Scala analysis: xen09-wilson-marwa-15b-03
Marwa permutation 3 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: 7/6 266.870906 septimal minor third 2: 11/9 347.407941 undecimal neutral third 3: 11/8 551.317942 undecimal semi-augmented 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: 7/6 266.8709 septimal minor third 2: 22/21 80.5370 undecimal minor semitone 3: 9/8 203.9100 major whole tone 4: 112/99 213.5980 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: 2 22/21 80.537 cents undecimal minor semitone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 112/99 213.598 cents 1: 1 7/6 266.871 cents septimal minor third 2: 2 33/28 284.447 cents undecimal minor third 2: 1 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: 2 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: 2 11/7 782.492 cents undecimal augmented fifth 5: 1 44/27 845.453 cents neutral sixth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 56/33 915.553 cents 6: 1 12/7 933.129 cents septimal major sixth 6: 1 99/56 986.402 cents 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 2 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 : 266.9 347.4 551.3 764.9 845.5 1049.4 1200.0 266.9 : 80.5 284.4 498.0 578.6 782.5 933.1 1200.0 347.4 : 203.9 417.5 498.0 702.0 852.6 1119.5 1200.0 551.3 : 213.6 294.1 498.0 648.7 915.6 996.1 1200.0 764.9 : 80.5 284.4 435.1 702.0 782.5 986.4 1200.0 845.5 : 203.9 354.5 621.4 702.0 905.9 1119.5 1200.0 1049.4: 150.6 417.5 498.0 702.0 915.6 996.1 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 : 9/8, 203.9100 cents, amount: 2 Least squares average step : 175.70533 cents, oct.: 1229.93733 cents Scale is not proper Step pattern alph. order: ABCDBCE Step pattern size order : EACDACB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.581147 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 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 : 99 (O: 99 U: 99) Highest odd numerator or denominator: 27 Scale harmonicity : 0.024115 Average absolute harmonicity : 0.186119 Specific harmonicity : 0.113474 Fundamental : 1/216, -7.7549 octaves, 1.2112 Hz. Guide tone : 308, 8.2668 octaves, 80580.674 Hz. Exponens Consonantiae : 6.652800E+04, 16.02167 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 83.0, average 11.85714 Mersenne's string divisions : 411418020 Sum of van Prooijen's expressibility: 6.35488, average 0.90784 Sum of Tenney's harmonic distance : 12.85913, average 1.83702 Vogel's harmonic complexity : 16.28571 Wille's k value : 148 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 75.24350, average 2.68727 Lattice compactness (without 2's) : 48.58129, average 1.73505 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.14286 9 1 3: -3 .. 0 -1.28571 9 7: 0 .. 1 0.28571 2 2 11: 0 .. 