Scala analysis: xen09-wilson-marwa-06-05
Marwa permutation 5 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: 128/81 792.179997 Pythagorean 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: 10/9 182.4037 minor whole tone 6: 9/8 203.9100 major 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: 2 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 1 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: 1 128/81 792.180 cents Pythagorean minor sixth 5: 2 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 2 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: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 111.7 294.1 498.0 609.8 792.2 996.1 1200.0 111.7 : 182.4 386.3 498.0 680.4 884.4 1088.3 1200.0 294.1 : 203.9 315.6 498.0 702.0 905.9 1017.6 1200.0 498.0 : 111.7 294.1 498.0 702.0 813.7 996.1 1200.0 609.8 : 182.4 386.3 590.2 702.0 884.4 1088.3 1200.0 792.2 : 203.9 407.8 519.6 702.0 905.9 1017.6 1200.0 996.1 : 203.9 315.6 498.0 702.0 813.7 996.1 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 .. 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 .. 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 : 164.07630 cents, oct.: 1148.53407 cents Scale is strictly proper Step pattern alph. order: ABCABCC Step pattern size order : SMLSMLL Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.415885 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.503263 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 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: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Mixolydian octave species of abstract tetrachord Scale is Lydian octave species of abstract tetrachord Scale contains two identical conjunct tetrachords Best major thirds form a closed circle Best minor thirds form a closed circle All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 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 classes 2 and 3 combined 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 113.6850 cents: 4 -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.041551 Average absolute harmonicity : 0.226839 Specific harmonicity : 0.224456 Fundamental : 1/405, -8.6618 octaves, 0.6460 Hz. Guide tone : 128, 7.0000 octaves, 33488.072 Hz. Exponens Consonantiae : 5.184000E+04, 15.66178 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 221.5, average 31.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.60052, average 1.08579 Sum of Tenney's harmonic distance : 16.33039, average 2.33291 Vogel's harmonic complexity : 14.14286 Wille's k value : 202 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 100.55529, average 3.59126 Lattice compactness (without 2's) : 52.17762, average 1.86349 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 7 4.14286 29 1 3: -4 .. 0 -1.85714 13 4 5: -1 .. 0 -0.28571 2 2 Average exponent except 2's :-15 / 7 =-2.14286 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 0 1 1 1 1 1 2 N T3 SD: 114.2577 c. M: 155.1879 c. 8: 1 1 1 1 1 2 1 P M ME S SD: 35.0270 c. M:-53.9100 c. 9: 1 1 2 1 1 2 1 P M ME S SD: 39.1794 c. M:-70.5767 c. 10: 1 1 2 1 1 2 2 P D3 S SD: 37.6689 c. M: 72.1800 c. 11: 1 2 2 1 1 2 2 P D3 S SD: 30.1791 c. M:-47.4095 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 7.0494 c. M: 11.7313 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 4 5 5 SP SD: 6.9685 c. M:-12.4066 c. 41: 4 6 7 4 6 7 7 SP SD: 2.9072 c. M:-5.3419 c. 53: 5 8 9 5 8 9 9 SP SD: 0.8198 c. M:-1.5445 c. 118: 11 18 20 11 18 20 20 SP SD: 0.5608 c. M:-1.0403 c. 171: 16 26 29 16 26 29 29 SP SD: 0.5440 c. M:-0.8025 c. 289: 27 44 49 27 44 49 49 SP SD: 0.5381 c. M:-0.8996 c. 323: 30 49 55 30 49 55 55 SP SD: 0.4878 c. M: 0.8487 c. 376: 35 57 64 35 57 64 64 SP SD: 0.3657 c. M: 0.6906 c. 388: 36 59 66 36 59 66 66 SP SD: 0.3259 c. M: 0.4979 c. 429: 40 65 73 40 65 73 73 SP SD: 0.3018 c. M: 0.5716 c. 441: 41 67 75 41 67 75 75 SP SD: 0.2113 c. M: 0.3433 c. 494: 46 75 84 46 75 84 84 SP SD: 0.1453 c. M: 0.2772 c. 547: 51 83 93 51 83 93 93 SP SD: 0.1342 c. M: 0.2239 c. 559: 52 85 95 52 85 95 95 SP SD: 0.0645 c. M: 0.1162 c. 612: 57 93 104 57 93 104 104 SP SD: 0.0203 c. M:-0.0334 c. 1783: 166 271 303 166 271 303 303 SP SD: 0.0182 c. M: 0.0319 c. 2395: 223 364 407 223 364 407 407 SP SD: 0.0155 c. M: 0.0297 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 45.1125 cents 3 x x 4 x 5 x 6 S SD: 30.7262 cents 4 x 5 x x 6:7:8 S SD: 32.9591 cents 5 x 6 x 7:8:9:10 S SD: 9.2323 cents 6 x 7:8 x 9:11:12 SD: 21.6535 cents 7 x 8:9:10:11:12:14 S SD: 18.2920 cents 8 x 9:11 x 13:14:16 SD: 23.7145 cents 9:10:11:12:13:14:16:18 S SD: 13.7740 cents 10:11:12:13:14:16:18:20 S SD: 11.8581 cents 12:13:14:16:17:19:21:24 SD: 6.7980 cents 15:16:18:20:21:24:27:30 S SD: 6.5945 cents 17:18:20:23:24:27:30:34 SD: 5.2837 cents 26:28:31:35:37:41:46:52 SD: 3.8875 cents 27:29:32:36:38:43:48:54 SD: 3.6525 cents 28:30:33:37:40:44:50:56 SD: 3.5202 cents 31:33:37:41:44:49:55:62 SD: 2.7903 cents 33:35:39:44:47:52:59:66 SD: 2.2501 cents 45:48:53:60:64:71:80:90 SD: 1.5981 cents 59:63:70:79:84:93:105:118 SD: 1.3251 cents 76:81:90:101:108:120:135:152 SD: 0.9333 cents 90:96:107:120:128:142:160:180 SD: 0.8632 cents 102:109:121:136:145:161:181:204 SD: 0.7475 cents 135:144:160:180:192:213:240:270 SD: 0.3867 cents 210:224:249:280:299:332:373:420 SD: 0.3864 cents 243:259:288:324:346:384:432:486 SD: 0.3439 cents 270:288:320:360:384:427:480:540 SD: 0.1931 cents 405:432:480:540:576:640:720:810 S SD: 0.0000 cents