Scala analysis: xen09-wilson-marwa-17a-10
Marwa permutation 10 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: 32/27 294.134997 Pythagorean minor third 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: 36/35 48.7704 septimal diesis, 1/4-tone 3: 9/8 203.9100 major whole 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 32/27 294.135 cents Pythagorean minor third 2: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 2: 1 45/32 590.224 cents diatonic tritone 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 64/45 609.776 cents 2nd tritone 5: 2 54/35 750.725 cents septimal semi-augmented fifth 5: 1 27/16 905.865 cents Pythagorean major 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 245.4 294.1 498.0 884.4 947.3 996.1 1200.0 245.4 : 48.8 252.7 639.0 702.0 750.7 954.6 1200.0 294.1 : 203.9 590.2 653.2 702.0 905.9 1151.2 1200.0 498.0 : 386.3 449.3 498.0 702.0 947.3 996.1 1200.0 884.4 : 63.0 111.7 315.6 561.0 609.8 813.7 1200.0 947.3 : 48.8 252.7 498.0 546.8 750.7 1137.0 1200.0 996.1 : 203.9 449.3 498.0 702.0 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 .. 590.2237 cents 675/512, 478.4924 cents 64/75,-274.5824 cents 3: 315.6413 .. 653.1846 cents 175/144, 337.5433 cents 64/75,-274.5824 cents 4: 546.8154 .. 884.3587 cents 175/144, 337.5433 cents 1152/1225,-106.3692 cents 5: 609.7763 .. 1088.2687 cents 675/512, 478.4924 cents 64/75,-274.5824 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 : 178.41673 cents, oct.: 1248.91713 cents Scale is not proper Step pattern alph. order: ABCDEBC Step pattern size order : DACEBAC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 1.594117 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 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 : 0.028556 Average absolute harmonicity : 0.224714 Specific harmonicity : 0.143574 Fundamental : 1/243, -7.9248 octaves, 1.0766 Hz. Guide tone : 1120, 10.1293 octaves, 293020.633 Hz. Exponens Consonantiae : 2.721600E+05, 18.05410 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 423.0, average 60.42857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.85579, average 1.12226 Sum of Tenney's harmonic distance : 16.53856, average 2.36265 Vogel's harmonic complexity : 14.71429 Wille's k value : 202 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 97.71720, average 3.48990 Lattice compactness (without 2's) : 68.14860, average 2.43388 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 5 2.42857 17 1 3: -5 .. 0 -2.28571 16 3 5: 0 .. 1 0.42857 3 1 7: 0 .. 1 0.28571 2 2 Average exponent except 2's :-11 / 7 =-1.57143 Average absolute exponent except 2's: 21 / 7 = 3.00000 Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 16 22| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 1 1 1 2 1 0 1 N T3 SD: 48.5530 c. M:-81.2518 c. 8: 2 0 1 3 0 1 1 N SD: 39.1295 c. M:-54.6354 c. 9: 2 0 2 3 0 0 2 N SD: 35.8291 c. M: 62.7567 c. 10: 2 0 2 3 1 0 2 N SD: 30.9746 c. M: 54.1350 c. 11: 2 1 2 3 1 0 2 N SD: 28.3191 c. M:-47.4095 c. 12: 2 1 2 4 0 1 2 N SD: 25.6216 c. M: 47.3196 c. 14: 3 0 3 4 1 1 2 N SD: 22.6355 c. M: 36.9921 c. 15: 3 1 2 5 1 0 3 N SD: 18.9197 c. M: 36.0900 c. 16: 3 1 3 5 1 0 3 N SD: 19.3882 