Scala analysis: xen09-wilson-marwa-12-04
Marwa permutation 4 from Figure 12, Helmholtz 16/15 16/15 75/64
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 5/4 386.313714 major third 3: 45/32 590.223716 diatonic tritone 4: 25/16 772.627428 classic augmented fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 15/8 1088.268715 classic major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 10/9 182.4037 minor whole tone 2: 9/8 203.9100 major whole tone 3: 9/8 203.9100 major whole tone 4: 10/9 182.4037 minor whole tone 5: 16/15 111.7313 minor diatonic semitone 6: 9/8 203.9100 major whole tone 7: 16/15 111.7313 minor diatonic semitone
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: 1 32/25 427.373 cents classic diminished fourth 3: 4 4/3 498.045 cents perfect fourth 3: 2 45/32 590.224 cents diatonic tritone 4: 2 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 25/16 772.627 cents classic augmented 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 : 182.4 386.3 590.2 772.6 884.4 1088.3 1200.0 182.4 : 203.9 407.8 590.2 702.0 905.9 1017.6 1200.0 386.3 : 203.9 386.3 498.0 702.0 813.7 996.1 1200.0 590.2 : 182.4 294.1 498.0 609.8 792.2 996.1 1200.0 772.6 : 111.7 315.6 427.4 609.8 813.7 1017.6 1200.0 884.4 : 203.9 315.6 498.0 702.0 905.9 1088.3 1200.0 1088.3: 111.7 294.1 498.0 702.0 884.4 996.1 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 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 427.3726 .. 590.2237 cents 1125/1024, 162.8511 cents 2048/2025, 19.5526 cents 4: 609.7763 .. 772.6274 cents 1125/1024, 162.8511 cents 2048/2025, 19.5526 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 2048/2025, 19.5526 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 : 179.76870 cents, oct.: 1258.38089 cents Scale is strictly proper Step pattern alph. order: ABBACBC Step pattern size order : MLLMSLS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.412795 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.385475 Rothenberg efficiency : 0.451701 redundancy: 0.548299 Efficiency x scale size : 3.161905 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: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Best minor thirds form a closed circle All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 2 at degree 0 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 Limited inverse transpositions : 4 Inversional symmetry on degrees : 2 Inversional symmetry on intervals : 5-6 -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 45 Scale harmonicity : 0.033937 Average absolute harmonicity : 0.215719 Specific harmonicity : 0.212671 Fundamental : 1/288, -8.1699 octaves, 0.9084 Hz. Guide tone : 450, 8.8138 octaves, 117731.504 Hz. Exponens Consonantiae : 1.296000E+05, 16.98371 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 90.0, average 12.85714 Mersenne's string divisions : 99331848 Sum of van Prooijen's expressibility: 6.57943, average 0.93992 Sum of Tenney's harmonic distance : 12.57200, average 1.79600 Vogel's harmonic complexity : 14.28571 Wille's k value : 202 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 95.82383, average 3.42228 Lattice compactness (without 2's) : 48.90169, average 1.74649 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -1.71429 16 1 3: -2 .. 