Scala analysis: xen09-wilson-marwa-18a-03
Marwa permutation 3 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: 11/10 165.004228 Ptolemy's second, 4/5-tone 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: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 10/9 182.4037 minor 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 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: 2 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: 2 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: 2 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: 2 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: 2 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: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 20/11 1034.996 cents large minor seventh 6: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 15/8 1088.269 cents classic 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 : 165.0 347.4 551.3 663.0 845.5 1049.4 1200.0 165.0 : 182.4 386.3 498.0 680.4 884.4 1035.0 1200.0 347.4 : 203.9 315.6 498.0 702.0 852.6 1017.6 1200.0 551.3 : 111.7 294.1 498.0 648.7 813.7 996.1 1200.0 663.0 : 182.4 386.3 537.0 702.0 884.4 1088.3 1200.0 845.5 : 203.9 354.5 519.6 702.0 905.9 1017.6 1200.0 1049.4: 150.6 315.6 498.0 702.0 813.7 996.1 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 .. 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 .. 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: 2 Least squares average step : 172.06724 cents, oct.: 1204.47066 cents Scale is strictly proper Step pattern alph. order: ABCDBCE Step pattern size order : CDEADEB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.438286 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.603949 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 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 4 at degree 6 Formal octave complements present : 1 = 14.2857% Scale is 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 : 27 (O: 27 U: 27) Highest odd numerator or denominator: 27 Scale harmonicity : 0.026609 Average absolute harmonicity : 0.177925 Specific harmonicity : 0.145681 Fundamental : 1/1080, -10.0768 octaves, 0.2422 Hz. Guide tone : 44, 5.4594 octaves, 11511.525 Hz. Exponens Consonantiae : 4.752000E+04, 15.53625 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 94.0, average 13.42857 Mersenne's string divisions : 356378820 Sum of van Prooijen's expressibility: 6.77303, average 0.96758 Sum of Tenney's harmonic distance : 13.69541, average 1.95649 Vogel's harmonic complexity : 21.85714 Wille's k value : 742 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 74.40775, average 2.65742 Lattice compactness (without 2's) : 46.79470, average 1.67124 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.14286 9 1 3: -3 .. 0 -1.00000 7 5: -1 .. 0 -0.28571 2 11: 0 .. 1 0.85714 6 6 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is weakly epimorphic with val: <7 10 15 26| 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: 18.9587 c. M: 37.0322 c. Lebeng 13: 2 2 2 1 2 2 2 SP M ME I SD: 18.9843 c. M: 33.9783 c. Horthatian 15: 2 2 3 1 2 3 2 P D3 SD: 22.4770 c. M: 45.4529 c. 16: 2 3 2 2 2 3 2 SP M ME I SD: 17.8911 c. M:-27.5921 c. Armodue-7, Antidorian 17: 2 3 3 1 3 3 2 SP D3 I SD: 15.3066 c. M: 27.7551 c. Naghmeh Abuata, Naghmeh Afshari 20: 3 3 3 2 3 3 3 SP M