Scala analysis: xen09-wilson-marwa-15b-08
Marwa permutation 8 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: 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: 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: 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: 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: 2 11/9 347.408 cents undecimal neutral third 2: 1 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 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: 1 11/7 782.492 cents undecimal augmented fifth 5: 1 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 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 : 266.9 347.4 498.0 764.9 845.5 996.1 1200.0 266.9 : 80.5 231.2 498.0 578.6 729.2 933.1 1200.0 347.4 : 150.6 417.5 498.0 648.7 852.6 1119.5 1200.0 498.0 : 266.9 347.4 498.0 702.0 968.8 1049.4 1200.0 764.9 : 80.5 231.2 435.1 702.0 782.5 933.1 1200.0 845.5 : 150.6 354.5 621.4 702.0 852.6 1119.5 1200.0 996.1 : 203.9 470.8 551.3 702.0 968.8 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 : 172.28064 cents, oct.: 1205.96450 cents Scale is not proper Step pattern alph. order: ABCABCD Step pattern size order : DABDABC Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.575227 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 : 243/242, 7.1391 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Mixolydian octave species of abstract tetrachord Scale contains two identical conjunct tetrachords 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 n-1 differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined -- Rational properties -- Prime limit : 11 Odd number limit : 63 (O: 63 U: 63) Highest odd numerator or denominator: 27 Scale harmonicity : 0.024115 Average absolute harmonicity : 0.218754 Specific harmonicity : 0.131702 Fundamental : 1/54, -5.7549 octaves, 4.8449 Hz. Guide tone : 1232, 10.2668 octaves, 322322.696 Hz. Exponens Consonantiae : 6.652800E+04, 16.02167 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 81.0, average 11.57143 Mersenne's string divisions : 44580900 Sum of van Prooijen's expressibility: 5.70346, average 0.81478 Sum of Tenney's harmonic distance : 12.33265, average 1.76181 Vogel's harmonic complexity : 11.71429 Wille's k value : 31 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 74.16306, average 2.64868 Lattice compactness (without 2's) : 45.31798, average 1.61850 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.28571 11 1 3: -3 .. 0 -1.57143 11 2 7: 0 .. 1 0.28571 2 2 11: 0 .. 1 0.28571 2 2 Average exponent except 2's :-7 / 7 =-1.00000 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is weakly epimorphic with val: <7 10 22 26| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 20 23| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 2 0 1 2 0 1 1 N T3 SD: 47.4430 c. M:-92.2270 c. 8: 2 0 1 2 1 1 1 N D3 SD: 40.9835 c. M:-54.5471 c. 10: 2 1 1 2 1 1 2 P D3 I SD: 25.5116 c. M: 44.9159 c. 13: 3 1 1 3 1 2 2 N SD: 21.3733 c. M: 36.5065 c. 14: 3 1 2 3 1 2 2 P T3 SD: 15.1809 c. M:-32.4814 c. 17: 4 1 2 4 1 2 3 N SD: 8.3111 c. M:-15.4820 c. 31: 7 2 4 7 2 4 5 N SD: 6.2788 c. M:-10.3616 c. 41: 9 3 5 9 3 5 7 N SD: 2.7837 c. M: 3.9403 c. 58: 13 4 7 13 4 7 10 N SD: 2.4639 c. M:-4.3162 c. 72: 16 5 9 16 5 9 12 N SD: 2.6622 c. M:-4.5471 c. 77: 17 5 10 17 5 10 13 N SD: 2.4904 c. M: 4.5508 c. 89: 20 6 11 20 6 11 15 N SD: 2.6782 c. M:-3.9853 c. 94: 21 6 12 21 6 12 16 N SD: 1.6280 c. M: 2.8997 c. 118: 26 8 15 26 8 15 20 N SD: 1.5068 c. M: 2.4641 c. 135: 30 9 17 30 9 17 23 N SD: 0.5590 c. M: 1.0085 c. 287: 64 19 36 64 19 36 49 N SD: 0.6118 c. M: 0.9680 c. 301: 67 20 38 67 20 38 51 N SD: 0.4077 c. M:-0.5877 c. 342: 76 23 43 76 23 43 58 N SD: 0.1966 c. M:-0.4012 c. 477: 106 32 60 106 32 60 81 N SD: 0.1554 c. M: 0.2381 c. 535: 119 36 67 119 36 67 91 N SD: 0.1442 c. M:-0.2556 c. 670: 149 45 84 149 45 84 114 N SD: 0.1306 c. M: 0.2691 c. 836: 186 56 105 186 56 105 142 N SD: 0.0824 c. M:-0.1559 c. 971: 216 65 122 216 65 122 165 N SD: 0.0826 c. M: 0.1388 c. 1012: 225 68 127 225 68 127 172 N SD: 0.0490 c. M: 0.0938 c. 1371: 305 92 172 305 92 172 233 N SD: 0.0580 c. M:-0.0875 c. 1506: 335 101 189 335 101 189 256 N SD: 0.0421 c. M: 0.0741 c. 1713: 381 115 215 381 115 215 291 N SD: 0.0502 c. M:-0.0812 c. 1848: 411 124 232 411 124 232 314 N SD: 0.0106 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: 19.7184 cents 5 x 6:7 x 8:9:10 S SD: 19.6117 cents 6:7 x 8:9:10:11:12 S SD: 15.1984 cents 7:8 x 9:11 x 12:14 SD: 19.5052 cents 8:9:10:11:12:13:14:16 S SD: 16.3179 cents 9 x 11:12:14:15:16:18 SD: 6.4843 cents 10 x 12:13 x 16:18:20 SD: 13.2694 cents 11:13 x 15:17:18:20:22 SD: 10.1441 cents 12:14:15:16:19:20:21:24 SD: 9.8038 cents 13:15:16:17:20:21:23:26 SD: 6.8634 cents 15 x 18:20:23:24:27:30 SD: 9.2815 cents 16:19:20:21:25:26:28:32 SD: 9.0610 cents 17:20:21:23:26:28:30:34 SD: 7.2159 cents 18:21:22:24:28:29:32:36 SD: 2.8265 cents 36:42:44:48:56:59:64:72 SD: 1.4012 cents 54:63:66:72:84:88:96:108 S SD: 0.0000 cents