Scala analysis: xen09-wilson-marwa-06-04
Marwa permutation 4 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: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 64/45 609.776284 2nd tritone 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: 10/9 182.4037 minor whole tone 3: 9/8 203.9100 major whole tone 4: 16/15 111.7313 minor diatonic semitone 5: 9/8 203.9100 major whole 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: 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 : 111.7 294.1 498.0 609.8 813.7 996.1 1200.0 111.7 : 182.4 386.3 498.0 702.0 884.4 1088.3 1200.0 294.1 : 203.9 315.6 519.6 702.0 905.9 1017.6 1200.0 498.0 : 111.7 315.6 498.0 702.0 813.7 996.1 1200.0 609.8 : 203.9 386.3 590.2 702.0 884.4 1088.3 1200.0 813.7 : 182.4 386.3 498.0 680.4 884.4 996.1 1200.0 996.1 : 203.9 315.6 498.0 702.0 813.7 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: 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 : 164.84438 cents, oct.: 1153.91064 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCACBC Step pattern size order : SMLSLML Scale is sum-free (all different intervals) 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 Phrygian 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 4 Length of longest subharmonic part : 2 at degree 1 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 Limited inverse transpositions with margin 92.1787 cents: 4 -- Rational properties -- Prime limit : 5 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 45 Scale harmonicity : 0.049020 Average absolute harmonicity : 0.233950 Specific harmonicity : 0.242730 Fundamental : 1/135, -7.0768 octaves, 1.9380 Hz. Guide tone : 64, 6.0000 octaves, 16744.036 Hz. Exponens Consonantiae : 8.640000E+03, 13.07682 octaves Euler's gradus suavitatis : 17 Sum of Mann's harmonic distance : 123.5, average 17.64286 Mersenne's string divisions : 1360638825 Sum of van Prooijen's expressibility: 6.39100, average 0.91300 Sum of Tenney's harmonic distance : 13.91675, average 1.98811 Vogel's harmonic complexity : 11.57143 Wille's k value : 67 Wilson's harmonic complexity : 14 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 85.14228, average 3.04080 Lattice compactness (without 2's) : 44.59183, average 1.59257 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 6 3.57143 25 1 3: -3 .. 0 -1.28571 9 3 5: -1 .. 0 -0.42857 3 3 Average exponent except 2's :-12 / 7 =-1.71429 Average absolute exponent except 2's: 12 / 7 = 1.71429 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: 46.1542 c. M:-75.9380 c. Lebeng 8: 1 1 1 1 1 2 1 P M ME S SD: 39.3973 c. M: 63.6863 c. 9: 1 1 2 1 1 1 2 P M ME S SD: 37.4712 c. M: 62.7567 c. Pseudo Pelog, Pelogic-7, Antiionian 10: 1 1 2 1 2 1 2 P M ME S SD: 27.8133 c. M: 54.1350 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 8.2291 c. M: 13.6863 c. G.Mixolydian, G.Hyperdorian, M.Hypophrygian, M.Locrian, G.M.Hyperaeolian, Rut biscale descending, Pien chih: China, Makam Lami, Yishtabach: Jewish 29: 3 4 5 3 5 4 5 SP T3 SD: 8.4300 c. M:-13.8999 c. 31: 3 5 5 3 5 5 5 SP M DE S SD: 8.3450 c. M:-15.5424 c. Intense Diatonic Mixolydian, M.Locrian 34: 3 5 6 3 6 5 6 P T3 SD: 7.0652 c. M: 11.7821 c. 41: 4 6 7 4 7 6 7 SP T3 SD: 3.5728 c. M:-5.8259 c. 53: 5 8 9 5 9 8 9 SP T3 SD: 0.9719 c. M:-1.5445 c. 65: 6 10 11 6 11 10 11 SP T3 SD: 0.8906 c. M: 1.3786 c. 118: 11 18 20 11 20 18 20 SP T3 SD: 0.4028 c. M:-0.7803 c. 171: 16 26 29 16 29 26 29 SP T3 SD: 0.4705 c. M:-0.7500 c. 289: 27 44 49 27 49 44 49 SP T3 SD: 0.4211 c. M:-0.6747 c. 323: 30 49 55 30 55 49 55 SP T3 SD: 0.3682 c. M: 0.6365 c. 376: 35 57 64 35 64 57 64 SP T3 SD: 0.2617 c. M: 0.5180 c. 388: 36 59 66 36 66 59 66 SP T3 SD: 0.3027 c. M: 0.4979 c. 429: 40 65 73 40 73 65 73 SP T3 SD: 0.2392 c. M: 0.4287 c. 441: 41 67 75 41 75 67 75 SP T3 SD: 0.1695 c. M: 0.2574 c. 494: 46 75 84 46 84 75 84 SP T3 SD: 0.1049 c. M: 0.2079 c. 547: 51 83 93 51 93 83 93 SP T3 SD: 0.1305 c. M:-0.2077 c. 559: 52 85 95 52 95 85 95 SP T3 SD: 0.0704 c. M: 0.1162 c. 612: 57 93 104 57 104 93 104 SP T3 SD: 0.0236 c. M:-0.0392 c. 1171: 109 178 199 109 199 178 199 SP T3 SD: 0.0250 c. M: 0.0410 c. 1783: 166 271 303 166 303 271 303 SP T3 SD: 0.0136 c. M: 0.0239 c. 1901: 177 289 323 177 323 289 323 SP T3 SD: 0.0131 c. M:-0.0260 c. 2395: 223 364 407 223 407 364 407 SP T3 SD: 0.0113 c. M: 0.0223 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: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 33.2952 cents 5 x 6 x 7:8:9:10 S SD: 8.1691 cents 6 x 7:8:9:10:11:12 S SD: 21.7772 cents 7 x 8:9:10:11:12:14 S SD: 18.9479 cents 8 x 9:11 x 13:14:16 SD: 22.3091 cents 9:10:11:12:13:14:16:18 S SD: 14.9363 cents 10:11:12:13:14:16:18:20 S SD: 11.4531 cents 12:13:14:16:17:19:21:24 SD: 7.2586 cents 15:16:18:20:21:24:27:30 S SD: 5.8351 cents 17:18:20:23:24:27:30:34 SD: 5.4492 cents 26:28:31:35:37:42:46:52 SD: 4.5213 cents 27:29:32:36:38:43:48:54 SD: 3.3096 cents 33:35:39:44:47:53:59:66 SD: 2.3328 cents 42:45:50:56:60:67:75:84 SD: 2.3233 cents 45:48:53:60:64:72:80:90 SD: 1.5506 cents 60:64:71:80:85:96:107:120 SD: 1.2969 cents 75:80:89:100:107:120:133:150 SD: 1.0364 cents 87:93:103:116:124:139:155:174 SD: 1.0237 cents 90:96:107:120:128:144:160:180 SD: 0.7717 cents 102:109:121:136:145:163:181:204 SD: 0.7549 cents 120:128:142:160:171:192:213:240 SD: 0.7294 cents 123:131:146:164:175:197:219:246 SD: 0.7058 cents 135:144:160:180:192:216:240:270 S SD: 0.0000 cents