Scala analysis: xen09-wilson-marwa-10-16
Marwa permutation 16 from Figure 10, Ptolemy 7/6 12/11 22/21
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22/21 80.537035 undecimal minor semitone 2: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 44/27 845.452940 neutral sixth 6: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 22/21 80.5370 undecimal minor semitone 2: 7/6 266.8709 septimal minor third 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 9/8 203.9100 major whole tone 5: 88/81 143.4979 2nd undecimal neutral second 6: 9/8 203.9100 major whole tone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 22/21 80.537 cents undecimal minor semitone 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: 2 9/8 203.910 cents major whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 3 11/9 347.408 cents undecimal neutral third 2: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 9/7 435.084 cents septimal major third, BP third 3: 4 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 63/44 621.418 cents 4: 1 88/63 578.582 cents 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 14/9 764.916 cents septimal minor sixth 5: 1 11/7 782.492 cents undecimal augmented fifth 5: 2 44/27 845.453 cents neutral sixth 5: 3 18/11 852.592 cents undecimal neutral sixth 5: 1 7/4 968.826 cents harmonic seventh 6: 1 12/7 933.129 cents septimal major sixth 6: 2 16/9 996.090 cents Pythagorean 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 6: 1 21/11 1119.463 cents undecimal major 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 : 80.5 347.4 498.0 702.0 845.5 1049.4 1200.0 80.5 : 266.9 417.5 621.4 764.9 968.8 1119.5 1200.0 347.4 : 150.6 354.5 498.0 702.0 852.6 933.1 1200.0 498.0 : 203.9 347.4 551.3 702.0 782.5 1049.4 1200.0 702.0 : 143.5 347.4 498.0 578.6 845.5 996.1 1200.0 845.5 : 203.9 354.5 435.1 702.0 852.6 1056.5 1200.0 1049.4: 150.6 231.2 498.0 648.7 852.6 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 266.8709 cents 49/44, 186.3339 cents 22/21, 80.5370 cents 2: 231.1741 .. 417.5080 cents 49/44, 186.3339 cents 48/49,-35.6968 cents 3: 435.0841 .. 621.4180 cents 49/44, 186.3339 cents 99/98, 17.5761 cents 4: 578.5820 .. 764.9159 cents 49/44, 186.3339 cents 3872/3969,-42.8359 cents 5: 782.4920 .. 968.8259 cents 49/44, 186.3339 cents 99/98, 17.5761 cents 6: 933.1291 .. 1119.4630 cents 49/44, 186.3339 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 2.128568 Largest / Average step : 1.556747 Largest / Smallest step : 3.313642 Median interval of one step : 12/11, 150.6371 cents, amount: 2 Least squares average step : 171.43393 cents, oct.: 1200.03751 cents Scale is not proper Step pattern alph. order: ABCDEDC Step pattern size order : AECDBDC Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.559442 Lumma stability : 0.163522 Lumma impropriety factor : 0.095191 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 Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.023734 Average absolute harmonicity : 0.234558 Specific harmonicity : 0.124940 Fundamental : 1/378, -8.5622 octaves, 0.6921 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 4.989600E+04, 15.60664 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 83.0, average 11.85714 Mersenne's string divisions : 21798420 Sum of van Prooijen's expressibility: 5.79061, average 0.82723 Sum of Tenney's harmonic distance : 11.71300, average 1.67329 Vogel's harmonic complexity : 19.85714 Wille's k value : 346 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 68.63086, average 2.45110 Lattice compactness (without 2's) : 49.77494, average 1.77768 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 8 1 3: -3 .. 