Scala analysis: xen09-wilson-marwa-17a-04
Marwa permutation 4 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: 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: 280/243 245.3646 2: 9/8 203.9100 major whole 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: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 3 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 280/243 245.365 cents 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 32/27 294.135 cents Pythagorean minor third 2: 1 81/64 407.820 cents Pythagorean major third 2: 1 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: 1 14/9 764.916 cents septimal minor sixth 5: 1 128/81 792.180 cents Pythagorean minor sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 1 140/81 947.320 cents 6: 1 243/140 954.635 cents 6: 1 7/4 968.826 cents harmonic seventh 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 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: 6 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 245.4 449.3 653.2 884.4 947.3 1151.2 1200.0 245.4 : 203.9 407.8 639.0 702.0 905.9 954.6 1200.0 449.3 : 203.9 435.1 498.0 702.0 750.7 996.1 1200.0 653.2 : 231.2 294.1 498.0 546.8 792.2 996.1 1200.0 884.4 : 63.0 266.9 315.6 561.0 764.9 968.8 1200.0 947.3 : 203.9 252.7 498.0 702.0 905.9 1137.0 1200.0 1151.2: 48.8 294.1 498.0 702.0 933.1 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 245.3646 cents 2450/2187, 196.5942 cents 36/35, 48.7704 cents 2: 252.6804 .. 449.2746 cents 2450/2187, 196.5942 cents 19683/19600, 7.3158 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: 954.6354 .. 1151.2296 cents 2450/2187, 196.5942 cents 19683/19600, 7.3158 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 : 280/243, 245.3646 cents Average / Smallest step : 3.515014 Largest / Average step : 1.431294 Largest / Smallest step : 5.031017 Median interval of one step : 9/8, 203.9100 cents, amount: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 190.60627 cents, oct.: 1334.24392 cents Scale is not proper Step pattern alph. order: ABBCDBE Step pattern size order : ECCDBCA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 1.456709 Lumma stability : 0.093477 Lumma impropriety factor : 0.311363 Rothenberg efficiency : 0.383673 redundancy: 0.616327 Efficiency x scale size : 2.685714 Number of different interval sizes : 30 = 5.00000 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.00000 = 5 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: 3 Number of recognisable fifths : 4, average 701.9550 cents Length of longest subharmonic part : 2 at degree 2 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 Limited inverse transpositions with margin 323.3528 cents: 4 -- Rational properties -- Prime limit : 7 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 243 Scale harmonicity : 0.027763 Average absolute harmonicity : 0.186191 Specific harmonicity : 0.140222 Fundamental : 1/1944, -10.9248 octaves, 0.1346 Hz. Guide tone : 280, 8.1293 octaves, 73255.158 Hz. Exponens Consonantiae : 5.443200E+05, 19.05410 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 464.5, average 66.35714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.62527, average 1.37504 Sum of Tenney's harmonic distance : 19.06355, average 2.72336 Vogel's harmonic complexity : 20.71429 Wille's k value : 1417 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 97.30544, average 3.47519 Lattice compactness (without 2's) : 68.63801, average 2.45136 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.28571 10 1 3: -5 .. 0 -2.28571 16 5: 0 .. 1 0.85714 6 1 7: 0 .. 