Scala analysis: 580_M88
Miscellaneous tetrachord 23/22 * 44/39 * 26/23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 23/22 76.956405 2: 46/39 285.791685 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 26/23 212.2533 1: 23/22 76.9564 2: 44/39 208.8353 3: 26/23 212.2533
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 23/22 76.956 cents 1: 1 44/39 208.835 cents 1: 1 26/23 212.253 cents 2: 1 46/39 285.792 cents 2: 1 13/11 289.210 cents tridecimal minor third 2: 1 88/69 421.089 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 : 77.0 285.8 498.0 77.0 : 208.8 421.1 498.0 285.8: 212.3 289.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.9564 .. 212.2533 cents 572/529, 135.2969 cents 23/22, 76.9564 cents 2: 285.7917 .. 421.0886 cents 572/529, 135.2969 cents 529/507, 73.5384 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 23/22, 76.9564 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 26/23, 212.2533 cents Average / Smallest step : 2.157260 Largest / Average step : 1.278519 Largest / Smallest step : 2.758098 Median interval of one step : 44/39, 208.8353 cents, amount: 1 Least squares average step : 153.04820 cents, oct.: 459.14459 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1016-tone equal temperament with octave 4/3 degrees: 157 583 1016 Least number of segments generator : 509 of 249.513 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 611 of 299.513 cents and inv. generated superset size: 34 = 31 more = 1133.333% 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 73.53837 cents Scale diversity : 0.901850 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.456688 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 : 507/506, 3.4180 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 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 131.8789 cents: 1 -- Rational properties -- Prime limit : 23 Odd number limit : 69 (O: 23 U: 69) Highest odd numerator or denominator: 39 Scale harmonicity : 0.011352 Average absolute harmonicity : 0.081777 Specific harmonicity : 0.051609 Fundamental : 1/858, -9.7448 octaves, 0.3049 Hz. Guide tone : 92, 6.5236 octaves, 24069.552 Hz. Exponens Consonantiae : 7.893600E+04, 16.26840 octaves Euler's gradus suavitatis : 50 Sum of Mann's harmonic distance : 68.5, average 22.83333 Mersenne's string divisions : 5355 Sum of van Prooijen's expressibility: 3.42991, average 1.14330 Sum of Tenney's harmonic distance : 7.03715, average 2.34572 Vogel's harmonic complexity : 34.00000 Wille's k value : 448 Wilson's harmonic complexity : 50 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.81002, average 2.30167 Lattice compactness (without 2's) : 9.02458, average 1.50410 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 0 -0.66667 2 1 11: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 23: 0 .. 1 0.66667 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 23 26 33| Scale is weakly epimorphic with val: <6 10 23 27 32| Scale is weakly epimorphic with val: <6 10 23 29 36| Scale is weakly epimorphic with val: <6 10 23 30 32| Scale is weakly epimorphic with val: <6 10 24 25 33| Scale is weakly epimorphic with val: <6 10 24 27 34| Scale is weakly epimorphic with val: <6 10 24 28 33| Scale is weakly epimorphic with val: <6 10 25 25 32| Scale is weakly epimorphic with val: <6 10 25 26 34| Scale is weakly epimorphic with val: <6 10 25 28 35| Scale is weakly epimorphic with val: <6 10 25 29 34| Scale is weakly epimorphic with val: <6 10 26 26 33| Scale is weakly epimorphic with val: <6 10 26 27 35| Scale is weakly epimorphic with val: <6 10 26 29 36| Scale is weakly epimorphic with val: <6 10 26 30 35| Scale is weakly epimorphic with val: <6 10 27 27 34| Scale is weakly epimorphic with val: <6 10 27 28 36| Scale is weakly epimorphic with val: <6 11 23 25 32| Scale is weakly epimorphic with val: <6 11 23 26 34| Scale is weakly epimorphic with val: <6 11 