Scala analysis: xen09-wilson-marwa-06-01
Marwa permutation 1 from Figure 6, Didymus/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: 16/15 111.731285 minor diatonic semitone 2: 6/5 315.641287 minor third 3: 27/20 519.551289 acute fourth 4: 64/45 609.776284 2nd tritone 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: 16/15 111.7313 minor diatonic semitone 2: 9/8 203.9100 major whole tone 3: 9/8 203.9100 major whole tone 4: 256/243 90.2250 limma, Pythagorean minor second 5: 9/8 203.9100 major whole tone 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: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 4 9/8 203.910 cents major whole tone 2: 3 32/27 294.135 cents Pythagorean minor third 2: 1 6/5 315.641 cents minor third 2: 1 5/4 386.314 cents major third 2: 2 81/64 407.820 cents Pythagorean 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: 2 128/81 792.180 cents Pythagorean minor sixth 5: 1 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 3 27/16 905.865 cents Pythagorean major sixth 6: 4 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 15/8 1088.269 cents classic major seventh 6: 1 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.66667 = 11/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 111.7 315.6 519.6 609.8 813.7 1017.6 1200.0 111.7 : 203.9 407.8 498.0 702.0 905.9 1088.3 1200.0 315.6 : 203.9 294.1 498.0 702.0 884.4 996.1 1200.0 519.6 : 90.2 294.1 498.0 680.4 792.2 996.1 1200.0 609.8 : 203.9 407.8 590.2 702.0 905.9 1109.8 1200.0 813.7 : 203.9 386.3 498.0 702.0 905.9 996.1 1200.0 1017.6: 182.4 294.1 498.0 702.0 792.2 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 203.9100 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 2: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 498.0450 .. 590.2237 cents 135/128, 92.1787 cents 256/243, 90.2250 cents 4: 609.7763 .. 701.9550 cents 135/128, 92.1787 cents 2048/2025, 19.5526 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 6: 996.0900 .. 1109.7750 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.900012 Largest / Average step : 1.189475 Largest / Smallest step : 2.260017 Median interval of one step : 9/8, 203.9100 cents, amount: 4 Most common interval of one step : 9/8, 203.9100 cents, amount: 4 Least squares average step : 166.53416 cents, oct.: 1165.73910 cents Scale is strictly proper Step pattern alph. order: ABBCBBD Step pattern size order : BDDADDC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.461397 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.467419 Rothenberg efficiency : 0.496599 redundancy: 0.503401 Efficiency x scale size : 3.476190 Number of different interval sizes : 22 = 3.66667 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.66667 = 11/3 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 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 5, average 701.9550 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Length of longest harmonic part : 2 at degree 5 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 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: 4 -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 45 Scale harmonicity : 0.036058 Average absolute harmonicity : 0.212120 Specific harmonicity : 0.211128 Fundamental : 1/180, -7.4919 octaves, 1.4535 Hz. Guide tone : 1728, 10.7549 octaves, 452088.977 Hz. Exponens Consonantiae : 3.110400E+05, 18.24674 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 114.0, average 16.28571 Mersenne's string divisions : 953830878 Sum of van Prooijen's expressibility: 6.61285, average 0.94469 Sum of Tenney's harmonic distance : 13.60542, average 1.94363 Vogel's harmonic complexity : 11.85714 Wille's k value : 121 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 106.24727, average 3.79455 Lattice compactness (without 2's) : 57.92568, average 2.06877 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 6 1.85714 17 1 3: -2 .. 