1 0.71429 5 5 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 27 / 7 = 3.85714 Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 1 1 1 2 0 1 1 N T3 SD: 92.5833 c. M: 138.8989 c. 8: 2 1 1 2 0 2 0 N D3 S SD: 39.0540 c. M:-54.6354 c. 9: 2 1 2 2 0 2 0 N SD: 33.8826 c. M: 49.2746 c. 11: 2 2 2 2 1 2 0 N SD: 25.6667 c. M:-48.7704 c. 14: 3 2 2 3 1 2 1 N T3 S SD: 28.0851 c. M: 53.1846 c. 15: 3 3 2 3 1 2 1 N SD: 18.1334 c. M: 31.2296 c. 16: 3 3 3 3 1 2 1 N G S SD: 19.2354 c. M:-27.6804 c. 18: 4 3 3 3 1 3 1 N SD: 15.8877 c. M:-21.3021 c. 19: 4 3 3 4 1 3 1 N S SD: 10.5427 c. M: 21.6057 c. 24: 5 4 4 5 1 4 1 N S SD: 6.3864 c. M:-15.6413 c. 29: 6 5 5 5 2 5 1 N SD: 7.8665 c. M: 15.3932 c. 30: 6 5 5 6 2 5 1 N SD: 8.8264 c. M: 13.1846 c. 33: 7 5 6 6 2 6 1 N SD: 8.8280 c. M: 12.9110 c. 35: 7 6 6 7 2 6 1 N SD: 8.1514 c. M:-14.4847 c. 38: 8 6 7 7 2 6 2 N SD: 7.6597 c. M: 14.3875 c. 39: 8 7 6 8 2 6 2 N SD: 8.1876 c. M: 12.7681 c. 41: 8 7 7 8 2 7 2 N S SD: 9.0039 c. M: 11.2183 c. 42: 9 7 7 8 2 7 2 N SD: 6.6349 c. M:-11.7782 c. 43: 9 7 7 9 2 7 2 N S SD: 6.5080 c. M: 11.3242 c. 46: 9 8 8 9 2 8 2 N S SD: 5.7569 c. M: 10.5820 c. 48: 10 8 8 9 3 8 2 N SD: 4.2835 c. M: 9.3587 c. 49: 10 8 9 9 3 8 2 N SD: 5.4042 c. M: 8.4583 c. 53: 11 9 9 10 3 9 2 N SD: 3.0485 c. M:-3.6920 c. 72: 15 12 12 14 4 12 3 N SD: 2.4466 c. M:-4.6354 c. 77: 16 13 13 15 4 13 3 N SD: 2.8201 c. M:-3.9860 c. 94: 19 16 16 18 5 16 4 N SD: 2.4788 c. M: 3.5076 c. 99: 20 17 17 19 5 17 4 N SD: 1.4600 c. M: 2.9404 c. 118: 24 20 20 23 6 20 5 N SD: 1.5736 c. M: 2.3372 c. 123: 25 21 21 24 6 21 5 N SD: 1.4851 c. M:-3.4462 c. 147: 30 25 25 28 8 25 6 N SD: 1.0650 c. M: 2.7261 c. 152: 31 26 26 29 8 26 6 N SD: 1.0163 c. M:-2.0785 c. 171: 35 29 29 33 9 29 7 N SD: 0.2777 c. M: 0.5530 c. 441: 90 75 75 85 23 75 18 N SD: 0.2696 c. M: 0.4667 c. 494: 101 84 84 95 26 84 20 N SD: 0.1413 c. M:-0.2567 c. 665: 136 113 113 128 35 113 27 N SD: 0.0695 c. M: 0.1482 c. 1277: 261 217 217 246 67 217 52 N SD: 0.0900 c. M: 0.1023 c. 1354: 277 230 230 261 71 230 55 N SD: 0.0827 c. M:-0.1317 c. 1453: 297 247 247 280 76 247 59 N SD: 0.0766 c. M:-0.1561 c. 1501: 307 255 255 289 79 255 61 N SD: 0.0661 c. M: 0.1482 c. 1624: 332 276 276 313 85 276 66 N SD: 0.0517 c. M:-0.1240 c. 1795: 367 305 305 346 94 305 73 N SD: 0.0438 c. M:-0.0981 c. 1848: 378 314 314 356 97 314 75 N SD: 0.0683 c. M:-0.0899 c. 1942: 397 330 330 374 102 330 79 N SD: 0.0591 c. M: 0.1157 c. 1966: 402 334 334 379 103 334 80 N SD: 0.0505 c. M: 0.0819 c. 2118: 433 360 360 408 111 360 86 N SD: 0.0431 c. M:-0.0732 c. 2289: 468 389 389 441 120 389 93 N SD: 0.0218 c. M:-0.0450 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 x 5:6 x 7 x 8 S SD: 20.6233 cents 5:6 x 7:8:9 x 10 S SD: 28.1899 cents 6:7:8:9:10 x x 12 S SD: 14.4494 cents 7:8:9:10 x 12 x 14 S SD: 8.6680 cents 8:9:10:12:13:14 x 16 S SD: 17.0333 cents 9:10:12:13:15:16 x 18 SD: 15.8076 cents 10:12:13:15 x 17:19:20 SD: 16.4710 cents 11:13:14:16:18:19:21:22 SD: 10.0725 cents 13:15:17:19:22 x 25:26 SD: 6.0422 cents 18:21:23:26:30:31:35:36 SD: 5.3373 cents 20:23:26:29:33:35:39:40 SD: 4.3427 cents 26:30:34:38:43:45:51:52 SD: 3.6803 cents 33:38:43:48:55:57:64:66 SD: 1.5878 cents 54:62:70:79:90:93:105:108 SD: 1.4766 cents 67:77:87:98:112:116:130:134 SD: 1.4626 cents 72:83:93:105:120:124:140:144 SD: 1.2562 cents 74:85:96:108:123:128:144:148 SD: 1.0944 cents 78:90:101:114:130:135:152:156 SD: 0.9456 cents 85:98:110:124:142:147:165:170 SD: 0.8563 cents 92:106:119:134:153:159:179:184 SD: 0.8356 cents 105:121:136:153:175:181:204:210 SD: 0.7448 cents 111:128:144:162:185:192:216:222 SD: 0.4269 cents 159:183:206:232:265:275:309:318 SD: 0.4018 cents 183:211:237:267:305:316:356:366 SD: 0.3995 cents 192:221:249:280:320:332:373:384 SD: 0.3768 cents 203:234:263:296:338:351:395:406 SD: 0.3587 cents 210:242:272:306:350:363:408:420 SD: 0.3516 cents 216:249:280:315:360:373:420:432 SD: 0.2470 cents 303:349:393:442:505:524:589:606 SD: 0.2412 cents 321:370:416:468:535:555:624:642 SD: 0.1634 cents 375:432:486:547:625:648:729:750 SD: 0.1264 cents 486:560:630:709:810:840:945:972 SD: 0.0872 cents