Scala analysis: xen09-wilson-marwa-10-09
Marwa permutation 9 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: 11/8 551.317942 undecimal semi-augmented fourth 4: 3/2 701.955001 perfect fifth 5: 11/7 782.492036 undecimal augmented fifth 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: 9/8 203.9100 major whole tone 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 22/21 80.5370 undecimal minor semitone 6: 7/6 266.8709 septimal minor third 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 22/21 80.537 cents undecimal minor semitone 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 7/6 266.871 cents septimal minor third 2: 2 8/7 231.174 cents septimal whole tone 2: 2 11/9 347.408 cents undecimal neutral third 2: 1 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 2: 1 21/16 470.781 cents narrow fourth 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 32/21 729.219 cents wide fifth 5: 1 11/7 782.492 cents undecimal augmented fifth 5: 1 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 2 7/4 968.826 cents harmonic seventh 6: 2 12/7 933.129 cents septimal major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 2 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 : 80.5 347.4 551.3 702.0 782.5 1049.4 1200.0 80.5 : 266.9 470.8 621.4 702.0 968.8 1119.5 1200.0 347.4 : 203.9 354.5 435.1 702.0 852.6 933.1 1200.0 551.3 : 150.6 231.2 498.0 648.7 729.2 996.1 1200.0 702.0 : 80.5 347.4 498.0 578.6 845.5 1049.4 1200.0 782.5 : 266.9 417.5 498.0 764.9 968.8 1119.5 1200.0 1049.4: 150.6 231.2 498.0 702.0 852.6 933.1 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 .. 470.7809 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 3: 435.0841 .. 621.4180 cents 49/44, 186.3339 cents 48/49,-35.6968 cents 4: 578.5820 .. 764.9159 cents 49/44, 186.3339 cents 3872/3969,-42.8359 cents 5: 729.2191 .. 968.8259 cents 147/128, 239.6068 cents 48/49,-35.6968 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 : 170.32689 cents, oct.: 1192.28823 cents Scale is not proper Step pattern alph. order: ABCDABD Step pattern size order : ADCBADB Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.575227 Lumma stability : 0.134228 Lumma impropriety factor : 0.154686 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 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 Number of recognisable fifths : 4, average 701.9550 cents Scale is Hypolydian octave species of abstract tetrachord All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 63 (O: 63 U: 63) Highest odd numerator or denominator: 21 Scale harmonicity : 0.024711 Average absolute harmonicity : 0.210640 Specific harmonicity : 0.124395 Fundamental : 1/504, -8.9773 octaves, 0.5191 Hz. Guide tone : 66, 6.0444 octaves, 17267.287 Hz. Exponens Consonantiae : 3.326400E+04, 15.02167 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 62.5, average 8.92857 Mersenne's string divisions : 2500020 Sum of van Prooijen's expressibility: 5.96491, average 0.85213 Sum of Tenney's harmonic distance : 11.38998, average 1.62714 Vogel's harmonic complexity : 20.14286 Wille's k value : 346 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 64.85674, average 2.31631 Lattice compactness (without 2's) : 42.06590, average 1.50235 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.42857 7 1 3: -2 .. 1 -0.42857 5 1 7: -1 .. 0 -0.28571 2 11: 0 .. 