Scala analysis: xen09-wilson-marwa-10-08
Marwa permutation 8 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: 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: 9/8 203.9100 major whole tone 2: 88/81 143.4979 2nd undecimal neutral second 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: 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 8/7 231.174 cents septimal whole tone 2: 3 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: 3 18/11 852.592 cents undecimal neutral sixth 5: 1 7/4 968.826 cents harmonic seventh 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 347.4 551.3 702.0 782.5 1049.4 1200.0 203.9 : 143.5 347.4 498.0 578.6 845.5 996.1 1200.0 347.4 : 203.9 354.5 435.1 702.0 852.6 1056.5 1200.0 551.3 : 150.6 231.2 498.0 648.7 852.6 996.1 1200.0 702.0 : 80.5 347.4 498.0 702.0 845.5 1049.4 1200.0 782.5 : 266.9 417.5 621.4 764.9 968.8 1119.5 1200.0 1049.4: 150.6 354.5 498.0 702.0 852.6 933.1 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 .. 417.5080 cents 49/44, 186.3339 cents 48/49,-35.6968 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 .. 968.8259 cents 49/44, 186.3339 cents 99/98, 17.5761 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 : 171.20813 cents, oct.: 1198.45688 cents Scale is not proper Step pattern alph. order: ABACDEC Step pattern size order : DBDCAEC Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.559442 Lumma stability : 0.163522 Lumma impropriety factor : 0.095191 Rothenberg efficiency : 0.423129 redundancy: 0.576871 Efficiency x scale size : 2.961905 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 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 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 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 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 : 0.023183 Average absolute harmonicity : 0.223337 Specific harmonicity : 0.125185 Fundamental : 1/504, -8.9773 octaves, 0.5191 Hz. Guide tone : 198, 7.6294 octaves, 51801.862 Hz. Exponens Consonantiae : 9.979200E+04, 16.60664 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 49.5, average 7.07143 Mersenne's string divisions : 58140 Sum of van Prooijen's expressibility: 5.59693, average 0.79956 Sum of Tenney's harmonic distance : 10.58267, average 1.51181 Vogel's harmonic complexity : 20.28571 Wille's k value : 346 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 73.60092, average 2.62860 Lattice compactness (without 2's) : 48.29482, average 1.72482 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.00000 9 1 3: -2 .. 2 0.00000 6 2 7: -1 .. 0 -0.14286 1 11: 0 .. 