Scala analysis: 588_M96
Miscellaneous tetrachord 120/113 * 113/101 * 101/90
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 120/113 104.053960 2: 120/101 298.414935 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 101/90 199.6301 1: 120/113 104.0540 2: 113/101 194.3610 3: 101/90 199.6301
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 120/113 104.054 cents 1: 1 113/101 194.361 cents 1: 1 101/90 199.630 cents 2: 1 120/101 298.415 cents 2: 1 404/339 303.684 cents 2: 1 113/90 393.991 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 : 104.1 298.4 498.0 104.1: 194.4 394.0 498.0 298.4: 199.6 303.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 104.0540 .. 199.6301 cents 11413/10800, 95.5761 cents 120/113, 104.0540 cents 2: 298.4149 .. 393.9910 cents 11413/10800, 95.5761 cents 10800/10201, 98.7849 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 120/113, 104.0540 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 101/90, 199.6301 cents Average / Smallest step : 1.595470 Largest / Average step : 1.202482 Largest / Smallest step : 1.918524 Median interval of one step : 113/101, 194.3610 cents, amount: 1 Least squares average step : 156.78706 cents, oct.: 470.36118 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1704-tone equal temperament with octave 4/3 degrees: 356 1021 1704 Least number of segments generator : 853 of 249.315 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1601 of 467.940 cents and inv. generated superset size: 44 = 41 more = 1466.667% 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 98.78487 cents Scale diversity : 1.125587 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.616195 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 : 10201/10170, 5.2691 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 90.3070 cents: 1 -- Rational properties -- Prime limit : 113 Odd number limit : 339 (O: 113 U: 339) Highest odd numerator or denominator: 113 Scale harmonicity : 0.067873 Fundamental : 1/34239, -15.0634 octaves, 0.0076 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 4.108680E+06, 21.97024 octaves Euler's gradus suavitatis : 224 Sum of Mann's harmonic distance : 230.5, average 76.83333 Mersenne's string divisions : 360451 Sum of van Prooijen's expressibility: 4.53452, average 1.51151 Sum of Tenney's harmonic distance : 9.29494, average 3.09831 Vogel's harmonic complexity : 152.66667 Wille's k value : 5706 Wilson's harmonic complexity : 225 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.76830, average 2.29472 Lattice compactness (without 2's) : 8.30056, average 1.38343 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.66667 2 101: -1 .. 