1 0.71429 5 5 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 22 26| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 20 23| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 0 2 1 1 0 2 1 N T3 SD: 50.6251 c. M: 96.7778 c. 9: 1 2 1 1 1 2 1 P M ME I SD: 33.2266 c. M:-52.7963 c. 11: 1 2 2 1 1 3 1 N D3 S SD: 28.2449 c. M: 47.4095 c. 13: 1 3 2 2 1 2 2 N T3 SD: 27.8750 c. M:-48.2772 c. 14: 1 3 2 2 1 3 2 P T3 SD: 17.8780 c. M: 37.0322 c. 15: 1 3 3 2 1 3 2 N SD: 14.8645 c. M: 27.4079 c. 17: 1 4 3 2 1 4 2 N SD: 8.0180 c. M:-13.3879 c. 31: 2 7 5 4 2 7 4 N SD: 5.5041 c. M: 9.3825 c. 41: 3 9 7 5 3 9 5 N SD: 4.9131 c. M:-7.7519 c. 46: 3 10 8 6 3 10 6 N SD: 4.2470 c. M: 8.2775 c. 48: 3 11 8 6 3 11 6 N SD: 3.7697 c. M: 7.4920 c. 55: 4 12 9 7 4 12 7 N SD: 3.9635 c. M:-6.7357 c. 58: 4 13 10 7 4 13 7 N SD: 4.2540 c. M:-7.3027 c. 63: 4 14 11 8 4 14 8 N SD: 2.7780 c. M: 4.5508 c. 72: 5 16 12 9 5 16 9 N SD: 1.7407 c. M:-2.7963 c. 89: 6 20 15 11 6 20 11 N SD: 1.6304 c. M:-3.1539 c. 104: 7 23 18 13 7 23 13 N SD: 1.5357 c. M:-2.5282 c. 118: 8 26 20 15 8 26 15 N SD: 1.3135 c. M: 2.1654 c. 135: 9 30 23 17 9 30 17 N SD: 0.4225 c. M: 0.7413 c. 207: 14 46 35 26 14 46 26 N SD: 0.4125 c. M:-0.6224 c. 311: 21 69 53 39 21 69 39 N SD: 0.4135 c. M:-0.7877 c. 342: 23 76 58 43 23 76 43 N SD: 0.2145 c. M: 0.4407 c. 359: 24 80 61 45 24 80 45 N SD: 0.2220 c. M: 0.3193 c. 477: 32 106 81 60 32 106 60 N SD: 0.2094 c. M: 0.3745 c. 494: 33 110 84 62 33 110 62 N SD: 0.1895 c. M: 0.3751 c. 566: 38 126 96 71 38 126 71 N SD: 0.1545 c. M:-0.2952 c. 670: 45 149 114 84 45 149 84 N SD: 0.1704 c. M:-0.3238 c. 701: 47 156 119 88 47 156 88 N SD: 0.0997 c. M: 0.1811 c. 836: 56 186 142 105 56 186 105 N SD: 0.1112 c. M: 0.1954 c. 940: 63 209 160 118 63 209 118 N SD: 0.1228 c. M: 0.1739 c. 1012: 68 225 172 127 68 225 127 N SD: 0.0654 c. M:-0.1167 c. 1147: 77 255 195 144 77 255 144 N SD: 0.0446 c. M:-0.0712 c. 1506: 101 335 256 189 101 335 189 N SD: 0.0427 c. M:-0.0765 c. 1713: 115 381 291 215 115 381 215 N SD: 0.0261 c. M:-0.0527 c. 1848: 124 411 314 232 124 411 232 N SD: 0.0147 c. M: 0.0245 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: 38.3186 cents 4 x 5 x 6 x 7:8 S SD: 22.3605 cents 5 x 6:7 x 8:9:10 S SD: 12.5927 cents 6 x 7:8:9 x 11:12 SD: 19.3124 cents 7 x 9:10 x 11:13:14 SD: 22.4184 cents 8:9:10:11:12:13:15:16 SD: 21.0036 cents 9:10:11:12 x 14:17:18 SD: 21.2098 cents 10:11:12:14:15:16:18:20 S SD: 15.0503 cents 11:12:13:15 x 17:20:22 SD: 16.2843 cents 12:13:15:17:18:19:22:24 SD: 12.5549 cents 13:14:16:18 x 20:24:26 S SD: 10.6264 cents 14:15:17:19:21:22:26:28 SD: 7.3569 cents 16:17:20:22:24:25:29:32 SD: 7.2825 cents 18:19:22:25:27:28:33:36 SD: 3.9959 cents 24:25:29:33:36:38:44:48 SD: 3.6687 cents 35:37:43:48:53:55:64:70 SD: 3.6020 cents 37:39:45:51:56:58:68:74 SD: 3.1313 cents 40:42:49:55:60:63:73:80 SD: 1.4884 cents 64:67:78:88:96:101:117:128 SD: 1.4584 cents 72:75:88:99:108:113:132:144 SD: 1.4435 cents 80:84:98:110:120:126:147:160 SD: 1.1229 cents 82:86:100:113:123:129:150:164 SD: 1.0262 cents 86:90:105:118:129:135:158:172 SD: 0.8672 cents 104:109:127:143:156:163:191:208 SD: 0.8166 cents 122:128:149:168:183:192:224:244 SD: 0.7593 cents 126:132:154:173:189:198:231:252 SD: 0.3571 cents 208:218:254:286:312:327:381:416 SD: 0.3419 cents 234:245:286:322:351:368:429:468 SD: 0.3075 cents 270:283:330:371:405:424:495:540 SD: 0.2667 cents 296:310:362:407:444:465:543:592 SD: 0.2401 cents 336:352:411:462:504:528:616:672 SD: 0.2007 cents 360:377:440:495:540:566:660:720 SD: 0.1561 cents 378:396:462:520:567:594:693:756 SD: 0.1189 cents 504:528:616:693:756:792:924:1008 S SD: 0.0000 cents