Scala analysis: xen09-wilson-marwa-17a-06
Marwa permutation 6 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: 4/3 498.044999 perfect fourth 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: 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: 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: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 7/6 266.871 cents septimal minor third 2: 2 9/7 435.084 cents septimal major third, BP third 2: 2 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: 2 54/35 750.725 cents septimal semi-augmented fifth 5: 2 14/9 764.916 cents septimal minor sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 1 140/81 947.320 cents 5: 1 15/8 1088.269 cents classic major seventh 6: 2 8/5 813.686 cents minor sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 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 : 386.3 449.3 498.0 884.4 947.3 1151.2 1200.0 386.3 : 63.0 111.7 498.0 561.0 764.9 813.7 1200.0 449.3 : 48.8 435.1 498.0 702.0 750.7 1137.0 1200.0 498.0 : 386.3 449.3 653.2 702.0 1088.3 1151.2 1200.0 884.4 : 63.0 266.9 315.6 702.0 764.9 813.7 1200.0 947.3 : 203.9 252.7 639.0 702.0 750.7 1137.0 1200.0 1151.2: 48.8 435.1 498.0 546.8 933.1 996.1 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: 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 : 28/27, 62.9609 cents, amount: 2 Least squares average step : 188.28863 cents, oct.: 1318.02043 cents Scale is not proper Step pattern alph. order: ABCABDC Step pattern size order : DBADBCA Scale is a Constant Structure, by a margin of 48.77038 cents Scale diversity : 1.569058 Lumma stability : 0.081284 Lumma impropriety factor : 0.651213 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 : 245/243, 14.1905 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Lydian octave species of abstract tetrachord All steps are superparticular (epimoric) 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 differentially coherent in interval class 1 Scale is differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 337.5433 cents: 4 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.031896 Average absolute harmonicity : 0.223092 Specific harmonicity : 0.149899 Fundamental : 1/324, -8.3399 octaves, 0.8075 Hz. Guide tone : 140, 7.1293 octaves, 36627.579 Hz. Exponens Consonantiae : 4.536000E+04, 15.46913 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 181.5, average 25.92857 Mersenne's string divisions : 183003912 Sum of van Prooijen's expressibility: 6.87168, average 0.98167 Sum of Tenney's harmonic distance : 13.68672, average 1.95525 Vogel's harmonic complexity : 16.14286 Wille's k value : 202 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 80.39206, average 2.87115 Lattice compactness (without 2's) : 58.09233, average 2.07473 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.28571 8 1 3: -4 .. 0 -1.57143 11 1 5: 0 .. 1 0.71429 5 2 7: 0 .. 1 0.42857 3 3 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 19 / 7 = 2.71429 Scale is weakly epimorphic with val: <7 10 15 21| 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 21|
FIT/MODE
