Scala analysis: xen09-wilson-marwa-18a-09
Marwa permutation 9 from Figure 18a, Ptolemy 12/11 11/10 10/9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88/81 143.497939 2nd undecimal neutral second 2: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 22/15 663.049228 undecimal diminished fifth 5: 44/27 845.452940 neutral 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: 88/81 143.4979 2nd undecimal neutral second 2: 9/8 203.9100 major whole tone 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 10/9 182.4037 minor whole tone 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 88/81 143.498 cents 2nd undecimal neutral second 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 2: 1 6/5 315.641 cents minor third 2: 1 40/33 333.041 cents 2: 3 11/9 347.408 cents undecimal neutral third 2: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 4 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 3: 1 15/11 536.951 cents undecimal augmented fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 1 22/15 663.049 cents undecimal diminished fifth 4: 1 40/27 680.449 cents grave fifth 4: 4 3/2 701.955 cents perfect fifth 5: 2 44/27 845.453 cents neutral sixth 5: 3 18/11 852.592 cents undecimal neutral sixth 5: 1 33/20 866.959 cents 5: 1 5/3 884.359 cents major sixth, BP sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 20/11 1034.996 cents large minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 81/44 1056.502 cents 2nd undecimal neutral seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 143.5 347.4 498.0 663.0 845.5 996.1 1200.0 143.5 : 203.9 354.5 519.6 702.0 852.6 1056.5 1200.0 347.4 : 150.6 315.6 498.0 648.7 852.6 996.1 1200.0 498.0 : 165.0 347.4 498.0 702.0 845.5 1049.4 1200.0 663.0 : 182.4 333.0 537.0 680.4 884.4 1035.0 1200.0 845.5 : 150.6 354.5 498.0 702.0 852.6 1017.6 1200.0 996.1 : 203.9 347.4 551.3 702.0 867.0 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 143.4979 .. 203.9100 cents 729/704, 60.4121 cents 88/81, 143.4979 cents 2: 315.6413 .. 354.5471 cents 45/44, 38.9058 cents 16/15, 111.7313 cents 3: 498.0450 .. 551.3179 cents 33/32, 53.2729 cents 88/81, 143.4979 cents 4: 648.6821 .. 701.9550 cents 33/32, 53.2729 cents 128/121, 97.3641 cents 5: 845.4529 .. 884.3587 cents 45/44, 38.9058 cents 88/81, 143.4979 cents 6: 996.0900 .. 1056.5021 cents 729/704, 60.4121 cents 16/15, 111.7313 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 88/81, 143.4979 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.194641 Largest / Average step : 1.189475 Largest / Smallest step : 1.420996 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 168.48893 cents, oct.: 1179.42252 cents Scale is strictly proper Step pattern alph. order: ABCDECB Step pattern size order : AEBCDBE Scale is a Constant Structure, by a margin of 97.36412 cents Scale diversity : 1.268819 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.745682 Rothenberg efficiency : 0.423129 redundancy: 0.576871 Efficiency x scale size : 2.961905 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 243/242, 7.1391 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, 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 subharmonic part : 3 at degree 2 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 3 and 4 combined Limited inverse transpositions with margin 60.4121 cents: 1 6 -- Rational properties -- Prime limit : 11 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.025479 Average absolute harmonicity : 0.209462 Specific harmonicity : 0.125973 Fundamental : 1/405, -8.6618 octaves, 0.6460 