Scala analysis: xen09-wilson-marwa-10-02
Marwa permutation 2 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: 9/8 203.910002 major whole tone 2: 33/28 284.447037 undecimal minor third 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major sixth 6: 99/56 986.402038 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 112/99 213.5980 1: 9/8 203.9100 major whole tone 2: 22/21 80.5370 undecimal minor semitone 3: 7/6 266.8709 septimal minor third 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 9/8 203.9100 major whole tone 6: 22/21 80.5370 undecimal minor semitone 7: 112/99 213.5980
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 22/21 80.537 cents undecimal minor semitone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 112/99 213.598 cents 1: 1 7/6 266.871 cents septimal minor third 2: 2 33/28 284.447 cents undecimal minor third 2: 1 32/27 294.135 cents Pythagorean 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 14/11 417.508 cents undecimal diminished fourth or major third 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: 2 11/7 782.492 cents undecimal augmented fifth 5: 1 44/27 845.453 cents neutral sixth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 56/33 915.553 cents 6: 1 12/7 933.129 cents septimal major sixth 6: 1 99/56 986.402 cents 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 2 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 : 203.9 284.4 551.3 702.0 905.9 986.4 1200.0 203.9 : 80.5 347.4 498.0 702.0 782.5 996.1 1200.0 284.4 : 266.9 417.5 621.4 702.0 915.6 1119.5 1200.0 551.3 : 150.6 354.5 435.1 648.7 852.6 933.1 1200.0 702.0 : 203.9 284.4 498.0 702.0 782.5 1049.4 1200.0 905.9 : 80.5 294.1 498.0 578.6 845.5 996.1 1200.0 986.4 : 213.6 417.5 498.0 764.9 915.6 1119.5 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: 284.4470 .. 417.5080 cents 392/363, 133.0609 cents 99/98, 17.5761 cents 3: 435.0841 .. 621.4180 cents 49/44, 186.3339 cents 99/98, 17.5761 cents 4: 578.5820 .. 764.9159 cents 49/44, 186.3339 cents 3872/3969,-42.8359 cents 5: 782.4920 .. 915.5530 cents 392/363, 133.0609 cents 99/98, 17.5761 cents 6: 933.1291 .. 1119.4630 cents 49/44, 186.3339 cents 99/98, 17.5761 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 : 9/8, 203.9100 cents, amount: 2 Least squares average step : 172.01654 cents, oct.: 1204.11576 cents Scale is not proper Step pattern alph. order: ABCDABE Step pattern size order : CAEBCAD Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.581147 Lumma stability : 0.192815 Lumma impropriety factor : 0.035697 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 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 : 99 (O: 99 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.024115 Average absolute harmonicity : 0.225803 Specific harmonicity : 0.115979 Fundamental : 1/112, -6.8074 octaves, 2.3359 Hz. Guide tone : 594, 9.2143 octaves, 155405.586 Hz. Exponens Consonantiae : 6.652800E+04, 16.02167 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 151.5, average 21.64286 Mersenne's string divisions : 393961485 Sum of van Prooijen's expressibility: 7.41827, average 1.05975 Sum of Tenney's harmonic distance : 14.22598, average 2.03228 Vogel's harmonic complexity : 15.42857 Wille's k value : 94 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 79.11220, average 2.82544 Lattice compactness (without 2's) : 48.29999, average 1.72500 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -2.14286 17 1 3: 0 .. 3 1.28571 9 3 7: -1 .. 0 -0.28571 2 11: 0 .. 