Scala analysis: xen09-wilson-marwa-17a-07
Marwa permutation 7 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: 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: 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: 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: 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: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 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: 1 14/9 764.916 cents septimal minor sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 2 140/81 947.320 cents 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 245.4 449.3 498.0 884.4 947.3 1151.2 1200.0 245.4 : 203.9 252.7 639.0 702.0 905.9 954.6 1200.0 449.3 : 48.8 435.1 498.0 702.0 750.7 996.1 1200.0 498.0 : 386.3 449.3 653.2 702.0 947.3 1151.2 1200.0 884.4 : 63.0 266.9 315.6 561.0 764.9 813.7 1200.0 947.3 : 203.9 252.7 498.0 702.0 750.7 1137.0 1200.0 1151.2: 48.8 294.1 498.0 546.8 933.1 996.1 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: 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 : 187.28185 cents, oct.: 1310.97297 cents Scale is not proper Step pattern alph. order: ABCDEBC Step pattern size order : DCAEBCA Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 1.470169 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 : 19683/19600, 7.3158 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 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 : 0.210412 Specific harmonicity : 0.135908 Fundamental : 1/486, -8.9248 octaves, 0.5383 Hz. Guide tone : 280, 8.1293 octaves, 73255.158 Hz. Exponens Consonantiae : 1.360800E+05, 17.05410 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 438.5, average 62.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.55832, average 1.22262 Sum of Tenney's harmonic distance : 17.21845, average 2.45978 Vogel's harmonic complexity : 17.71429 Wille's k value : 472 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 87.62474, average 3.12946 Lattice compactness (without 2's) : 68.91471, average 2.46124 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.00000 9 1 3: -5 .. 0 -2.28571 16 1 5: 0 .. 1 0.71429 5 1 7: 0 .. 1 0.57143 4 4 Average exponent except 2's :-7 / 7 =-1.00000 Average absolute exponent except 2's: 25 / 7 = 3.57143 Scale is weakly epimorphic with val: <7 10 18 21| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 17 21| Scale is weakly epimorphic with val: <7 12 16 21| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 1 1 0 3 0 1 1 N T3 I SD: 96.2082 c. M: 155.1879 c. 8: 2 1 0 3 0 2 0 N SD: 38.0905 c. M:-54.6354 c. 9: 2 1 1 3 0 2 0 N SD: 36.0549 c. M: 49.2746 c. 10: 2 2 0 3 1 2 0 N SD: 28.7985 c. M:-48.7704 c. 14: 3 2 1 4 1 2 1 N SD: 20.5516 c. M: 36.9439 c. 15: 3 3 0 5 1 2 1 N SD: 18.7218 c. M: 31.2296 c. 16: 3 3 1 5 1 2 1 N SD: 20.1447 c. M:-27.6804 c. 19: 4 3 1 6 1 3 1 N SD: 7.2045 c. M: 14.3875 c. 24: 5 4 1 8 1 4 1 N SD: 6.3153 c. M:-15.6413 c. 33: 7 5 2 10 2 6 1 N SD: 9.7518 c. M: 12.9110 c. 34: 7 6 1 11 2 6 1 N SD: 6.8318 c. M:-13.4763 c. 39: 8 7 1 13 2 6 2 N