Scala analysis: 426_D10
Diatonic tetrachord 201/191 * 191/171 * 76/67
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 201/191 88.347436 2: 67/57 279.839012 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 76/67 218.2060 1: 201/191 88.3474 2: 191/171 191.4916 3: 76/67 218.2060
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 201/191 88.347 cents 1: 1 191/171 191.492 cents 1: 1 76/67 218.206 cents 2: 1 67/57 279.839 cents 2: 1 228/191 306.553 cents 2: 1 764/603 409.698 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 : 88.3 279.8 498.0 88.3 : 191.5 409.7 498.0 279.8: 218.2 306.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.3474 .. 218.2060 cents 14516/13467, 129.8586 cents 201/191, 88.3474 cents 2: 279.8390 .. 409.6976 cents 14516/13467, 129.8586 cents 4489/4332, 61.6330 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 201/191, 88.3474 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 76/67, 218.2060 cents Average / Smallest step : 1.879115 Largest / Average step : 1.314375 Largest / Smallest step : 2.469862 Median interval of one step : 191/171, 191.4916 cents, amount: 1 Least squares average step : 153.01146 cents, oct.: 459.03438 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1212-tone equal temperament with octave 4/3 degrees: 215 681 1212 Least number of segments generator : 607 of 249.433 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 923 of 379.287 cents and inv. generated superset size: 38 = 35 more = 1266.667% 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 61.63302 cents Scale diversity : 1.082558 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.478527 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 : 12996/12797, 26.7144 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 103.1441 cents: 1 -- Rational properties -- Prime limit : 191 Odd number limit : 603 (O: 201 U: 603) Highest odd numerator or denominator: 201 Scale harmonicity : 0.024132 Fundamental : 1/10887, -13.4103 octaves, 0.0240 Hz. Guide tone : 804, 9.6511 octaves, 210346.955 Hz. Exponens Consonantiae : 8.753148E+06, 23.06137 octaves Euler's gradus suavitatis : 281 Sum of Mann's harmonic distance : 261.5, average 87.16667 Mersenne's string divisions : 12152 Sum of van Prooijen's expressibility: 4.60639, average 1.53546 Sum of Tenney's harmonic distance : 9.24536, average 3.08179 Vogel's harmonic complexity : 187.33333 Wille's k value : 6398 Wilson's harmonic complexity : 283 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 11.95084, average 1.99181 Lattice compactness (without 2's) : 8.65028, average 1.44171 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -1 .. 1 -0.33333 3 1 19: -1 .. 0 -0.33333 1 67: 0 .. 1 0.66667 2 1 191: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 30 43 55| Scale is weakly epimorphic with val: <6 10 31 44 56| Scale is weakly epimorphic with val: <6 10 32 45 54| Scale is weakly epimorphic with val: <6 11 29 43 55| Scale is weakly epimorphic with val: <6 11 30 44 56| Scale is weakly epimorphic with val: <6 11 31 45 54| Scale is weakly epimorphic with val: <7 10 30 43 54| Scale is weakly epimorphic with val: <7 10 31 44 55| Scale is weakly epimorphic with val: <7 10 32 45 56| Scale is weakly epimorphic with val: <7 11 28 43 55| Scale is weakly epimorphic with val: <7 11 28 44 54| Scale is weakly epimorphic with val: <7 11 29 44 56| Scale is weakly epimorphic with val: <7 11 29 45 55| Scale is weakly epimorphic with val: <7 11 30 43 56| Scale is weakly epimorphic with val: <7 11 30 45 54| Scale is weakly epimorphic with val: <7 11 31 43 55| Scale is JI-epimorphic with val: <7 11 31 44 54| Scale is weakly epimorphic with val: <7 11 32 44 56| Scale is JI-epimorphic with val: <7 11 32 45 55| Scale is weakly epimorphic with val: <7 11 33 43 56| Scale is weakly epimorphic with val: <7 11 33 45 54| Scale is weakly epimorphic with val: <7 11 34 43 55| Scale is weakly epimorphic with val: <7 11 34 44 54| Scale is weakly epimorphic with val: <7 12 28 43 54| Scale is weakly epimorphic with val: <7 12 29 44 55| Scale is weakly epimorphic with val: <7 12 29 45 54| Scale is weakly epimorphic with val: <7 12 30 45 56| Scale is weakly epimorphic with val: <7 12 32 45 54| Scale is weakly epimorphic with val: <8 11 29 43 56| Scale is weakly epimorphic with val: <8 11 30 44 54| Scale is weakly epimorphic with val: <8 11 31 45 55| Scale is weakly epimorphic with val: <8 12 28 43 56| Scale is weakly epimorphic with val: <8 12 28 45 54| Scale is weakly epimorphic with val: <8 12 29 44 54| Scale is weakly epimorphic with val: <8 12 30 45 55| Scale is weakly epimorphic with val: <8 12 31 45 54| Scale is weakly epimorphic with val: <8 12 34 45 54|
FIT/MODE
3: 0 1 2 N G T3 SD: 83.1889 c. M: 113.8240 c. 4: 1 1 2 P M ME S SD: 27.4316 c. M:-36.1638 c. 5: 1 2 2 SP M ME S SD: 12.7458 c. M:-18.9880 c. 7: 1 3 3 SP M DE S SD: 10.3024 c. M: 17.1982 c. 11: 2 4 5 SP T3 SD: 4.8904 c. M: 8.1781 c. 16: 3 6 7 SP T3 SD: 2.9131 c. M:-5.0360 c. 23: 4 9 10 SP T3 SD: 1.3865 c. M: 1.7309 c. 34: 6 13 15 SP T3 SD: 0.9163 c. M: 1.5197 c. 39: 7 15 17 SP T3 SD: 0.8800 c. M:-1.1094 c. 57: 10 22 25 SP T3 SD: 0.5768 c. M: 0.9711 c. 73: 13 28 32 SP T3 SD: 0.2103 c. M:-0.3455 c. 96: 17 37 42 SP T3 SD: 0.2000 c. M:-0.3113 c. 130: 23 50 57 SP T3 SD: 0.1651 c. M: 0.2318 c. 169: 30 65 74 SP T3 SD: 0.0819 c. M:-0.1271 c. 299: 53 115 131 SP T3 SD: 0.0377 c. M: 0.0652 c. 372: 66 143 163 SP T3 SD: 0.0162 c. M: 0.0234 c. 671: 119 258 294 SP T3 SD: 0.0142 c. M: 0.0205 c. 840: 149 323 368 SP T3 SD: 0.0088 c. M:-0.0148 c. 1212: 215 466 531 SP T3 SD: 0.0022 c. M:-0.0031 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: 106.4747 cents 5 x 6:7 S SD: 45.8708 cents 6 x 7:8 S SD: 6.4841 cents 7 x 8:9 S SD: 39.7880 cents 8 x 9:11 SD: 46.3768 cents 9:10:11:12 H SD: 38.6036 cents 10:11:12:13 H SD: 31.7617 cents 11:12:13:15 SD: 24.6790 cents 12:13:14:16 S SD: 17.2908 cents 15:16:18:20 S SD: 14.2541 cents 16:17:19:21 SD: 12.1634 cents 17:18:20:23 SD: 9.1505 cents 18:19:21:24 SD: 4.6642 cents 39:41:46:52 SD: 2.0699 cents 57:60:67:76 SD: 0.1511 cents