Scala analysis: xen09-wilson-marwa-18a-01
Marwa permutation 1 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: 99/80 368.914230 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 22/15 663.049228 undecimal diminished fifth 5: 33/20 866.959229 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: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 9/8 203.9100 major whole tone 3: 10/9 182.4037 minor whole tone 4: 16/15 111.7313 minor diatonic semitone 5: 9/8 203.9100 major whole tone 6: 10/9 182.4037 minor whole tone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 2 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 1 40/33 333.041 cents 2: 1 99/80 368.914 cents 2: 2 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: 2 8/5 813.686 cents minor sixth 5: 1 160/99 831.086 cents 5: 1 33/20 866.959 cents 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 20/11 1034.996 cents large minor seventh 6: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 15/8 1088.269 cents classic 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 : 165.0 368.9 551.3 663.0 867.0 1049.4 1200.0 165.0 : 203.9 386.3 498.0 702.0 884.4 1035.0 1200.0 368.9 : 182.4 294.1 498.0 680.4 831.1 996.1 1200.0 551.3 : 111.7 315.6 498.0 648.7 813.7 1017.6 1200.0 663.0 : 203.9 386.3 537.0 702.0 905.9 1088.3 1200.0 867.0 : 182.4 333.0 498.0 702.0 884.4 996.1 1200.0 1049.4: 150.6 315.6 519.6 702.0 813.7 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 203.9100 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 2: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 256/243, 90.2250 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 .. 905.8650 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 6: 996.0900 .. 1088.2687 cents 135/128, 92.1787 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.534293 Largest / Average step : 1.189475 Largest / Smallest step : 1.825004 Median interval of one step : 10/9, 182.4037 cents, amount: 2 Least squares average step : 173.14255 cents, oct.: 1211.99786 cents Scale is strictly proper Step pattern alph. order: ABCDBCE Step pattern size order : CEDAEDB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.440363 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.603949 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 : 121/120, 14.3672 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 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 : 2 at degree 1 Length of longest subharmonic part : 2 at degree 6 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 classes 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.026609 Average absolute harmonicity : 0.175877 Specific harmonicity : 0.137857 Fundamental : 1/240, -7.9069 octaves, 1.0901 Hz. Guide tone : 198, 7.6294 octaves, 51801.862 Hz. Exponens Consonantiae : 4.752000E+04, 15.53625 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 164.5, average 23.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.81442, average 1.11635 Sum of Tenney's harmonic distance : 15.34323, average 2.19189 Vogel's harmonic complexity : 17.71429 Wille's k value : 148 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 79.03194, average 2.82257 Lattice compactness (without 2's) : 44.36109, average 1.58432 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.28571 13 1 3: -1 .. 2 0.14286 5 5: -1 .. 