Scala analysis: xen09-wilson-marwa-18a-04
Marwa permutation 4 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: 11/8 551.317942 undecimal semi-augmented 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: 9/8 203.9100 major whole tone 4: 16/15 111.7313 minor diatonic semitone 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 16/15 111.731 cents minor diatonic semitone 1: 1 88/81 143.498 cents 2nd undecimal neutral second 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 10/9 182.404 cents minor whole tone 1: 3 9/8 203.910 cents major whole tone 2: 2 32/27 294.135 cents Pythagorean minor third 2: 1 6/5 315.641 cents minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 5/4 386.314 cents major third 2: 1 81/64 407.820 cents Pythagorean 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: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 8/5 813.686 cents minor sixth 5: 1 44/27 845.453 cents neutral sixth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 81/44 1056.502 cents 2nd undecimal neutral seventh 6: 1 15/8 1088.269 cents classic major seventh 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 : 143.5 347.4 551.3 663.0 845.5 1049.4 1200.0 143.5 : 203.9 407.8 519.6 702.0 905.9 1056.5 1200.0 347.4 : 203.9 315.6 498.0 702.0 852.6 996.1 1200.0 551.3 : 111.7 294.1 498.0 648.7 792.2 996.1 1200.0 663.0 : 182.4 386.3 537.0 680.4 884.4 1088.3 1200.0 845.5 : 203.9 354.5 498.0 702.0 905.9 1017.6 1200.0 1049.4: 150.6 294.1 498.0 702.0 813.7 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 203.9100 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 2: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 498.0450 .. 551.3179 cents 33/32, 53.2729 cents 256/243, 90.2250 cents 4: 648.6821 .. 701.9550 cents 33/32, 53.2729 cents 128/121, 97.3641 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 6: 996.0900 .. 1088.2687 cents 135/128, 92.1787 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.534293 Largest / Average step : 1.189475 Largest / Smallest step : 1.825004 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 171.91362 cents, oct.: 1203.39535 cents Scale is strictly proper Step pattern alph. order: ABBCDBE Step pattern size order : BEEADEC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.485325 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.568106 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 : 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: 3 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 4 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.024243 Average absolute harmonicity : 0.176826 Specific harmonicity : 0.140768 Fundamental : 1/3240, -11.6618 octaves, 0.0807 Hz. Guide tone : 88, 6.4594 octaves, 23023.050 Hz. Exponens Consonantiae : 2.851200E+05, 18.12121 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 168.0, average 24.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.64012, average 1.09145 Sum of Tenney's harmonic distance : 15.50699, average 2.21528 Vogel's harmonic complexity : 24.42857 Wille's k value : 2227 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 88.18559, average 3.14949 Lattice compactness (without 2's) : 56.56220, average 2.02008 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.42857 11 1 3: -4 .. 0 -1.57143 11 5: -1 .. 0 -0.14286 1 11: 0 .. 