Scala analysis: 453_D15
Diatonic tetrachord 96/91 * 91/81 * 9/8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 96/91 92.601433 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: 96/91 92.6014 2: 91/81 201.5336 3: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 96/91 92.601 cents 1: 1 91/81 201.534 cents 1: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 108/91 296.511 cents 2: 1 91/72 405.444 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 : 92.6 294.1 498.0 92.6 : 201.5 405.4 498.0 294.1: 203.9 296.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.6014 .. 203.9100 cents 273/256, 111.3086 cents 96/91, 92.6014 cents 2: 294.1350 .. 405.4436 cents 273/256, 111.3086 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 96/91, 92.6014 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.792791 Largest / Average step : 1.228263 Largest / Smallest step : 2.202018 Median interval of one step : 91/81, 201.5336 cents, amount: 1 Least squares average step : 155.35760 cents, oct.: 466.07281 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1463-tone equal temperament with octave 4/3 degrees: 272 864 1463 Least number of segments generator : 732 of 249.193 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1284 of 437.109 cents and inv. generated superset size: 37 = 34 more = 1233.333% 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 : 1.030534 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.553018 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 : 729/728, 2.3764 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 108.9321 cents: 1 -- Rational properties -- Prime limit : 13 Odd number limit : 91 (O: 91 U: 91) Highest odd numerator or denominator: 91 Scale harmonicity : 0.020787 Average absolute harmonicity : 0.105380 Specific harmonicity : 0.106677 Fundamental : 1/2457, -11.2627 octaves, 0.1065 Hz. Guide tone : 96, 6.5850 octaves, 25116.054 Hz. Exponens Consonantiae : 2.358720E+05, 17.84764 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 126.5, average 42.16667 Mersenne's string divisions : 77231 Sum of van Prooijen's expressibility: 3.86753, average 1.28918 Sum of Tenney's harmonic distance : 7.95701, average 2.65234 Vogel's harmonic complexity : 23.33333 Wille's k value : 409 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 25.07970, average 4.17995 Lattice compactness (without 2's) : 14.42418, average 2.40403 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 5 4.00000 12 3: -3 .. 1 -1.00000 5 2 7: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is JI-epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 18 30| Scale is JI-epimorphic with val: <7 11 19 26| Scale is weakly epimorphic with val: <7 11 19 29| Scale is JI-epimorphic with val: <7 11 20 25| Scale is weakly epimorphic with val: <7 11 20 28| Scale is weakly epimorphic with val: <7 11 21 27| Scale is weakly epimorphic with val: <7 11 21 30| Scale is weakly epimorphic with val: <7 11 22 26| Scale is weakly epimorphic with val: <7 11 22 29| Scale is weakly epimorphic with val: <8 11 18 30| Scale is weakly epimorphic with val: <8 11 19 29| Scale is weakly epimorphic with val: <8 11 20 28| Scale is weakly epimorphic with val: <8 11 21 27| Scale is weakly epimorphic with val: <8 11 22 26|
FIT/MODE
3: 1 1 1 SP B ME I SD: 47.6990 c. M:-73.4136 c. 4: 1 1 2 P M ME S SD: 31.9028 c. M: 45.1125 c. 5: 1 2 2 SP M ME S SD: 4.8690 c. M:-7.0076 c. 17: 3 7 7 SP M DE S SD: 2.8022 c. M: 4.7111 c. 22: 4 9 9 SP M DE S SD: 1.1861 c. M: 2.0478 c. 27: 5 11 11 SP M DE S SD: 0.6173 c. M:-1.0028 c. 76: 14 31 31 SP M DE S SD: 0.6610 c. M: 0.8563 c. 86: 16 35 35 SP M DE S SD: 0.7036 c. M:-1.2173 c. 102: 19 41 42 SP T3 SD: 0.6812 c. M: 1.1674 c. 103: 19 42 42 SP M DE S SD: 0.6351 c. M:-0.8237 c. 107: 20 43 44 SP T3 SD: 0.5887 c. M: 0.8935 c. 112: 21 45 46 SP T3 SD: 0.5850 c. M:-0.7820 c. 113: 21 46 46 SP M DE S SD: 0.6737 c. M:-1.1660 c. 117: 22 47 48 SP T3 SD: 0.6511 c. M:-1.0481 c. 119: 22 48 49 SP T3 SD: 0.7392 c. M: 1.1674 c. 124: 23 50 51 SP T3 SD: 0.5526 c. M: 0.9311 c. 129: 24 52 53 SP T3 SD: 0.4131 c. M: 0.7131 c. 134: 25 54 55 SP T3 SD: 0.3475 c. M: 0.5115 c. 151: 28 61 62 SP T3 SD: 0.3672 c. M: 0.5853 c. 156: 29 63 64 SP T3 SD: 0.2404 c. M: 0.4162 c. 161: 30 65 66 SP T3 SD: 0.1890 c. M: 0.2575 c. 183: 34 74 75 SP T3 SD: 0.1258 c. M: 0.2068 c. 188: 35 76 77 SP T3 SD: 0.0820 c. M:-0.1197 c. 210: 39 85 86 SP T3 SD: 0.0687 c. M: 0.1074 c. 215: 40 87 88 SP T3 SD: 0.0478 c. M:-0.0590 c. 398: 74 161 163 SP T3 SD: 0.0365 c. M: 0.0632 c. 425: 79 172 174 SP T3 SD: 0.0139 c. M: 0.0237 c. 613: 114 248 251 SP T3 SD: 0.0166 c. M: 0.0203 c. 640: 119 259 262 SP T3 SD: 0.0134 c. M:-0.0228 c. 1038: 193 420 425 SP T3 SD: 0.0060 c. M: 0.0102 c. 1253: 233 507 513 SP T3 SD: 0.0069 c. M:-0.0119 c. 1463: 272 592 599 SP T3 SD: 0.0046 c. M: 0.0059 c. 1678: 312 679 687 SP T3 SD: 0.0022 c. M:-0.0029 c. 2103: 391 851 861 SP T3 SD: 0.0022 c. M:-0.0028 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 x 9:11 SD: 52.3893 cents 9:10:11:12 H SD: 34.8049 cents 10:11:12:13 H SD: 29.1087 cents 11:12:13:15 SD: 23.3477 cents 12:13:14:16 S SD: 17.8160 cents 15:16:18:20 S SD: 9.5944 cents 18:19:21:24 SD: 9.0942 cents 21:22:25:28 SD: 4.7728 cents 33:35:39:44 SD: 3.4977 cents 39:41:46:52 SD: 3.4298 cents 53:56:63:71 SD: 3.3291 cents 54:57:64:72 SD: 0.3339 cents 237:250:281:316 SD: 0.2338 cents 291:307:345:388 SD: 0.1870 cents 345:364:409:460 SD: 0.1716 cents 438:462:519:584 SD: 0.1485 cents 492:519:583:656 SD: 0.1159 cents 546:576:647:728 SD: 0.0991 cents 600:633:711:800 SD: 0.0951 cents