0 -0.57143 4 11: 0 .. 1 0.85714 6 6 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 12 18 24|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 21.1592 c. M: 37.0322 c. Lebeng 13: 2 2 2 1 2 2 2 SP M ME I SD: 21.1822 c. M: 36.1900 c. Horthatian 15: 2 3 2 1 3 2 2 P D3 SD: 16.2821 c. M:-31.0858 c. 17: 2 3 3 1 3 3 2 SP D3 I SD: 17.9603 c. M: 27.7551 c. Naghmeh Abuata, Naghmeh Afshari 20: 3 3 3 2 3 3 3 SP M ME I SD: 17.0324 c. M: 29.3629 c. 21: 3 3 4 2 3 3 3 SP T3 SD: 17.5948 c. M: 26.0571 c. 22: 3 4 3 2 4 3 3 SP D3 SD: 8.2577 c. M: 12.9993 c. 29: 4 5 4 3 5 4 4 SP D3 SD: 7.7287 c. M: 14.8802 c. 39: 5 7 6 3 7 6 5 SP SD: 8.0723 c. M: 16.8954 c. 40: 5 7 6 4 7 6 5 SP SD: 8.0324 c. M: 15.0042 c. 42: 6 7 6 4 7 7 5 SP SD: 6.6650 c. M: 9.8164 c. 43: 6 7 7 4 7 7 5 SP SD: 6.1151 c. M:-11.1022 c. 46: 6 8 7 4 8 7 6 SP SD: 6.4120 c. M: 10.8753 c. 50: 7 8 8 5 8 8 6 SP SD: 5.6294 c. M:-8.9508 c. 53: 7 9 8 5 9 8 7 SP SD: 6.5022 c. M: 7.9217 c. 54: 7 10 8 5 9 8 7 SP SD: 5.6462 c. M: 9.4487 c. 56: 8 9 9 5 9 9 7 SP SD: 5.2769 c. M: 9.8164 c. 58: 8 10 9 5 10 9 7 SP SD: 3.8652 c. M:-7.3027 c. 65: 9 11 10 6 11 10 8 SP SD: 1.6680 c. M:-2.9448 c. 87: 12 15 13 8 15 13 11 SP SD: 1.6407 c. M:-3.4996 c. 94: 13 16 14 9 16 14 12 SP SD: 1.5432 c. M: 2.5544 c. 137: 19 23 21 13 23 21 17 SP SD: 1.3817 c. M:-2.6442 c. 152: 21 26 23 14 26 23 19 SP SD: 1.1631 c. M:-2.1384 c. 159: 22 27 24 15 27 24 20 SP SD: 0.7794 c. M:-1.1017 c. 224: 31 38 34 21 38 34 28 SP SD: 0.8132 c. M:-1.2365 c. 248: 34 42 38 23 42 38 31 SP SD: 0.6342 c. M: 1.1723 c. 270: 37 46 41 25 46 41 34 SP SD: 0.4393 c. M: 0.8270 c. 335: 46 57 51 31 57 51 42 SP SD: 0.2187 c. M: 0.3627 c. 494: 68 84 75 46 84 75 62 SP SD: 0.1755 c. M:-0.3165 c. 677: 93 115 103 63 115 103 85 SP SD: 0.1392 c. M: 0.2289 c. 742: 102 126 113 69 126 113 93 SP SD: 0.1359 c. M:-0.2327 c. 764: 105 130 116 71 130 116 96 SP SD: 0.1308 c. M: 0.2220 c. 829: 114 141 126 77 141 126 104 SP SD: 0.1230 c. M:-0.2052 c. 836: 115 142 127 78 142 127 105 SP SD: 0.0743 c. M: 0.1218 c. 1171: 161 199 178 109 199 178 147 SP SD: 0.0124 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: 18.6808 cents 4 x 5 x 6 x 7:8 S SD: 22.7797 cents 5 x 6:7 x 8:9:10 S SD: 17.5022 cents 6:7 x 8:9:10:11:12 S SD: 20.4337 cents 7:8:9 x 10:12:13:14 S SD: 20.8901 cents 8:9:10:11:12:13:15:16 SD: 10.6353 cents 11:12:14:15:16:18:20:22 S SD: 8.3219 cents 13:14:16:18:19:21:24:26 SD: 7.9689 cents 17:19:21:23:25:28:31:34 SD: 5.8375 cents 21:23:26:29:31:35:39:42 SD: 4.6078 cents 26:29:32:36:38:43:48:52 SD: 4.5433 cents 29:32:36:40:43:48:53:58 SD: 3.2067 cents 30:33:37:41:44:50:55:60 SD: 3.0223 cents 37:41:46:51:54:61:68:74 SD: 2.6215 cents 42:46:52:58:62:69:77:84 SD: 2.4537 cents 43:47:53:59:63:71:79:86 SD: 2.0251 cents 51:56:63:70:75:84:94:102 SD: 1.7189 cents 60:66:74:83:88:99:110:120 SD: 1.7114 cents 62:68:77:85:91:102:114:124 SD: 1.7097 cents 67:74:83:92:98:111:123:134 SD: 1.6624 cents 71:78:88:98:104:117:130:142 SD: 1.2043 cents 80:88:99:110:117:132:147:160 SD: 0.9002 cents 88:97:109:121:129:145:161:176 SD: 0.8404 cents 101:111:125:139:148:167:185:202 SD: 0.6842 cents 109:120:135:150:160:180:200:218 SD: 0.5050 cents 131:144:162:180:192:216:240:262 SD: 0.4206 cents 229:252:283:315:336:378:420:458 SD: 0.4034 cents 232:255:287:319:340:383:425:464 SD: 0.3700 cents 240:264:297:330:352:396:440:480 S SD: 0.0000 cents