Scala analysis: xen09-wilson-marwa-18a-07
Marwa permutation 7 from Figure 18a, Ptolemy 12/11 11/10 10/9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88/81 143.497939 2nd undecimal neutral second 2: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 22/15 663.049228 undecimal diminished 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: 88/81 143.4979 2nd undecimal neutral second 2: 9/8 203.9100 major whole tone 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 10/9 182.4037 minor whole tone 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 88/81 143.498 cents 2nd undecimal neutral second 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 6/5 315.641 cents 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 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 3: 1 15/11 536.951 cents undecimal augmented fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 1 22/15 663.049 cents undecimal diminished fifth 4: 1 40/27 680.449 cents grave fifth 4: 4 3/2 701.955 cents perfect fifth 5: 1 8/5 813.686 cents minor sixth 5: 2 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 20/11 1034.996 cents large 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 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 : 143.5 347.4 498.0 663.0 845.5 1049.4 1200.0 143.5 : 203.9 354.5 519.6 702.0 905.9 1056.5 1200.0 347.4 : 150.6 315.6 498.0 702.0 852.6 996.1 1200.0 498.0 : 165.0 347.4 551.3 702.0 845.5 1049.4 1200.0 663.0 : 182.4 386.3 537.0 680.4 884.4 1035.0 1200.0 845.5 : 203.9 354.5 498.0 702.0 852.6 1017.6 1200.0 1049.4: 150.6 294.1 498.0 648.7 813.7 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 143.4979 .. 203.9100 cents 729/704, 60.4121 cents 88/81, 143.4979 cents 2: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 256/243, 90.2250 cents 3: 498.0450 .. 551.3179 cents 33/32, 53.2729 cents 16/15, 111.7313 cents 4: 648.6821 .. 701.9550 cents 33/32, 53.2729 cents 128/121, 97.3641 cents 5: 813.6863 .. 905.8650 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 6: 996.0900 .. 1056.5021 cents 729/704, 60.4121 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 88/81, 143.4979 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.194641 Largest / Average step : 1.189475 Largest / Smallest step : 1.420996 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 170.77206 cents, oct.: 1195.40440 cents Scale is strictly proper Step pattern alph. order: ABCDEBC Step pattern size order : AEBCDEB Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.365754 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.656894 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 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Length of longest subharmonic part : 4 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 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 60.4121 cents: 3 -- Rational properties -- Prime limit : 11 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.025479 Average absolute harmonicity : 0.200694 Specific harmonicity : 0.132178 Fundamental : 1/810, -9.6618 octaves, 0.3230 Hz. Guide tone : 88, 6.4594 octaves, 23023.050 Hz. Exponens Consonantiae : 7.128000E+04, 16.12121 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 162.0, average 23.14286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.07585, average 1.01084 Sum of Tenney's harmonic distance : 14.64169, average 2.09167 Vogel's harmonic complexity : 21.14286 Wille's k value : 742 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 74.32068, average 2.65431 Lattice compactness (without 2's) : 54.37476, average 1.94196 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.14286 10 1 3: -4 .. 