Scala analysis: xen09-wilson-marwa-10-10
Marwa permutation 10 from Figure 10, Ptolemy 7/6 12/11 22/21
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22/21 80.537035 undecimal minor semitone 2: 11/9 347.407941 undecimal neutral third 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 3/2 701.955001 perfect fifth 5: 44/27 845.452940 neutral sixth 6: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 22/21 80.5370 undecimal minor semitone 2: 7/6 266.8709 septimal minor third 3: 9/8 203.9100 major whole tone 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 88/81 143.4979 2nd undecimal neutral second 6: 9/8 203.9100 major whole tone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 88/81 143.498 cents 2nd undecimal neutral second 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 11/9 347.408 cents undecimal neutral third 2: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 21/16 470.781 cents narrow fourth 3: 1 9/7 435.084 cents septimal major third, BP third 3: 4 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 63/44 621.418 cents 4: 1 88/63 578.582 cents 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 14/9 764.916 cents septimal minor sixth 5: 1 32/21 729.219 cents wide fifth 5: 2 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 7/4 968.826 cents harmonic seventh 6: 1 12/7 933.129 cents septimal major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 81/44 1056.502 cents 2nd undecimal neutral seventh 6: 1 21/11 1119.463 cents undecimal major seventh 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 : 80.5 347.4 551.3 702.0 845.5 1049.4 1200.0 80.5 : 266.9 470.8 621.4 764.9 968.8 1119.5 1200.0 347.4 : 203.9 354.5 498.0 702.0 852.6 933.1 1200.0 551.3 : 150.6 294.1 498.0 648.7 729.2 996.1 1200.0 702.0 : 143.5 347.4 498.0 578.6 845.5 1049.4 1200.0 845.5 : 203.9 354.5 435.1 702.0 905.9 1056.5 1200.0 1049.4: 150.6 231.2 498.0 702.0 852.6 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 266.8709 cents 49/44, 186.3339 cents 22/21, 80.5370 cents 2: 231.1741 .. 470.7809 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 3: 435.0841 .. 621.4180 cents 49/44, 186.3339 cents 48/49,-35.6968 cents 4: 578.5820 .. 764.9159 cents 49/44, 186.3339 cents 3872/3969,-42.8359 cents 5: 729.2191 .. 968.8259 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 6: 933.1291 .. 1119.4630 cents 49/44, 186.3339 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 2.128568 Largest / Average step : 1.556747 Largest / Smallest step : 3.313642 Median interval of one step : 12/11, 150.6371 cents, amount: 2 Least squares average step : 172.57549 cents, oct.: 1208.02845 cents Scale is not proper Step pattern alph. order: ABCDECD Step pattern size order : AEDCBDC Scale is a Constant Structure, by a margin of 27.26409 cents Scale diversity : 1.600163 Lumma stability : 0.134228 Lumma impropriety factor : 0.154686 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 : 243/242, 7.1391 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 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 n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.022658 Average absolute harmonicity : 0.210690 Specific harmonicity : 0.126051 Fundamental : 1/1512, -10.5622 octaves, 0.1730 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 1.995840E+05, 17.60664 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 89.0, average 12.71429 Mersenne's string divisions : 59167140 Sum of van Prooijen's expressibility: 6.35488, average 0.90784 Sum of Tenney's harmonic distance : 12.57830, average 1.79690 Vogel's harmonic complexity : 23.14286 Wille's k value : 1039 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 77.44523, average 2.76590 Lattice compactness (without 2's) : 50.53887, average 1.80496 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.14286 9 1 3: -3 .. 