Scala analysis: xen09-wilson-marwa-10-01
Marwa permutation 1 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: 81/64 407.820003 Pythagorean major third 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major sixth 6: 99/56 986.402038 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 112/99 213.5980 1: 9/8 203.9100 major whole tone 2: 9/8 203.9100 major whole tone 3: 88/81 143.4979 2nd undecimal neutral second 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 9/8 203.9100 major whole tone 6: 22/21 80.5370 undecimal minor semitone 7: 112/99 213.5980
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 : 203.9 407.8 551.3 702.0 905.9 986.4 1200.0 203.9 : 203.9 347.4 498.0 702.0 782.5 996.1 1200.0 407.8 : 143.5 294.1 498.0 578.6 792.2 996.1 1200.0 551.3 : 150.6 354.5 435.1 648.7 852.6 1056.5 1200.0 702.0 : 203.9 284.4 498.0 702.0 905.9 1049.4 1200.0 905.9 : 80.5 294.1 498.0 702.0 845.5 996.1 1200.0 986.4 : 213.6 417.5 621.4 764.9 915.6 1119.5 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 : 173.77901 cents, oct.: 1216.45305 cents Scale is not proper Step pattern alph. order: AABCADE Step pattern size order : DDBCDAE Scale is sum-free (all different intervals) 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 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% -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.021676 Average absolute harmonicity : 0.230063 Specific harmonicity : 0.128381 Fundamental : 1/448, -8.8074 octaves, 0.5840 Hz. Guide tone : 1782, 10.7993 octaves, 466216.757 Hz. Exponens Consonantiae : 7.983360E+05, 19.60664 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 193.5, average 27.64286 Mersenne's string divisions : 187293165 Sum of van Prooijen's expressibility: 7.80824, average 1.11546 Sum of Tenney's harmonic distance : 14.97497, average 2.13928 Vogel's harmonic complexity : 17.57143 Wille's k value : 283 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 98.87969, average 3.53142 Lattice compactness (without 2's) : 57.39852, average 2.04995 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -6 .. 1 -2.71429 21 1 3: 0 .. 4 1.71429 12 4 7: -1 .. 0 -0.14286 1 11: 0 .. 1 0.28571 2 2 Average exponent except 2's : 13 / 7 = 1.85714 Average absolute exponent except 2's: 15 / 7 = 2.14286 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: 39.7536 c. M: 64.9629 c. Lebeng 9: 1 2 1 1 2 0 2 N D3 SD: 38.1383 c. M: 70.5767 c. 11: 2 2 1 1 2 1 2 N D3 SD: 25.1271 c. M: 47.4095 c. 12: 2 2 2 1 2 1 2 P D3 S SD: 19.5284 c. M:-48.6821 c. Lydian Dominant, Mela Vacaspati, Raga Bhusavati, Bhusavali, Vachaspati, Overtone, Lydian-Mixolydian, Bartok 13: 2 2 2 2 2 1 2 SP M ME S SD: 24.8905 c. M: 38.5892 c. Karakalian 15: 3 2 2 2 2 1 3 N SD: 21.1481 c. M:-36.0900 c. 17: 3 3 2 2 3 1 3 N SD: 9.6015 c. M:-15.7094 c. 24: 4 