Scala analysis: 452_D15
Diatonic tetrachord 48/43 * 86/81 * 9/8, Safiyu-d-Din
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 48/43 190.437295 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 48/43 190.4373 2: 86/81 103.6977 3: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 86/81 103.698 cents 1: 1 48/43 190.437 cents 1: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 43/36 307.608 cents 2: 1 54/43 394.347 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 190.4 294.1 498.0 190.4: 103.7 307.6 498.0 294.1: 203.9 394.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 103.6977 .. 203.9100 cents 729/688, 100.2123 cents 86/81, 103.6977 cents 2: 294.1350 .. 394.3473 cents 729/688, 100.2123 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 86/81, 103.6977 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.600952 Largest / Average step : 1.228263 Largest / Smallest step : 1.966389 Median interval of one step : 48/43, 190.4373 cents, amount: 1 Least squares average step : 162.34588 cents, oct.: 487.03763 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1849-tone equal temperament with octave 4/3 degrees: 707 1092 1849 Least number of segments generator : 925 of 249.157 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1303 of 350.975 cents and inv. generated superset size: 26 = 23 more = 866.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.157925 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.597577 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 129/128, 13.4727 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 43 Odd number limit : 81 (O: 43 U: 81) Highest odd numerator or denominator: 43 Scale harmonicity : 0.063830 Fundamental : 1/1161, -10.1812 octaves, 0.2253 Hz. Guide tone : 96, 6.5850 octaves, 25116.054 Hz. Exponens Consonantiae : 1.114560E+05, 16.76611 octaves Euler's gradus suavitatis : 56 Sum of Mann's harmonic distance : 78.5, average 26.16667 Mersenne's string divisions : 5369 Sum of van Prooijen's expressibility: 3.54195, average 1.18065 Sum of Tenney's harmonic distance : 7.33040, average 2.44347 Vogel's harmonic complexity : 38.33333 Wille's k value : 193 Wilson's harmonic complexity : 55 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 22.74721, average 3.79120 Lattice compactness (without 2's) : 13.00000, average 2.16667 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 5 3.66667 11 3: -3 .. 1 -1.00000 5 2 43: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is JI-epimorphic with val: <7 11 38| Scale is weakly epimorphic with val: <7 11 41| Scale is weakly epimorphic with val: <8 11 40|
FIT/MODE
3: 1 1 1 SP B ME I SD: 26.0287 c. M:-37.8950 c. 5: 2 1 2 SP M ME I SD: 5.7479 c. M:-8.7807 c. 19: 7 4 8 SP T3 SD: 5.2224 c. M: 6.9470 c. 24: 9 5 10 SP T3 SD: 2.9718 c. M: 3.6704 c. 29: 11 6 12 SP T3 SD: 1.5344 c. M: 2.1776 c. 34: 13 7 14 SP T3 SD: 0.6740 c. M: 1.1674 c. 39: 15 8 16 SP T3 SD: 0.6890 c. M:-1.1185 c. 71: 27 15 29 SP T3 SD: 0.6620 c. M: 1.0399 c. 73: 28 15 30 SP T3 SD: 0.5595 c. M: 0.7660 c. 76: 29 16 31 SP T3 SD: 0.4942 c. M:-0.7601 c. 81: 31 17 33 SP T3 SD: 0.5875 c. M:-1.0028 c. 105: 40 22 43 SP T3 SD: 0.4086 c. M: 0.7059 c. 110: 42 23 45 SP T3 SD: 0.1848 c. M: 0.2747 c. 115: 44 24 47 SP T3 SD: 0.2196 c. M:-0.3612 c. 144: 55 30 59 SP T3 SD: 0.1499 c. M: 0.2118 c. 149: 57 31 61 SP T3 SD: 0.0524 c. M:-0.0900 c. 259: 99 54 106 SP T3 SD: 0.0581 c. M:-0.0769 c. 293: 112 61 120 SP T3 SD: 0.0515 c. M: 0.0675 c. 408: 156 85 167 SP T3 SD: 0.0312 c. M:-0.0533 c. 442: 169 92 181 SP T3 SD: 0.0239 c. M: 0.0406 c. 557: 213 116 228 SP T3 SD: 0.0266 c. M:-0.0424 c. 591: 226 123 242 SP T3 SD: 0.0184 c. M: 0.0272 c. 701: 268 146 287 SP T3 SD: 0.0170 c. M: 0.0292 c. 850: 325 177 348 SP T3 SD: 0.0055 c. M: 0.0083 c. 999: 382 208 409 SP T3 SD: 0.0049 c. M:-0.0063 c. 1849: 707 385 757 SP T3 SD: 0.0030 c. M:-0.0052 c. 2291: 876 477 938 SP T3 SD: 0.0024 c. M: 0.0037 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x 5 x S SD: 92.1787 cents 5 x 6:7 S SD: 43.5810 cents 6 x 7:8 S SD: 13.6320 cents 7:8 x 9 S SD: 37.4952 cents 8:9 x 11 SD: 27.4751 cents 9:10:11:12 H SD: 17.9584 cents 13 x 15:17 SD: 28.6466 cents 14:16:17:19 SD: 22.0151 cents 15:17:18:20 SD: 11.3115 cents 16:18:19:21 SD: 10.1994 cents 17:19:20:23 SD: 9.4664 cents 25:28:30:33 SD: 9.4190 cents 26:29:31:35 SD: 6.5319 cents 27:30:32:36 S SD: 2.6779 cents 60:67:71:80 SD: 0.9244 cents 102:114:121:136 SD: 0.8835 cents 129:144:153:172 SD: 0.4192 cents 189:211:224:252 SD: 0.0636 cents 594:663:704:792 SD: 0.0607 cents