Scala analysis: xen09-wilson-marwa-10-11
Marwa permutation 11 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: 9/8 203.910002 major whole tone 2: 33/28 284.447037 undecimal minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major 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: 9/8 203.9100 major whole tone 2: 22/21 80.5370 undecimal minor semitone 3: 112/99 213.5980 4: 9/8 203.9100 major whole tone 5: 9/8 203.9100 major whole tone 6: 88/81 143.4979 2nd undecimal neutral second 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: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 3 9/8 203.910 cents major whole tone 1: 1 112/99 213.598 cents 2: 1 33/28 284.447 cents undecimal minor third 2: 2 32/27 294.135 cents Pythagorean minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 81/64 407.820 cents Pythagorean major third 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: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 44/27 845.453 cents neutral sixth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 5: 1 56/33 915.553 cents 6: 1 99/56 986.402 cents 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 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: 6 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 284.4 498.0 702.0 905.9 1049.4 1200.0 203.9 : 80.5 294.1 498.0 702.0 845.5 996.1 1200.0 284.4 : 213.6 417.5 621.4 764.9 915.6 1119.5 1200.0 498.0 : 203.9 407.8 551.3 702.0 905.9 986.4 1200.0 702.0 : 203.9 347.4 498.0 702.0 782.5 996.1 1200.0 905.9 : 143.5 294.1 498.0 578.6 792.2 996.1 1200.0 1049.4: 150.6 354.5 435.1 648.7 852.6 1056.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 213.5980 cents 392/363, 133.0609 cents 22/21, 80.5370 cents 2: 284.4470 .. 417.5080 cents 392/363, 133.0609 cents 3267/3136, 70.8491 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 .. 915.5530 cents 392/363, 133.0609 cents 99/98, 17.5761 cents 6: 986.4020 .. 1119.4630 cents 392/363, 133.0609 cents 3267/3136, 70.8491 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 : 112/99, 213.5980 cents Average / Smallest step : 2.128568 Largest / Average step : 1.245988 Largest / Smallest step : 2.652171 Median interval of one step : 9/8, 203.9100 cents, amount: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 173.57330 cents, oct.: 1215.01309 cents Scale is not proper Step pattern alph. order: ABCAADE Step pattern size order : DAEDDBC Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.582054 Lumma stability : 0.281604 Lumma impropriety factor : 0.035697 Rothenberg efficiency : 0.383673 redundancy: 0.616327 Efficiency x scale size : 2.685714 Number of different interval sizes : 30 = 5.00000 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.00000 = 5 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: 3 Number of recognisable fifths : 4, average 701.9550 cents Best major thirds form a closed circle Best minor thirds 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% -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 33 Scale harmonicity : 0.022156 Average absolute harmonicity : 0.252328 Specific harmonicity : 0.132364 Fundamental : 1/336, -8.3923 octaves, 0.7786 Hz. Guide tone : 1188, 10.2143 octaves, 310811.172 Hz. Exponens Consonantiae : 3.991680E+05, 18.60664 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 76.5, average 10.92857 Mersenne's string divisions : 4682055 Sum of van Prooijen's expressibility: 5.89976, average 0.84282 Sum of Tenney's harmonic distance : 11.43639, average 1.63377 Vogel's harmonic complexity : 17.14286 Wille's k value : 283 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 89.67729, average 3.20276 Lattice compactness (without 2's) : 54.09529, average 1.93197 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.14286 14 1 3: -1 .. 