23 28 32| Scale is weakly epimorphic with val: <6 11 24 26 33| Scale is weakly epimorphic with val: <6 11 24 27 35| Scale is weakly epimorphic with val: <6 11 24 29 33| Scale is weakly epimorphic with val: <6 11 25 25 33| Scale is weakly epimorphic with val: <6 11 25 27 34| Scale is weakly epimorphic with val: <6 11 25 28 36| Scale is weakly epimorphic with val: <6 11 25 30 34| Scale is weakly epimorphic with val: <6 11 26 26 34| Scale is weakly epimorphic with val: <6 11 26 28 35| Scale is weakly epimorphic with val: <6 11 27 27 35| Scale is weakly epimorphic with val: <6 11 27 29 36| Scale is weakly epimorphic with val: <7 10 23 25 33| Scale is weakly epimorphic with val: <7 10 23 26 32| Scale is weakly epimorphic with val: <7 10 23 28 33| Scale is weakly epimorphic with val: <7 10 23 29 35| Scale is weakly epimorphic with val: <7 10 24 26 34| Scale is weakly epimorphic with val: <7 10 24 27 33| Scale is weakly epimorphic with val: <7 10 24 29 34| Scale is weakly epimorphic with val: <7 10 24 30 36| Scale is weakly epimorphic with val: <7 10 25 25 31| Scale is weakly epimorphic with val: <7 10 25 27 35| Scale is weakly epimorphic with val: <7 10 25 28 34| Scale is weakly epimorphic with val: <7 10 25 30 35| Scale is weakly epimorphic with val: <7 10 26 26 32| Scale is weakly epimorphic with val: <7 10 26 28 36| Scale is weakly epimorphic with val: <7 10 26 29 35| Scale is weakly epimorphic with val: <7 10 27 27 33| Scale is weakly epimorphic with val: <7 10 27 30 36| Scale is JI-epimorphic with val: <7 11 23 25 31| Scale is weakly epimorphic with val: <7 11 23 25 34| Scale is weakly epimorphic with val: <7 11 23 27 32| Scale is weakly epimorphic with val: <7 11 23 27 35| Scale is weakly epimorphic with val: <7 11 23 28 31| Scale is weakly epimorphic with val: <7 11 23 28 34| Scale is weakly epimorphic with val: <7 11 23 30 32| Scale is weakly epimorphic with val: <7 11 23 30 35| Scale is weakly epimorphic with val: <7 11 24 25 30| Scale is weakly epimorphic with val: <7 11 24 25 33| Scale is weakly epimorphic with val: <7 11 24 25 36| Scale is JI-epimorphic with val: <7 11 24 26 32| Scale is weakly epimorphic with val: <7 11 24 26 35| Scale is weakly epimorphic with val: <7 11 24 28 30| Scale is weakly epimorphic with val: <7 11 24 28 33| Scale is weakly epimorphic with val: <7 11 24 28 36| Scale is weakly epimorphic with val: <7 11 24 29 32| Scale is weakly epimorphic with val: <7 11 24 29 35| Scale is weakly epimorphic with val: <7 11 25 26 31| Scale is weakly epimorphic with val: <7 11 25 26 34| Scale is weakly epimorphic with val: <7 11 25 27 30| Scale is JI-epimorphic with val: <7 11 25 27 33| = patent Scale is weakly epimorphic with val: <7 11 25 27 36| Scale is weakly epimorphic with val: <7 11 25 29 31| Scale is weakly epimorphic with val: <7 11 25 29 34| Scale is weakly epimorphic with val: <7 11 25 30 30| Scale is weakly epimorphic with val: <7 11 25 30 33| Scale is weakly epimorphic with val: <7 11 25 30 36| Scale is weakly epimorphic with val: <7 11 26 27 32| Scale is weakly epimorphic with val: <7 11 26 27 35| Scale is weakly epimorphic with val: <7 11 26 28 31| Scale is JI-epimorphic with val: <7 11 26 28 34| Scale is weakly epimorphic with val: <7 11 26 30 32| Scale is weakly epimorphic with val: <7 11 26 30 35| Scale is weakly epimorphic with val: <7 11 27 28 30| Scale is weakly epimorphic with val: <7 11 27 28 33| Scale is weakly epimorphic with val: <7 11 27 28 36| Scale is weakly epimorphic with val: <7 11 27 29 32| Scale is JI-epimorphic with val: <7 11 27 29 35| Scale is weakly epimorphic with val: <7 12 23 26 34| Scale is weakly epimorphic with val: <7 12 23 27 33| Scale is weakly epimorphic with val: <7 12 23 30 33| Scale is weakly epimorphic with val: <7 12 24 25 34| Scale is weakly epimorphic with val: <7 12 24 27 35| Scale is weakly epimorphic with val: <7 12 24 28 34| Scale is weakly epimorphic