Scala analysis: xen09-wilson-marwa-10-17
Marwa permutation 17 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: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole 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: 112/99 213.5980 7: 9/8 203.9100 major whole 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 : 203.9 347.4 498.0 702.0 782.5 996.1 1200.0 203.9 : 143.5 294.1 498.0 578.6 792.2 996.1 1200.0 347.4 : 150.6 354.5 435.1 648.7 852.6 1056.5 1200.0 498.0 : 203.9 284.4 498.0 702.0 905.9 1049.4 1200.0 702.0 : 80.5 294.1 498.0 702.0 845.5 996.1 1200.0 782.5 : 213.6 417.5 621.4 764.9 915.6 1119.5 1200.0 996.1 : 203.9 407.8 551.3 702.0 905.9 986.4 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 : 167.78344 cents, oct.: 1174.48405 cents Scale is not proper Step pattern alph. order: ABCADEA Step pattern size order : DBCDAED 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 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 71.4286% -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 11 Scale harmonicity : 0.021676 Average absolute harmonicity : 0.255972 Specific harmonicity : 0.133375 Fundamental : 1/504, -8.9773 octaves, 0.5191 Hz. Guide tone : 1584, 10.6294 octaves, 414414.895 Hz. Exponens Consonantiae : 7.983360E+05, 19.60664 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 47.5, average 6.78571 Mersenne's string divisions : 107100 Sum of van Prooijen's expressibility: 4.94551, average 0.70650 Sum of Tenney's harmonic distance : 10.05618, average 1.43660 Vogel's harmonic complexity : 17.71429 Wille's k value : 283 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 90.52307, average 3.23297 Lattice compactness (without 2's) : 53.59931, average 1.91426 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.42857 11 1 3: -2 .. 2 -0.28571 8 4 7: -1 .. 0 -0.14286 1 11: 0 .. 1 0.28571 2 2 Average exponent except 2's :-1 / 7 =-0.14286 Average absolute exponent except 2's: 11 / 7 = 1.57143 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: 34.2909 c. M:-74.6508 c. Lebeng 10: 2 1 1 2 1 1 2 P D3 I SD: 30.9884 c. M:-57.5080 c. 11: 2 1 1 2 1 2 2 N D3 SD: 32.1172 c. M: 61.6814 c. 12: 2 1 2 2 1 2 2 P M ME S SD: 19.2438 c. M: 47.4079 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: 19.9310 c. M:-32.4814 c. 17: 3 2 2 3 1 3 3 N SD: 5.6203 c. M:-7.8547 c. 41: 7 5 5 7 3 7 7 N SD: 3.3158 c. M:-7.7519 c. 48: 8 6 6 8 3 9 8 N SD: 3.7998 c. M: 7.4920 c. 58: 10 7 7 10 4 10 10 N SD: 2.7961 c. M:-4.3162 c. 72: 12 9 9 12 5 13 12 N SD: 2.5536 c. M:-3.9100 c. 77: 13 9 10 13 5 14 13 N SD: 2.2589 c. M: 4.5508 c. 87: 15 10 11 15 6 15 15 N SD: 2.4715 c. M:-3.7149 c. 89: 15 11 11 15 6 16 15 N SD: 1.5620 c. M:-3.1539 c. 94: 16 11 12 16 6 17 16 N SD: 1.7703 c. M: 3.7686 c. 101: 17 12 13 17 7 18 17 N SD: 1.7000 c. M: 2.8535 c. 106: 18 13 13 18 7 19 18 N SD: 1.4340 c. M:-3.5355 c. 118: 20 14 15 20 8 21 20 N SD: 0.7266 c. M: 1.6452 c. 135: 23 16 17 23 9 24 23 N SD: 0.4369 c. M: 0.7413 c. 224: 38 27 28 38 15 40 38 N SD: 0.3889 c. M:-0.8063 c. 342: 58 41 43 58 23 61 58 N SD: 0.2406 c. M:-0.4012 c. 359: 61 43 45 61 24 64 61 N SD: 0.1476 c. M: 0.3193 c. 477: 81 57 60 81 32 85 81 N SD: 0.1274 c. M: 0.2381 c. 701: 119 84 88 119 47 125 119 N SD: 0.1429 c. M:-0.2010 c. 836: 142 100 105 142 56 149 142 N SD: 0.0900 c. M: 0.1954 c. 877: 149 105 110 149 59 156 149 N SD: 0.0874 c. M:-0.1762 c. 1012: 172 121 127 172 68 180 172 N SD: 0.0516 c. M:-0.1167 c. 1147: 195 137 144 195 77 204 195 N SD: 0.0705 c. M:-0.1005 c. 1236: 210 148 155 210 83 220 210 N SD: 0.0654 c. M:-0.1649 c. 1354: 230 162 170 230 91 241 230 N SD: 0.0510 c. M:-0.0781 c. 1371: 233 164 172 233 92 244 233 N SD: 0.0334 c. M:-0.0756 c. 1489: 253 178 187 253 100 265 253 N SD: 0.0302 c. M: 0.0607 c. 1713: 291 205 215 291 115 305 291 N SD: 0.0396 c. M:-0.0571 c. 1848: 314 221 232 314 124 329 314 N SD: 0.0126 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: 11.8769 cents 5 x 6:7 x 8:9:10 S SD: 19.5749 cents 6:7 x 8:9 x 11:12 SD: 16.4949 cents 7:8 x 9 x 11:12:14 SD: 18.6242 cents 8:9:10:11:12:13:14:16 S SD: 13.1422 cents 9:10:11:12 x 14:16:18 S SD: 4.6291 cents 11:12:13:15 x 17:20:22 SD: 16.7373 cents 12:14:15:16:18:19:21:24 SD: 11.4212 cents 13:15:16:17 x 20:23:26 SD: 11.3208 cents 14:16:17:19:21:22:25:28 SD: 6.1759 cents 18:20:22:24:27:28:32:36 S SD: 3.9678 cents 24:27:29:32:36:38:43:48 SD: 3.8959 cents 30:34:37:40:45:47:53:60 SD: 3.3629 cents 32:36:39:43:48:50:57:64 SD: 2.5334 cents 40:45:49:53:60:63:71:80 SD: 1.7845 cents 54:61:66:72:81:85:96:108 SD: 1.0976 cents 72:81:88:96:108:113:128:144 SD: 0.3125 cents 198:223:242:264:297:311:352:396 SD: 0.2998 cents 270:304:330:360:405:424:480:540 SD: 0.2630 cents 288:324:352:384:432:453:512:576 SD: 0.2341 cents 306:344:374:408:459:481:544:612 SD: 0.1941 cents 360:405:440:480:540:566:640:720 SD: 0.1249 cents 432:486:528:576:648:679:768:864 SD: 0.0520 cents 504:567:616:672:756:792:896:1008 SD: 0.0000 cents