Scala analysis: xen18-secor-neutral-third-mos-2-just
Transposition of a mode of MOS generated by a neutral third, just
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: 39/32 342.482663 39th harmonic, Zalzal wosta of Ibn Sina 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 3/2 701.955001 perfect fifth 5: 13/8 840.527662 tridecimal 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: 9/8 203.9100 major whole tone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 44/39 208.8353 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 13/12 138.5727 tridecimal 2/3-tone 6: 44/39 208.8353 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 44/39 208.835 cents 2: 1 13/11 289.210 cents tridecimal minor third 2: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 2 11/9 347.408 cents undecimal neutral third 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 2 16/13 359.472 cents tridecimal neutral third 3: 1 117/88 493.120 cents tridecimal gentle fourth 3: 4 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 18/13 563.382 cents tridecimal augmented fourth 4: 1 13/9 636.618 cents tridecimal diminished fifth 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 176/117 706.880 cents 5: 2 13/8 840.528 cents tridecimal neutral sixth 5: 1 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 1 64/39 857.517 cents 39th subharmonic 5: 1 22/13 910.790 cents tridecimal major sixth 6: 2 39/22 991.165 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 2 24/13 1061.427 cents tridecimal neutral seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 342.5 551.3 702.0 840.5 1049.4 1200.0 203.9 : 138.6 347.4 498.0 636.6 845.5 996.1 1200.0 342.5 : 208.8 359.5 498.0 706.9 857.5 1061.4 1200.0 551.3 : 150.6 289.2 498.0 648.7 852.6 991.2 1200.0 702.0 : 138.6 347.4 498.0 702.0 840.5 1049.4 1200.0 840.5 : 208.8 359.5 563.4 702.0 910.8 1061.4 1200.0 1049.4: 150.6 354.5 493.1 702.0 852.6 991.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.5727 .. 208.8353 cents 176/169, 70.2626 cents 13/12, 138.5727 cents 2: 289.2097 .. 359.4723 cents 176/169, 70.2626 cents 507/484, 80.3744 cents 3: 493.1197 .. 563.3823 cents 176/169, 70.2626 cents 1521/1408, 133.6474 cents 4: 636.6177 .. 706.8803 cents 176/169, 70.2626 cents 169/162, 73.2353 cents 5: 840.5277 .. 910.7903 cents 176/169, 70.2626 cents 1521/1408, 133.6474 cents 6: 991.1647 .. 1061.4273 cents 176/169, 70.2626 cents 507/484, 80.3744 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 13/12, 138.5727 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 44/39, 208.8353 cents Average / Smallest step : 1.237102 Largest / Average step : 1.218206 Largest / Smallest step : 1.507045 Median interval of one step : 12/11, 150.6371 cents, amount: 2 Least squares average step : 173.21047 cents, oct.: 1212.47326 cents Scale is strictly proper Step pattern alph. order: ABCDBCD Step pattern size order : CADBADB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 73.23532 cents Scale diversity : 1.320222 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.648687 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 352/351, 4.9253 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 5, average 702.9401 cents Scale is Hypodorian octave species of abstract tetrachord Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 70.2626 cents: 1 -- Rational properties -- Prime limit : 13 Odd number limit : 117 (O: 117 U: 117) Highest odd numerator or denominator: 39 Scale harmonicity : 