Scala analysis: xen09-wilson-marwa-18b-08
Marwa permutation 8 from Figure 18b, Ptolemy 10/9 11/10 12/11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 22/15 663.049228 undecimal diminished fifth 5: 8/5 813.686286 minor 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: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 10/9 182.4037 minor whole tone 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 10/9 182.4037 minor whole tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 2 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 2: 2 6/5 315.641 cents minor third 2: 2 40/33 333.041 cents 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 99/80 368.914 cents 2: 1 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 3: 1 15/11 536.951 cents undecimal augmented fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 1 22/15 663.049 cents undecimal diminished fifth 4: 1 40/27 680.449 cents grave fifth 4: 4 3/2 701.955 cents perfect fifth 5: 1 8/5 813.686 cents minor sixth 5: 1 160/99 831.086 cents 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 2 33/20 866.959 cents 5: 2 5/3 884.359 cents major sixth, BP sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 20/11 1034.996 cents large minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 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 : 165.0 315.6 498.0 663.0 813.7 996.1 1200.0 165.0 : 150.6 333.0 498.0 648.7 831.1 1035.0 1200.0 315.6 : 182.4 347.4 498.0 680.4 884.4 1049.4 1200.0 498.0 : 165.0 315.6 498.0 702.0 867.0 1017.6 1200.0 663.0 : 150.6 333.0 537.0 702.0 852.6 1035.0 1200.0 813.7 : 182.4 386.3 551.3 702.0 884.4 1049.4 1200.0 996.1 : 203.9 368.9 519.6 702.0 867.0 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 203.9100 cents 33/32, 53.2729 cents 12/11, 150.6371 cents 2: 315.6413 .. 386.3137 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 3: 498.0450 .. 551.3179 cents 33/32, 53.2729 cents 16/15, 111.7313 cents 4: 648.6821 .. 701.9550 cents 33/32, 53.2729 cents 128/121, 97.3641 cents 5: 813.6863 .. 884.3587 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 6: 996.0900 .. 1049.3629 cents 33/32, 53.2729 cents 16/15, 111.7313 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.138024 Largest / Average step : 1.189475 Largest / Smallest step : 1.353651 Median interval of one step : 11/10, 165.0042 cents, amount: 2 Least squares average step : 167.05422 cents, oct.: 1169.37951 cents Scale is strictly proper Step pattern alph. order: ABCABCD Step pattern size order : BACBACD Scale is a Constant Structure, by a margin of 97.36412 cents Scale diversity : 1.315972 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.704636 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 : 121/120, 14.3672 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 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle All steps are superparticular (epimoric) Length of longest harmonic part : 3 at degree 2 Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions with margin 70.6724 cents: 5 6 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 15 Scale harmonicity : 0.026609 Average absolute harmonicity : 0.228805 Specific harmonicity : 0.141933 Fundamental : 1/90, -6.4919 octaves, 2.9070 Hz. Guide tone : 528, 9.0444 octaves, 138138.298 Hz. Exponens Consonantiae : 4.752000E+04, 15.53625 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 58.5, average 8.35714 Mersenne's string divisions : 2777775 Sum of van Prooijen's expressibility: 5.04679, average 0.72097 Sum of Tenney's harmonic distance : 11.17766, average 1.59681 Vogel's harmonic complexity : 12.57143 Wille's k value : 49 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 72.37047, average 2.58466 Lattice compactness (without 2's) : 42.56188, average 1.52007 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.57143 13 1 3: -2 .. 