0 -0.33333 1 1 113: -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: <7 10 19 47 48| Scale is weakly epimorphic with val: <7 11 15 48 49| Scale is weakly epimorphic with val: <7 11 16 47 49| Scale is weakly epimorphic with val: <7 11 16 49 50| Scale is JI-epimorphic with val: <7 11 17 47 48| Scale is weakly epimorphic with val: <7 11 17 48 50| Scale is JI-epimorphic with val: <7 11 18 48 49| Scale is weakly epimorphic with val: <7 11 19 47 49| Scale is JI-epimorphic with val: <7 11 19 49 50| Scale is weakly epimorphic with val: <7 12 17 47 49| Scale is weakly epimorphic with val: <7 12 18 47 48| Scale is weakly epimorphic with val: <7 12 18 48 50| Scale is weakly epimorphic with val: <7 12 19 48 49| Scale is weakly epimorphic with val: <8 11 15 47 49| Scale is weakly epimorphic with val: <8 11 16 47 48| Scale is weakly epimorphic with val: <8 11 16 48 50| Scale is weakly epimorphic with val: <8 11 17 48 49| Scale is weakly epimorphic with val: <8 11 18 49 50| Scale is weakly epimorphic with val: <8 12 15 48 49| Scale is weakly epimorphic with val: <8 12 16 47 49| Scale is weakly epimorphic with val: <8 12 16 49 50| Scale is weakly epimorphic with val: <8 12 17 48 50|
FIT/MODE
3: 1 1 1 SP B ME I SD: 40.6987 c. M:-61.9610 c. 4: 1 1 2 P M ME S SD: 30.8659 c. M: 49.3924 c. 5: 1 2 2 SP M ME S SD: 2.5773 c. M: 4.4450 c. 28: 6 11 11 SP M DE S SD: 2.7620 c. M:-3.9695 c. 33: 7 13 13 SP M DE S SD: 2.1835 c. M:-3.4305 c. 38: 8 15 15 SP M DE S SD: 1.8108 c. M:-3.0334 c. 42: 9 16 17 SP T3 SD: 1.9121 c. M:-2.6700 c. 43: 9 17 17 SP M DE S SD: 1.5791 c. M:-2.7286 c. 47: 10 18 19 SP T3 SD: 1.4804 c. M:-1.9131 c. 48: 10 19 19 SP M DE S SD: 1.4461 c. M:-2.4873 c. 52: 11 20 21 SP T3 SD: 1.1482 c. M: 1.5035 c. 57: 12 22 23 SP T3 SD: 0.8981 c. M: 1.3355 c. 62: 13 24 25 SP T3 SD: 0.7228 c. M: 1.1945 c. 67: 14 26 27 SP T3 SD: 0.6205 c. M: 1.0746 c. 72: 15 28 29 SP T3 SD: 0.5861 c. M: 0.9714 c. 77: 16 30 31 SP T3 SD: 0.6042 c. M: 0.8816 c. 82: 17 32 33 SP T3 SD: 0.6546 c. M: 0.8027 c. 95: 20 37 38 SP T3 SD: 0.5183 c. M:-0.7976 c. 100: 21 39 40 SP T3 SD: 0.3901 c. M:-0.5355 c. 105: 22 41 42 SP T3 SD: 0.2937 c. M:-0.4121 c. 110: 23 43 44 SP T3 SD: 0.2427 c. M:-0.4121 c. 167: 35 65 67 SP T3 SD: 0.2166 c. M:-0.3267 c. 172: 36 67 69 SP T3 SD: 0.1452 c. M:-0.1880 c. 177: 37 69 71 SP T3 SD: 0.0931 c. M: 0.1507 c. 182: 38 71 73 SP T3 SD: 0.0870 c. M: 0.1352 c. 287: 60 112 115 SP T3 SD: 0.0539 c. M:-0.0669 c. 292: 61 114 117 SP T3 SD: 0.0414 c. M:-0.0709 c. 464: 97 181 186 SP T3 SD: 0.0378 c. M:-0.0632 c. 469: 98 183 188 SP T3 SD: 0.0114 c. M:-0.0151 c. 761: 159 297 305 SP T3 SD: 0.0116 c. M:-0.0194 c. 943: 197 368 378 SP T3 SD: 0.0078 c. M: 0.0105 c. 1230: 257 480 493 SP T3 SD: 0.0067 c. M:-0.0091 c. 1235: 258 482 495 SP T3 SD: 0.0072 c. M: 0.0089 c. 1412: 295 551 566 SP T3 SD: 0.0065 c. M: 0.0112 c. 1699: 355 663 681 SP T3 SD: 0.0063 c. M:-0.0108 c. 1704: 356 665 683 SP T3 SD: 0.0021 c. M:-0.0029 c. 2173: 454 848 871 SP T3 SD: 0.0009 c. M:-0.0015 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: 87.8988 cents 5 x 6:7 S SD: 43.1029 cents 6 x 7:8 S SD: 15.7720 cents 7 x 8:9 S SD: 46.0581 cents 8 x 10:11 S SD: 51.3912 cents 9:10:11:12 H SD: 30.8022 cents 10:11:12:13 H SD: 25.6750 cents 11:12:13:15 SD: 20.4624 cents 12:13:14:16 S SD: 15.5869 cents 15:16:18:20 S SD: 6.2866 cents 31:33:37:41 SD: 5.5409 cents 32:34:38:43 SD: 4.5110 cents 33:35:39:44 SD: 3.1538 cents 48:51:57:64 SD: 0.4251 cents 228:242:271:304 SD: 0.3756 cents 276:293:328:368 SD: 0.2370 cents 324:344:385:432 SD: 0.1400 cents 372:395:442:496 SD: 0.0696 cents 420:446:499:560 SD: 0.0256 cents