c. M:-27.6804 c. 17: 3 1 3 5 1 1 3 N SD: 22.7302 c. M: 37.2999 c. 19: 4 1 3 6 1 1 3 N SD: 10.5712 c. M:-21.6545 c. 24: 5 1 4 8 1 1 4 N SD: 6.8330 c. M:-15.6413 c. 29: 6 1 5 9 2 1 5 N SD: 6.5032 c. M: 15.3932 c. 33: 7 1 6 10 2 1 6 N SD: 8.9376 c. M: 14.2718 c. 34: 7 1 6 11 2 1 6 N SD: 6.0289 c. M: 11.7821 c. 41: 8 2 7 13 2 2 7 N SD: 6.3715 c. M: 11.2183 c. 43: 9 2 7 14 2 2 7 N SD: 7.2459 c. M:-12.8417 c. 46: 9 2 8 15 2 2 8 N SD: 6.1638 c. M: 10.5820 c. 48: 10 2 8 15 3 2 8 N SD: 4.9246 c. M: 9.3587 c. 49: 10 2 8 16 3 2 8 N SD: 5.3478 c. M: 8.2491 c. 53: 11 2 9 17 3 2 9 N SD: 2.0221 c. M:-3.6920 c. 94: 19 4 16 30 5 4 16 N SD: 1.9852 c. M: 3.5076 c. 99: 20 4 17 32 5 4 17 N SD: 2.0196 c. M: 3.2259 c. 113: 23 5 19 36 6 5 19 N SD: 2.0949 c. M:-3.2101 c. 118: 24 5 20 38 6 5 20 N SD: 0.8621 c. M: 1.5569 c. 152: 31 6 26 49 8 6 26 N SD: 0.9876 c. M: 2.0297 c. 171: 35 7 29 55 9 7 29 N SD: 0.3047 c. M:-0.6018 c. 323: 66 13 55 104 17 13 55 N SD: 0.3120 c. M: 0.6365 c. 376: 77 15 64 121 20 15 64 N SD: 0.3717 c. M:-0.5527 c. 441: 90 18 75 142 23 18 75 N SD: 0.2580 c. M: 0.4667 c. 494: 101 20 84 159 26 20 84 N SD: 0.1146 c. M: 0.2079 c. 665: 136 27 113 214 35 27 113 N SD: 0.0618 c. M: 0.1482 c. 1277: 261 52 217 411 67 52 217 N SD: 0.0657 c. M: 0.1023 c. 1448: 296 59 246 466 76 59 246 N SD: 0.0629 c. M: 0.1046 c. 1624: 332 66 276 523 85 66 276 N SD: 0.0555 c. M:-0.1240 c. 1677: 343 68 285 540 88 68 285 N SD: 0.0551 c. M:-0.0865 c. 1771: 362 72 301 570 93 72 301 N SD: 0.0640 c. M: 0.1125 c. 1795: 367 73 305 578 94 73 305 N SD: 0.0392 c. M:-0.0981 c. 1966: 402 80 334 633 103 80 334 N SD: 0.0431 c. M:-0.0767 c. 2289: 468 93 389 737 120 93 389 N SD: 0.0240 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: 31.5514 cents 5 x 6:7:8 x 9:10 S SD: 22.8511 cents 6:7 x 8:10 x 11:12 S SD: 11.4900 cents 7:8 x 9 x 12 x 14 S SD: 16.5205 cents 8:9 x 11:13:14 x 16 SD: 16.6615 cents 9:10:11:12:15 x 16:18 S SD: 13.7458 cents 10 x 12:13 x 17:18:20 SD: 12.1138 cents 11 x 13:15:18:19:20:22 SD: 10.6223 cents 12:14 x 16:20:21 x 24 S SD: 6.0829 cents 13:15 x 17:22 x 23:26 SD: 8.7270 cents 15:17:18:20:25:26:27:30 SD: 6.0134 cents 16:18:19:21:27:28 x 32 SD: 9.7158 cents 17 x 20:23:28:29:30:34 SD: 7.2652 cents 18:21 x 24:30:31:32:36 S SD: 3.7301 cents 23 x 27:31:38:40:41:46 SD: 5.2430 cents 24:28 x 32:40:41:43:48 SD: 5.4072 cents 26:30:31:35:43:45:46:52 SD: 3.6188 cents 27:31:32:36:45:47:48:54 SD: 1.9702 cents 33:38:39:44:55:57:59:66 SD: 1.5844 cents 54:62:64:72:90:93:96:108 SD: 1.2514 cents 60:69:71:80:100:104:107:120 SD: 1.2163 cents 66:76:78:88:110:114:117:132 SD: 1.0207 cents 81:93:96:108:135:140:144:162 SD: 0.8849 cents 99:114:117:132:165:171:176:198 SD: 0.7394 cents 117:135:139:156:195:202:208:234 SD: 0.7361 cents 125:144:148:167:208:216:222:250 SD: 0.7279 cents 126:145:149:168:210:218:224:252 SD: 0.6846 cents 144:166:171:192:240:249:256:288 SD: 0.5072 cents 162:187:192:216:270:280:288:324 SD: 0.4412 cents 177:204:210:236:295:306:315:354 SD: 0.3799 cents 189:218:224:252:315:327:336:378 SD: 0.3567 cents 210:242:249:280:350:363:373:420 SD: 0.2495 cents 216:249:256:288:360:373:384:432 SD: 0.2470 cents 243:280:288:324:405:420:432:486 SD: 0.0000 cents