Scala analysis: xen09-wilson-marwa-18a-10
Marwa permutation 10 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: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 22/15 663.049228 undecimal diminished fifth 5: 44/27 845.452940 neutral sixth 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: 88/81 143.4979 2nd undecimal neutral second 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 9/8 203.9100 major whole tone 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 10/9 182.4037 minor whole tone 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 9/8 203.9100 major whole 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 40/33 333.041 cents 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 99/80 368.914 cents 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: 1 160/99 831.086 cents 5: 2 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 1 33/20 866.959 cents 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 : 143.5 294.1 498.0 663.0 845.5 996.1 1200.0 143.5 : 150.6 354.5 519.6 702.0 852.6 1056.5 1200.0 294.1 : 203.9 368.9 551.3 702.0 905.9 1049.4 1200.0 498.0 : 165.0 347.4 498.0 702.0 845.5 996.1 1200.0 663.0 : 182.4 333.0 537.0 680.4 831.1 1035.0 1200.0 845.5 : 150.6 354.5 498.0 648.7 852.6 1017.6 1200.0 996.1 : 203.9 347.4 498.0 702.0 867.0 1049.4 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 .. 368.9142 cents 2673/2560, 74.7792 cents 256/243, 90.2250 cents 3: 498.0450 .. 551.3179 cents 33/32, 53.2729 cents 320/297, 129.1308 cents 4: 648.6821 .. 701.9550 cents 33/32, 53.2729 cents 128/121, 97.3641 cents 5: 831.0858 .. 905.8650 cents 2673/2560, 74.7792 cents 320/297, 129.1308 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 : 167.72789 cents, oct.: 1174.09523 cents Scale is strictly proper Step pattern alph. order: ABCDEBC Step pattern size order : ABECDBE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.330006 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.685893 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 : 2 at degree 3 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 74.7792 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 81 Scale harmonicity : 0.024846 Average absolute harmonicity : 0.214376 Specific harmonicity : 0.126267 Fundamental : 1/405, -8.6618 octaves, 0.6460 Hz. Guide tone : 352, 8.4594 octaves, 92092.199 Hz. Exponens Consonantiae : 1.425600E+05, 17.12121 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 185.5, average 26.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.37867, average 1.05410 Sum of Tenney's harmonic distance : 15.92139, average 2.27448 Vogel's harmonic complexity : 17.57143 Wille's k value : 202 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 84.84205, average 3.03007 Lattice compactness (without 2's) : 57.49181, average 2.05328 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 5 2.57143 18 1 3: -4 .. 0 -2.00000 14 3 5: -1 .. 0 -0.14286 1 11: 0 .. 