1 0.42857 3 3 Average exponent except 2's : 10 / 7 = 1.42857 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is weakly epimorphic with val: <7 10 21 26| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 21 23| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 38.2735 c. M:-58.4101 c. Lebeng 8: 1 1 2 1 1 1 1 P M ME S SD: 41.2407 c. M:-63.5980 c. 9: 1 1 2 1 2 0 2 N D3 SD: 38.6129 c. M: 70.5767 c. 11: 2 0 3 1 2 1 2 N SD: 33.7976 c. M: 66.2652 c. 12: 2 1 3 1 2 1 2 P D3 SD: 20.1787 c. M:-48.6821 c. Mela Hemavati, Raga Desisimharavam, Maqam Nakriz, Tunisian, Dorian sharp 4, Misheberekh: Jewish, Nigriz, Pimenikos, Souzinak (Peiraiotikos Minor): Greece, Ukrainian Dorian, Ukrainian Minor, Kaffa, Gnossiennes 13: 2 1 3 2 2 1 2 N T3 SD: 20.3689 c. M:-36.5065 c. 16: 3 1 3 2 3 1 3 P T3 I SD: 18.0091 c. M: 26.9550 c. 17: 3 1 4 2 3 1 3 N SD: 7.5868 c. M:-13.3879 c. 29: 5 2 6 4 5 2 5 N SD: 6.3523 c. M: 13.3869 c. 41: 7 3 9 5 7 3 7 N SD: 4.9279 c. M:-8.7199 c. 46: 8 3 10 6 8 3 8 N SD: 4.1864 c. M:-7.1785 c. 58: 10 4 13 7 10 4 10 N SD: 4.7296 c. M:-7.3027 c. 63: 11 4 14 8 11 4 11 N SD: 4.3034 c. M:-8.4207 c. 65: 11 4 15 8 11 4 12 N SD: 4.2842 c. M: 7.9405 c. 69: 12 4 16 8 12 5 12 N SD: 4.6951 c. M: 6.3028 c. 70: 12 5 15 9 12 5 12 N SD: 4.3067 c. M:-7.8837 c. 72: 12 5 16 9 12 5 13 N SD: 3.0683 c. M: 5.8650 c. 77: 13 5 17 10 13 5 14 N SD: 3.3133 c. M: 5.8634 c. 85: 14 6 19 11 14 6 15 N SD: 3.1255 c. M: 6.2629 c. 89: 15 6 20 11 15 6 16 N SD: 1.6098 c. M: 2.4942 c. 106: 18 7 24 13 18 7 19 N SD: 1.5070 c. M:-3.3990 c. 118: 20 8 26 15 20 8 21 N SD: 0.9045 c. M: 2.1654 c. 135: 23 9 30 17 23 9 24 N SD: 0.3987 c. M:-0.8017 c. 224: 38 15 50 28 38 15 40 N SD: 0.4411 c. M: 0.6878 c. 253: 43 17 56 32 43 17 45 N SD: 0.4319 c. M: 1.1203 c. 342: 58 23 76 43 58 23 61 N SD: 0.3789 c. M: 0.6018 c. 359: 61 24 80 45 61 24 64 N SD: 0.1928 c. M: 0.3296 c. 477: 81 32 106 60 81 32 85 N SD: 0.2040 c. M: 0.3745 c. 494: 84 33 110 62 84 33 88 N SD: 0.1516 c. M: 0.2365 c. 612: 104 41 136 77 104 41 109 N SD: 0.1456 c. M: 0.3376 c. 742: 126 50 165 93 126 50 132 N SD: 0.1427 c. M: 0.2046 c. 836: 142 56 186 105 142 56 149 N SD: 0.1565 c. M: 0.2776 c. 877: 149 59 195 110 149 59 156 N SD: 0.0936 c. M:-0.1596 c. 1012: 172 68 225 127 172 68 180 N SD: 0.0886 c. M:-0.1592 c. 1236: 210 83 275 155 210 83 220 N SD: 0.0561 c. M:-0.1384 c. 1354: 230 91 301 170 230 91 241 N SD: 0.0570 c. M: 0.1043 c. 1371: 233 92 305 172 233 92 244 N SD: 0.0464 c. M:-0.1044 c. 1489: 253 100 331 187 253 100 265 N SD: 0.0359 c. M: 0.0755 c. 1848: 314 124 411 232 314 124 329 N SD: 0.0224 c. M: 0.0384 c. 1983: 337 133 441 249 337 133 353 N SD: 0.0243 c. M:-0.0351 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: 19.1501 cents 4 x 5 x 6 x 7:8 S SD: 25.8430 cents 5 x 6:7 x 8:9:10 S SD: 21.3693 cents 6 x 7:8:9:10:11:12 S SD: 14.5043 cents 7:8 x 10:11:12 x 14 S SD: 22.2273 cents 8:9 x 11:12 x 14:16 SD: 3.5152 cents 11:12:13:15:17 x 19:22 SD: 14.2933 cents 12 x 14:17:18:20:21:24 SD: 10.2082 cents 13 x 15:18:20:22:23:26 SD: 9.7754 cents 16:18:19:22:24:27:28:32 SD: 3.1287 cents 32:36:38:44:48:54:57:64 SD: 2.6397 cents 38:43:45:52:57:64:67:76 SD: 2.3551 cents 40:45:47:55:60:68:71:80 SD: 2.2112 cents 48:54:57:66:72:81:85:96 SD: 1.9124 cents 56:63:66:77:84:95:99:112 SD: 1.3051 cents 72:81:85:99:108:122:127:144 SD: 1.2303 cents 74:83:87:102:111:125:131:148 SD: 1.2111 cents 78:88:92:107:117:132:138:156 SD: 1.1820 cents 80:90:94:110:120:135:141:160 SD: 1.0615 cents 90:101:106:124:135:152:159:180 SD: 0.8485 cents 96:108:113:132:144:162:170:192 SD: 0.5203 cents 112:126:132:154:168:189:198:224 SD: 0.0000 cents