Scala analysis: xen09-wilson-marwa-17a-03
Marwa permutation 3 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: 5/4 386.313714 major third 2: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 3: 35/24 653.184619 septimal semi-diminished fifth 4: 5/3 884.358713 major sixth, BP sixth 5: 140/81 947.319617 6: 35/18 1151.229619 septimal semi-diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 5/4 386.3137 major third 2: 28/27 62.9609 Archytas' 1/3-tone 3: 9/8 203.9100 major whole tone 4: 8/7 231.1741 septimal whole tone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 9/8 203.9100 major whole tone 7: 36/35 48.7704 septimal diesis, 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 5/4 386.314 cents major third 2: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 2 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 9/7 435.084 cents septimal major third, BP third 2: 1 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: 1 54/35 750.725 cents septimal semi-augmented fifth 5: 2 14/9 764.916 cents septimal minor sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 12/7 933.129 cents septimal major sixth 5: 1 140/81 947.320 cents 6: 1 8/5 813.686 cents minor sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/14 1137.039 cents septimal major seventh 6: 1 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 386.3 449.3 653.2 884.4 947.3 1151.2 1200.0 386.3 : 63.0 266.9 498.0 561.0 764.9 813.7 1200.0 449.3 : 203.9 435.1 498.0 702.0 750.7 1137.0 1200.0 653.2 : 231.2 294.1 498.0 546.8 933.1 996.1 1200.0 884.4 : 63.0 266.9 315.6 702.0 764.9 968.8 1200.0 947.3 : 203.9 252.7 639.0 702.0 905.9 1137.0 1200.0 1151.2: 48.8 435.1 498.0 702.0 933.1 996.1 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: 252.6804 .. 449.2746 cents 2450/2187, 196.5942 cents 162/175,-133.6333 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 .. 947.3196 cents 2450/2187, 196.5942 cents 162/175,-133.6333 cents 6: 813.6863 .. 1151.2296 cents 175/144, 337.5433 cents 162/175,-133.6333 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 : 191.61305 cents, oct.: 1341.29137 cents Scale is not proper Step pattern alph. order: ABCDBCE Step pattern size order : EBCDBCA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 21.50629 cents Scale diversity : 1.477280 Lumma stability : 0.081284 Lumma impropriety factor : 0.416298 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 : 245/243, 14.1905 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 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.030910 Average absolute harmonicity : 0.198871 Specific harmonicity : 0.150574 Fundamental : 1/648, -9.3399 octaves, 0.4037 Hz. Guide tone : 140, 7.1293 octaves, 36627.579 Hz. Exponens Consonantiae : 9.072000E+04, 16.46913 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 207.5, average 29.64286 Mersenne's string divisions : 1542461544 Sum of van Prooijen's expressibility: 7.93863, average 1.13409 Sum of Tenney's harmonic distance : 15.53182, average 2.21883 Vogel's harmonic complexity : 18.14286 Wille's k value : 472 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 84.70997, average 3.02536 Lattice compactness (without 2's) : 58.05826, average 2.07351 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.42857 9 1 3: -4 .. 0 -1.57143 11 5: 0 .. 1 0.85714 6 2 7: 0 .. 