2 0.00000 6 5: 0 .. 2 1.00000 7 6 Average exponent except 2's : 7 / 7 = 1.00000 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 16| Scale is JI-epimorphic with val: <7 11 16| = patent Scale is weakly epimorphic with val: <7 12 15|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 52.9607 c. M: 86.9131 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 32.5635 c. M:-63.6863 c. 9: 1 2 1 2 1 1 1 N D3 S SD: 36.7349 c. M: 56.8904 c. 10: 1 2 2 1 1 2 1 P D3 S SD: 36.8160 c. M: 62.4037 c. 11: 2 2 1 2 1 2 1 P M ME S SD: 29.3074 c. M:-50.0499 c. 12: 2 2 2 2 1 2 1 P D3 S SD: 15.6937 c. M:-27.3726 c. Lydian Augmented, Lydian sharp 5 19: 3 3 3 3 2 3 2 SP D3 S SD: 12.0082 c. M: 21.8027 c. 22: 3 4 4 3 2 4 2 P S SD: 9.9362 c. M: 18.7673 c. 28: 4 5 5 4 3 4 3 P S SD: 10.3238 c. M: 16.8401 c. 31: 5 5 5 5 3 5 3 SP D3 S SD: 6.2556 c. M:-11.1447 c. 34: 5 6 6 5 3 6 3 P S SD: 5.1751 c. M:-9.7763 c. 47: 7 8 8 7 5 8 4 SP SD: 6.0479 c. M:-9.6036 c. 53: 8 9 9 8 5 9 5 SP S SD: 1.5987 c. M: 2.8161 c. 65: 10 11 11 10 6 11 6 SP S SD: 1.6405 c. M:-2.7572 c. 118: 18 20 20 18 11 20 11 SP S SD: 0.3426 c. M:-0.6471 c. 289: 44 49 49 44 27 49 27 SP S SD: 0.3209 c. M: 0.6043 c. 323: 49 55 55 49 30 55 30 SP S SD: 0.2638 c. M:-0.4884 c. 376: 57 64 64 57 35 64 35 SP S SD: 0.2628 c. M: 0.4888 c. 441: 67 75 75 67 41 75 41 SP S SD: 0.1376 c. M:-0.2525 c. 494: 75 84 84 75 46 84 46 SP S SD: 0.1219 c. M: 0.2175 c. 559: 85 95 95 85 52 95 52 SP S SD: 0.1038 c. M:-0.1812 c. 612: 93 104 104 93 57 104 57 SP S SD: 0.0450 c. M: 0.0784 c. 1171: 178 199 199 178 109 199 109 SP S SD: 0.0280 c. M:-0.0455 c. 1783: 271 303 303 271 166 303 166 SP S SD: 0.0097 c. M:-0.0175 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: 35.3362 cents 3 x x 4 x 5 x 6 S SD: 30.7262 cents 4 x 5 x 6:7 x 8 S SD: 27.5333 cents 5 x 6:7:8 x 9:10 S SD: 21.6652 cents 6:7 x 8:9:10:11:12 S SD: 24.7991 cents 7:8:9:10:11:12:13:14 H SD: 12.9762 cents 8:9:10:11 x 13:15:16 SD: 10.4048 cents 9:10:11:13:14:15:17:18 SD: 8.9086 cents 15:17:19:21:23:25:28:30 SD: 7.6722 cents 16:18:20:23:25:27:30:32 SD: 6.9589 cents 17:19:21:24:27:28:32:34 SD: 6.1185 cents 19:21:24:27:30:32:36:38 SD: 5.9361 cents 20:22:25:28:31:33:38:40 SD: 5.3148 cents 24:27:30:34:38:40:45:48 SD: 4.8478 cents 25:28:31:35:39:42:47:50 SD: 3.6766 cents 27:30:34:38:42:45:51:54 SD: 2.8139 cents 36:40:45:51:56:60:68:72 SD: 2.8065 cents 37:41:46:52:58:62:69:74 SD: 2.5461 cents 39:43:49:55:61:65:73:78 SD: 2.4467 cents 44:49:55:62:69:73:83:88 SD: 2.2075 cents 45:50:56:63:70:75:84:90 SD: 2.2033 cents 52:58:65:73:81:87:98:104 SD: 2.0404 cents 55:61:69:77:86:92:103:110 SD: 1.7749 cents 57:63:71:80:89:95:107:114 SD: 1.6750 cents 64:71:80:90:100:107:120:128 SD: 0.8632 cents 96:107:120:135:150:160:180:192 SD: 0.7717 cents 108:120:135:152:169:180:203:216 SD: 0.7399 cents 128:142:160:180:200:213:240:256 SD: 0.5469 cents 135:150:169:190:211:225:253:270 SD: 0.4424 cents 153:170:191:215:239:255:287:306 SD: 0.3908 cents 192:213:240:270:300:320:360:384 SD: 0.3867 cents 217:241:271:305:339:362:407:434 SD: 0.3752 cents 224:249:280:315:350:373:420:448 SD: 0.2470 cents 288:320:360:405:450:480:540:576 S SD: 0.0000 cents