3 0.42857 9 5: -1 .. 0 -0.85714 6 6 Average exponent except 2's :-3 / 7 =-0.42857 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: 41.5893 c. M:-75.9380 c. Lebeng 8: 1 1 1 1 1 2 1 P M ME S SD: 40.9670 c. M: 69.5513 c. 9: 1 1 2 1 1 2 1 P M ME S SD: 35.6307 c. M:-56.8904 c. 10: 1 2 1 1 2 1 2 P M ME S SD: 33.1785 c. M: 57.5963 c. 11: 1 2 2 1 1 2 2 P D3 S SD: 30.7120 c. M: 50.0499 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 13.9235 c. M: 19.5513 c. G.Mixolydian, G.Hyperdorian, M.Hypophrygian, M.Locrian, G.M.Hyperaeolian, Rut biscale descending, Pien chih: China, Makam Lami, Yishtabach: Jewish 19: 2 3 3 2 3 3 3 SP M ME S SD: 11.9313 c. M:-21.8027 c. Nineteen-tone Locrian 26: 2 5 4 2 5 4 4 P SD: 11.7443 c. M: 19.4236 c. 28: 3 4 5 2 5 5 4 P SD: 10.5041 c. M:-16.8401 c. 30: 3 5 5 2 5 5 5 P T3 SD: 9.8568 c. M: 17.5963 c. 31: 3 5 5 3 5 5 5 SP M DE S SD: 8.7668 c. M: 16.3255 c. Intense Diatonic Mixolydian, M.Locrian 32: 3 5 6 2 6 5 5 P SD: 8.6559 c. M: 15.6413 c. 33: 3 6 5 3 5 6 5 SP T3 SD: 8.5356 c. M: 13.6863 c. 34: 3 6 6 2 6 6 5 P SD: 6.2098 c. M:-9.8605 c. 41: 4 7 7 3 7 7 6 SP SD: 5.6697 c. M:-7.2780 c. 46: 4 8 8 3 8 8 7 P SD: 5.1627 c. M: 9.7763 c. 53: 5 9 9 4 9 9 8 SP SD: 1.2766 c. M:-1.5445 c. 118: 11 20 20 9 20 20 18 SP SD: 0.4751 c. M: 0.9072 c. 171: 16 29 29 13 29 29 26 SP SD: 0.3918 c. M:-0.7500 c. 289: 27 49 49 22 49 49 44 SP SD: 0.3577 c. M:-0.6043 c. 323: 30 55 55 24 55 55 49 SP SD: 0.3377 c. M:-0.5726 c. 388: 36 66 66 29 66 66 59 SP SD: 0.2724 c. M: 0.4979 c. 441: 41 75 75 33 75 75 67 SP SD: 0.1402 c. M: 0.2525 c. 494: 46 84 84 37 84 84 75 SP SD: 0.1518 c. M:-0.2868 c. 559: 52 95 95 42 95 95 85 SP SD: 0.0805 c. M: 0.1162 c. 612: 57 104 104 46 104 104 93 SP SD: 0.0400 c. M:-0.0566 c. 1171: 109 199 199 88 199 199 178 SP SD: 0.0222 c. M: 0.0410 c. 1783: 166 303 303 134 303 303 271 SP SD: 0.0128 c. M:-0.0225 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: 46.0894 cents 3 x x 4 x 5 x 6 S SD: 24.6241 cents 4 x 5 x 6 x 7:8 S SD: 31.4941 cents 5 x 6 x 7:8:9:10 S SD: 5.4528 cents 6 x 7:8:9:10:11:12 S SD: 21.9480 cents 7 x 8:9:10:11:13:14 SD: 22.5027 cents 8:9:10:11 x 13:14:16 SD: 22.1106 cents 9:10:11:12:13:14:16:18 S SD: 14.3055 cents 10:11:12 x 14:16:18:20 S SD: 9.9740 cents 13:14:16:18 x 21:23:26 SD: 12.1132 cents 14:15:17:19:20:22:25:28 SD: 6.0365 cents 15:16:18:20:21:24:27:30 S SD: 4.9608 cents 25:27:30:34:36:40:45:50 SD: 4.7127 cents 26:28:31:35:37:42:47:52 SD: 3.9198 cents 29:31:35:39:41:46:52:58 SD: 3.2926 cents 31:33:37:42:44:50:56:62 SD: 2.7907 cents 40:43:48:54:57:64:72:80 SD: 1.9842 cents 45:48:54:61:64:72:81:90 SD: 1.0157 cents 60:64:72:81:85:96:108:120 SD: 0.9680 cents 100:107:120:135:142:160:180:200 SD: 0.8632 cents 105:112:126:142:149:168:189:210 SD: 0.7038 cents 120:128:144:162:171:192:216:240 SD: 0.4826 cents 135:144:162:182:192:216:243:270 SD: 0.3395 cents 180:192:216:243:256:288:324:360 SD: 0.0000 cents