1 0.85714 6 6 Average exponent except 2's :-6 / 7 =-0.85714 Average absolute exponent except 2's: 18 / 7 = 2.57143 Scale is weakly epimorphic with val: <7 10 15 22| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 12 18 25|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 21.5634 c. M: 37.0322 c. Lebeng 15: 2 2 3 1 3 2 2 SP D3 I SD: 20.3937 c. M:-34.5471 c. 16: 2 3 2 2 2 3 2 SP M ME I SD: 17.1455 c. M:-27.5921 c. Armodue-7, Antidorian 17: 2 3 3 1 3 3 2 SP D3 I SD: 12.4078 c. M: 27.7551 c. Naghmeh Abuata, Naghmeh Afshari 18: 2 3 3 2 3 3 2 SP D3 I SD: 14.0783 c. M:-21.2137 c. 23: 3 4 4 2 3 4 3 SP SD: 14.0266 c. M:-22.5951 c. 24: 3 4 4 2 4 4 3 SP D3 I SD: 5.8809 c. M: 13.0492 c. Maqam Su'ar, Naghmeh Abuata, Naghmeh Afshari 31: 4 5 5 3 5 5 4 SP D3 I SD: 6.5252 c. M:-11.3408 c. 34: 4 6 6 3 5 6 4 SP SD: 7.2127 c. M:-13.3879 c. 41: 5 7 7 4 6 7 5 SP SD: 5.0346 c. M:-10.1215 c. 53: 6 9 9 5 8 9 7 SP SD: 7.0168 c. M: 7.9217 c. 54: 6 10 9 5 8 9 7 SP SD: 5.6815 c. M: 10.1646 c. 56: 7 9 10 5 8 10 7 SP SD: 5.2603 c. M: 9.7387 c. 58: 7 10 10 5 9 10 7 SP SD: 4.0779 c. M:-7.3027 c. 61: 7 11 10 6 9 10 8 SP SD: 4.7491 c. M: 6.7400 c. 65: 8 11 11 6 10 11 8 SP SD: 2.9442 c. M:-4.1944 c. 87: 10 15 15 8 13 15 11 SP SD: 2.8423 c. M: 5.5669 c. 94: 11 16 16 9 14 16 12 SP SD: 2.3328 c. M: 3.0724 c. 111: 13 19 19 10 17 19 14 SP SD: 2.0412 c. M: 3.5898 c. 118: 14 20 20 11 18 20 15 SP SD: 1.6187 c. M: 2.1654 c. 135: 16 23 23 13 20 23 17 SP SD: 1.5375 c. M:-3.6174 c. 152: 18 26 26 14 23 26 19 SP SD: 0.8104 c. M: 1.3927 c. 159: 19 27 27 15 24 27 20 SP SD: 0.4696 c. M:-1.1017 c. 183: 22 31 31 17 28 31 23 SP SD: 0.4860 c. M:-0.7644 c. 311: 37 53 53 29 47 53 39 SP SD: 0.4399 c. M: 0.7327 c. 335: 40 57 57 31 51 57 42 SP SD: 0.2163 c. M: 0.3627 c. 494: 59 84 84 46 75 84 62 SP SD: 0.0983 c. M: 0.1781 c. 677: 81 115 115 63 103 115 85 SP SD: 0.0631 c. M: 0.1246 c. 836: 100 142 142 78 127 142 105 SP SD: 0.0722 c. M: 0.1218 c. 1171: 140 199 199 109 178 199 147 SP SD: 0.0182 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: 21.9891 cents 4 x 5 x 6 x 7:8 S SD: 24.3843 cents 5 x 6:7 x 8:9:10 S SD: 12.6498 cents 6 x 7:8:9:10:11:12 S SD: 18.5229 cents 7:8:9 x 10:11:13:14 SD: 24.6718 cents 8:9:10:11:12:13:15:16 SD: 12.9480 cents 10:11:12:14:15:16:18:20 S SD: 11.0441 cents 11:12:13:15:16:18:20:22 SD: 9.1565 cents 13:14:16:18:19:21:24:26 SD: 4.3694 cents 22:24:27:30:32:36:40:44 S SD: 3.9696 cents 24:26:29:33:35:39:44:48 SD: 3.3114 cents 32:35:39:44:47:52:59:64 SD: 2.4172 cents 35:38:43:48:51:57:64:70 SD: 2.2621 cents 45:49:55:62:66:73:83:90 SD: 2.0167 cents 49:53:60:67:72:80:90:98 SD: 1.9847 cents 54:59:66:74:79:88:99:108 SD: 1.7465 cents 58:63:71:80:85:95:106:116 SD: 1.7238 cents 59:64:72:81:87:96:108:118 SD: 1.5801 cents 67:73:82:92:98:109:123:134 SD: 1.2135 cents 90:98:110:124:132:147:165:180 SD: 0.9379 cents 94:102:115:129:138:153:172:188 SD: 0.8671 cents 103:112:126:142:151:168:189:206 SD: 0.7938 cents 126:137:154:173:185:205:231:252 SD: 0.6331 cents 139:151:170:191:204:227:255:278 SD: 0.6171 cents 152:165:186:209:223:248:279:304 SD: 0.5560 cents 162:176:198:223:238:264:297:324 SD: 0.5000 cents 176:191:215:242:258:287:323:352 SD: 0.4440 cents 184:200:225:253:270:300:337:368 SD: 0.3457 cents 197:214:241:271:289:321:361:394 SD: 0.2881 cents 221:240:270:304:324:360:405:442 SD: 0.2492 cents 347:377:424:477:509:565:636:694 SD: 0.2410 cents 360:391:440:495:528:587:660:720 SD: 0.1571 cents 486:528:594:668:713:792:891:972 SD: 0.1157 cents 589:640:720:810:864:960:1080:1178 SD: 0.0935 cents