3 0.71429 9 4 7: -1 .. 0 -0.14286 1 11: 0 .. 1 0.28571 2 2 Average exponent except 2's : 6 / 7 = 0.85714 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 12 19 25| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 33.3819 c. M:-58.4101 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 33.3801 c. M: 53.9100 c. 9: 2 0 2 1 2 1 1 N D3 SD: 33.3788 c. M:-62.7567 c. 10: 2 0 2 2 2 1 1 N SD: 33.3777 c. M:-54.1350 c. 12: 2 1 2 2 2 1 2 P M ME I SD: 19.7698 c. M: 49.3629 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 14: 2 1 3 2 2 2 2 P T3 SD: 27.0825 c. M: 48.7221 c. 16: 3 1 3 2 3 2 2 P D3 SD: 17.6256 c. M:-26.9550 c. 17: 3 1 3 3 3 2 2 N SD: 6.8165 c. M:-11.7821 c. Altered Melodic Minor 24: 4 2 4 4 4 3 3 P SD: 6.5425 c. M:-15.5530 c. 29: 5 2 5 5 5 3 4 N SD: 6.3470 c. M: 14.8802 c. 37: 6 3 6 7 6 4 5 N SD: 8.8420 c. M:-11.5585 c. 38: 6 3 7 6 7 4 5 N SD: 8.1402 c. M: 14.4363 c. 41: 7 3 7 7 7 5 5 N SD: 3.5816 c. M:-8.2359 c. 46: 8 3 8 8 8 5 6 N SD: 4.2563 c. M:-7.1785 c. 58: 10 4 10 10 10 7 7 N SD: 3.6708 c. M:-5.8095 c. 65: 11 4 12 11 11 8 8 N SD: 3.1141 c. M: 7.5240 c. 72: 12 5 13 12 12 9 9 N SD: 2.9026 c. M: 5.8650 c. 77: 13 5 14 13 13 9 10 N SD: 2.6458 c. M: 5.2071 c. 89: 15 6 16 15 15 11 11 N SD: 1.5791 c. M: 2.4942 c. 94: 16 6 17 16 16 11 12 N SD: 1.6862 c. M: 3.5960 c. 106: 18 7 19 18 18 13 13 N SD: 1.4208 c. M:-3.4672 c. 118: 20 8 21 20 20 14 15 N SD: 0.8224 c. M: 1.9053 c. 135: 23 9 24 23 23 16 17 N SD: 0.4303 c. M:-0.8017 c. 224: 38 15 40 38 38 27 28 N SD: 0.3972 c. M:-0.6371 c. 342: 58 23 61 58 58 41 43 N SD: 0.3201 c. M: 0.6018 c. 359: 61 24 64 61 61 43 45 N SD: 0.1482 c. M: 0.3245 c. 477: 81 32 85 81 81 57 60 N SD: 0.1659 c. M: 0.3063 c. 494: 84 33 88 84 84 59 62 N SD: 0.1357 c. M: 0.2365 c. 742: 126 50 132 126 126 89 93 N SD: 0.1510 c. M:-0.2327 c. 836: 142 56 149 142 142 100 105 N SD: 0.1120 c. M: 0.2365 c. 877: 149 59 156 149 149 105 110 N SD: 0.0801 c. M:-0.1596 c. 1012: 172 68 180 172 172 121 127 N SD: 0.0630 c. M:-0.1379 c. 1236: 210 83 220 210 210 148 155 N SD: 0.0609 c. M:-0.1516 c. 1354: 230 91 241 230 230 162 170 N SD: 0.0545 c. M: 0.1043 c. 1371: 233 92 244 233 233 164 172 N SD: 0.0405 c. M:-0.0900 c. 1489: 253 100 265 253 253 178 187 N SD: 0.0316 c. M: 0.0681 c. 1848: 314 124 329 314 314 221 232 N SD: 0.0163 c. M: 0.0315 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: 7.1688 cents 4 x 5 x 6:7 x 8 S SD: 29.9384 cents 5 x 6:7 x 8:9:10 S SD: 26.5434 cents 6 x 7:8:9:10:11:12 S SD: 4.6291 cents 7:8 x 9:11:12:13:14 SD: 18.5861 cents 8:9 x 11:12:14:15:16 SD: 15.1984 cents 10:11:12:13:15:17:18:20 SD: 10.6716 cents 12 x 14:16:18:20:22:24 S SD: 4.6291 cents 13 x 15:17:20:22:24:26 SD: 11.2650 cents 14:16:17:19:21:24:26:28 SD: 10.6863 cents 15:17:18:20:23:25:28:30 SD: 9.0574 cents 16:18:19:21:24:27:29:32 SD: 5.1617 cents 18:20:21:24:27:30:33:36 S SD: 5.0183 cents 22:25:26:29:33:37:40:44 SD: 4.4203 cents 24:27:28:32:36:41:44:48 SD: 3.9387 cents 30:34:35:40:45:51:55:60 SD: 3.6010 cents 32:36:38:43:48:54:59:64 SD: 3.0252 cents 38:43:45:51:57:64:70:76 SD: 2.7803 cents 40:45:47:53:60:68:73:80 SD: 2.7511 cents 46:52:54:61:69:78:84:92 SD: 2.5645 cents 48:54:57:64:72:81:88:96 SD: 1.8666 cents 54:61:64:72:81:91:99:108 SD: 1.7499 cents 66:74:78:88:99:111:121:132 SD: 1.3618 cents 72:81:85:96:108:122:132:144 SD: 1.0976 cents 78:88:92:104:117:132:143:156 SD: 1.0134 cents 90:101:106:120:135:152:165:180 SD: 0.6656 cents 96:108:113:128:144:162:176:192 SD: 0.3125 cents 240:270:283:320:360:405:440:480 SD: 0.1249 cents 336:378:396:448:504:567:616:672 SD: 0.0000 cents