Scala analysis: xen09-wilson-marwa-15b-10
Marwa permutation 10 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: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 14/9 764.915905 septimal minor sixth 5: 44/27 845.452940 neutral sixth 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: 88/81 143.4979 2nd undecimal neutral second 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 9/8 203.9100 major whole tone 4: 7/6 266.8709 septimal minor third 5: 22/21 80.5370 undecimal minor semitone 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 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: 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: 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 21/16 470.781 cents narrow fourth 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 32/21 729.219 cents wide 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 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 143.5 294.1 498.0 764.9 845.5 996.1 1200.0 143.5 : 150.6 354.5 621.4 702.0 852.6 1056.5 1200.0 294.1 : 203.9 470.8 551.3 702.0 905.9 1049.4 1200.0 498.0 : 266.9 347.4 498.0 702.0 845.5 996.1 1200.0 764.9 : 80.5 231.2 435.1 578.6 729.2 933.1 1200.0 845.5 : 150.6 354.5 498.0 648.7 852.6 1119.5 1200.0 996.1 : 203.9 347.4 498.0 702.0 968.8 1049.4 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 .. 470.7809 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 3: 435.0841 .. 621.4180 cents 49/44, 186.3339 cents 48/49,-35.6968 cents 4: 578.5820 .. 764.9159 cents 49/44, 186.3339 cents 3872/3969,-42.8359 cents 5: 729.2191 .. 968.8259 cents 147/128, 239.6068 cents 48/49,-35.6968 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 : 170.63837 cents, oct.: 1194.46856 cents Scale is not proper Step pattern alph. order: ABCDEBC Step pattern size order : BCDEACD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 27.26409 cents Scale diversity : 1.600163 Lumma stability : 0.134228 Lumma impropriety factor : 0.154686 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 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 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 -- Rational properties -- Prime limit : 11 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.022658 Average absolute harmonicity : 0.217915 Specific harmonicity : 0.134214 Fundamental : 1/81, -6.3399 octaves, 3.2299 Hz. Guide tone : 2464, 11.2668 octaves, 644645.393 Hz. Exponens Consonantiae : 1.995840E+05, 17.60664 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 178.5, average 25.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.15682, average 1.02240 Sum of Tenney's harmonic distance : 15.50324, average 2.21475 Vogel's harmonic complexity : 12.28571 Wille's k value : 40 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 84.01709, average 3.00061 Lattice compactness (without 2's) : 55.51571, average 1.98270 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 5 2.57143 18 1 3: -4 .. 0 -2.14286 15 3 7: 0 .. 1 0.14286 1 1 11: 0 .. 1 0.28571 2 2 Average exponent except 2's :-12 / 7 =-1.71429 Average absolute exponent except 2's: 18 / 7 = 2.57143 Scale is weakly epimorphic with val: <7 10 22 22| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 12 18 25| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 1 1 1 2 0 1 1 N T3 SD: 43.2852 c. M:-92.2270 c. 8: 1 1 1 2 1 1 1 P M ME I SD: 34.8244 c. M:-54.5471 c. 10: 1 1 2 2 1 1 2 P D3 S SD: 31.9777 c. M: 54.1350 c. 11: 1 2 2 2 1 1 2 N D3 SD: 27.9766 c. M:-47.4095 c. 12: 1 2 2 3 0 2 2 N SD: 27.3664 c. M: 45.4529 c. 14: 2 2 2 3 1 2 2 P T3 SD: 25.7788 c. M:-48.7221 c. 16: 2 2 3 3 1 2 3 P SD: 16.4266 c. M:-26.9550 c. 17: 2 2 3 4 1 2 3 N SD: 7.1456 c. M: 11.7821 c. 24: 3 3 4 5 2 3 4 P SD: 6.9585 c. M: 14.9159 c. 36: 4 5 6 8 2 5 6 N SD: 6.6201 c. M: 12.1196 c. 41: 5 5 7 9 3 5 7 N SD: 2.3288 c. M: 3.9403 c. 77: 9 10 13 17 5 10 13 N SD: 2.1818 c. M: 3.8945 c. 94: 11 12 16 21 6 12 16 N SD: 1.6626 c. M: 3.0724 c. 111: 13 14 19 25 7 14 19 N SD: 2.0173 c. M: 2.9574 c. 118: 14 15 20 26 8 15 20 N SD: 1.1332 c. M: 2.2040 c. 135: 16 17 23 30 9 17 23 N SD: 0.7432 c. M: 1.2757 c. 176: 21 22 30 39 12 22 30 N SD: 0.6709 c. M: 1.2795 c. 224: 27 28 38 50 15 28 38 N SD: 0.7558 c. M:-1.1555 c. 265: 32 33 45 59 18 33 45 N SD: 0.7536 c. M:-1.4077 c. 294: 35 37 50 65 20 37 50 N SD: 0.7118 c. M: 1.6506 c. 301: 36 38 51 67 20 38 51 N SD: 0.4730 c. M:-0.8816 c. 318: 38 40 54 71 21 40 54 N SD: 0.4412 c. M:-1.1218 c. 342: 41 43 58 76 23 43 58 N SD: 0.3208 c. M:-0.6018 c. 359: 43 45 61 80 24 45 61 N SD: 0.2402 c. M:-0.5437 c. 436: 52 55 74 97 29 55 74 N SD: 0.3032 c. M: 0.4988 c. 477: 57 60 81 106 32 60 81 N SD: 0.1325 c. M:-0.2046 c. 836: 100 105 142 186 56 105 142 N SD: 0.0843 c. M:-0.1559 c. 971: 116 122 165 216 65 122 165 N SD: 0.0791 c. M: 0.1406 c. 1012: 121 127 172 225 68 127 172 N SD: 0.0471 c. M: 0.0938 c. 1371: 164 172 233 305 92 172 233 N SD: 0.0450 c. M:-0.0732 c. 1848: 221 232 314 411 124 232 314 N SD: 0.0126 c. M:-0.0208 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: 28.7275 cents 5 x 6:7 x 8:9:10 S SD: 19.0461 cents 6 x 7:8:9:10:11:12 S SD: 15.8632 cents 7 x 8:9:11 x 12:14 SD: 22.0918 cents 8:9 x 11:12:13:14:16 SD: 17.6535 cents 9:10:11:12:14:15:16:18 S SD: 10.9408 cents 10:11:12:13 x 16:18:20 SD: 10.9517 cents 11:12:13:15:17:18:20:22 SD: 8.1825 cents 16:17:19:21:25:26:28:32 SD: 7.9119 cents 18:20:21:24:28:29:32:36 SD: 7.3519 cents 20:22:24:27:31:33:36:40 SD: 6.9267 cents 21:23:25:28:33:34:37:42 SD: 4.3625 cents 22:24:26:29:34:36:39:44 SD: 3.6954 cents 27:29:32:36:42:44:48:54 SD: 2.8265 cents 33:36:39:44:51:54:59:66 SD: 2.6711 cents 36:39:43:48:56:59:64:72 SD: 2.4825 cents 45:49:53:60:70:73:80:90 SD: 1.9973 cents 48:52:57:64:75:78:85:96 SD: 1.8367 cents 54:59:64:72:84:88:96:108 SD: 1.4012 cents 59:64:70:79:92:96:105:118 SD: 1.3709 cents 70:76:83:93:109:114:124:140 SD: 1.3013 cents 81:88:96:108:126:132:144:162 SD: 0.0000 cents