1 0.57143 4 4 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is weakly epimorphic with val: <7 10 21 26| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 21 23| 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: 49.7755 c. M: 95.4423 c. Lebeng 8: 2 0 2 1 1 1 1 P D3 S SD: 35.6837 c. M:-54.5471 c. 9: 2 1 1 2 0 2 1 N D3 SD: 30.9047 c. M:-52.5921 c. 10: 2 1 2 1 1 2 1 P M ME S SD: 29.8481 c. M:-48.6821 c. 11: 2 1 2 2 1 2 1 P M ME S SD: 27.4696 c. M: 48.6891 c. 13: 3 1 2 2 1 2 2 N T3 SD: 19.4703 c. M: 33.9783 c. 14: 3 1 2 3 1 2 2 P T3 SD: 17.3126 c. M: 37.0322 c. 16: 4 1 2 3 1 3 2 N SD: 21.3565 c. M:-33.1291 c. 17: 4 1 3 3 1 3 2 N SD: 9.8208 c. M:-15.4820 c. 24: 5 2 4 4 2 4 3 P SD: 8.7558 c. M: 16.8709 c. 30: 7 2 5 5 2 5 4 N SD: 8.8469 c. M:-13.1291 c. 31: 7 2 5 6 2 5 4 N SD: 5.9456 c. M: 9.3825 c. 41: 9 3 7 7 3 7 5 N SD: 3.6717 c. M:-4.7796 c. 58: 13 4 10 10 4 10 7 N SD: 4.1132 c. M:-7.3027 c. 63: 14 4 11 11 4 11 8 N SD: 3.5481 c. M: 7.3577 c. 72: 16 5 12 13 5 12 9 N SD: 2.1595 c. M:-4.5471 c. 89: 20 6 15 16 6 15 11 N SD: 2.7870 c. M:-3.9853 c. 94: 21 6 16 17 6 16 12 N SD: 2.0909 c. M: 2.8997 c. 111: 25 7 19 20 7 19 14 N SD: 1.9316 c. M:-3.3994 c. 118: 26 8 20 21 8 20 15 N SD: 1.8468 c. M: 2.4641 c. 135: 30 9 23 24 9 23 17 N SD: 0.5475 c. M: 1.0085 c. 207: 46 14 35 37 14 35 26 N SD: 0.4661 c. M:-0.9239 c. 287: 64 19 49 51 19 49 36 N SD: 0.5099 c. M: 0.8536 c. 311: 69 21 53 55 21 53 39 N SD: 0.4929 c. M: 0.9288 c. 342: 76 23 58 61 23 58 43 N SD: 0.2142 c. M: 0.4407 c. 477: 106 32 81 85 32 81 60 N SD: 0.2330 c. M: 0.3745 c. 494: 110 33 84 88 33 84 62 N SD: 0.1722 c. M:-0.3356 c. 629: 140 42 107 112 42 107 79 N SD: 0.1667 c. M: 0.3019 c. 670: 149 45 114 119 45 114 84 N SD: 0.1557 c. M:-0.3238 c. 701: 156 47 119 125 47 119 88 N SD: 0.1541 c. M:-0.2767 c. 805: 179 54 137 143 54 137 101 N SD: 0.1524 c. M: 0.2355 c. 836: 186 56 142 149 56 142 105 N SD: 0.0929 c. M:-0.1559 c. 877: 195 59 149 156 59 149 110 N SD: 0.1037 c. M:-0.1571 c. 971: 216 65 165 173 65 165 122 N SD: 0.1095 c. M: 0.1388 c. 1012: 225 68 172 180 68 172 127 N SD: 0.0545 c. M: 0.0938 c. 1354: 301 91 230 241 91 230 170 N SD: 0.0569 c. M: 0.1058 c. 1506: 335 101 256 268 101 256 189 N SD: 0.0430 c. M:-0.0765 c. 1713: 381 115 291 305 115 291 215 N SD: 0.0450 c. M:-0.0812 c. 1848: 411 124 314 329 124 314 232 N SD: 0.0124 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: 21.9891 cents 4 x 5 x 6 x 7:8 S SD: 27.3450 cents 5 x 6:7 x 8:9:10 S SD: 12.6498 cents 6:7 x 8:9:10:11:12 S SD: 15.1984 cents 7:8:9:10:11 x 13:14 SD: 19.8241 cents 8:9:10:11:12:13:15:16 SD: 14.9692 cents 9 x 11:12:14:15:17:18 SD: 13.9670 cents 10 x 12:14 x 16:18:20 S SD: 12.6498 cents 11:13 x 15:17:18:20:22 SD: 5.5026 cents 13:15:16:18:20:21:24:26 SD: 5.3444 cents 15 x 18:21:23:24:28:30 SD: 11.2853 cents 16:19:20:22:25:26:29:32 SD: 7.7299 cents 17:20:21:23:26:28:31:34 SD: 7.3115 cents 18:21:22:25:28:29:33:36 SD: 3.7640 cents 24:28:29:33:37:39:44:48 SD: 3.6612 cents 30:35:37:41:47:49:55:60 SD: 3.2686 cents 32:37:39:44:50:52:59:64 SD: 3.0145 cents 35:41:43:48:54:57:64:70 SD: 2.7604 cents 40:47:49:55:62:65:73:80 SD: 2.4416 cents 41:48:50:56:64:67:75:82 SD: 2.2969 cents 48:56:59:66:75:78:88:96 SD: 1.9163 cents 49:57:60:67:76:80:90:98 SD: 1.8918 cents 54:63:66:74:84:88:99:108 SD: 0.8341 cents 72:84:88:99:112:117:132:144 SD: 0.7036 cents 126:147:154:173:196:205:231:252 SD: 0.5376 cents 144:168:176:198:224:235:264:288 SD: 0.3511 cents 162:189:198:223:252:264:297:324 SD: 0.2774 cents 216:252:264:297:336:352:396:432 SD: 0.0000 cents