Hz. Guide tone : 176, 7.4594 octaves, 46046.099 Hz. Exponens Consonantiae : 7.128000E+04, 16.12121 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 166.0, average 23.71429 Mersenne's string divisions : 932322300 Sum of van Prooijen's expressibility: 6.98870, average 0.99839 Sum of Tenney's harmonic distance : 14.98051, average 2.14007 Vogel's harmonic complexity : 18.85714 Wille's k value : 247 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 77.52097, average 2.76861 Lattice compactness (without 2's) : 54.92867, average 1.96174 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 4 1.85714 13 1 3: -4 .. 0 -1.85714 13 2 5: -1 .. 0 -0.14286 1 11: 0 .. 1 0.57143 4 4 Average exponent except 2's :-10 / 7 =-1.42857 Average absolute exponent except 2's: 18 / 7 = 2.57143 Scale is JI-epimorphic with val: <7 11 16 24| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 19.8925 c. M:-32.4814 c. Lebeng 16: 2 3 2 2 2 2 3 P D3 S SD: 19.0342 c. M:-27.5921 c. 17: 2 3 2 2 3 2 3 SP M ME S SD: 11.2507 c. M: 27.7551 c. 23: 3 4 3 3 3 3 4 SP D3 S SD: 14.2245 c. M:-23.6941 c. 24: 3 4 3 3 4 3 4 SP M ME S SD: 6.0835 c. M: 13.0492 c. Neutral Mixolydian, Iced Blizzard 31: 4 5 4 4 5 4 5 SP M ME S SD: 6.8303 c. M:-11.3408 c. Neutral Mixolydian 34: 4 6 4 5 5 4 6 SP D3 S SD: 4.9648 c. M: 7.8547 c. 41: 5 7 5 6 6 5 7 SP D3 S SD: 4.4288 c. M:-10.1215 c. 51: 6 9 6 7 8 6 9 SP SD: 4.3681 c. M: 7.8547 c. 53: 6 9 7 7 8 7 9 SP SD: 5.6091 c. M: 7.7853 c. 58: 7 10 7 8 9 7 10 SP SD: 2.4047 c. M:-4.3162 c. 65: 8 11 8 9 10 8 11 SP SD: 2.5769 c. M:-4.1944 c. 94: 11 16 12 13 14 12 16 SP SD: 1.9289 c. M: 3.0724 c. 101: 12 17 13 14 15 13 17 SP SD: 1.7926 c. M: 2.8535 c. 111: 13 19 14 15 17 14 19 SP SD: 2.1196 c. M: 3.5898 c. 118: 14 20 15 16 18 15 20 SP SD: 1.2165 c. M: 2.0323 c. 152: 18 26 19 21 23 19 26 SP SD: 0.8241 c. M: 1.3927 c. 159: 19 27 20 22 24 20 27 SP SD: 0.4364 c. M:-1.1017 c. 183: 22 31 23 25 28 23 31 SP SD: 0.5169 c. M:-0.7644 c. 277: 33 47 35 38 42 35 47 SP SD: 0.4826 c. M: 0.8375 c. 311: 37 53 39 43 47 39 53 SP SD: 0.4728 c. M: 0.7327 c. 335: 40 57 42 46 51 42 57 SP SD: 0.1991 c. M: 0.3627 c. 494: 59 84 62 68 75 62 84 SP SD: 0.1075 c. M: 0.1781 c. 677: 81 115 85 93 103 85 115 SP SD: 0.0646 c. M: 0.1246 c. 836: 100 142 105 115 127 105 142 SP SD: 0.0581 c. M:-0.1087 c. 1171: 140 199 147 161 178 147 199 SP SD: 0.0196 c. M: 0.0308 c. 2007: 240 341 252 276 305 252 341 SP SD: 0.0181 c. M:-0.0300 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: 19.4529 cents 3 x x 4 x 5 x 6 S SD: 12.9686 cents 4 x 5 x 6 x 7:8 S SD: 15.3514 cents 5 x 6 x 7:8:9:10 S SD: 18.9388 cents 6 x 7:8:9:10:11:12 S SD: 18.5229 cents 7:8 x 9:10:11:12:14 S SD: 24.5262 cents 8:9:10:11:12:13:14:16 S SD: 14.4861 cents 9:10:11:12:13:15:16:18 SD: 8.7201 cents 13:14:16:17:19:21:23:26 SD: 6.1347 cents 21:23:26:28:31:34:37:42 SD: 4.9255 cents 22:24:27:29:32:36:39:44 SD: 3.9771 cents 24:26:29:32:35:39:43:48 SD: 3.8301 cents 27:29:33:36:40:44:48:54 SD: 3.7640 cents 32:35:39:43:47:52:57:64 SD: 2.7958 cents 36:39:44:48:53:59:64:72 SD: 1.8256 cents 45:49:55:60:66:73:80:90 SD: 1.2589 cents 81:88:99:108:119:132:144:162 SD: 0.4160 cents 208:226:254:277:305:339:370:416 SD: 0.4021 cents 216:235:264:288:317:352:384:432 SD: 0.3842 cents 221:240:270:295:324:360:393:442 SD: 0.3528 cents 234:254:286:312:343:381:416:468 SD: 0.3381 cents 243:264:297:324:356:396:432:486 SD: 0.2777 cents 279:303:341:372:409:455:496:558 SD: 0.2360 cents 315:342:385:420:462:513:560:630 SD: 0.2272 cents 324:352:396:432:475:528:576:648 SD: 0.1041 cents 405:440:495:540:594:660:720:810 SD: 0.0000 cents