1 0.57143 4 4 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is weakly epimorphic with val: <7 10 18 22| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 1 1 1 1 0 2 1 N T3 SD: 42.2731 c. M: 96.7778 c. 9: 2 1 1 1 1 2 1 N D3 S SD: 35.6150 c. M:-62.7567 c. 10: 2 1 2 1 1 2 1 P M ME S SD: 34.6460 c. M:-57.5080 c. 11: 2 1 2 1 1 2 2 N D3 SD: 33.4001 c. M: 67.5448 c. 12: 2 1 2 2 1 2 2 P M ME S SD: 33.0441 c. M: 51.3179 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 13: 2 2 2 1 1 3 2 N SD: 31.7623 c. M: 55.8012 c. 14: 2 2 2 2 1 3 2 P T3 SD: 21.5989 c. M: 37.0322 c. 15: 3 1 3 2 1 3 2 N T3 SD: 20.1738 c. M:-36.0900 c. 16: 3 2 2 2 1 4 2 N SD: 22.9330 c. M: 32.4920 c. 17: 3 2 3 2 1 4 2 N SD: 7.6787 c. M:-13.3879 c. 24: 4 3 4 3 2 5 3 P SD: 6.9127 c. M:-17.5080 c. 31: 5 4 5 4 2 7 4 N SD: 6.6517 c. M: 10.3616 c. 41: 7 5 7 5 3 9 5 N SD: 4.0898 c. M:-7.7519 c. 48: 8 6 8 6 3 11 6 N SD: 3.4662 c. M: 7.4920 c. 58: 10 7 10 7 4 13 7 N SD: 4.3204 c. M:-7.3027 c. 61: 10 8 10 8 4 13 8 N SD: 5.3502 c. M: 7.1887 c. 63: 11 7 11 8 4 14 8 N SD: 3.0856 c. M:-5.6138 c. 72: 12 9 12 9 5 16 9 N SD: 2.0241 c. M: 3.9100 c. 87: 15 10 15 11 6 19 11 N SD: 2.1697 c. M:-3.7149 c. 89: 15 11 15 11 6 20 11 N SD: 1.7419 c. M:-3.1539 c. 118: 20 14 20 15 8 26 15 N SD: 1.2915 c. M: 2.1654 c. 135: 23 16 23 17 9 30 17 N SD: 0.4220 c. M: 0.7413 c. 311: 53 37 53 39 21 69 39 N SD: 0.4317 c. M:-0.7877 c. 342: 58 41 58 43 23 76 43 N SD: 0.2552 c. M: 0.4407 c. 359: 61 43 61 45 24 80 45 N SD: 0.1876 c. M: 0.3193 c. 477: 81 57 81 60 32 106 60 N SD: 0.2153 c. M: 0.3745 c. 494: 84 59 84 62 33 110 62 N SD: 0.1362 c. M: 0.3058 c. 629: 107 75 107 79 42 140 79 N SD: 0.1668 c. M: 0.2981 c. 653: 111 78 111 82 44 145 82 N SD: 0.1435 c. M:-0.3564 c. 701: 119 84 119 88 47 156 88 N SD: 0.1216 c. M: 0.2010 c. 836: 142 100 142 105 56 186 105 N SD: 0.0997 c. M: 0.1954 c. 877: 149 105 149 110 59 195 110 N SD: 0.1063 c. M:-0.1762 c. 1012: 172 121 172 127 68 225 127 N SD: 0.0569 c. M:-0.1167 c. 1147: 195 137 195 144 77 255 144 N SD: 0.0580 c. M:-0.1005 c. 1354: 230 162 230 170 91 301 170 N SD: 0.0491 c. M:-0.0781 c. 1489: 253 178 253 187 100 331 187 N SD: 0.0485 c. M: 0.0755 c. 1506: 256 180 256 189 101 335 189 N SD: 0.0459 c. M:-0.0765 c. 1713: 291 205 291 215 115 381 215 N SD: 0.0327 c. M: 0.0571 c. 1848: 314 221 314 232 124 411 232 N SD: 0.0141 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 6:7 x 8:9 x 11:12 SD: 16.4949 cents 7:8:9:10 x 11:13:14 SD: 19.2267 cents 8:9:10:11:12:13:15:16 SD: 11.4245 cents 9:10:11:12 x 14:17:18 SD: 13.2083 cents 10:11:12:14:15:16:18:20 S SD: 10.5734 cents 11:12:13:15 x 17:20:22 SD: 14.4053 cents 12:14:15:17:18:19:22:24 SD: 13.0302 cents 13:15:16:18 x 20:24:26 SD: 10.1450 cents 14:16:17:19:21:22:26:28 SD: 6.1970 cents 18:20:22:25:27:28:33:36 SD: 4.6821 cents 24:27:29:33:36:38:44:48 SD: 3.3872 cents 30:34:37:41:45:47:55:60 SD: 3.3414 cents 32:36:39:44:48:50:59:64 SD: 2.1082 cents 40:45:49:55:60:63:73:80 SD: 1.3784 cents 72:81:88:99:108:113:132:144 SD: 0.3125 cents 184:207:225:253:276:289:337:368 SD: 0.2994 cents 224:252:274:308:336:352:411:448 SD: 0.2838 cents 248:279:303:341:372:390:455:496 SD: 0.2719 cents 256:288:313:352:384:402:469:512 SD: 0.2636 cents 280:315:342:385:420:440:513:560 SD: 0.2272 cents 320:360:391:440:480:503:587:640 SD: 0.1721 cents 360:405:440:495:540:566:660:720 SD: 0.1249 cents 432:486:528:594:648:679:792:864 SD: 0.0520 cents 504:567:616:693:756:792:924:1008 SD: 0.0000 cents