1 -1.00000 9 2 7: -1 .. 0 -0.14286 1 11: 0 .. 1 0.57143 4 4 Average exponent except 2's :-4 / 7 =-0.57143 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is weakly epimorphic with val: <7 10 18 22| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 0 2 1 1 1 1 1 N T3 SD: 32.9575 c. M: 80.5370 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 21.8289 c. M:-39.4630 c. 13: 1 3 1 3 1 2 2 N D3 S SD: 25.7748 c. M:-36.5065 c. 14: 1 3 2 2 2 2 2 P T3 SD: 12.7838 c. M: 20.7915 c. 17: 1 4 2 3 2 3 2 N SD: 6.0062 c. M: 9.9488 c. 31: 2 7 4 5 4 5 4 N SD: 4.1397 c. M:-6.1600 c. 41: 3 9 5 7 5 7 5 N SD: 3.7291 c. M:-7.2678 c. 48: 3 11 6 8 6 8 6 N SD: 3.0730 c. M: 5.5370 c. 58: 4 13 7 10 7 10 7 N SD: 3.1565 c. M:-5.8095 c. 70: 5 15 9 12 8 12 9 N SD: 3.6290 c. M: 5.4529 c. 72: 5 16 9 12 9 12 9 N SD: 2.4861 c. M:-4.5471 c. 87: 6 19 11 15 10 15 11 N SD: 2.1984 c. M: 4.0736 c. 89: 6 20 11 15 11 15 11 N SD: 2.1625 c. M:-3.9853 c. 94: 6 21 12 16 11 16 12 N SD: 2.3288 c. M: 3.9413 c. 101: 7 22 13 17 12 17 13 N SD: 2.2385 c. M: 3.8184 c. 104: 7 23 13 18 12 18 13 N SD: 1.6509 c. M: 3.1452 c. 118: 8 26 15 20 14 20 15 N SD: 1.1378 c. M: 1.9053 c. 135: 9 30 17 23 16 23 17 N SD: 0.5635 c. M: 1.0085 c. 207: 14 46 26 35 25 35 26 N SD: 0.5258 c. M:-0.9239 c. 294: 20 65 37 50 35 50 37 N SD: 0.5196 c. M:-1.0956 c. 301: 20 67 38 51 36 51 38 N SD: 0.5271 c. M: 0.8580 c. 311: 21 69 39 53 37 53 39 N SD: 0.3051 c. M:-0.4919 c. 342: 23 76 43 58 41 58 43 N SD: 0.1660 c. M: 0.2401 c. 477: 32 106 60 81 57 81 60 N SD: 0.1647 c. M: 0.3063 c. 494: 33 110 62 84 59 84 62 N SD: 0.1533 c. M: 0.3751 c. 653: 44 145 82 111 78 111 82 N SD: 0.1368 c. M:-0.3205 c. 670: 45 149 84 114 80 114 84 N SD: 0.1102 c. M:-0.1893 c. 701: 47 156 88 119 84 119 88 N SD: 0.1030 c. M:-0.1961 c. 836: 56 186 105 142 100 142 105 N SD: 0.0710 c. M: 0.1543 c. 1012: 68 225 127 172 121 172 127 N SD: 0.0422 c. M:-0.0954 c. 1371: 92 305 172 233 164 233 172 N SD: 0.0509 c. M:-0.0900 c. 1489: 100 331 187 253 178 253 187 N SD: 0.0450 c. M: 0.0681 c. 1506: 101 335 189 256 180 256 189 N SD: 0.0358 c. M: 0.0589 c. 1713: 115 381 215 291 205 291 215 N SD: 0.0416 c. M:-0.0812 c. 1848: 124 411 232 314 221 314 232 N SD: 0.0092 c. M: 0.0176 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 12.9686 cents 4 x 5 x 6 x 7:8 S SD: 22.3605 cents 5 x 6:7 x 8:9:10 S SD: 20.1614 cents 6 x 7:8:9:10:11:12 S SD: 14.9070 cents 7 x x 9 x 11:13:14 SD: 22.9499 cents 8:9:10:11:12:13:15:16 SD: 20.7563 cents 9:10:11:12:14:15:17:18 SD: 19.4441 cents 10:11:12:13:15:16:18:20 SD: 15.7034 cents 12:13:15:16:18:20:22:24 SD: 11.4245 cents 13:14:16:17:20:21:24:26 SD: 10.9307 cents 14:15:17:19:21:23:26:28 SD: 8.1750 cents 16:17:20:21:24:26:29:32 SD: 8.1679 cents 17:18:21:23:26:28:31:34 SD: 7.6568 cents 18:19:22:24:27:29:33:36 SD: 3.3872 cents 24:25:29:32:36:39:44:48 SD: 3.2358 cents 36:38:44:48:54:59:66:72 SD: 2.3340 cents 40:42:49:53:60:65:73:80 SD: 2.1908 cents 46:48:56:61:69:75:84:92 SD: 2.1702 cents 48:50:59:64:72:78:88:96 SD: 2.1082 cents 54:57:66:72:81:88:99:108 SD: 1.8666 cents 60:63:73:80:90:98:110:120 SD: 1.3784 cents 78:82:95:104:117:127:143:156 SD: 1.2419 cents 84:88:103:112:126:137:154:168 SD: 0.8264 cents 102:107:125:136:153:166:187:204 SD: 0.8092 cents 108:113:132:144:162:176:198:216 SD: 0.3125 cents 234:245:286:312:351:381:429:468 SD: 0.2599 cents 252:264:308:336:378:411:462:504 SD: 0.2007 cents 270:283:330:360:405:440:495:540 SD: 0.1249 cents 378:396:462:504:567:616:693:756 SD: 0.0000 cents