Scala analysis: xen09-wilson-marwa-15a-02
Marwa permutation 2 from Figure 15a, Ptolemy 12/11 22/21 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: 14/11 417.507964 undecimal diminished fourth or major third 3: 63/44 621.417966 4: 14/9 764.915905 septimal minor sixth 5: 7/4 968.825906 harmonic seventh 6: 21/11 1119.462965 undecimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 22/21 80.5370 undecimal minor semitone 1: 7/6 266.8709 septimal minor third 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 9/8 203.9100 major whole tone 4: 88/81 143.4979 2nd undecimal neutral second 5: 9/8 203.9100 major whole tone 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 22/21 80.5370 undecimal minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 88/81 143.498 cents 2nd undecimal neutral second 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 3 11/9 347.408 cents undecimal neutral third 2: 2 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 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 11/7 782.492 cents undecimal augmented fifth 5: 2 44/27 845.453 cents neutral sixth 5: 3 18/11 852.592 cents undecimal neutral sixth 5: 1 7/4 968.826 cents harmonic seventh 6: 1 12/7 933.129 cents septimal major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 81/44 1056.502 cents 2nd undecimal neutral seventh 6: 1 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 : 266.9 417.5 621.4 764.9 968.8 1119.5 1200.0 266.9 : 150.6 354.5 498.0 702.0 852.6 933.1 1200.0 417.5 : 203.9 347.4 551.3 702.0 782.5 1049.4 1200.0 621.4 : 143.5 347.4 498.0 578.6 845.5 996.1 1200.0 764.9 : 203.9 354.5 435.1 702.0 852.6 1056.5 1200.0 968.8 : 150.6 231.2 498.0 648.7 852.6 996.1 1200.0 1119.5: 80.5 347.4 498.0 702.0 845.5 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 .. 417.5080 cents 49/44, 186.3339 cents 48/49,-35.6968 cents 3: 435.0841 .. 621.4180 cents 49/44, 186.3339 cents 99/98, 17.5761 cents 4: 578.5820 .. 764.9159 cents 49/44, 186.3339 cents 3872/3969,-42.8359 cents 5: 782.4920 .. 968.8259 cents 49/44, 186.3339 cents 99/98, 17.5761 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 : 185.61937 cents, oct.: 1299.33558 cents Scale is not proper Step pattern alph. order: ABCDCBE Step pattern size order : ECDBDCA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.559442 Lumma stability : 0.163522 Lumma impropriety factor : 0.095191 Rothenberg efficiency : 0.423129 redundancy: 0.576871 Efficiency x scale size : 2.961905 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 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 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Best fifths form a closed circle 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 n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 63 Scale harmonicity : 0.023734 Average absolute harmonicity : 0.186746 Specific harmonicity : 0.118630 Fundamental : 1/396, -8.6294 octaves, 0.6607 Hz. Guide tone : 126, 6.9773 octaves, 32964.821 Hz. Exponens Consonantiae : 4.989600E+04, 15.60664 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 107.0, average 15.28571 Mersenne's string divisions : 844615200 Sum of van Prooijen's expressibility: 6.80739, average 0.97248 Sum of Tenney's harmonic distance : 13.46573, average 1.92368 Vogel's harmonic complexity : 20.00000 Wille's k value : 346 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 70.40584, average 2.51449 Lattice compactness (without 2's) : 49.47636, average 1.76701 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.28571 8 1 3: -2 .. 