4 3 3 4 2 4 P SD: 6.5607 c. M:-13.5980 c. 29: 5 5 3 4 5 2 5 N SD: 6.4477 c. M: 13.3869 c. 41: 7 7 5 5 7 3 7 N SD: 3.8897 c. M:-8.7199 c. 57: 10 9 7 7 10 4 10 N SD: 5.1050 c. M: 7.8200 c. 58: 10 10 7 7 10 4 10 N SD: 4.8570 c. M:-7.3027 c. 61: 10 11 7 8 10 4 11 N SD: 4.2700 c. M: 7.1887 c. 65: 11 11 8 8 11 4 12 N SD: 3.2656 c. M: 7.9405 c. 74: 13 12 9 9 13 5 13 N SD: 3.5445 c. M:-6.9008 c. 77: 13 13 9 10 13 5 14 N SD: 3.1239 c. M: 5.8634 c. 82: 14 14 10 10 14 5 15 N SD: 3.0438 c. M: 5.9142 c. 89: 15 15 11 11 15 6 16 N SD: 1.9823 c. M: 3.3256 c. 94: 16 16 11 12 16 6 17 N SD: 1.6163 c. M: 3.4233 c. 106: 18 18 13 13 18 7 19 N SD: 1.4108 c. M:-3.3990 c. 111: 19 19 13 14 19 7 20 N SD: 1.8372 c. M:-2.9908 c. 118: 20 20 14 15 20 8 21 N SD: 0.9798 c. M: 2.1654 c. 135: 23 23 16 17 23 9 24 N SD: 0.5676 c. M:-1.0689 c. 224: 38 38 27 28 38 15 40 N SD: 0.4708 c. M: 0.6878 c. 253: 43 43 30 32 43 17 45 N SD: 0.4300 c. M: 1.1203 c. 342: 58 58 41 43 58 23 61 N SD: 0.4770 c. M: 0.8025 c. 359: 61 61 43 45 61 24 64 N SD: 0.1489 c. M: 0.3296 c. 494: 84 84 59 62 84 33 88 N SD: 0.1612 c. M:-0.2772 c. 612: 104 104 73 77 104 41 109 N SD: 0.1369 c. M: 0.3376 c. 742: 126 126 89 93 126 50 132 N SD: 0.1609 c. M: 0.2728 c. 836: 142 142 100 105 142 56 149 N SD: 0.1428 c. M: 0.2776 c. 853: 145 145 102 107 145 57 152 N SD: 0.1312 c. M: 0.2356 c. 877: 149 149 105 110 149 59 156 N SD: 0.0758 c. M:-0.1430 c. 1012: 172 172 121 127 172 68 180 N SD: 0.0786 c. M:-0.1592 c. 1236: 210 210 148 155 210 83 220 N SD: 0.0591 c. M:-0.1384 c. 1371: 233 233 164 172 233 92 244 N SD: 0.0508 c. M:-0.1044 c. 1489: 253 253 178 187 253 100 265 N SD: 0.0345 c. M: 0.0755 c. 1848: 314 314 221 232 314 124 329 N SD: 0.0217 c. M: 0.0384 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: 19.1501 cents 4 x 5 x 6 x 7:8 S SD: 6.9437 cents 5 x 6:7 x 8:9:10 S SD: 27.5245 cents 6:7 x 8:9:10:11:12 S SD: 17.6609 cents 7:8:9:10:11:12 x 14 S SD: 19.0720 cents 8:9:10:11:12 x 14:16 S SD: 4.6291 cents 11:12:14:15:17 x 19:22 SD: 14.3623 cents 12:14:15:17:18:20:21:24 SD: 12.6726 cents 13:15:16:18:20:22:23:26 SD: 11.3851 cents 14:16:18:19:21:24:25:28 SD: 7.8829 cents 16:18:20:22:24:27:28:32 S SD: 3.9678 cents 22:25:28:30:33:37:39:44 SD: 3.6695 cents 26:29:33:36:39:44:46:52 SD: 2.9162 cents 34:38:43:47:51:57:60:68 SD: 2.6883 cents 38:43:48:52:57:64:67:76 SD: 2.0942 cents 42:47:53:58:63:71:74:84 SD: 2.0685 cents 48:54:61:66:72:81:85:96 SD: 1.0976 cents 64:72:81:88:96:108:113:128 SD: 0.3125 cents 176:198:223:242:264:297:311:352 SD: 0.2998 cents 240:270:304:330:360:405:424:480 SD: 0.2630 cents 256:288:324:352:384:432:453:512 SD: 0.2341 cents 272:306:344:374:408:459:481:544 SD: 0.1941 cents 320:360:405:440:480:540:566:640 SD: 0.1249 cents 384:432:486:528:576:648:679:768 SD: 0.0520 cents 448:504:567:616:672:756:792:896 SD: 0.0000 cents