Scala analysis: 427_D10
Diatonic tetrachord 256/243 * 76/67 * 5427/4864, Euler
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/243 90.224996 limma, Pythagorean minor second 2: 19456/16281 308.430983 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 5427/4864 189.6140 1: 256/243 90.2250 limma, Pythagorean minor second 2: 76/67 218.2060 3: 5427/4864 189.6140
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 5427/4864 189.614 cents 1: 1 76/67 218.206 cents 2: 1 67/57 279.839 cents 2: 1 19456/16281 308.431 cents 2: 1 81/64 407.820 cents Pythagorean major third 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 : 90.2 308.4 498.0 90.2 : 218.2 407.8 498.0 308.4: 189.6 279.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 218.2060 cents 4617/4288, 127.9810 cents 256/243, 90.2250 cents 2: 279.8390 .. 407.8200 cents 4617/4288, 127.9810 cents 4489/4332, 61.6330 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 76/67, 218.2060 cents Average / Smallest step : 1.840011 Largest / Average step : 1.314375 Largest / Smallest step : 2.418465 Median interval of one step : 5427/4864, 189.6140 cents, amount: 1 Least squares average step : 157.23014 cents, oct.: 471.69042 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1358-tone equal temperament with octave 4/3 degrees: 246 841 1358 Least number of segments generator : 681 of 249.756 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1235 of 452.935 cents and inv. generated superset size: 52 = 49 more = 1733.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 61.63302 cents Scale diversity : 1.103739 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.486067 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 : 369664/363609, 28.5920 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 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 67 Odd number limit : 16281 (O: 5427 U: 16281) Highest odd numerator or denominator: 16281 Scale harmonicity : 0.017410 Fundamental : 1/16281, -13.9909 octaves, 0.0161 Hz. Guide tone : 19456, 14.2479 octaves, 5090186.998 Hz. Exponens Consonantiae : 3.167631E+08, 28.23883 octaves Euler's gradus suavitatis : 105 Sum of Mann's harmonic distance : 18121.5, average 6040.50000 Mersenne's string divisions : 124829341 Sum of van Prooijen's expressibility: 7.07441, average 2.35814 Sum of Tenney's harmonic distance : 14.37376, average 4.79125 Vogel's harmonic complexity : 61.66667 Wille's k value : 2713 Wilson's harmonic complexity : 101 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 41.34219, average 6.89037 Lattice compactness (without 2's) : 20.22213, average 3.37035 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 10 6.66667 20 3: -5 ..-1 -3.66667 11 2 19: 0 .. 1 0.33333 1 67: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-11 / 3 =-3.66667 Average absolute exponent except 2's: 13 / 3 = 4.33333 Scale is weakly epimorphic with val: <7 11 28 44| Scale is weakly epimorphic with val: <7 11 29 45| Scale is JI-epimorphic with val: <7 11 30 43| Scale is JI-epimorphic with val: <7 11 31 44| = patent Scale is JI-epimorphic with val: <7 11 32 45| Scale is weakly epimorphic with val: <7 11 33 43| Scale is weakly epimorphic with val: <7 11 34 44|
FIT/MODE
3: 1 1 1 SP B ME I SD: 45.8295 c. M:-75.7900 c. 4: 1 2 1 P M ME I SD: 42.4810 c. M:-65.1028 c. 5: 1 2 2 SP M ME S SD: 7.7523 c. M: 9.6040 c. 11: 2 5 4 SP T3 SD: 4.9150 c. M:-8.5067 c. 16: 3 7 6 SP T3 SD: 2.4551 c. M:-3.1584 c. 34: 6 15 13 SP T3 SD: 1.4277 c. M: 2.3347 c. 39: 7 17 15 SP T3 SD: 1.2197 c. M: 1.9418 c. 45: 8 20 17 SP T3 SD: 1.2880 c. M: 1.6837 c. 50: 9 22 19 SP T3 SD: 0.3917 c. M: 0.5769 c. 55: 10 24 21 SP T3 SD: 0.3692 c. M: 0.5486 c. 105: 19 46 40 SP T3 SD: 0.0900 c. M: 0.1174 c. 276: 50 121 105 SP T3 SD: 0.0810 c. M:-0.1404 c. 331: 60 145 126 SP T3 SD: 0.0351 c. M:-0.0551 c. 436: 79 191 166 SP T3 SD: 0.0111 c. M:-0.0171 c. 922: 167 404 351 SP T3 SD: 0.0109 c. M: 0.0151 c. 1253: 227 549 477 SP T3 SD: 0.0089 c. M:-0.0151 c. 1358: 246 595 517 SP T3 SD: 0.0039 c. M:-0.0048 c. 1794: 325 786 683 SP T3 SD: 0.0010 c. M:-0.0016 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: 77.8827 cents 5 x 6:7 S SD: 42.3872 cents 6 x 7:8 S SD: 20.7800 cents 7 x 8:9 S SD: 49.8315 cents 8 x 10:11 S SD: 47.1798 cents 9:10:11:12 H SD: 33.3602 cents 10:11:12:13 H SD: 28.9925 cents 11:12:13:15 SD: 24.7941 cents 12:13:14:16 S SD: 21.2518 cents 14:15:17:19 SD: 16.8649 cents 15:16:18:20 S SD: 7.5609 cents 21:22:25:28 SD: 3.9046 cents 36:38:43:48 SD: 1.1590 cents 57:60:68:76 SD: 1.0900 cents 93:98:111:124 SD: 0.7223 cents 129:136:154:172 SD: 0.7210 cents 168:177:201:224 SD: 0.6846 cents 189:199:226:252 SD: 0.4863 cents 225:237:269:300 SD: 0.2772 cents 261:275:312:348 SD: 0.2036 cents 282:297:337:376 SD: 0.1683 cents 318:335:380:424 SD: 0.0301 cents