2 0.00000 6 7: 0 .. 1 0.85714 6 3 11: -1 .. 0 -0.42857 3 3 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is weakly epimorphic with val: <7 10 18 22| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 87.1506 c. M: 111.6830 c. Lebeng 8: 2 1 1 1 1 1 1 P M ME S SD: 42.0826 c. M: 69.4630 c. 9: 2 1 2 1 1 1 1 N D3 S SD: 33.0197 c. M: 52.7963 c. 10: 2 1 2 1 2 1 1 P M ME S SD: 34.1020 c. M: 57.5080 c. 11: 2 2 2 1 2 1 1 N D3 SD: 26.2117 c. M: 48.6891 c. 12: 3 1 2 2 2 1 1 N T3 SD: 25.1973 c. M:-35.0841 c. 14: 3 2 2 2 2 2 1 P T3 SD: 14.2396 c. M: 25.9688 c. 17: 4 2 3 2 3 2 1 N SD: 12.4080 c. M:-19.4094 c. 25: 6 3 4 3 4 3 2 N SD: 11.8902 c. M:-21.1291 c. 27: 6 3 5 3 5 3 2 N SD: 8.8214 c. M: 17.5080 c. 31: 7 4 5 4 5 4 2 N SD: 5.1669 c. M:-9.2776 c. 41: 9 5 7 5 7 5 3 N SD: 5.2812 c. M: 7.7519 c. 46: 10 6 8 5 8 6 3 N SD: 4.5747 c. M: 8.3942 c. 58: 13 7 10 7 10 7 4 N SD: 2.2956 c. M: 3.7149 c. 72: 16 9 12 9 12 9 5 N SD: 2.3565 c. M: 4.7513 c. 77: 17 10 13 9 13 10 5 N SD: 2.1870 c. M:-3.2713 c. 89: 20 11 15 11 15 11 6 N SD: 1.9473 c. M:-3.6234 c. 104: 23 13 18 12 18 13 7 N SD: 1.7360 c. M: 3.3774 c. 118: 26 15 20 14 20 15 8 N SD: 1.7112 c. M: 2.7242 c. 135: 30 17 23 16 23 17 9 N SD: 0.4269 c. M:-0.8043 c. 328: 73 41 56 39 56 41 22 N SD: 0.3904 c. M:-0.6863 c. 342: 76 43 58 41 58 43 23 N SD: 0.2291 c. M: 0.4049 c. 477: 106 60 81 57 81 60 32 N SD: 0.1450 c. M: 0.2724 c. 612: 136 77 104 73 104 77 41 N SD: 0.1640 c. M: 0.2100 c. 670: 149 84 114 80 114 84 45 N SD: 0.1091 c. M: 0.1945 c. 836: 186 105 142 100 142 105 56 N SD: 0.1296 c. M:-0.1954 c. 1012: 225 127 172 121 172 127 68 N SD: 0.0801 c. M: 0.1167 c. 1147: 255 144 195 137 195 144 77 N SD: 0.0703 c. M: 0.1382 c. 1371: 305 172 233 164 233 172 92 N SD: 0.0588 c. M:-0.1019 c. 1506: 335 189 256 180 256 189 101 N SD: 0.0623 c. M:-0.0984 c. 1713: 381 215 291 205 291 215 115 N SD: 0.0327 c. M:-0.0578 c. 1848: 411 232 314 221 314 232 124 N SD: 0.0150 c. M:-0.0245 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 4 x x 5 x 6 S SD: 38.9029 cents 4 x 5 x 6:7 x 8 S SD: 17.5662 cents 5:6 x 7:8:9 x 10 S SD: 18.6003 cents 6:7:8 x 9 x 11:12 SD: 24.7906 cents 7:8:9:10:11:12:13:14 H SD: 10.5588 cents 9 x 11:13:14:16:17:18 SD: 13.1525 cents 11:13:14:16:17:19:21:22 SD: 6.1970 cents 18:21:23:26:28:32:34:36 SD: 5.2694 cents 23:27:29:33:36:40:44:46 SD: 3.5983 cents 25:29:32:36:39:44:48:50 SD: 3.2327 cents 32:37:41:46:50:56:61:64 SD: 3.1549 cents 36:42:46:52:56:63:69:72 SD: 2.5756 cents 41:48:52:59:64:72:78:82 SD: 2.2917 cents 44:51:56:63:68:77:84:88 SD: 2.2786 cents 47:55:60:67:73:82:90:94 SD: 1.8928 cents 48:56:61:69:75:84:92:96 SD: 1.8078 cents 55:64:70:79:86:96:105:110 SD: 1.7562 cents 56:65:71:80:87:98:107:112 SD: 1.7200 cents 65:76:83:93:101:114:124:130 SD: 1.1798 cents 77:90:98:110:120:135:147:154 SD: 0.9725 cents 88:103:112:126:137:154:168:176 SD: 0.8264 cents 113:132:144:162:176:198:216:226 SD: 0.7654 cents 120:140:153:172:187:210:229:240 SD: 0.6837 cents 121:141:154:173:188:212:231:242 SD: 0.6192 cents 132:154:168:189:205:231:252:264 SD: 0.4018 cents 180:210:229:258:280:315:344:360 SD: 0.3827 cents 187:218:238:268:291:327:357:374 SD: 0.3656 cents 209:244:266:299:325:366:399:418 SD: 0.3271 cents 216:252:275:309:336:378:412:432 SD: 0.3192 cents 241:281:307:345:375:422:460:482 SD: 0.3185 cents 252:294:321:361:392:441:481:504 SD: 0.2488 cents 264:308:336:378:411:462:504:528 SD: 0.2007 cents 385:449:490:551:599:674:735:770 SD: 0.1776 cents 396:462:504:567:616:693:756:792 SD: 0.0000 cents