1 -0.42857 5 2 5: -1 .. 0 -0.57143 4 2 11: 0 .. 1 0.28571 2 2 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is weakly epimorphic with val: <7 10 18 23| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 11 17 26| Scale is weakly epimorphic with val: <7 12 16 22|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 25.3630 c. M:-43.4566 c. Lebeng 12: 2 1 2 2 1 2 2 P M ME S SD: 20.8434 c. M:-36.9508 c. G.M.Hypodorian, G.M.Aeolian, G.Hyperphrygian, Natural Minor, Melodic Minor descending, Asavari That, Mela Natabhairavi, Raga Jaunpuri, Adana, Darbari, Dhanyasi, Jingla, Gregorian nr.2, Makam Buselik, Nihavend, Peruvian Minor, Se, Chiao: China, Geez, Ezel: Ethiopia, Kiourdi descending: Greece, Cushak: Armenia 15: 2 2 2 2 2 2 3 SP M ME S SD: 18.4806 c. M: 36.0900 c. 16: 2 2 3 2 2 2 3 SP M ME S SD: 16.5269 c. M:-26.9550 c. Pseudo Pelog, Pelogic-7, Antiionian 19: 3 2 3 3 2 3 3 SP M ME S SD: 16.5514 c. M:-31.6876 c. Nineteen-tone Natural Minor, Aeolian 22: 3 3 3 3 3 3 4 SP M ME S SD: 8.3177 c. M: 14.2718 c. 29: 4 4 4 4 4 4 5 SP M ME S SD: 7.9510 c. M:-15.3932 c. 31: 4 4 5 4 4 5 5 SP D3 S SD: 6.5309 c. M:-10.3616 c. Neutral Diatonic Mixolydian 34: 5 4 5 5 4 5 6 SP T3 S SD: 6.2467 c. M:-11.4664 c. 41: 6 5 6 6 5 6 7 SP T3 S SD: 6.4348 c. M:-10.6055 c. 43: 6 5 7 6 5 7 7 SP SD: 5.8185 c. M: 8.6645 c. 46: 6 6 7 6 6 7 8 SP SD: 5.9822 c. M: 10.8753 c. 49: 7 6 7 7 6 8 8 SP SD: 5.5350 c. M: 8.2491 c. 53: 7 7 8 7 7 8 9 SP SD: 3.5410 c. M: 6.5137 c. 58: 8 7 9 8 7 9 10 SP SD: 3.5158 c. M: 6.7897 c. 60: 8 8 9 8 8 9 10 SP SD: 4.0056 c. M:-6.3137 c. 65: 9 8 10 9 8 10 11 SP SD: 1.1811 c. M: 1.7951 c. 118: 16 15 18 16 15 18 20 SP SD: 1.1886 c. M: 2.2924 c. 152: 21 19 23 21 19 23 26 SP SD: 0.6781 c. M: 1.3532 c. 183: 25 23 28 25 23 28 31 SP SD: 0.6892 c. M: 1.0698 c. 217: 30 27 33 30 27 33 37 SP SD: 0.5986 c. M:-0.8944 c. 224: 31 28 34 31 28 34 38 SP SD: 0.6924 c. M:-1.2365 c. 248: 34 31 38 34 31 38 42 SP SD: 0.6238 c. M: 1.1252 c. 270: 37 34 41 37 34 41 46 SP SD: 0.4608 c. M: 0.8270 c. 277: 38 35 42 38 35 42 47 SP SD: 0.4222 c. M:-0.7541 c. 335: 46 42 51 46 42 51 57 SP SD: 0.3280 c. M: 0.5520 c. 342: 47 43 52 47 43 52 58 SP SD: 0.2284 c. M:-0.4012 c. 494: 68 62 75 68 62 75 84 SP SD: 0.1169 c. M:-0.1780 c. 677: 93 85 103 93 85 103 115 SP SD: 0.1026 c. M: 0.1593 c. 829: 114 104 126 114 104 126 141 SP SD: 0.1134 c. M: 0.1913 c. 836: 115 105 127 115 105 127 142 SP SD: 0.1086 c. M:-0.1893 c. 1019: 140 128 155 140 128 155 173 SP SD: 0.0970 c. M:-0.1809 c. 1106: 152 139 168 152 139 168 188 SP SD: 0.0747 c. M: 0.1198 c. 1171: 161 147 178 161 147 178 199 SP SD: 0.0173 c. M: 0.0262 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: 19.4529 cents 3 x x 4 x 5 x 6 S SD: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 21.2891 cents 5 x 6 x 7:8:9:10 S SD: 16.6718 cents 6 x 7:8:9:10:11:12 S SD: 18.0469 cents 7:8 x 9:10:11:12:14 S SD: 20.6529 cents 8:9:10:11:12:13:14:16 S SD: 15.8589 cents 9:10:11:12:13:14:16:18 S SD: 9.4643 cents 10:11:12:13:15:16:18:20 SD: 8.9184 cents 15:17:18:20:22:24:27:30 SD: 7.9969 cents 17:19:20:23:25:27:30:34 SD: 7.7211 cents 18:20:22:24:26:29:32:36 SD: 6.6302 cents 19:21:23:25:28:30:34:38 SD: 5.6165 cents 20:22:24:27:29:32:36:40 SD: 5.1834 cents 21:23:25:28:31:34:37:42 SD: 4.5917 cents 28:31:34:37:41:45:50:56 SD: 4.3172 cents 30:33:36:40:44:48:53:60 SD: 1.5506 cents 60:66:72:80:88:96:107:120 SD: 0.7717 cents 90:99:108:120:132:144:160:180 S SD: 0.0000 cents