Scala analysis: xen09-wilson-marwa-17a-09
Marwa permutation 9 from Figure 17a, Archytas 28/27 36/35 5/4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 280/243 245.364616 2: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 3: 4/3 498.044999 perfect fourth 4: 5/3 884.358713 major sixth, BP sixth 5: 140/81 947.319617 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: 280/243 245.3646 2: 9/8 203.9100 major whole tone 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 5/4 386.3137 major third 5: 28/27 62.9609 Archytas' 1/3-tone 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 280/243 245.365 cents 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 9/7 435.084 cents septimal major third, BP third 2: 3 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 3: 1 6/5 315.641 cents minor third 3: 4 4/3 498.045 cents perfect fourth 3: 1 81/56 638.994 cents 3: 1 35/24 653.185 cents septimal semi-diminished fifth 4: 1 48/35 546.815 cents septimal semi-augmented fourth 4: 1 112/81 561.006 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 5/3 884.359 cents major sixth, BP sixth 5: 3 54/35 750.725 cents septimal semi-augmented fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 2 140/81 947.320 cents 5: 1 15/8 1088.269 cents classic major seventh 6: 1 8/5 813.686 cents minor sixth 6: 1 243/140 954.635 cents 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 27/14 1137.039 cents septimal major seventh 6: 2 35/18 1151.230 cents septimal semi-diminished octave 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 : 245.4 449.3 498.0 884.4 947.3 996.1 1200.0 245.4 : 203.9 252.7 639.0 702.0 750.7 954.6 1200.0 449.3 : 48.8 435.1 498.0 546.8 750.7 996.1 1200.0 498.0 : 386.3 449.3 498.0 702.0 947.3 1151.2 1200.0 884.4 : 63.0 111.7 315.6 561.0 764.9 813.7 1200.0 947.3 : 48.8 252.7 498.0 702.0 750.7 1137.0 1200.0 996.1 : 203.9 449.3 653.2 702.0 1088.3 1151.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 386.3137 cents 175/144, 337.5433 cents 36/35, 48.7704 cents 2: 111.7313 .. 449.2746 cents 175/144, 337.5433 cents 64/75,-274.5824 cents 3: 315.6413 .. 653.1846 cents 175/144, 337.5433 cents 162/175,-133.6333 cents 4: 546.8154 .. 884.3587 cents 175/144, 337.5433 cents 1152/1225,-106.3692 cents 5: 750.7254 .. 1088.2687 cents 175/144, 337.5433 cents 162/175,-133.6333 cents 6: 813.6863 .. 1151.2296 cents 175/144, 337.5433 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 3.515014 Largest / Average step : 2.253497 Largest / Smallest step : 7.921072 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 180.63301 cents, oct.: 1264.43109 cents Scale is not proper Step pattern alph. order: ABCDECB Step pattern size order : DCAEBAC Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 1.557433 Lumma stability : 0.081284 Lumma impropriety factor : 0.651213 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 : 19683/19600, 7.3158 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval class 1 Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 243 Scale harmonicity : 0.029395 Average absolute harmonicity : 0.219512 Specific harmonicity : 0.135587 Fundamental : 1/243, -7.9248 octaves, 1.0766 Hz. Guide tone : 560, 9.1293 octaves, 146510.317 Hz. Exponens Consonantiae : 1.360800E+05, 17.05410 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 424.5, average 60.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.96849, average 1.13836 Sum of Tenney's harmonic distance : 16.57747, average 2.36821 Vogel's harmonic complexity : 15.71429 Wille's k value : 202 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 92.14247, average 3.29080 Lattice compactness (without 2's) : 68.78185, average 2.45649 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 4 1.71429 12 1 3: -5 .. 0 -2.28571 16 2 5: 0 .. 1 0.57143 4 1 7: 0 .. 1 0.42857 3 3 Average exponent except 2's :-9 / 7 =-1.28571 Average absolute exponent except 2's: 23 / 7 = 3.28571 Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 12 17 18| Scale is weakly epimorphic with val: <7 12 18 19|