0 -1.71429 12 1 5: -1 .. 0 -0.14286 1 11: 0 .. 1 0.71429 5 5 Average exponent except 2's :-8 / 7 =-1.14286 Average absolute exponent except 2's: 18 / 7 = 2.57143 Scale is weakly epimorphic with val: <7 10 18 22| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 12 16 25|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 17.5142 c. M:-27.9306 c. Lebeng 16: 2 3 2 2 2 3 2 SP M ME I SD: 17.2863 c. M:-27.5921 c. Armodue-7, Antidorian 17: 2 3 2 2 3 3 2 SP D3 S SD: 11.4259 c. M: 27.7551 c. Dastgah-e Sehgah 23: 3 4 3 3 3 4 3 SP M ME I SD: 14.2833 c. M:-23.6941 c. Armodue-7, Antidorian 24: 3 4 3 3 4 4 3 SP D3 S SD: 5.9062 c. M: 13.0492 c. Dastgah-e Sehgah, Neutral Diatonic Lydian 31: 4 5 4 4 5 5 4 SP D3 S SD: 5.8170 c. M:-11.3408 c. Neutral Diatonic Lydian 34: 4 6 4 5 5 6 4 SP SD: 5.3499 c. M:-9.4606 c. 41: 5 7 5 6 6 7 5 SP SD: 4.7028 c. M:-10.1215 c. 53: 6 9 7 7 8 9 7 SP SD: 6.3459 c. M: 7.8535 c. 55: 7 9 7 7 9 9 7 SP D3 S SD: 5.4603 c. M:-9.2293 c. 56: 7 9 7 8 8 10 7 SP SD: 5.1641 c. M: 9.7387 c. 58: 7 10 7 8 9 10 7 SP SD: 3.0544 c. M:-5.8095 c. 65: 8 11 8 9 10 11 8 SP SD: 2.7893 c. M:-4.1944 c. 94: 11 16 12 13 14 16 12 SP SD: 2.1531 c. M: 3.0724 c. 111: 13 19 14 15 17 19 14 SP SD: 2.0606 c. M: 3.5898 c. 118: 14 20 15 16 18 20 15 SP SD: 1.4000 c. M: 2.0323 c. 152: 18 26 19 21 23 26 19 SP SD: 0.6896 c. M: 1.3927 c. 159: 19 27 20 22 24 27 20 SP SD: 0.4485 c. M:-1.1017 c. 183: 22 31 23 25 28 31 23 SP SD: 0.4637 c. M:-0.7644 c. 311: 37 53 39 43 47 53 39 SP SD: 0.4207 c. M: 0.7327 c. 335: 40 57 42 46 51 57 42 SP SD: 0.1855 c. M: 0.3627 c. 342: 41 58 43 47 52 58 43 SP SD: 0.1957 c. M:-0.3617 c. 494: 59 84 62 68 75 84 62 SP SD: 0.0946 c. M: 0.1781 c. 677: 81 115 85 93 103 115 85 SP SD: 0.0600 c. M: 0.1246 c. 836: 100 142 105 115 127 142 105 SP SD: 0.0578 c. M:-0.1087 c. 1171: 140 199 147 161 178 199 147 SP SD: 0.0184 c. M: 0.0308 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: 19.4529 cents 3 x x 4 x 5 x 6 S SD: 12.9686 cents 4 x 5 x 6 x 7:8 S SD: 24.3843 cents 5 x 6 x 7:8:9:10 S SD: 19.5075 cents 6 x 7:8:9:10:11:12 S SD: 16.2562 cents 7:8 x 9:10:11:13:14 SD: 22.4785 cents 8:9:10:11:12:13:15:16 SD: 15.0189 cents 9:10:11:12:13:15:17:18 SD: 11.4259 cents 11:12:13:15:16:18:20:22 SD: 10.5128 cents 12:13:15:16:18:20:22:24 SD: 9.6524 cents 13:14:16:17:19:21:24:26 SD: 6.2598 cents 19:21:23:25:28:31:35:38 SD: 6.1113 cents 21:23:26:28:31:34:39:42 SD: 5.4336 cents 22:24:27:29:32:36:40:44 SD: 4.4198 cents 24:26:29:32:35:39:44:48 SD: 3.3114 cents 32:35:39:43:47:52:59:64 SD: 3.0898 cents 35:38:43:47:51:57:64:70 SD: 2.7932 cents 36:39:44:48:53:59:66:72 SD: 1.8256 cents 54:59:66:72:79:88:99:108 SD: 1.5344 cents 60:65:73:80:88:98:110:120 SD: 1.4422 cents 71:77:87:95:104:116:130:142 SD: 1.3952 cents 72:78:88:96:106:117:132:144 SD: 1.3654 cents 81:88:99:108:119:132:149:162 SD: 0.9296 cents 90:98:110:120:132:147:165:180 SD: 0.7940 cents 103:112:126:137:151:168:189:206 SD: 0.7507 cents 126:137:154:168:185:205:231:252 SD: 0.5228 cents 162:176:198:216:238:264:297:324 SD: 0.4160 cents 197:214:241:263:289:321:361:394 SD: 0.4103 cents 210:228:257:280:308:342:385:420 SD: 0.3933 cents 216:235:264:288:317:352:396:432 SD: 0.3842 cents 221:240:270:295:324:360:405:442 SD: 0.3605 cents 234:254:286:312:343:381:429:468 SD: 0.3381 cents 270:293:330:360:396:440:495:540 SD: 0.2812 cents 300:326:367:400:440:489:550:600 SD: 0.2384 cents 324:352:396:432:475:528:594:648 SD: 0.1041 cents 486:528:594:648:713:792:891:972 SD: 0.0694 cents