Scala analysis: xen09-wilson-marwa-18a-08
Marwa permutation 8 from Figure 18a, Ptolemy 12/11 11/10 10/9
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: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 22/15 663.049228 undecimal diminished fifth 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: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 10/9 182.4037 minor whole tone 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 10/9 182.4037 minor whole tone 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 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: 1 6/5 315.641 cents minor third 2: 2 40/33 333.041 cents 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 99/80 368.914 cents 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: 1 160/99 831.086 cents 5: 1 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 2 33/20 866.959 cents 5: 1 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 : 165.0 347.4 498.0 663.0 845.5 996.1 1200.0 165.0 : 182.4 333.0 498.0 680.4 831.1 1035.0 1200.0 347.4 : 150.6 315.6 498.0 648.7 852.6 1017.6 1200.0 498.0 : 165.0 347.4 498.0 702.0 867.0 1049.4 1200.0 663.0 : 182.4 333.0 537.0 702.0 884.4 1035.0 1200.0 845.5 : 150.6 354.5 519.6 702.0 852.6 1017.6 1200.0 996.1 : 203.9 368.9 551.3 702.0 867.0 1049.4 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 .. 368.9142 cents 33/32, 53.2729 cents 16/15, 111.7313 cents 3: 498.0450 .. 551.3179 cents 33/32, 53.2729 cents 320/297, 129.1308 cents 4: 648.6821 .. 701.9550 cents 33/32, 53.2729 cents 128/121, 97.3641 cents 5: 831.0858 .. 884.3587 cents 33/32, 53.2729 cents 320/297, 129.1308 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 : 168.64255 cents, oct.: 1180.49784 cents Scale is strictly proper Step pattern alph. order: ABCABCD Step pattern size order : BCABCAD Scale is a Constant Structure, by a margin of 97.36412 cents Scale diversity : 1.283021 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.733635 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 Most common triad is 0.0 701.955 1049.363 cents, amount: 2 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 : 1 at degree 0 Length of longest subharmonic part : 3 at degree 2 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 Limited inverse transpositions with margin 53.2729 cents: 6 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 27 Scale harmonicity : 0.026609 Average absolute harmonicity : 0.210561 Specific harmonicity : 0.123701 Fundamental : 1/270, -8.0768 octaves, 0.9690 Hz. Guide tone : 176, 7.4594 octaves, 46046.099 Hz. Exponens Consonantiae : 4.752000E+04, 15.53625 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 92.0, average 13.14286 Mersenne's string divisions : 5516700 Sum of van Prooijen's expressibility: 6.12160, average 0.87451 Sum of Tenney's harmonic distance : 13.16893, average 1.88128 Vogel's harmonic complexity : 17.28571 Wille's k value : 148 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 75.56970, average 2.69892 Lattice compactness (without 2's) : 48.53015, average 1.73322 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.28571 11 1 3: -3 .. 0 -1.28571 9 2 5: -1 .. 0 -0.28571 2 11: 0 .. 