with val: <7 12 25 25 33| Scale is weakly epimorphic with val: <7 12 25 26 35| Scale is weakly epimorphic with val: <7 12 25 28 36| Scale is weakly epimorphic with val: <7 12 25 29 35| Scale is weakly epimorphic with val: <7 12 26 26 34| Scale is weakly epimorphic with val: <7 12 26 27 36| Scale is weakly epimorphic with val: <7 12 26 30 36| Scale is weakly epimorphic with val: <7 12 27 27 35| Scale is weakly epimorphic with val: <8 11 23 26 32| Scale is weakly epimorphic with val: <8 11 23 27 34| Scale is weakly epimorphic with val: <8 11 23 29 35| Scale is weakly epimorphic with val: <8 11 23 30 34| Scale is weakly epimorphic with val: <8 11 24 25 35| Scale is weakly epimorphic with val: <8 11 24 27 33| Scale is weakly epimorphic with val: <8 11 24 28 35| Scale is weakly epimorphic with val: <8 11 24 30 36| Scale is weakly epimorphic with val: <8 11 25 25 31| Scale is weakly epimorphic with val: <8 11 25 26 36| Scale is weakly epimorphic with val: <8 11 25 28 34| Scale is weakly epimorphic with val: <8 11 25 29 36| Scale is weakly epimorphic with val: <8 11 26 26 32| Scale is weakly epimorphic with val: <8 11 26 29 35| Scale is weakly epimorphic with val: <8 11 27 27 33| Scale is weakly epimorphic with val: <8 11 27 30 36| Scale is weakly epimorphic with val: <8 12 23 25 34| Scale is weakly epimorphic with val: <8 12 23 26 33| Scale is weakly epimorphic with val: <8 12 23 28 34| Scale is weakly epimorphic with val: <8 12 23 29 36| Scale is weakly epimorphic with val: <8 12 24 26 35| Scale is weakly epimorphic with val: <8 12 24 27 34| Scale is weakly epimorphic with val: <8 12 24 29 35| Scale is weakly epimorphic with val: <8 12 25 25 32| Scale is weakly epimorphic with val: <8 12 25 27 36| Scale is weakly epimorphic with val: <8 12 25 28 35| Scale is weakly epimorphic with val: <8 12 25 30 36| Scale is weakly epimorphic with val: <8 12 26 26 33| Scale is weakly epimorphic with val: <8 12 26 29 36| Scale is weakly epimorphic with val: <8 12 27 27 34|
FIT/MODE
3: 1 1 1 SP B ME I SD: 57.9351 c. M:-89.0586 c. 4: 0 2 2 P M DE S SD: 49.2418 c. M: 76.9564 c. 5: 1 2 2 SP M ME S SD: 15.0893 c. M:-22.6526 c. 7: 1 3 3 SP M DE S SD: 3.4229 c. M: 5.8071 c. 19: 3 8 8 SP M DE S SD: 1.7638 c. M:-2.5502 c. 26: 4 11 11 SP M DE S SD: 0.9109 c. M:-1.5420 c. 33: 5 14 14 SP M DE S SD: 1.0263 c. M: 1.4950 c. 59: 9 25 25 SP M DE S SD: 0.9035 c. M:-1.2173 c. 71: 11 30 30 SP M DE S SD: 1.0527 c. M:-1.8118 c. 77: 12 32 33 SP T3 SD: 0.7882 c. M: 1.1945 c. 84: 13 35 36 SP T3 SD: 0.6933 c. M: 1.1945 c. 91: 14 38 39 SP T3 SD: 0.7161 c. M: 1.1945 c. 92: 14 39 39 SP M DE S SD: 0.9361 c. M: 1.1669 c. 96: 15 40 41 SP T3 SD: 0.5629 c. M:-0.8631 c. 103: 16 43 44 SP T3 SD: 0.3749 c. M: 0.5038 c. 110: 17 46 47 SP T3 SD: 0.3163 c. M: 0.5477 c. 129: 20 54 55 SP T3 SD: 0.1591 c. M:-0.2599 c. 136: 21 57 58 SP T3 SD: 0.0908 c. M: 0.1482 c. 162: 25 68 69 SP T3 SD: 0.0907 c. M:-0.1230 c. 265: 41 111 113 SP T3 SD: 0.0903 c. M: 0.1206 c. 291: 45 122 124 SP T3 SD: 0.0387 c. M:-0.0609 c. 427: 66 179 182 SP T3 SD: 0.0217 c. M: 0.0282 c. 589: 91 247 251 SP T3 SD: 0.0093 c. M:-0.0134 c. 1016: 157 426 433 SP T3 SD: 0.0038 c. M:-0.0053 c. 1605: 248 673 684 SP T3 SD: 0.0014 c. M:-0.0024 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: 100.5220 cents 5 x 6:7 S SD: 44.7932 cents 6 x 7:8 S SD: 9.4604 cents 7 x 8:9 S SD: 41.6748 cents 8 x 9:11 SD: 48.8432 cents 9 x 11:12 SD: 30.8081 cents 11:12:13:15 SD: 27.7972 cents 12:13:14:16 S SD: 21.4853 cents 15:16:18:20 S SD: 15.2763 cents 16:17:19:21 SD: 13.6001 cents 17:18:20:23 SD: 11.2662 cents 18:19:21:24 SD: 8.4004 cents 21:22:25:28 SD: 5.4831 cents 27:28:32:36 S SD: 5.4312 cents 39:41:46:52 SD: 3.2078 cents 45:47:53:60 SD: 1.0058 cents 111:116:131:148 SD: 0.4074 cents 156:163:184:208 SD: 0.3218 cents 240:251:283:320 SD: 0.2613 cents 306:320:361:408 SD: 0.2050 cents 351:367:414:468 SD: 0.0715 cents 507:530:598:676 SD: 0.0495 cents