Scala analysis: xen09-wilson-marwa-10-14
Marwa permutation 14 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: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect 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: 9/8 203.9100 major whole tone 2: 88/81 143.4979 2nd undecimal neutral second 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 9/8 203.9100 major whole 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: 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 33/28 284.447 cents undecimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 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: 2 18/11 852.592 cents undecimal neutral sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 56/33 915.553 cents 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 347.4 498.0 702.0 782.5 1049.4 1200.0 203.9 : 143.5 294.1 498.0 578.6 845.5 996.1 1200.0 347.4 : 150.6 354.5 435.1 702.0 852.6 1056.5 1200.0 498.0 : 203.9 284.4 551.3 702.0 905.9 1049.4 1200.0 702.0 : 80.5 347.4 498.0 702.0 845.5 996.1 1200.0 782.5 : 266.9 417.5 621.4 764.9 915.6 1119.5 1200.0 1049.4: 150.6 354.5 498.0 648.7 852.6 933.1 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: 284.4470 .. 417.5080 cents 392/363, 133.0609 cents 99/98, 17.5761 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: 933.1291 .. 1119.4630 cents 49/44, 186.3339 cents 99/98, 17.5761 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 : 170.06656 cents, oct.: 1190.46594 cents Scale is not proper Step pattern alph. order: ABCADEC Step pattern size order : DBCDAEC Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.579089 Lumma stability : 0.192815 Lumma impropriety factor : 0.035697 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 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 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: 11 Scale harmonicity : 0.022658 Average absolute harmonicity : 0.247205 Specific harmonicity : 0.127474 Fundamental : 1/504, -8.9773 octaves, 0.5191 Hz. Guide tone : 396, 8.6294 octaves, 103603.724 Hz. Exponens Consonantiae : 1.995840E+05, 17.60664 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 43.5, average 6.21429 Mersenne's string divisions : 21420 Sum of van Prooijen's expressibility: 5.03266, average 0.71895 Sum of Tenney's harmonic distance : 9.71736, average 1.38819 Vogel's harmonic complexity : 19.00000 Wille's k value : 283 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 73.97039, average 2.64180 Lattice compactness (without 2's) : 49.79081, average 1.77824 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.28571 8 1 3: -2 .. 2 -0.14286 7 3 7: -1 .. 0 -0.14286 1 11: 0 .. 1 0.42857 3 3 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is weakly epimorphic with val: <7 10 21 22| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 12 21 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: 32.9682 c. M:-74.6508 c. Lebeng 9: 2 1 1 1 1 2 1 N D3 S SD: 37.4181 c. M:-62.7567 c. 10: 2 1 1 2 1 2 1 P M ME S SD: 30.1380 c. M:-57.5080 c. Sethares Neutral, Beatles-7, Dichotic-7 12: 2 1 2 2 1 2 2 P M ME S SD: 26.7626 c. M: 49.3629 c. G.M.Hypodorian, G.M.Aeolian, G.Hyperphrygian, Natural Minor, Melodic Minor descending, Asavari That, Mela Natabhairavi, Raga Jaunpuri, Adana, Darbari, Dhanyasi, Jingla, Gregorian nr.2, Makam Buselik, Nihavend, Peruvian