SD: 8.0423 c. M: 12.7681 c. 41: 8 7 2 13 2 7 2 N SD: 8.2943 c. M: 11.2183 c. 43: 9 7 2 14 2 7 2 N SD: 5.1626 c. M:-8.6645 c. 46: 9 8 2 15 2 8 2 N SD: 5.8150 c. M: 10.5820 c. 48: 10 8 2 15 3 8 2 N SD: 4.1768 c. M: 9.3587 c. 49: 10 8 2 16 3 8 2 N SD: 5.4491 c. M: 8.4583 c. 53: 11 9 2 17 3 9 2 N SD: 2.7611 c. M:-3.6920 c. 72: 15 12 3 23 4 12 3 N SD: 2.2546 c. M:-4.6354 c. 94: 19 16 4 30 5 16 4 N SD: 2.3465 c. M: 3.5076 c. 99: 20 17 4 32 5 17 4 N SD: 1.4256 c. M: 2.9404 c. 118: 24 20 5 38 6 20 5 N SD: 1.3060 c. M: 2.0771 c. 147: 30 25 6 47 8 25 6 N SD: 1.0645 c. M: 2.7261 c. 152: 31 26 6 49 8 26 6 N SD: 0.6936 c. M:-1.4020 c. 171: 35 29 7 55 9 29 7 N SD: 0.1979 c. M: 0.3524 c. 494: 101 84 20 159 26 84 20 N SD: 0.1060 c. M:-0.1874 c. 665: 136 113 27 214 35 113 27 N SD: 0.0670 c. M: 0.1482 c. 1277: 261 217 52 411 67 217 52 N SD: 0.0831 c. M: 0.1023 c. 1448: 296 246 59 466 76 246 59 N SD: 0.0828 c. M: 0.1246 c. 1453: 297 247 59 468 76 247 59 N SD: 0.0714 c. M:-0.1561 c. 1501: 307 255 61 483 79 255 61 N SD: 0.0662 c. M: 0.1482 c. 1624: 332 276 66 523 85 276 66 N SD: 0.0516 c. M:-0.1240 c. 1771: 362 301 72 570 93 301 72 N SD: 0.0591 c. M: 0.1125 c. 1795: 367 305 73 578 94 305 73 N SD: 0.0416 c. M:-0.0981 c. 1848: 378 314 75 595 97 314 75 N SD: 0.0642 c. M:-0.0899 c. 1942: 397 330 79 625 102 330 79 N SD: 0.0568 c. M: 0.1157 c. 1947: 398 331 79 627 102 331 79 N SD: 0.0539 c. M:-0.0801 c. 1966: 402 334 80 633 103 334 80 N SD: 0.0408 c. M:-0.0767 c. 2118: 433 360 86 682 111 360 86 N SD: 0.0347 c. M:-0.0606 c. 2289: 468 389 93 737 120 389 93 N SD: 0.0198 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 7:8:9 x 10 S SD: 29.6695 cents 6:7 x 8:10 x x 12 S SD: 5.3766 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 12:15:16 x 18 S SD: 15.9281 cents 10:12:13 x x 17:19:20 SD: 17.1908 cents 11:13:14:15:18:19:21:22 SD: 11.4862 cents 12:14 x 16:20:21:23:24 SD: 6.5523 cents 13:15:17 x 22 x 25:26 SD: 7.2107 cents 14:16:18:19:23:24:27:28 SD: 6.9472 cents 16:18:21 x 27:28:31:32 SD: 9.3458 cents 17:20:22:23:28:29:33:34 SD: 7.6748 cents 18:21:23:24:30:31:35:36 SD: 4.7839 cents 19:22 x 25:32:33:37:38 SD: 5.2802 cents 20:23:26:27:33:35:39:40 SD: 5.1273 cents 21:24:27:28:35:36:41:42 SD: 3.6529 cents 22:25 x 29:37:38:43:44 SD: 6.0031 cents 24:28:31:32:40:41:47:48 SD: 4.6538 cents 26:30:34:35:43:45:51:52 SD: 4.3418 cents 27:31:35:36:45:47:53:54 SD: 3.0622 cents 33:38:43:44:55:57:64:66 SD: 1.4517 cents 51:59:66:68:85:88:99:102 SD: 1.2206 cents 78:90:101:104:130:135:152:156 SD: 0.7741 cents 105:121:136:140:175:181:204:210 SD: 0.7169 cents 111:128:144:148:185:192:216:222 SD: 0.3818 cents 159:183:206:212:265:275:309:318 SD: 0.3791 cents 165:190:214:220:275:285:321:330 SD: 0.2909 cents 210:242:272:280:350:363:408:420 SD: 0.2879 cents 216:249:280:288:360:373:420:432 SD: 0.2470 cents 270:311:350:360:450:467:525:540 SD: 0.1975 cents 321:370:416:428:535:555:624:642 SD: 0.1495 cents 375:432:486:500:625:648:729:750 SD: 0.1131 cents 453:522:587:604:755:783:881:906 SD: 0.1060 cents 486:560:630:648:810:840:945:972 SD: 0.0000 cents