1 0.42857 3 3 Average exponent except 2's :-12 / 7 =-1.71429 Average absolute exponent except 2's: 18 / 7 = 2.57143 Scale is weakly epimorphic with val: <7 10 17 22| Scale is JI-epimorphic with val: <7 11 16 24| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 27.0532 c. M:-48.7221 c. Lebeng 11: 1 2 2 1 2 1 2 P M ME S SD: 28.1565 c. M:-47.4095 c. Orgone-7 13: 1 2 2 2 2 2 2 SP M ME S SD: 27.0522 c. M: 51.1902 c. Zo-Kalarian 15: 2 2 2 2 3 1 3 SP D3 S SD: 24.7680 c. M: 36.0900 c. 16: 2 2 3 2 2 2 3 SP M ME S SD: 16.0765 c. M:-26.9550 c. Pseudo Pelog, Pelogic-7, Antiionian 17: 2 2 3 2 3 2 3 SP M ME S SD: 11.9179 c. M: 27.7551 c. Safi al-Din's maqam Higazi 23: 3 3 4 3 3 3 4 SP M ME S SD: 14.4257 c. M:-23.6941 c. 24: 3 3 4 3 4 3 4 SP M ME S SD: 6.4003 c. M: 13.0492 c. Neutral Phrygian, Iced Locrian 34: 4 4 6 5 5 4 6 SP SD: 6.3329 c. M: 11.7821 c. 41: 5 5 7 6 6 5 7 SP SD: 4.2238 c. M:-10.1215 c. 52: 6 7 9 7 8 6 9 SP SD: 6.2769 c. M:-9.6473 c. 53: 6 7 9 7 8 7 9 SP SD: 4.7760 c. M: 7.7171 c. 58: 7 7 10 8 9 7 10 SP SD: 2.4470 c. M: 4.4798 c. 65: 8 8 11 9 10 8 11 SP SD: 2.2912 c. M:-4.1944 c. 94: 11 12 16 13 14 12 16 SP SD: 1.6421 c. M: 3.0724 c. 101: 12 13 17 14 15 13 17 SP SD: 1.8021 c. M:-2.8947 c. 118: 14 15 20 16 18 15 20 SP SD: 1.0864 c. M: 2.0323 c. 152: 18 19 26 21 23 19 26 SP SD: 1.1258 c. M: 2.0297 c. 159: 19 20 27 22 24 20 27 SP SD: 0.4339 c. M:-1.1017 c. 183: 22 23 31 25 28 23 31 SP SD: 0.6267 c. M:-0.9470 c. 217: 26 27 37 30 33 27 37 SP SD: 0.5952 c. M: 1.0474 c. 277: 33 35 47 38 42 35 47 SP SD: 0.4020 c. M: 0.6876 c. 335: 40 42 57 46 51 42 57 SP SD: 0.2499 c. M: 0.4037 c. 494: 59 62 84 68 75 62 84 SP SD: 0.1323 c. M: 0.2079 c. 677: 81 85 115 93 103 85 115 SP SD: 0.0757 c. M: 0.1246 c. 836: 100 105 142 115 127 105 142 SP SD: 0.0730 c. M:-0.1234 c. 1171: 140 147 199 161 178 147 199 SP SD: 0.0216 c. M: 0.0308 c. 2007: 240 252 341 276 305 252 341 SP SD: 0.0207 c. M:-0.0354 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: 25.9253 cents 5 x 6 x 7:8:9:10 S SD: 18.3525 cents 6 x 7:8:9:10:11:12 S SD: 13.5489 cents 7 x 8:9:10:11:12:14 S SD: 22.3185 cents 8:9 x 11:12:13:14:16 SD: 15.6070 cents 9:10:11:12:13:15:16:18 SD: 11.5740 cents 10:11:12:13:15:16:18:20 SD: 10.9092 cents 11:12:13:15:16:18:20:22 SD: 8.2807 cents 15:16:18:20:22:24:27:30 S SD: 7.7503 cents 20:22:24:27:29:33:36:40 SD: 7.4287 cents 21:23:25:28:31:34:37:42 SD: 3.9102 cents 22:24:26:29:32:36:39:44 SD: 3.9080 cents 27:29:32:36:40:44:48:54 SD: 3.7640 cents 32:35:38:43:47:52:57:64 SD: 2.7485 cents 36:39:43:48:53:59:64:72 SD: 2.6528 cents 43:47:51:57:63:70:76:86 SD: 2.5641 cents 45:49:53:60:66:73:80:90 SD: 1.9973 cents 49:53:58:65:72:80:87:98 SD: 1.8474 cents 54:59:64:72:79:88:96:108 SD: 1.5344 cents 60:65:71:80:88:98:107:120 SD: 1.2471 cents 81:88:96:108:119:132:144:162 SD: 0.4160 cents 184:200:218:245:270:300:327:368 SD: 0.4147 cents 195:212:231:260:286:318:347:390 SD: 0.3611 cents 210:228:249:280:308:342:373:420 SD: 0.3356 cents 243:264:288:324:356:396:432:486 SD: 0.2777 cents 291:316:345:388:427:474:517:582 SD: 0.2684 cents 302:328:358:403:443:492:537:604 SD: 0.2441 cents 324:352:384:432:475:528:576:648 SD: 0.1041 cents 405:440:480:540:594:660:720:810 SD: 0.0000 cents