Minor, Se, Chiao: China, Geez, Ezel: Ethiopia, Kiourdi descending: Greece, Cushak: Armenia 14: 2 2 2 2 1 3 2 P T3 SD: 17.5579 c. M: 32.4814 c. 17: 3 2 2 3 1 4 2 N SD: 5.9632 c. M:-9.4606 c. Turkish Minor 31: 5 4 4 5 2 7 4 N SD: 5.9585 c. M: 10.3616 c. 41: 7 5 5 7 3 9 5 N SD: 3.6738 c. M:-7.7519 c. 48: 8 6 6 8 3 11 6 N SD: 3.5089 c. M: 7.4920 c. 58: 10 7 7 10 4 13 7 N SD: 3.3713 c. M:-5.8095 c. 63: 11 7 8 11 4 14 8 N SD: 3.2380 c. M:-5.6138 c. 65: 11 8 8 11 4 15 8 N SD: 3.1966 c. M: 7.1074 c. 72: 12 9 9 12 5 16 9 N SD: 2.0964 c. M: 3.9100 c. 87: 15 10 11 15 6 19 11 N SD: 2.2367 c. M:-3.7149 c. 89: 15 11 11 15 6 20 11 N SD: 1.6779 c. M:-3.1539 c. 94: 16 11 12 16 6 21 12 N SD: 2.0122 c. M: 3.7686 c. 104: 18 12 13 18 7 23 13 N SD: 1.9981 c. M:-3.7823 c. 106: 18 13 13 18 7 24 13 N SD: 1.9420 c. M:-3.5355 c. 111: 19 13 14 19 7 25 14 N SD: 1.8097 c. M: 4.1137 c. 118: 20 14 15 20 8 26 15 N SD: 1.0039 c. M: 1.9053 c. 135: 23 16 17 23 9 30 17 N SD: 0.4269 c. M: 0.7413 c. 311: 53 37 39 53 21 69 39 N SD: 0.4122 c. M:-0.7877 c. 342: 58 41 43 58 23 76 43 N SD: 0.2077 c. M: 0.4012 c. 359: 61 43 45 61 24 80 45 N SD: 0.1693 c. M: 0.3193 c. 477: 81 57 60 81 32 106 60 N SD: 0.1643 c. M: 0.3063 c. 494: 84 59 62 84 33 110 62 N SD: 0.1335 c. M: 0.3058 c. 629: 107 75 79 107 42 140 79 N SD: 0.1716 c. M: 0.2981 c. 653: 111 78 82 111 44 145 82 N SD: 0.1440 c. M:-0.3564 c. 670: 114 80 84 114 45 149 84 N SD: 0.1627 c. M:-0.2691 c. 701: 119 84 88 119 47 156 88 N SD: 0.1210 c. M: 0.2010 c. 836: 142 100 105 142 56 186 105 N SD: 0.0898 c. M: 0.1954 c. 877: 149 105 110 149 59 195 110 N SD: 0.0984 c. M:-0.1762 c. 1012: 172 121 127 172 68 225 127 N SD: 0.0518 c. M:-0.1167 c. 1147: 195 137 144 195 77 255 144 N SD: 0.0597 c. M:-0.1005 c. 1354: 230 162 170 230 91 301 170 N SD: 0.0450 c. M:-0.0781 c. 1371: 233 164 172 233 92 305 172 N SD: 0.0464 c. M:-0.0900 c. 1489: 253 178 187 253 100 331 187 N SD: 0.0393 c. M: 0.0681 c. 1506: 256 180 189 256 101 335 189 N SD: 0.0383 c. M:-0.0741 c. 1713: 291 205 215 291 115 381 215 N SD: 0.0344 c. M: 0.0571 c. 1848: 314 221 232 314 124 411 232 N SD: 0.0124 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: 33.9556 cents 4 x 5 x 6 x 7:8 S SD: 22.3605 cents 5 x 6:7 x 8:9:10 S SD: 20.1256 cents 6:7 x 8:9 x 11:12 SD: 12.5922 cents 7:8 x 9 x 11:13:14 SD: 14.4311 cents 8:9:10:11:12:13:15:16 SD: 13.7273 cents 9:10:11:12 x 14:17:18 SD: 9.7788 cents 11:12:13:15 x 17:20:22 SD: 15.6149 cents 12:14:15:16:18:19:22:24 SD: 10.7366 cents 13:15:16:17 x 20:24:26 SD: 11.4136 cents 14:16:17:19:21:22:26:28 SD: 6.8638 cents 18:20:22:24:27:28:33:36 SD: 3.9678 cents 24:27:29:32:36:38:44:48 SD: 3.3872 cents 30:34:37:40:45:47:55:60 SD: 2.9840 cents 32:36:39:43:48:50:59:64 SD: 2.8546 cents 40:45:49:53:60:63:73:80 SD: 2.0747 cents 48:54:59:64:72:75:88:96 SD: 1.9873 cents 54:61:66:72:81:85:99:108 SD: 1.0976 cents 72:81:88:96:108:113:132:144 SD: 0.3125 cents 198:223:242:264:297:311:363:396 SD: 0.2998 cents 240:270:293:320:360:377:440:480 SD: 0.2964 cents 264:297:323:352:396:415:484:528 SD: 0.2692 cents 270:304:330:360:405:424:495:540 SD: 0.2630 cents 288:324:352:384:432:453:528:576 SD: 0.2341 cents 306:344:374:408:459:481:561:612 SD: 0.1941 cents 360:405:440:480:540:566:660:720 SD: 0.1249 cents 432:486:528:576:648:679:792:864 SD: 0.0520 cents 504:567:616:672:756:792:924:1008 SD: 0.0000 cents