7: 2 1 0 2 1 1 0 N T3 SD: 47.9580 c. M:-81.2518 c. 8: 3 0 0 3 0 2 0 N T3 S SD: 40.0484 c. M:-63.6863 c. 9: 3 0 1 3 0 2 0 N SD: 35.5231 c. M: 49.2746 c. 10: 3 1 0 3 1 2 0 N SD: 30.4000 c. M:-48.7704 c. 13: 4 1 0 4 1 2 1 N SD: 31.9151 c. M: 53.5895 c. 14: 4 1 1 4 1 2 1 N T3 S SD: 25.9294 c. M: 43.4566 c. 15: 5 1 0 5 1 2 1 N SD: 19.3171 c. M: 31.2296 c. 16: 5 1 1 5 1 2 1 N T3 S SD: 19.1010 c. M:-27.6804 c. 18: 6 1 0 6 1 3 1 N SD: 18.1395 c. M: 31.3783 c. 19: 6 1 1 6 1 3 1 N T3 S SD: 7.2189 c. M: 14.3875 c. 27: 9 1 1 9 1 5 1 N T3 S SD: 8.6959 c. M: 13.9863 c. 34: 11 2 1 11 2 6 1 N SD: 6.8404 c. M:-13.4763 c. 41: 13 2 2 13 2 7 2 N T3 S SD: 7.4610 c. M: 10.7343 c. 43: 14 2 2 14 2 7 2 N T3 S SD: 4.9593 c. M:-8.6645 c. 46: 15 2 2 15 2 8 2 N T3 S SD: 4.6233 c. M: 8.1892 c. 53: 17 3 2 17 3 9 2 N SD: 2.4413 c. M:-3.6238 c. 72: 23 4 3 23 4 12 3 N SD: 1.8118 c. M: 2.9804 c. 99: 32 5 4 32 5 17 4 N SD: 1.0710 c. M: 1.8651 c. 118: 38 6 5 38 6 20 5 N SD: 1.2114 c. M: 2.0771 c. 152: 49 8 6 49 8 26 6 N SD: 0.6817 c. M:-1.4020 c. 171: 55 9 7 55 9 29 7 N SD: 0.2183 c. M: 0.3524 c. 441: 142 23 18 142 23 75 18 N SD: 0.2035 c. M: 0.3808 c. 494: 159 26 20 159 26 84 20 N SD: 0.1098 c. M:-0.1874 c. 665: 214 35 27 214 35 113 27 N SD: 0.0854 c. M: 0.1483 c. 935: 301 49 38 301 49 159 38 N SD: 0.0775 c. M: 0.1538 c. 1106: 356 58 45 356 58 188 45 N SD: 0.0741 c. M: 0.1225 c. 1258: 405 66 51 405 66 214 51 N SD: 0.0824 c. M:-0.1217 c. 1277: 411 67 52 411 67 217 52 N SD: 0.0821 c. M: 0.0996 c. 1354: 436 71 55 436 71 230 55 N SD: 0.0769 c. M:-0.1317 c. 1429: 460 75 58 460 75 243 58 N SD: 0.0639 c. M: 0.1040 c. 1525: 491 80 62 491 80 259 62 N SD: 0.0596 c. M:-0.1003 c. 1600: 515 84 65 515 84 272 65 N SD: 0.0583 c. M: 0.1087 c. 1696: 546 89 69 546 89 288 69 N SD: 0.0543 c. M:-0.0860 c. 1795: 578 94 73 578 94 305 73 N SD: 0.0541 c. M:-0.0981 c. 1848: 595 97 75 595 97 314 75 N SD: 0.0576 c. M:-0.0830 c. 1867: 601 98 76 601 98 317 76 N SD: 0.0574 c. M:-0.0826 c. 1966: 633 103 80 633 103 334 80 N SD: 0.0456 c. M:-0.0767 c. 2019: 650 106 82 650 106 343 82 N SD: 0.0433 c. M:-0.0801 c. 2190: 705 115 89 705 115 372 89 N SD: 0.0375 c. M:-0.0776 c. 2289: 737 120 93 737 120 389 93 N SD: 0.0282 c. M:-0.0559 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 4:5 x x x 7 x 8 SD: 7.1688 cents 5:6 x 7:8:9 x 10 S SD: 29.7070 cents 6 x x 8:10 x x 12 S SD: 0.0000 cents 7 x 9 x x 12 x 14 SD: 6.6895 cents 8:10 x 11:13:14 x 16 SD: 14.4522 cents 9:11 x 12:15:16 x 18 SD: 12.4775 cents 10 x 13 x x 17:19:20 SD: 12.3725 cents 11:14 x 15:18:19:21:22 SD: 11.1881 cents 12:15 x 16:20:21:23:24 SD: 5.4849 cents 13:16:17 x 22 x 25:26 SD: 8.9770 cents 14 x 18:19:23:24:27:28 SD: 7.7524 cents 15:19 x 20:25:26:29:30 SD: 4.2447 cents 16:20:21 x 27:28:31:32 SD: 6.2936 cents 18 x 23:24:30:31:35:36 SD: 4.2781 cents 19:24 x 25:32:33:37:38 SD: 5.9186 cents 20:25:26:27:33:35:39:40 SD: 5.1042 cents 21:26:27:28:35:36:41:42 SD: 3.8517 cents 22:28 x 29:37:38:43:44 SD: 6.8552 cents 23:29:30:31:38:40:45:46 SD: 4.8410 cents 24:30:31:32:40:41:47:48 SD: 3.4956 cents 27:34:35:36:45:47:53:54 SD: 3.4534 cents 33:41:43:44:55:57:64:66 SD: 2.0838 cents 36:45:47:48:60:62:70:72 SD: 1.9702 cents 48:60:62:64:80:83:93:96 SD: 1.2562 cents 51:64:66:68:85:88:99:102 SD: 1.2067 cents 75:94:97:100:125:130:146:150 SD: 1.1540 cents 81:101:105:108:135:140:158:162 SD: 0.9941 cents 84:105:109:112:140:145:163:168 SD: 0.6469 cents 108:135:140:144:180:187:210:216 SD: 0.4412 cents 132:165:171:176:220:228:257:264 SD: 0.3933 cents 165:206:214:220:275:285:321:330 SD: 0.3857 cents 180:225:233:240:300:311:350:360 SD: 0.3644 cents 192:240:249:256:320:332:373:384 SD: 0.2705 cents 216:270:280:288:360:373:420:432 SD: 0.2209 cents 276:345:358:368:460:477:537:552 SD: 0.2180 cents 321:401:416:428:535:555:624:642 SD: 0.1982 cents 324:405:420:432:540:560:630:648 S SD: 0.0000 cents