1 0.57143 4 4 Average exponent except 2's :-1 / 7 =-0.14286 Average absolute exponent except 2's: 21 / 7 = 3.00000 Scale is weakly epimorphic with val: <7 10 18 18| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 2 0 1 2 0 1 1 N T3 SD: 89.7804 c. M: 138.8989 c. 8: 3 0 1 2 0 2 0 N SD: 40.9659 c. M:-63.6863 c. 9: 3 0 2 2 0 2 0 N SD: 33.3161 c. M: 49.2746 c. 11: 4 0 2 2 1 2 0 N G SD: 30.1840 c. M:-50.0499 c. 13: 4 1 2 2 1 2 1 N SD: 28.9006 c. M: 53.5895 c. 14: 4 1 2 3 1 2 1 N SD: 32.2295 c. M: 53.1846 c. 15: 5 1 2 3 1 2 1 N SD: 18.7475 c. M: 31.2296 c. 16: 5 1 3 3 1 2 1 N SD: 18.1395 c. M:-27.6804 c. 18: 6 1 3 3 1 3 1 N SD: 14.6408 c. M: 17.8963 c. 19: 6 1 3 4 1 3 1 N SD: 10.5525 c. M: 21.6057 c. 22: 7 1 4 4 1 4 1 N D3 SD: 10.4148 c. M: 20.0469 c. 24: 8 1 4 5 1 4 1 N SD: 8.0297 c. M:-15.6413 c. 27: 9 1 5 5 1 5 1 N D3 SD: 9.4662 c. M: 13.9863 c. 29: 9 2 5 5 2 5 1 N SD: 9.3953 c. M: 15.3932 c. 30: 10 1 5 6 2 5 1 N SD: 10.0277 c. M:-13.6863 c. 33: 11 1 6 6 2 6 1 N SD: 9.6255 c. M:-13.6863 c. 34: 11 2 6 6 2 6 1 N SD: 9.3732 c. M:-17.4036 c. 35: 11 2 6 7 2 6 1 N SD: 8.6226 c. M:-14.4847 c. 37: 12 2 6 7 2 6 2 N SD: 7.8565 c. M: 16.0945 c. 38: 12 2 7 7 2 6 2 N SD: 7.6733 c. M: 14.3875 c. 41: 13 2 7 8 2 7 2 N SD: 8.2426 c. M: 10.7343 c. 42: 14 2 7 8 2 7 2 N SD: 7.1388 c. M:-13.6863 c. 43: 14 2 7 9 2 7 2 N SD: 6.3480 c. M: 11.3242 c. 46: 15 2 8 9 2 8 2 N SD: 4.5501 c. M: 8.1892 c. 53: 17 3 9 10 3 9 2 N SD: 2.7621 c. M:-3.6238 c. 72: 23 4 12 14 4 12 3 N SD: 2.0458 c. M: 3.1846 c. 99: 32 5 17 19 5 17 4 N SD: 1.1164 c. M: 1.8651 c. 152: 49 8 26 29 8 26 6 N SD: 1.0082 c. M:-2.0785 c. 171: 55 9 29 33 9 29 7 N SD: 0.2926 c. M: 0.5530 c. 395: 127 21 67 76 21 67 16 N SD: 0.3298 c. M:-0.5285 c. 441: 142 23 75 85 23 75 18 N SD: 0.2062 c. M: 0.3808 c. 494: 159 26 84 95 26 84 20 N SD: 0.1442 c. M:-0.2567 c. 665: 214 35 113 128 35 113 27 N SD: 0.0874 c. M: 0.1483 c. 836: 269 44 142 161 44 142 34 N SD: 0.0978 c. M: 0.1893 c. 935: 301 49 159 180 49 159 38 N SD: 0.0775 c. M: 0.1538 c. 1106: 356 58 188 213 58 188 45 N SD: 0.0734 c. M: 0.1225 c. 1277: 411 67 217 246 67 217 52 N SD: 0.0890 c. M: 0.0996 c. 1354: 436 71 230 261 71 230 55 N SD: 0.0759 c. M:-0.1317 c. 1525: 491 80 259 294 80 259 62 N SD: 0.0620 c. M:-0.1003 c. 1600: 515 84 272 308 84 272 65 N SD: 0.0610 c. M: 0.1087 c. 1771: 570 93 301 341 93 301 72 N SD: 0.0610 c. M: 0.1125 c. 1795: 578 94 305 346 94 305 73 N SD: 0.0558 c. M:-0.0981 c. 1848: 595 97 314 356 97 314 75 N SD: 0.0621 c. M:-0.0830 c. 1966: 633 103 334 379 103 334 80 N SD: 0.0545 c. M: 0.0819 c. 2019: 650 106 343 389 106 343 82 N SD: 0.0425 c. M:-0.0801 c. 2190: 705 115 372 422 115 372 89 N SD: 0.0370 c. M:-0.0776 c. 2289: 737 120 389 441 120 389 93 N SD: 0.0296 c. M:-0.0559 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 24.3852 cents 3 x 4 x 5 x x 6 S SD: 16.2568 cents 4:5 x 6 x 7 x 8 S SD: 13.3254 cents 5:6 x 7:8:9 x 10 S SD: 28.2295 cents 6 x 8:9:10 x x 12 S SD: 17.2429 cents 7 x 9:10 x 12 x 14 SD: 10.2378 cents 8:10 x 12:13:14 x 16 S SD: 13.8018 cents 9:11:12:13:15:16 x 18 SD: 13.4838 cents 10 x 13:15 x 17:19:20 SD: 13.8965 cents 11:14 x 16:18:19:21:22 SD: 9.1483 cents 13:16:17:19:22 x 25:26 SD: 7.5076 cents 14 x 18:20:23:24:27:28 SD: 8.3315 cents 15:19 x 22:25:26:29:30 SD: 4.5520 cents 18 x 23:26:30:31:35:36 SD: 5.0918 cents 20:25:26:29:33:35:39:40 SD: 4.3153 cents 24:30:31:35:40:41:47:48 SD: 3.4956 cents 33:41:43:48:55:57:64:66 SD: 2.1808 cents 37:46:48:54:62:64:72:74 SD: 1.9288 cents 44:55:57:64:73:76:86:88 SD: 1.8377 cents 48:60:62:70:80:83:93:96 SD: 1.2562 cents 72:90:93:105:120:124:140:144 SD: 1.2514 cents 81:101:105:118:135:140:158:162 SD: 1.0281 cents 85:106:110:124:142:147:165:170 SD: 1.0254 cents 87:109:113:127:145:150:169:174 SD: 1.0248 cents 88:110:114:128:147:152:171:176 SD: 0.8980 cents 92:115:119:134:153:159:179:184 SD: 0.8354 cents 111:139:144:162:185:192:216:222 SD: 0.5865 cents 129:161:167:188:215:223:251:258 SD: 0.5578 cents 144:180:187:210:240:249:280:288 SD: 0.4548 cents 159:199:206:232:265:275:309:318 SD: 0.4216 cents 192:240:249:280:320:332:373:384 SD: 0.2705 cents 216:270:280:315:360:373:420:432 SD: 0.2209 cents 321:401:416:468:535:555:624:642 SD: 0.2089 cents 327:409:424:477:545:565:636:654 SD: 0.2050 cents 360:450:467:525:600:622:700:720 SD: 0.1975 cents 375:469:486:547:625:648:729:750 SD: 0.1737 cents 408:510:529:595:680:705:793:816 SD: 0.1331 cents 432:540:560:630:720:747:840:864 SD: 0.1104 cents 600:750:778:875:1000:1037:1167:1200 SD: 0.1003 cents