1 -0.85714 8 1 7: -1 .. 0 -0.14286 1 11: 0 .. 1 0.71429 5 5 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is weakly epimorphic with val: <7 10 22 22| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 12 18 25| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 0 2 1 1 1 1 1 N T3 SD: 35.2765 c. M: 80.5370 c. 9: 1 2 1 1 1 2 1 P M ME I SD: 36.8151 c. M:-52.7963 c. 10: 1 2 2 1 1 2 1 P D3 S SD: 27.7226 c. M:-48.6821 c. 11: 1 2 2 1 2 2 1 P D3 I SD: 29.2105 c. M: 47.4095 c. 13: 1 3 2 2 1 2 2 N T3 SD: 21.7914 c. M:-36.5065 c. 14: 1 3 2 2 2 2 2 P T3 SD: 17.9348 c. M: 37.0322 c. 15: 1 3 3 2 2 2 2 N SD: 18.6457 c. M:-34.5471 c. 17: 1 4 3 2 2 3 2 N SD: 7.7121 c. M:-13.3879 c. 24: 2 5 4 3 3 4 3 P SD: 7.6734 c. M:-19.4630 c. 31: 2 7 5 4 4 5 4 N SD: 5.0871 c. M: 9.3825 c. 41: 3 9 7 5 5 7 5 N SD: 4.1396 c. M:-7.2678 c. 48: 3 11 8 6 6 8 6 N SD: 3.0241 c. M: 5.5370 c. 70: 5 15 12 9 8 12 9 N SD: 3.7591 c. M: 5.4529 c. 72: 5 16 12 9 9 12 9 N SD: 2.4254 c. M:-4.5471 c. 87: 6 19 15 11 10 15 11 N SD: 2.1302 c. M: 4.0736 c. 89: 6 20 15 11 11 15 11 N SD: 2.2126 c. M:-3.9853 c. 94: 6 21 16 12 11 16 12 N SD: 2.4959 c. M: 3.9413 c. 104: 7 23 18 13 12 18 13 N SD: 1.7685 c. M: 3.1452 c. 118: 8 26 20 15 14 20 15 N SD: 1.3981 c. M: 2.1654 c. 135: 9 30 23 17 16 23 17 N SD: 0.5598 c. M: 1.0085 c. 207: 14 46 35 26 25 35 26 N SD: 0.5387 c. M:-0.9239 c. 294: 20 65 50 37 35 50 37 N SD: 0.5307 c. M:-1.0956 c. 311: 21 69 53 39 37 53 39 N SD: 0.3310 c. M:-0.4919 c. 342: 23 76 58 43 41 58 43 N SD: 0.2226 c. M: 0.4407 c. 359: 24 80 61 45 43 61 45 N SD: 0.2055 c. M: 0.3142 c. 477: 32 106 81 60 57 81 60 N SD: 0.2156 c. M: 0.3745 c. 494: 33 110 84 62 59 84 62 N SD: 0.1557 c. M: 0.3751 c. 653: 44 145 111 82 78 111 82 N SD: 0.1363 c. M:-0.3205 c. 670: 45 149 114 84 80 114 84 N SD: 0.1567 c. M:-0.3238 c. 701: 47 156 119 88 84 119 88 N SD: 0.1037 c. M:-0.1961 c. 836: 56 186 142 105 100 142 105 N SD: 0.0831 c. M: 0.1543 c. 1012: 68 225 172 127 121 172 127 N SD: 0.0483 c. M:-0.0954 c. 1489: 100 331 253 187 178 253 187 N SD: 0.0532 c. M: 0.0755 c. 1506: 101 335 256 189 180 256 189 N SD: 0.0438 c. M:-0.0765 c. 1713: 115 381 291 215 205 291 215 N SD: 0.0402 c. M:-0.0812 c. 1848: 124 411 314 232 221 314 232 N SD: 0.0114 c. M: 0.0192 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 21.9891 cents 4 x 5 x 6 x 7:8 S SD: 22.3605 cents 5 x 6:7 x 8:9:10 S SD: 12.6498 cents 6 x 7:8:9:10:11:12 S SD: 17.3509 cents 7 x 9:10 x 11:13:14 SD: 25.7128 cents 8:9:10:11:12:13:15:16 SD: 19.3108 cents 10:11:12:14:15:16:18:20 S SD: 15.0747 cents 12:13:15:17:18:20:22:24 SD: 13.6026 cents 13:14:16:18:20:21:24:26 S SD: 9.9693 cents 14:15:17:19:21:23:26:28 SD: 7.6237 cents 16:17:20:22:24:26:29:32 SD: 7.1794 cents 18:19:22:25:27:29:33:36 SD: 4.2014 cents 22:23:27:30:33:36:40:44 SD: 3.2813 cents 24:25:29:33:36:39:44:48 SD: 3.2358 cents 38:40:46:52:57:62:70:76 SD: 3.1523 cents 40:42:49:55:60:65:73:80 SD: 1.5476 cents 62:65:76:85:93:101:114:124 SD: 1.2719 cents 64:67:78:88:96:104:117:128 SD: 1.2313 cents 80:84:98:110:120:130:147:160 SD: 1.2003 cents 86:90:105:118:129:140:158:172 SD: 0.8672 cents 104:109:127:143:156:169:191:208 SD: 0.8603 cents 122:128:149:168:183:199:224:244 SD: 0.7028 cents 126:132:154:173:189:205:231:252 SD: 0.5376 cents 144:151:176:198:216:235:264:288 SD: 0.4219 cents 192:201:235:264:288:313:352:384 SD: 0.4023 cents 208:218:254:286:312:339:381:416 SD: 0.3255 cents 216:226:264:297:324:352:396:432 SD: 0.3125 cents 248:260:303:341:372:404:455:496 SD: 0.2866 cents 256:268:313:352:384:417:469:512 SD: 0.2855 cents 270:283:330:371:405:440:495:540 SD: 0.2082 cents 360:377:440:495:540:587:660:720 SD: 0.1689 cents 378:396:462:520:567:616:693:756 SD: 0.1189 cents 486:509:594:668:729:792:891:972 SD: 0.1157 cents 504:528:616:693:756:821:924:1008 SD: 0.1004 cents