Scala analysis: xen09-wilson-marwa-15b-07
Marwa permutation 7 from Figure 15b, Ptolemy 22/21 12/11 7/6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88/81 143.497939 2nd undecimal neutral second 2: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 14/9 764.915905 septimal minor sixth 5: 44/27 845.452940 neutral 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: 88/81 143.4979 2nd undecimal neutral second 2: 9/8 203.9100 major whole tone 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 7/6 266.8709 septimal minor third 5: 22/21 80.5370 undecimal minor semitone 6: 9/8 203.9100 major whole tone 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 : 143.5 347.4 498.0 764.9 845.5 1049.4 1200.0 143.5 : 203.9 354.5 621.4 702.0 905.9 1056.5 1200.0 347.4 : 150.6 417.5 498.0 702.0 852.6 996.1 1200.0 498.0 : 266.9 347.4 551.3 702.0 845.5 1049.4 1200.0 764.9 : 80.5 284.4 435.1 578.6 782.5 933.1 1200.0 845.5 : 203.9 354.5 498.0 702.0 852.6 1119.5 1200.0 1049.4: 150.6 294.1 498.0 648.7 915.6 996.1 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 : 173.68253 cents, oct.: 1215.77774 cents Scale is not proper Step pattern alph. order: ABCDEBC Step pattern size order : BDCEADC 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 minor thirds form a closed circle 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: 81 Scale harmonicity : 0.023183 Average absolute harmonicity : 0.204233 Specific harmonicity : 0.120246 Fundamental : 1/162, -7.3399 octaves, 1.6150 Hz. Guide tone : 616, 9.2668 octaves, 161161.348 Hz. Exponens Consonantiae : 9.979200E+04, 16.60664 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 155.0, average 22.14286 Mersenne's string divisions : 1970475780 Sum of van Prooijen's expressibility: 6.85400, average 0.97914 Sum of Tenney's harmonic distance : 14.22355, average 2.03194 Vogel's harmonic complexity : 15.85714 Wille's k value : 148 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 74.65500, average 2.66625 Lattice compactness (without 2's) : 54.89804, average 1.96064 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.14286 10 1 3: -4 .. 0 -1.85714 13 1 7: 0 .. 1 0.14286 1 1 11: 0 .. 1 0.57143 4 4 Average exponent except 2's :-8 / 7 =-1.14286 Average absolute exponent except 2's: 18 / 7 = 2.57143 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: 33.6079 c. M: 79.2016 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 33.3732 c. M:-54.5471 c. 9: 1 2 1 2 0 2 1 N D3 SD: 33.1895 c. M:-52.5921 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 23.9706 c. M: 44.9159 c. 14: 2 2 2 3 1 2 2 P T3 SD: 15.4732 c. M:-27.9306 c. 16: 2 3 2 3 1 3 2 P D3 SD: 17.6124 c. M:-27.5921 c. 17: 2 3 2 4 1 3 2 N SD: 6.2908 c. M:-11.5547 c. 31: 4 5 4 7 2 5 4 N SD: 6.5256 c. M:-11.3408 c. 41: 5 7 5 9 3 7 5 N SD: 3.1145 c. M:-4.2956 c. 58: 7 10 7 13 4 10 7 N SD: 3.0404 c. M:-5.8095 c. 72: 9 12 9 16 5 12 9 N SD: 3.3159 c. M:-6.5021 c. 77: 9 13 10 17 5 13 10 N SD: 3.2851 c. M: 5.2071 c. 89: 11 15 11 20 6 15 11 N SD: 3.1224 c. M:-4.8167 c. 91: 11 15 12 20 6 16 11 N SD: 3.0675 c. M:-5.5821 c. 94: 11 16 12 21 6 16 12 N SD: 2.1688 c. M: 3.0724 c. 111: 13 19 14 25 7 19 14 N SD: 1.8465 c. M: 2.9574 c. 118: 14 20 15 26 8 20 15 N SD: 1.4366 c. M: 2.2040 c. 135: 16 23 17 30 9 23 17 N SD: 0.7282 c. M: 1.2757 c. 176: 21 30 22 39 12 30 22 N SD: 0.5789 c. M: 1.2795 c. 224: 27 38 28 50 15 38 28 N SD: 0.8179 c. M:-1.1555 c. 284: 34 48 36 63 19 48 36 N SD: 0.7100 c. M: 1.4756 c. 287: 34 49 36 64 19 49 36 N SD: 0.6503 c. M: 1.3377 c. 301: 36 51 38 67 20 51 38 N SD: 0.4626 c. M: 0.8580 c. 311: 37 53 39 69 21 53 39 N SD: 0.4959 c. M: 0.9288 c. 318: 38 54 40 71 21 54 40 N SD: 0.4556 c. M:-1.1218 c. 325: 39 55 41 72 22 55 41 N SD: 0.4584 c. M: 0.7476 c. 342: 41 58 43 76 23 58 43 N SD: 0.1913 c. M:-0.3617 c. 477: 57 81 60 106 32 81 60 N SD: 0.1744 c. M: 0.3063 c. 494: 59 84 62 110 33 84 62 N SD: 0.1319 c. M:-0.2663 c. 670: 80 114 84 149 45 114 84 N SD: 0.1356 c. M: 0.2144 c. 836: 100 142 105 186 56 142 105 N SD: 0.0716 c. M:-0.1559 c. 971: 116 165 122 216 65 165 122 N SD: 0.1075 c. M: 0.1406 c. 1012: 121 172 127 225 68 172 127 N SD: 0.0416 c. M: 0.0938 c. 1354: 162 230 170 301 91 230 170 N SD: 0.0458 c. M:-0.0767 c. 1506: 180 256 189 335 101 256 189 N SD: 0.0375 c. M: 0.0716 c. 1848: 221 314 232 411 124 314 232 N SD: 0.0098 c. M:-0.0192 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: 31.4805 cents 3 x x 4 x 5 x 6 S SD: 12.9686 cents 4 x 5 x 6 x 7:8 S SD: 27.3450 cents 5 x 6:7 x 8:9:10 S SD: 20.1614 cents 6 x 7:8:9:10:11:12 S SD: 18.2300 cents 7:8 x 9:11 x 13:14 SD: 22.3241 cents 8:9:10:11:12:13:15:16 SD: 16.6005 cents 9:10:11:12:14:15:17:18 SD: 10.7840 cents 10:11:12:13 x 16:18:20 SD: 12.2600 cents 11:12:13:15:17:18:20:22 SD: 10.4357 cents 12:13:15:16:19:20:22:24 SD: 9.0244 cents 13:14:16:17:20:21:24:26 SD: 6.7752 cents 18:20:22:24:28:29:33:36 SD: 6.2354 cents 21:23:26:28:33:34:39:42 SD: 5.7677 cents 22:24:27:29:34:36:40:44 SD: 4.2330 cents 24:26:29:32:37:39:44:48 SD: 3.7282 cents 32:35:39:43:50:52:59:64 SD: 3.2615 cents 35:38:43:47:54:57:64:70 SD: 3.0522 cents 36:39:44:48:56:59:66:72 SD: 1.5680 cents 54:59:66:72:84:88:99:108 SD: 1.4012 cents 72:78:88:96:112:117:132:144 SD: 0.9951 cents 81:88:99:108:126:132:149:162 SD: 0.8313 cents 90:98:110:120:140:147:165:180 SD: 0.7940 cents 108:117:132:144:168:176:198:216 SD: 0.7036 cents 126:137:154:168:196:205:231:252 SD: 0.4491 cents 162:176:198:216:252:264:297:324 SD: 0.0000 cents