SD: 11.8538 c. M: 21.6545 c. Nineteen-tone Dorian 27: 5 2 5 4 4 3 4 SP SD: 11.5834 c. M:-18.3122 c. 28: 5 2 5 4 5 3 4 P SD: 10.6814 c. M: 16.2407 c. 29: 5 3 5 4 5 3 4 SP T3 SD: 11.2830 c. M:-18.3797 c. 30: 5 3 5 5 5 2 5 P T3 SD: 11.1454 c. M:-18.0450 c. 31: 5 3 5 5 5 3 5 SP M DE I SD: 10.7042 c. M: 16.3255 c. Intense Diatonic Phrygian, M.Dorian 32: 5 3 6 5 5 3 5 P SD: 10.1079 c. M: 16.4100 c. 33: 6 3 5 5 6 3 5 SP SD: 9.1117 c. M:-14.2718 c. 34: 6 3 6 5 6 3 5 P T3 SD: 7.0952 c. M:-11.7821 c. 41: 7 4 7 6 7 4 6 SP T3 SD: 4.5075 c. M:-7.2780 c. 46: 8 4 8 7 8 4 7 P T3 SD: 3.6201 c. M:-7.1785 c. 53: 9 5 9 8 9 5 8 SP T3 SD: 0.8388 c. M:-1.3398 c. 118: 20 11 20 18 20 11 18 SP T3 SD: 0.5780 c. M: 0.9072 c. 171: 29 16 29 26 29 16 26 SP T3 SD: 0.3052 c. M: 0.6018 c. 224: 38 21 38 34 38 21 34 SP T3 SD: 0.3077 c. M: 0.5079 c. 335: 57 31 57 51 57 31 51 SP T3 SD: 0.2751 c. M: 0.4174 c. 388: 66 36 66 59 66 36 59 SP T3 SD: 0.1680 c. M:-0.3206 c. 441: 75 41 75 67 75 41 67 SP T3 SD: 0.1427 c. M:-0.2574 c. 506: 86 47 86 77 86 47 77 SP T3 SD: 0.1380 c. M: 0.2263 c. 559: 95 52 95 85 95 52 85 SP T3 SD: 0.0467 c. M: 0.0778 c. 612: 104 57 104 93 104 57 93 SP T3 SD: 0.0344 c. M:-0.0566 c. 1171: 199 109 199 178 199 109 178 SP T3 SD: 0.0141 c. M:-0.0274 c. 1783: 303 166 303 271 303 166 271 SP T3 SD: 0.0153 c. M:-0.0239 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: 10.1382 cents 4 x 5 x 6 x 7:8 S SD: 21.4668 cents 5 x 6:7 x 8:9:10 S SD: 22.3258 cents 6 x 7:8:9:10:11:12 S SD: 10.9452 cents 7:8 x 9:11:12:13:14 SD: 22.3824 cents 8:9:10:11:12 x 14:16 S SD: 15.2591 cents 9:10:11:12:14:15:16:18 S SD: 11.8004 cents 10:11:12:14:15:17:18:20 SD: 10.7295 cents 12 x 14:16:18:20:22:24 S SD: 10.9452 cents 14:16:17:19:21:24:25:28 SD: 6.6704 cents 16:18:19:22:24:27:29:32 SD: 5.4982 cents 24:27:29:32:36:41:43:48 SD: 4.7848 cents 25:28:30:34:38:42:45:50 SD: 4.0607 cents 26:29:31:35:39:44:47:52 SD: 3.0235 cents 34:38:41:46:51:57:61:68 SD: 2.7691 cents 40:45:48:54:60:68:72:80 SD: 1.8252 cents 54:61:65:73:81:91:97:108 SD: 1.4499 cents 64:72:77:86:96:108:115:128 SD: 1.3840 cents 74:83:89:100:111:125:133:148 SD: 1.0599 cents 80:90:96:108:120:135:144:160 S SD: 0.0000 cents