Scala analysis: 434_D11
Diatonic tetrachord 120/109 * 109/102 * 17/15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 120/109 166.447525 2: 20/17 281.358304 septendecimal augmented second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 17/15 216.6867 septendecimal whole tone 1: 120/109 166.4475 2: 109/102 114.9108 3: 17/15 216.6867 septendecimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 109/102 114.911 cents 1: 1 120/109 166.448 cents 1: 1 17/15 216.687 cents septendecimal whole tone 2: 1 20/17 281.358 cents septendecimal augmented second 2: 1 109/90 331.597 cents 2: 1 136/109 383.134 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 : 166.4 281.4 498.0 166.4: 114.9 331.6 498.0 281.4: 216.7 383.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 114.9108 .. 216.6867 cents 578/545, 101.7759 cents 109/102, 114.9108 cents 2: 281.3583 .. 383.1342 cents 578/545, 101.7759 cents 300/289, 64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 109/102, 114.9108 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/15, 216.6867 cents Average / Smallest step : 1.444730 Largest / Average step : 1.305224 Largest / Smallest step : 1.885695 Median interval of one step : 120/109, 166.4475 cents, amount: 1 Least squares average step : 158.80708 cents, oct.: 476.42124 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1517-tone equal temperament with octave 4/3 degrees: 507 857 1517 Least number of segments generator : 759 of 249.187 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1348 of 442.561 cents and inv. generated superset size: 33 = 30 more = 1100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 64.67161 cents Scale diversity : 1.309140 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.591298 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 : 1853/1800, 50.2392 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle 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 : 109 Odd number limit : 109 (O: 109 U: 109) Highest odd numerator or denominator: 109 Scale harmonicity : 0.022296 Fundamental : 1/5559, -12.4406 octaves, 0.0471 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 6.670800E+05, 19.34750 octaves Euler's gradus suavitatis : 136 Sum of Mann's harmonic distance : 136.5, average 45.50000 Mersenne's string divisions : 59311 Sum of van Prooijen's expressibility: 3.74500, average 1.24833 Sum of Tenney's harmonic distance : 7.72727, average 2.57576 Vogel's harmonic complexity : 92.66667 Wille's k value : 926 Wilson's harmonic complexity : 137 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.91577, average 2.31930 Lattice compactness (without 2's) : 9.21076, average 1.53513 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.66667 2 17: -1 .. 0 -0.33333 1 1 109: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 18 27 48| Scale is weakly epimorphic with val: <6 10 19 28 49| Scale is weakly epimorphic with val: <6 11 18 27 48| Scale is weakly epimorphic with val: <6 11 19 28 49| Scale is weakly epimorphic with val: <7 10 16 27 48| Scale is weakly epimorphic with val: <7 10 17 28 49| Scale is weakly epimorphic with val: <7 10 18 29 50| Scale is weakly epimorphic with val: <7 10 19 30 48| Scale is weakly epimorphic with val: <7 11 15 27 49| Scale is weakly epimorphic with val: <7 11 15 28 48| Scale is weakly epimorphic with val: <7 11 15 30 49| Scale is weakly epimorphic with val: <7 11 15 31 48| Scale is weakly epimorphic with val: <7 11 15 33 49| Scale is weakly epimorphic with val: <7 11 16 28 50| Scale is weakly epimorphic with val: <7 11 16 29 49| Scale is weakly epimorphic with val: <7 11 16 31 50| Scale is weakly epimorphic with val: <7 11 16 32 49| Scale is weakly epimorphic with val: <7 11 17 27 50| Scale is JI-epimorphic with val: <7 11 17 29 48| Scale is weakly epimorphic with val: <7 11 17 30 50| Scale is weakly epimorphic with val: <7 11 17 32 48| Scale is weakly epimorphic with val: <7 11 17 33 50| Scale is weakly epimorphic with val: <7 11 18 27 49| Scale is weakly epimorphic with val: <7 11 18 28 48| Scale is JI-epimorphic with val: <7 11 18 30 49| Scale is weakly epimorphic with val: <7 11 18 31 48| Scale is weakly epimorphic with val: <7 11 18 33 49| Scale is weakly epimorphic with val: <7 11 19 28 50| Scale is weakly epimorphic with val: <7 11 19 29 49| Scale is JI-epimorphic with val: <7 11 19 31 50| Scale is weakly epimorphic with val: <7 11 19 32 49| Scale is weakly epimorphic with val: <7 12 16 27 48| Scale is weakly epimorphic with val: <7 12 17 28 49| Scale is weakly epimorphic with val: <7 12 18 28 48| Scale is weakly epimorphic with val: <7 12 18 29 50| Scale is weakly epimorphic with val: <7 12 18 31 48| Scale is weakly epimorphic with val: <7 12 19 29 49| Scale is weakly epimorphic with val: <7 12 19 30 48| Scale is weakly epimorphic with val: <7 12 19 32 49| Scale is weakly epimorphic with val: <8 11 15 28 49| Scale is weakly epimorphic with val: <8 11 16 28 48| Scale is weakly epimorphic with val: <8 11 16 29 50| Scale is weakly epimorphic with val: <8 11 16 31 48| Scale is weakly epimorphic with val: <8 11 17 29 49| Scale is weakly epimorphic with val: <8 11 17 30 48| Scale is weakly epimorphic with val: <8 11 17 32 49| Scale is weakly epimorphic with val: <8 11 18 27 50| Scale is weakly epimorphic with val: <8 11 18 30 50| Scale is weakly epimorphic with val: <8 11 18 31 49| Scale is weakly epimorphic with val: <8 11 18 33 50| Scale is weakly epimorphic with val: <8 11 19 32 50| Scale is weakly epimorphic with val: <8 12 15 28 49| Scale is weakly epimorphic with val: <8 12 15 29 48| Scale is weakly epimorphic with val: <8 12 15 32 48| Scale is weakly epimorphic with val: <8 12 16 27 49| Scale is weakly epimorphic with val: <8 12 16 29 50| Scale is weakly epimorphic with val: <8 12 16 30 49| Scale is weakly epimorphic with val: <8 12 16 33 49| Scale is weakly epimorphic with val: <8 12 17 28 50| Scale is weakly epimorphic with val: <8 12 17 30 48| Scale is weakly epimorphic with val: <8 12 17 31 50| Scale is weakly epimorphic with val: <8 12 18 31 49| Scale is weakly epimorphic with val: <8 12 19 32 50|
FIT/MODE
3: 1 1 1 SP B ME I SD: 29.2564 c. M:-50.6717 c. 4: 1 1 2 P M ME S SD: 30.5737 c. M: 41.9363 c. 5: 2 1 2 SP M ME I SD: 21.4403 c. M:-32.7705 c. 6: 2 1 3 P T3 SD: 18.6708 c. M: 32.3358 c. 7: 2 2 3 SP M ME S SD: 14.0672 c. M: 24.1490 c. 9: 3 2 4 SP T3 SD: 2.7058 c. M: 4.6666 c. 21: 7 5 9 SP T3 SD: 1.8865 c. M:-3.2388 c. 30: 10 7 13 SP T3 SD: 0.5595 c. M:-0.8672 c. 39: 13 9 17 SP T3 SD: 0.3440 c. M: 0.4325 c. 69: 23 16 30 SP T3 SD: 0.2634 c. M: 0.4325 c. 108: 36 25 47 SP T3 SD: 0.2517 c. M: 0.4325 c. 147: 49 34 64 SP T3 SD: 0.2642 c. M: 0.4325 c. 177: 59 41 77 SP T3 SD: 0.2501 c. M: 0.4325 c. 186: 62 43 81 SP T3 SD: 0.2761 c. M: 0.4325 c. 200: 67 46 87 SP T3 SD: 0.2305 c. M:-0.3975 c. 209: 70 48 91 SP T3 SD: 0.2297 c. M:-0.3618 c. 218: 73 50 95 SP T3 SD: 0.2779 c. M: 0.3513 c. 221: 74 51 96 SP T3 SD: 0.2696 c. M:-0.3414 c. 230: 77 53 100 SP T3 SD: 0.1869 c. M:-0.2893 c. 239: 80 55 104 SP T3 SD: 0.1527 c. M:-0.2621 c. 248: 83 57 108 SP T3 SD: 0.1804 c. M:-0.2369 c. 260: 87 60 113 SP T3 SD: 0.1777 c. M:-0.2287 c. 269: 90 62 117 SP T3 SD: 0.1130 c. M:-0.1846 c. 278: 93 64 121 SP T3 SD: 0.1079 c. M:-0.1647 c. 299: 100 69 130 SP T3 SD: 0.1098 c. M:-0.1454 c. 308: 103 71 134 SP T3 SD: 0.0615 c. M:-0.1065 c. 338: 113 78 147 SP T3 SD: 0.0579 c. M:-0.0813 c. 347: 116 80 151 SP T3 SD: 0.0359 c. M:-0.0459 c. 377: 126 87 164 SP T3 SD: 0.0182 c. M:-0.0305 c. 724: 242 167 315 SP T3 SD: 0.0152 c. M:-0.0261 c. 763: 255 176 332 SP T3 SD: 0.0145 c. M: 0.0249 c. 793: 265 183 345 SP T3 SD: 0.0095 c. M: 0.0138 c. 1140: 381 263 496 SP T3 SD: 0.0046 c. M: 0.0066 c. 1517: 507 350 660 SP T3 SD: 0.0034 c. M:-0.0052 c. 1933: 646 446 841 SP T3 SD: 0.0018 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: 104.9554 cents 5 x 6:7 S SD: 45.5797 cents 6 x 7:8 S SD: 7.2437 cents 7 x 8:9 S SD: 40.2571 cents 8:9 x 11 SD: 32.5632 cents 9:10:11:12 H SD: 22.6499 cents 10:11:12:13 H SD: 18.5549 cents 11:12:13:15 SD: 14.2411 cents 12:13:14:16 S SD: 10.4716 cents 18:20:21:24 S SD: 7.1840 cents 27:30:32:36 S SD: 6.8137 cents 28:31:33:37 SD: 6.1997 cents 29:32:34:39 SD: 5.5015 cents 30:33:35:40 SD: 4.8530 cents 39:43:46:52 SD: 1.7111 cents 51:56:60:68 SD: 1.5107 cents 69:76:81:92 SD: 1.2864 cents 90:99:106:120 SD: 0.8013 cents 108:119:127:144 SD: 0.5578 cents 159:175:187:212 SD: 0.2363 cents 198:218:233:264 SD: 0.1536 cents 357:393:420:476 SD: 0.0404 cents