FIT/MODE
7: 2 1 0 2 1 0 1 N T3 SD: 56.5592 c. M:-97.4925 c. 8: 2 1 0 3 0 1 1 N SD: 39.0676 c. M:-54.6354 c. 9: 2 1 1 3 0 0 2 N SD: 39.0230 c. M: 62.7567 c. 10: 2 2 0 3 1 0 2 N SD: 25.9929 c. M: 44.3587 c. 11: 2 2 1 3 1 0 2 N G SD: 25.8633 c. M:-47.4095 c. 13: 3 2 0 5 0 1 2 N SD: 26.5603 c. M:-38.7182 c. 14: 3 2 1 4 1 1 2 N SD: 19.4450 c. M:-32.4814 c. 16: 3 3 1 5 1 0 3 N SD: 19.2631 c. M:-27.6804 c. 18: 4 3 0 6 1 1 3 N SD: 17.9872 c. M: 31.3783 c. 19: 4 3 1 6 1 1 3 N SD: 7.2184 c. M:-14.4363 c. 24: 5 4 1 8 1 1 4 N SD: 6.4692 c. M:-15.6413 c. 34: 7 6 1 11 2 1 6 N SD: 5.4353 c. M:-9.5489 c. 43: 9 7 2 14 2 2 7 N SD: 5.4804 c. M:-8.6645 c. 48: 10 8 2 15 3 2 8 N SD: 4.4061 c. M: 9.3587 c. 49: 10 8 2 16 3 2 8 N SD: 6.2298 c. M: 8.4583 c. 53: 11 9 2 17 3 2 9 N SD: 2.4267 c. M:-3.6920 c. 72: 15 12 3 23 4 3 12 N SD: 2.6554 c. M:-4.6354 c. 77: 16 13 3 25 4 3 13 N SD: 2.7230 c. M:-3.9860 c. 94: 19 16 4 30 5 4 16 N SD: 2.1844 c. M: 3.5076 c. 99: 20 17 4 32 5 4 17 N SD: 1.6375 c. M: 2.9404 c. 118: 24 20 5 38 6 5 20 N SD: 1.0620 c. M: 1.8170 c. 147: 30 25 6 47 8 6 25 N SD: 1.0636 c. M: 2.7261 c. 152: 31 26 6 49 8 6 26 N SD: 0.6796 c. M: 1.3532 c. 171: 35 29 7 55 9 7 29 N SD: 0.2107 c. M:-0.4012 c. 494: 101 84 20 159 26 20 84 N SD: 0.0947 c. M: 0.1482 c. 665: 136 113 27 214 35 27 113 N SD: 0.0645 c. M: 0.1482 c. 1277: 261 217 52 411 67 52 217 N SD: 0.0752 c. M: 0.1023 c. 1354: 277 230 55 436 71 55 230 N SD: 0.0871 c. M:-0.1317 c. 1448: 296 246 59 466 76 59 246 N SD: 0.0700 c. M: 0.1046 c. 1501: 307 255 61 483 79 61 255 N SD: 0.0684 c. M: 0.1482 c. 1600: 327 272 65 515 84 65 272 N SD: 0.0761 c. M: 0.1146 c. 1619: 331 275 66 521 85 66 275 N SD: 0.0729 c. M: 0.1092 c. 1624: 332 276 66 523 85 66 276 N SD: 0.0529 c. M:-0.1240 c. 1677: 343 285 68 540 88 68 285 N SD: 0.0651 c. M:-0.0993 c. 1771: 362 301 72 570 93 72 301 N SD: 0.0609 c. M: 0.1125 c. 1795: 367 305 73 578 94 73 305 N SD: 0.0400 c. M:-0.0981 c. 1848: 378 314 75 595 97 75 314 N SD: 0.0588 c. M:-0.0899 c. 1942: 397 330 79 625 102 79 330 N SD: 0.0542 c. M: 0.1157 c. 1966: 402 334 80 633 103 80 334 N SD: 0.0379 c. M:-0.0767 c. 2118: 433 360 86 682 111 86 360 N SD: 0.0369 c. M:-0.0606 c. 2289: 468 389 93 737 120 93 389 N SD: 0.0206 c. M:-0.0450 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: 91.2019 cents 3 x x 4:5 x x 6 S SD: 0.0000 cents 4 x 5 x x 7 x 8 SD: 22.1776 cents 5:6 x 7:8 x 9:10 S SD: 26.4807 cents 6:7 x 8:10 x 11:12 S SD: 11.4900 cents 7:8:9 x x 12 x 14 S SD: 6.1447 cents 8:9:10:11:13:14 x 16 SD: 17.4039 cents 9:10 x 12:15 x 16:18 S SD: 12.5922 cents 10:12:13 x x 17:18:20 SD: 15.8090 cents 11:13:14:15:18:19:20:22 SD: 11.9260 cents 12:14 x 16:20:21 x 24 S SD: 6.0829 cents 13:15:17 x 22 x 23:26 SD: 6.3356 cents 16:18:21 x 27:28 x 32 SD: 11.1464 cents 17:20:22:23:28:29:30:34 SD: 7.8779 cents 18:21:23:24:30:31:32:36 SD: 4.7839 cents 19:22 x 25:32:33:34:38 SD: 5.5922 cents 21:24:27:28:35:36:37:42 SD: 4.1532 cents 22:25 x 29:37:38:39:44 SD: 5.8716 cents 24:28:31:32:40:41:43:48 SD: 4.7185 cents 26:30:34:35:43:45:46:52 SD: 3.9479 cents 27:31:35:36:45:47:48:54 SD: 1.9702 cents 33:38:43:44:55:57:59:66 SD: 1.9124 cents 45:52:58:60:75:78:80:90 SD: 1.7334 cents 51:59:66:68:85:88:91:102 SD: 1.4631 cents 54:62:70:72:90:93:96:108 SD: 1.2514 cents 78:90:101:104:130:135:139:156 SD: 0.8106 cents 99:114:128:132:165:171:176:198 SD: 0.6822 cents 111:128:144:148:185:192:197:222 SD: 0.5331 cents 132:152:171:176:220:228:235:264 SD: 0.4480 cents 162:187:210:216:270:280:288:324 SD: 0.4412 cents 165:190:214:220:275:285:293:330 SD: 0.3837 cents 189:218:245:252:315:327:336:378 SD: 0.3567 cents 210:242:272:280:350:363:373:420 SD: 0.3015 cents 216:249:280:288:360:373:384:432 SD: 0.2470 cents 243:280:315:324:405:420:432:486 SD: 0.0000 cents