0.018404 Average absolute harmonicity : 0.222713 Specific harmonicity : 0.102177 Fundamental : 1/96, -6.5850 octaves, 2.7253 Hz. Guide tone : 2574, 11.3298 octaves, 673424.205 Hz. Exponens Consonantiae : 2.471040E+05, 17.91476 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 76.5, average 10.92857 Mersenne's string divisions : 2407965 Sum of van Prooijen's expressibility: 6.21916, average 0.88845 Sum of Tenney's harmonic distance : 11.81379, average 1.68768 Vogel's harmonic complexity : 14.00000 Wille's k value : 58 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 82.86661, average 2.95952 Lattice compactness (without 2's) : 41.09778, average 1.46778 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -2.14286 17 1 3: -1 .. 2 0.42857 5 2 11: 0 .. 1 0.28571 2 2 13: 0 .. 1 0.28571 2 2 Average exponent except 2's : 7 / 7 = 1.00000 Average absolute exponent except 2's: 9 / 7 = 1.28571 Scale is weakly epimorphic with val: <7 10 26 29| Scale is weakly epimorphic with val: <7 11 23 27| Scale is JI-epimorphic with val: <7 11 24 26| = patent Scale is weakly epimorphic with val: <7 12 23 29|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 22.0347 c. M: 37.0322 c. Lebeng 13: 2 2 2 2 1 2 2 SP M ME S SD: 22.9179 c. M:-36.5065 c. Glacial-7, Lobonian 17: 3 2 3 2 2 3 2 SP M ME S SD: 8.4337 c. M:-13.3879 c. 24: 4 3 4 3 3 4 3 SP M ME S SD: 4.8915 c. M:-9.4723 c. Neutral Hypodorian, Iced Dark Lydian 41: 7 5 7 5 5 7 5 SP M DE S SD: 5.1673 c. M:-8.7368 c. 46: 8 5 8 6 5 8 6 SP T3 SD: 4.1351 c. M: 5.8847 c. 53: 9 6 9 7 6 9 7 SP T3 SD: 4.4790 c. M: 7.9217 c. 63: 11 7 11 8 7 11 8 SP T3 SD: 2.6625 c. M:-5.6138 c. 70: 12 8 12 9 8 12 9 SP T3 SD: 1.9028 c. M: 3.6487 c. 87: 15 10 15 11 10 15 11 SP T3 SD: 1.6353 c. M:-2.9865 c. 94: 16 11 16 12 11 16 12 SP T3 SD: 1.7436 c. M: 2.5544 c. 113: 19 13 20 14 13 20 14 SP SD: 1.6897 c. M: 2.6597 c. 130: 22 15 23 16 15 23 16 SP SD: 1.5630 c. M:-2.9448 c. 137: 23 16 24 17 16 24 17 SP SD: 1.2901 c. M: 2.4501 c. 159: 27 18 28 20 18 28 20 SP SD: 1.5227 c. M: 2.8600 c. 161: 27 19 28 20 19 28 20 SP SD: 1.4378 c. M: 2.6678 c. 166: 28 19 29 21 19 29 21 SP SD: 1.6554 c. M: 2.7236 c. 176: 30 20 31 22 20 31 22 SP SD: 1.0607 c. M: 1.8913 c. 183: 31 21 32 23 21 32 23 SP SD: 0.7953 c. M: 1.4991 c. 200: 34 23 35 25 23 35 25 SP SD: 0.4460 c. M:-0.6821 c. 207: 35 24 36 26 24 36 26 SP SD: 0.5137 c. M: 1.0115 c. 224: 38 26 39 28 26 39 28 SP SD: 0.4147 c. M:-0.6371 c. 270: 46 31 47 34 31 47 34 SP SD: 0.3724 c. M:-0.5344 c. 294: 50 34 51 37 34 51 37 SP SD: 0.2662 c. M: 0.3833 c. 407: 69 47 71 51 47 71 51 SP SD: 0.2983 c. M: 0.4702 c. 470: 80 54 82 59 54 82 59 SP SD: 0.2886 c. M: 0.5277 c. 477: 81 55 83 60 55 83 60 SP SD: 0.2542 c. M: 0.3745 c. 494: 84 57 86 62 57 86 62 SP SD: 0.0729 c. M:-0.1386 c. 1195: 203 138 208 150 138 208 150 SP SD: 0.0357 c. M: 0.0606 c. 1689: 287 195 294 212 195 294 212 SP SD: 0.0184 c. M: 0.0315 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: 22.9956 cents 4 x 5 x 6 x 7:8 S SD: 22.9229 cents 5 x 6:7 x 8:9:10 S SD: 11.7015 cents 6:7 x 8:9:10:11:12 S SD: 15.5664 cents 7:8:9:10 x 11:13:14 SD: 22.0882 cents 8:9:10:11:12:13:15:16 SD: 8.3725 cents 14:16:17:19:21:23:26:28 SD: 6.6284 cents 18:20:22:25:27:29:33:36 SD: 4.5409 cents 22:25:27:30:33:36:40:44 SD: 4.5326 cents 24:27:29:33:36:39:44:48 SD: 2.1229 cents 32:36:39:44:48:52:59:64 SD: 1.4012 cents 56:63:68:77:84:91:103:112 SD: 1.2110 cents 64:72:78:88:96:104:117:128 SD: 0.7036 cents 96:108:117:132:144:156:176:192 SD: 0.0000 cents