Scala analysis: 451_D15
Diatonic tetrachord 64/59 * 59/54 * 9/8, Safiyu-d-Din
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 64/59 140.828341 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: 64/59 140.8283 2: 59/54 153.3067 3: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 64/59 140.828 cents 1: 1 59/54 153.307 cents 1: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 72/59 344.738 cents Ibn Sina's neutral third 2: 1 59/48 357.217 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 : 140.8 294.1 498.0 140.8: 153.3 357.2 498.0 294.1: 203.9 344.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 140.8283 .. 203.9100 cents 531/512, 63.0817 cents 64/59, 140.8283 cents 2: 294.1350 .. 357.2167 cents 531/512, 63.0817 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 64/59, 140.8283 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.178847 Largest / Average step : 1.228263 Largest / Smallest step : 1.447933 Median interval of one step : 59/54, 153.3067 cents, amount: 1 Least squares average step : 158.80238 cents, oct.: 476.40714 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 679-tone equal temperament with octave 4/3 degrees: 192 401 679 Least number of segments generator : 340 of 249.389 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 383 of 280.930 cents and inv. generated superset size: 23 = 20 more = 766.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.353726 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.746683 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 : 3481/3456, 12.4783 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 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 50.6033 cents: 2 -- Rational properties -- Prime limit : 59 Odd number limit : 59 (O: 59 U: 59) Highest odd numerator or denominator: 59 Scale harmonicity : 0.071429 Fundamental : 1/1593, -10.6375 octaves, 0.1642 Hz. Guide tone : 64, 6.0000 octaves, 16744.036 Hz. Exponens Consonantiae : 1.019520E+05, 16.63753 octaves Euler's gradus suavitatis : 71 Sum of Mann's harmonic distance : 94.5, average 31.50000 Mersenne's string divisions : 50799 Sum of van Prooijen's expressibility: 3.67934, average 1.22645 Sum of Tenney's harmonic distance : 7.59273, average 2.53091 Vogel's harmonic complexity : 48.66667 Wille's k value : 265 Wilson's harmonic complexity : 68 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 24.95795, average 4.15966 Lattice compactness (without 2's) : 10.00000, average 1.66667 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 6 4.33333 13 3: -3 .. 0 -1.33333 4 2 59: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <7 11 44|
FIT/MODE
3: 1 1 1 SP B ME I SD: 26.2704 c. M:-37.8950 c. 5: 1 2 2 SP M ME S SD: 23.9517 c. M: 41.2193 c. 7: 2 2 3 SP M ME S SD: 5.5717 c. M: 9.5379 c. 10: 3 3 4 SP M ME S SD: 5.6486 c. M:-8.5852 c. 15: 4 5 6 SP T3 SD: 5.3627 c. M: 8.0163 c. 17: 5 5 7 SP M DE S SD: 3.3340 c. M:-5.6555 c. 22: 6 7 9 SP T3 SD: 2.8871 c. M: 4.9979 c. 24: 7 7 10 SP M DE S SD: 3.3010 c. M:-4.4348 c. 25: 7 8 10 SP T3 SD: 2.8230 c. M:-4.6920 c. 29: 8 9 12 SP T3 SD: 2.3489 c. M: 3.4366 c. 32: 9 10 13 SP T3 SD: 1.0102 c. M:-1.5792 c. 39: 11 12 16 SP T3 SD: 0.3155 c. M: 0.4162 c. 110: 31 34 45 SP T3 SD: 0.2876 c. M: 0.4702 c. 127: 36 39 52 SP T3 SD: 0.2021 c. M:-0.3498 c. 159: 45 49 65 SP T3 SD: 0.1918 c. M:-0.3067 c. 166: 47 51 68 SP T3 SD: 0.1235 c. M:-0.1844 c. 198: 56 61 81 SP T3 SD: 0.0967 c. M:-0.1643 c. 237: 67 73 97 SP T3 SD: 0.0435 c. M:-0.0688 c. 276: 78 85 113 SP T3 SD: 0.0442 c. M: 0.0765 c. 403: 114 124 165 SP T3 SD: 0.0335 c. M:-0.0578 c. 442: 125 136 181 SP T3 SD: 0.0265 c. M: 0.0406 c. 640: 181 197 262 SP T3 SD: 0.0196 c. M:-0.0250 c. 679: 192 209 278 SP T3 SD: 0.0023 c. M:-0.0032 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 x 8:9 S SD: 44.5201 cents 8:9 x 11 SD: 41.2835 cents 9:10:11:12 H SD: 22.5253 cents 10:11:12:13 H SD: 18.1603 cents 11:12:13:15 SD: 13.4748 cents 12:13:14:16 S SD: 9.1191 cents 21:23:25:28 SD: 6.1209 cents 27:29:32:36 SD: 5.7054 cents 33:36:39:44 SD: 3.6586 cents 48:52:57:64 SD: 1.3540 cents 60:65:71:80 SD: 1.1746 cents 81:88:96:108 SD: 0.8899 cents 108:117:128:144 SD: 0.7519 cents 129:140:153:172 SD: 0.5039 cents 141:153:167:188 SD: 0.4291 cents 189:205:224:252 SD: 0.0477 cents