Scala analysis: xen09-wilson-marwa-15b-05
Marwa permutation 5 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: 4/3 498.044999 perfect fourth 4: 14/9 764.915905 septimal minor sixth 5: 7/4 968.825906 harmonic seventh 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: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 7/6 266.8709 septimal minor third 5: 9/8 203.9100 major whole tone 6: 22/21 80.5370 undecimal minor semitone 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: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 7/6 266.871 cents septimal minor third 2: 2 8/7 231.174 cents septimal whole tone 2: 1 33/28 284.447 cents undecimal minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 2 14/11 417.508 cents undecimal diminished fourth or major third 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 11/7 782.492 cents undecimal augmented fifth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 1 56/33 915.553 cents 5: 2 7/4 968.826 cents harmonic seventh 6: 2 12/7 933.129 cents septimal major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 266.9 347.4 498.0 764.9 968.8 1049.4 1200.0 266.9 : 80.5 231.2 498.0 702.0 782.5 933.1 1200.0 347.4 : 150.6 417.5 621.4 702.0 852.6 1119.5 1200.0 498.0 : 266.9 470.8 551.3 702.0 968.8 1049.4 1200.0 764.9 : 203.9 284.4 435.1 702.0 782.5 933.1 1200.0 968.8 : 80.5 231.2 498.0 578.6 729.2 996.1 1200.0 1049.4: 150.6 417.5 498.0 648.7 915.6 1119.5 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 : 178.96995 cents, oct.: 1252.78963 cents Scale is not proper Step pattern alph. order: ABCADBC Step pattern size order : DABDCAB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.595742 Lumma stability : 0.134228 Lumma impropriety factor : 0.154686 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 99/98, 17.5761 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Phrygian octave species of abstract tetrachord All steps are superparticular (epimoric) 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 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 63 (O: 63 U: 63) Highest odd numerator or denominator: 11 Scale harmonicity : 0.026454 Average absolute harmonicity : 0.216545 Specific harmonicity : 0.131022 Fundamental : 1/36, -5.1699 octaves, 7.2674 Hz. Guide tone : 308, 8.2668 octaves, 80580.674 Hz. Exponens Consonantiae : 1.108800E+04, 13.43671 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 47.0, average 6.71429 Mersenne's string divisions : 23483460 Sum of van Prooijen's expressibility: 5.20435, average 0.74348 Sum of Tenney's harmonic distance : 10.36617, average 1.48088 Vogel's harmonic complexity : 11.14286 Wille's k value : 31 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 64.15590, average 2.29128 Lattice compactness (without 2's) : 40.31784, average 1.43992 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.00000 8 1 3: -2 .. 0 -1.00000 7 1 7: 0 .. 1 0.42857 3 3 11: 0 .. 1 0.28571 2 2 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 22 23| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 20 26| Scale is weakly epimorphic with val: <7 12 18 22| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 2 0 1 2 1 0 1 N T3 SD: 51.5004 c. M:-92.2270 c. 8: 2 0 1 2 1 1 1 N D3 SD: 38.9382 c. M: 68.8259 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 31.1707 c. M:-52.5921 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 24.6118 c. M: 44.9159 c. Pseudo Rast 14: 3 1 2 3 2 1 2 P T3 SD: 14.7754 c. M: 25.9688 c. 17: 4 1 2 4 3 1 2 N SD: 11.2470 c. M:-19.4094 c. 22: 5 1 3 5 4 1 3 N SD: 10.8895 c. M: 20.1352 c. 24: 5 2 3 5 4 2 3 P SD: 11.1642 c. M: 18.8259 c. Soft Diatonic Phrygian 27: 6 2 3 6 5 2 3 N SD: 9.3917 c. M:-17.3037 c. 31: 7 2 4 7 5 2 4 N SD: 4.6212 c. M:-9.2776 c. 41: 9 3 5 9 7 3 5 N SD: 3.1514 c. M:-4.2956 c. 58: 13 4 7 13 10 4 7 N SD: 3.2123 c. M:-5.8095 c. 63: 14 4 8 14 11 4 8 N SD: 2.6053 c. M: 4.5508 c. 72: 16 5 9 16 12 5 9 N SD: 1.6351 c. M:-2.5921 c. 94: 21 6 12 21 16 6 12 N SD: 1.6246 c. M: 2.7271 c. 118: 26 8 15 26 20 8 15 N SD: 1.8806 c. M: 2.7242 c. 121: 27 8 15 27 21 8 15 N SD: 1.7009 c. M:-3.0749 c. 135: 30 9 17 30 23 9 17 N SD: 0.3989 c. M: 0.7413 c. 207: 46 14 26 46 35 14 26 N SD: 0.3919 c. M: 0.7100 c. 328: 73 22 41 73 56 22 41 N SD: 0.4234 c. M:-0.6863 c. 342: 76 23 43 76 58 23 43 N SD: 0.2088 c. M: 0.4049 c. 477: 106 32 60 106 81 32 60 N SD: 0.2034 c. M: 0.3063 c. 535: 119 36 67 119 91 36 67 N SD: 0.1810 c. M:-0.3567 c. 629: 140 42 79 140 107 42 79 N SD: 0.1791 c. M:-0.3315 c. 670: 149 45 84 149 114 45 84 N SD: 0.1154 c. M:-0.1893 c. 701: 156 47 88 156 119 47 88 N SD: 0.1376 c. M:-0.2767 c. 805: 179 54 101 179 137 54 101 N SD: 0.1137 c. M: 0.1954 c. 836: 186 56 105 186 142 56 105 N SD: 0.0867 c. M:-0.1559 c. 877: 195 59 110 195 149 59 110 N SD: 0.0794 c. M:-0.1405 c. 971: 216 65 122 216 165 65 122 N SD: 0.0862 c. M: 0.1371 c. 1012: 225 68 127 225 172 68 127 N SD: 0.0529 c. M: 0.0938 c. 1506: 335 101 189 335 256 101 189 N SD: 0.0492 c. M:-0.0984 c. 1713: 381 115 215 381 291 115 215 N SD: 0.0346 c. M:-0.0578 c. 1848: 411 124 232 411 314 124 232 N SD: 0.0105 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: 28.1557 cents 4 x 5 x 6:7 x 8 S SD: 18.5029 cents 5 x 6:7:8 x 9:10 S SD: 21.4770 cents 6:7 x 8:9 x 11:12 SD: 12.5922 cents 7:8 x 9:11:12:13:14 SD: 14.2600 cents 9 x 11:12:14:16:17:18 SD: 9.7388 cents 10 x 12:13:16 x 18:20 SD: 15.8971 cents 11:13 x 15:17:19:20:22 SD: 8.9108 cents 12:14:15:16:19:21:22:24 SD: 7.0748 cents 15 x 18:20:23:26:28:30 SD: 8.9399 cents 16:19:20:21:25:28:29:32 SD: 8.6270 cents 17:20:21:23:26:30:31:34 SD: 6.9178 cents 18:21:22:24:28:32:33:36 S SD: 3.8949 cents 24:28:29:32:37:42:44:48 SD: 3.5930 cents 31:36:38:41:48:54:57:62 SD: 2.9957 cents 36:42:44:48:56:63:66:72 S SD: 0.0000 cents