1 0.57143 4 4 Average exponent except 2's :-7 / 7 =-1.00000 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is JI-epimorphic with val: <7 11 16 24| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 17.0342 c. M:-32.4814 c. Lebeng 16: 2 3 2 2 2 2 3 P D3 S SD: 19.7084 c. M:-27.5921 c. 17: 2 3 2 2 3 2 3 SP M ME S SD: 14.3846 c. M: 27.7551 c. 20: 3 3 2 3 3 3 3 SP M ME S SD: 13.7310 c. M:-23.9100 c. 22: 3 3 3 3 3 3 4 SP M ME S SD: 14.5304 c. M: 27.2711 c. 23: 3 4 3 3 3 3 4 SP D3 S SD: 13.7253 c. M:-23.6941 c. 24: 3 4 3 3 4 3 4 SP M ME S SD: 7.9455 c. M: 15.0042 c. Neutral Mixolydian, Iced Blizzard 29: 4 4 4 4 4 4 5 SP M ME S SD: 9.2558 c. M: 17.8667 c. 31: 4 5 4 4 5 4 5 SP M ME S SD: 6.5606 c. M:-10.3616 c. Neutral Mixolydian 34: 5 5 4 5 5 4 6 SP T3 SD: 6.5316 c. M:-11.4664 c. 41: 6 6 5 6 6 5 7 SP T3 SD: 5.8760 c. M:-10.6055 c. 45: 6 7 6 6 7 5 8 SP SD: 6.1402 c. M: 9.4233 c. 51: 7 8 6 7 8 6 9 SP SD: 4.2805 c. M: 7.8547 c. 53: 7 8 7 7 8 7 9 SP T3 S SD: 5.4005 c. M: 7.7853 c. 58: 8 9 7 8 9 7 10 SP SD: 2.3595 c. M:-4.3162 c. 65: 9 10 8 9 10 8 11 SP SD: 2.0775 c. M:-3.7778 c. 94: 13 14 12 13 14 12 16 SP SD: 1.5817 c. M: 2.8997 c. 101: 14 15 13 14 15 13 17 SP SD: 1.8290 c. M: 2.8535 c. 111: 15 17 14 15 17 14 19 SP SD: 2.0969 c. M: 3.5898 c. 118: 16 18 15 16 18 15 20 SP SD: 1.4317 c. M: 2.2924 c. 125: 17 19 16 17 19 16 21 SP SD: 1.4163 c. M:-2.3100 c. 152: 21 23 19 21 23 19 26 SP SD: 0.7002 c. M: 1.3532 c. 159: 22 24 20 22 24 20 27 SP SD: 0.5844 c. M:-1.1017 c. 183: 25 28 23 25 28 23 31 SP SD: 0.5892 c. M: 1.0698 c. 217: 30 33 27 30 33 27 37 SP SD: 0.6614 c. M:-0.9792 c. 270: 37 41 34 37 41 34 46 SP SD: 0.6460 c. M: 1.0085 c. 277: 38 42 35 38 42 35 47 SP SD: 0.4611 c. M: 0.8375 c. 335: 46 51 42 46 51 42 57 SP SD: 0.2012 c. M: 0.3627 c. 342: 47 52 43 47 52 43 58 SP SD: 0.1886 c. M:-0.4012 c. 494: 68 75 62 68 75 62 84 SP SD: 0.1075 c. M:-0.1780 c. 677: 93 103 85 93 103 85 115 SP SD: 0.0835 c. M: 0.1593 c. 829: 114 126 104 114 126 104 141 SP SD: 0.0942 c. M: 0.1913 c. 836: 115 127 105 115 127 105 142 SP SD: 0.0614 c. M:-0.1087 c. 1171: 161 178 147 161 178 147 199 SP SD: 0.0170 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: 12.9686 cents 4 x 5 x 6 x 7:8 S SD: 15.3514 cents 5 x 6 x 7:8:9:10 S SD: 18.9388 cents 6 x 7:8:9:10:11:12 S SD: 18.5229 cents 7:8 x 9:10:11:12:14 S SD: 22.5749 cents 8:9:10:11:12:13:14:16 S SD: 12.8941 cents 9:10:11:12:13:15:16:18 SD: 7.1643 cents 17:19:21:23:25:28:30:34 SD: 6.7928 cents 18:20:22:24:26:29:32:36 SD: 5.3315 cents 19:21:23:25:28:31:34:38 SD: 4.6788 cents 21:23:26:28:31:34:37:42 SD: 4.6275 cents 22:24:27:29:32:36:39:44 SD: 4.3577 cents 27:30:33:36:40:44:48:54 S SD: 3.5152 cents 30:33:37:40:44:49:53:60 SD: 2.7801 cents 32:35:39:43:47:52:57:64 SD: 2.6526 cents 40:44:49:53:59:65:71:80 SD: 2.3082 cents 41:45:50:55:60:67:73:82 SD: 1.9430 cents 49:54:60:65:72:80:87:98 SD: 1.5939 cents 60:66:73:80:88:98:107:120 SD: 1.4766 cents 68:75:83:91:100:111:121:136 SD: 1.4239 cents 71:78:87:95:104:116:126:142 SD: 1.3952 cents 72:79:88:96:106:117:128:144 SD: 1.3268 cents 81:89:99:108:119:132:144:162 SD: 0.5002 cents 171:188:209:228:251:279:304:342 SD: 0.3789 cents 180:198:220:240:264:293:320:360 SD: 0.2812 cents 189:208:231:252:277:308:336:378 SD: 0.2145 cents 270:297:330:360:396:440:480:540 S SD: 0.0000 cents