ME I SD: 14.2064 c. M: 29.3629 c. 21: 3 3 4 2 3 3 3 SP T3 SD: 14.8760 c. M:-22.6651 c. 22: 3 3 4 2 3 4 3 SP D3 SD: 14.2763 c. M: 27.2711 c. 23: 3 4 4 2 3 4 3 SP SD: 13.5201 c. M:-22.5951 c. 24: 3 4 4 2 4 4 3 SP D3 I SD: 7.7914 c. M: 15.0042 c. Maqam Su'ar, Naghmeh Abuata, Naghmeh Afshari 31: 4 5 5 3 5 5 4 SP D3 I SD: 6.2424 c. M: 10.1655 c. 41: 6 6 7 4 6 7 5 SP SD: 6.3451 c. M:-10.6055 c. 45: 6 7 8 4 7 7 6 SP SD: 6.1391 c. M: 9.3629 c. 51: 7 8 8 5 8 9 6 SP SD: 5.8979 c. M: 10.1415 c. 53: 7 8 9 5 8 9 7 SP SD: 6.8511 c. M: 7.9217 c. 54: 7 9 9 5 8 9 7 SP SD: 5.5021 c. M: 9.4487 c. 56: 8 8 10 5 8 10 7 SP SD: 5.2466 c. M: 9.7387 c. 58: 8 9 10 5 9 10 7 SP SD: 4.0515 c. M:-7.3027 c. 65: 9 10 11 6 10 11 8 SP SD: 2.5187 c. M:-3.7778 c. 87: 12 13 15 8 13 15 11 SP SD: 1.9207 c. M: 4.0736 c. 94: 13 14 16 9 14 16 12 SP SD: 2.0550 c. M: 2.8997 c. 111: 15 17 19 10 17 19 14 SP SD: 2.0176 c. M: 3.5898 c. 118: 16 18 20 11 18 20 15 SP SD: 1.7860 c. M: 2.2924 c. 145: 20 22 25 13 22 25 18 SP SD: 1.5022 c. M:-3.1648 c. 152: 21 23 26 14 23 26 19 SP SD: 0.6839 c. M:-1.3136 c. 159: 22 24 27 15 24 27 20 SP SD: 0.6096 c. M:-1.1017 c. 183: 25 28 31 17 28 31 23 SP SD: 0.5624 c. M: 1.0698 c. 270: 37 41 46 25 41 46 34 SP SD: 0.6360 c. M: 1.0085 c. 311: 43 47 53 29 47 53 39 SP SD: 0.4855 c. M:-0.9122 c. 335: 46 51 57 31 51 57 42 SP SD: 0.2183 c. M: 0.3627 c. 342: 47 52 58 32 52 58 43 SP SD: 0.2069 c. M: 0.4407 c. 494: 68 75 84 46 75 84 62 SP SD: 0.0983 c. M:-0.1780 c. 677: 93 103 115 63 103 115 85 SP SD: 0.0823 c. M: 0.1593 c. 836: 115 127 142 78 127 142 105 SP SD: 0.0749 c. M: 0.1218 c. 1171: 161 178 199 109 178 199 147 SP SD: 0.0153 c. M: 0.0262 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: 22.7331 cents 8:9:10:11:12:13:15:16 SD: 11.1382 cents 10:11:12:14:15:16:18:20 S SD: 10.6081 cents 11:12:13:15:16:18:20:22 SD: 9.3281 cents 13:14:16:18:19:21:24:26 SD: 6.4709 cents 18:20:22:25:26:29:33:36 SD: 5.8825 cents 19:21:23:26:28:31:35:38 SD: 3.3661 cents 30:33:37:41:44:49:55:60 SD: 2.7541 cents 32:35:39:44:47:52:59:64 SD: 2.2501 cents 40:44:49:55:59:65:73:80 SD: 2.0108 cents 49:54:60:67:72:80:90:98 SD: 1.7194 cents 59:65:72:81:87:96:108:118 SD: 1.5799 cents 62:68:76:85:91:101:114:124 SD: 1.4646 cents 67:74:82:92:98:109:123:134 SD: 1.4053 cents 72:79:88:99:106:117:132:144 SD: 1.3268 cents 80:88:98:110:117:130:147:160 SD: 1.2730 cents 90:99:110:124:132:147:165:180 SD: 0.7512 cents 122:134:149:168:179:199:224:244 SD: 0.7091 cents 130:143:159:179:191:212:238:260 SD: 0.6969 cents 131:144:160:180:192:213:240:262 SD: 0.6777 cents 139:153:170:191:204:227:255:278 SD: 0.6376 cents 149:164:182:205:219:243:273:298 SD: 0.6364 cents 152:167:186:209:223:248:279:304 SD: 0.5961 cents 157:173:192:216:230:256:288:314 SD: 0.5902 cents 162:178:198:223:238:264:297:324 SD: 0.5720 cents 170:187:208:234:249:277:312:340 SD: 0.5659 cents 171:188:209:235:251:279:314:342 SD: 0.5623 cents 181:199:221:249:265:295:332:362 SD: 0.5462 cents 189:208:231:260:277:308:347:378 SD: 0.4328 cents 208:229:254:286:305:339:381:416 SD: 0.3793 cents 221:243:270:304:324:360:405:442 SD: 0.2492 cents 270:297:330:371:396:440:495:540 SD: 0.1666 cents 360:396:440:495:528:587:660:720 SD: 0.1405 cents 491:540:600:675:720:800:900:982 SD: 0.1122 cents 581:639:710:799:852:947:1065:1162 SD: 0.0991 cents 589:648:720:810:864:960:1080:1178 SD: 0.0935 cents