Scala analysis: 428_D11
Diatonic tetrachord 40/37 * 37/34 * 17/15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/37 134.969675 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: 40/37 134.9697 2: 37/34 146.3886 3: 17/15 216.6867 septendecimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/37 134.970 cents 1: 1 37/34 146.389 cents 1: 1 17/15 216.687 cents septendecimal whole tone 2: 1 20/17 281.358 cents septendecimal augmented second 2: 1 136/111 351.656 cents 2: 1 37/30 363.075 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 : 135.0 281.4 498.0 135.0: 146.4 363.1 498.0 281.4: 216.7 351.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 134.9697 .. 216.6867 cents 629/600, 81.7170 cents 40/37, 134.9697 cents 2: 281.3583 .. 363.0753 cents 629/600, 81.7170 cents 300/289, 64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/37, 134.9697 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/15, 216.6867 cents Average / Smallest step : 1.230017 Largest / Average step : 1.305224 Largest / Smallest step : 1.605447 Median interval of one step : 37/34, 146.3886 cents, amount: 1 Least squares average step : 156.55866 cents, oct.: 469.67599 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2310-tone equal temperament with octave 4/3 degrees: 626 1305 2310 Least number of segments generator : 1157 of 249.454 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2077 of 447.809 cents and inv. generated superset size: 83 = 80 more = 2766.667% 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 64.67161 cents Scale diversity : 1.338661 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.671849 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 : 1369/1360, 11.4190 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 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 70.2981 cents: 2 -- Rational properties -- Prime limit : 37 Odd number limit : 111 (O: 37 U: 111) Highest odd numerator or denominator: 37 Scale harmonicity : 0.023705 Fundamental : 1/1887, -10.8819 octaves, 0.1386 Hz. Guide tone : 40, 5.3219 octaves, 10465.023 Hz. Exponens Consonantiae : 7.548000E+04, 16.20381 octaves Euler's gradus suavitatis : 62 Sum of Mann's harmonic distance : 60.5, average 20.16667 Mersenne's string divisions : 2849 Sum of van Prooijen's expressibility: 3.27577, average 1.09192 Sum of Tenney's harmonic distance : 6.78092, average 2.26031 Vogel's harmonic complexity : 43.66667 Wille's k value : 314 Wilson's harmonic complexity : 62 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 12.72615, average 2.12103 Lattice compactness (without 2's) : 7.56048, average 1.26008 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 0 -0.33333 1 1 5: 0 .. 1 0.66667 2 17: -1 .. 0 -0.33333 1 1 37: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 18 27 35| Scale is weakly epimorphic with val: <6 10 18 27 38| Scale is weakly epimorphic with val: <6 10 18 27 41| Scale is weakly epimorphic with val: <6 10 19 28 36| Scale is weakly epimorphic with val: <6 10 19 28 39| Scale is weakly epimorphic with val: <6 11 18 27 37| Scale is weakly epimorphic with val: <6 11 18 27 40| Scale is weakly epimorphic with val: <6 11 19 28 35| Scale is weakly epimorphic with val: <6 11 19 28 38| Scale is weakly epimorphic with val: <6 11 19 28 41| Scale is weakly epimorphic with val: <7 10 16 27 35| Scale is weakly epimorphic with val: <7 10 16 27 38| Scale is weakly epimorphic with val: <7 10 16 27 41| Scale is weakly epimorphic with val: <7 10 17 28 36| Scale is weakly epimorphic with val: <7 10 17 28 39| Scale is weakly epimorphic with val: <7 10 17 29 35| Scale is weakly epimorphic with val: <7 10 17 32 35| Scale is weakly epimorphic with val: <7 10 18 27 36| Scale is weakly epimorphic with val: <7 10 18 29 37| Scale is weakly epimorphic with val: <7 10 18 29 40| Scale is weakly epimorphic with val: <7 10 18 30 36| Scale is weakly epimorphic with val: <7 10 18 33 36| Scale is weakly epimorphic with val: <7 10 19 28 37| Scale is weakly epimorphic with val: <7 10 19 30 35| Scale is weakly epimorphic with val: <7 10 19 30 38| Scale is weakly epimorphic with val: <7 10 19 30 41| Scale is weakly epimorphic with val: <7 10 19 31 37| Scale is JI-epimorphic with val: <7 11 15 27 35| Scale is weakly epimorphic with val: <7 11 15 27 38| Scale is weakly epimorphic with val: <7 11 15 27 41| Scale is weakly epimorphic with val: <7 11 15 28 37| Scale is weakly epimorphic with val: <7 11 15 28 40| Scale is weakly epimorphic with val: <7 11 15 30 35| Scale is weakly epimorphic with val: <7 11 15 30 38| Scale is weakly epimorphic with val: <7 11 15 30 41| Scale is weakly epimorphic with val: <7 11 15 31 37| Scale is weakly epimorphic with val: <7 11 15 31 40| Scale is weakly epimorphic with val: <7 11 15 33 35| Scale is weakly epimorphic with val: <7 11 15 33 38| Scale is weakly epimorphic with val: <7 11 15 33 41| Scale is JI-epimorphic with val: <7 11 16 28 36| Scale is weakly epimorphic with val: <7 11 16 28 39| Scale is weakly epimorphic with val: <7 11 16 29 35| Scale is weakly epimorphic with val: <7 11 16 29 38| Scale is weakly epimorphic with val: <7 11 16 29 41| Scale is weakly epimorphic with val: <7 11 16 31 36| Scale is weakly epimorphic with val: <7 11 16 31 39| Scale is weakly epimorphic with val: <7 11 16 32 35| Scale is weakly epimorphic with val: <7 11 16 32 38| Scale is weakly epimorphic with val: <7 11 16 32 41| Scale is weakly epimorphic with val: <7 11 17 27 36| Scale is weakly epimorphic with val: <7 11 17 27 39| Scale is JI-epimorphic with val: <7 11 17 29 37| Scale is weakly epimorphic with val: <7 11 17 29 40| Scale is weakly epimorphic with val: <7 11 17 30 36| Scale is weakly epimorphic with val: <7 11 17 30 39| Scale is weakly epimorphic with val: <7 11 17 32 37| Scale is weakly epimorphic with val: <7 11 17 32 40| Scale is weakly epimorphic with val: <7 11 17 33 36| Scale is weakly epimorphic with val: <7 11 17 33 39| Scale is weakly epimorphic with val: <7 11 18 27 35| Scale is weakly epimorphic with val: <7 11 18 27 38| Scale is weakly epimorphic with val: <7 11 18 27 41| Scale is weakly epimorphic with val: <7 11 18 28 37| Scale is weakly epimorphic with val: <7 11 18 28 40| Scale is weakly epimorphic with val: <7 11 18 30 35| Scale is JI-epimorphic with val: <7 11 18 30 38| Scale is weakly epimorphic with val: <7 11 18 30 41| Scale is weakly epimorphic with val: <7 11 18 31 37| Scale is weakly epimorphic with val: <7 11 18 31 40| Scale is weakly epimorphic with val: <7 11 18 33 35| Scale is weakly epimorphic with val: <7 11 18 33 38| Scale is weakly epimorphic with val: <7 11 18 33 41| Scale is weakly epimorphic with val: <7 11 19 28 36| Scale is weakly epimorphic with val: <7 11 19 28 39| Scale is weakly epimorphic with val: <7 11 19 29 35| Scale is weakly epimorphic with val: <7 11 19 29 38| Scale is weakly epimorphic with val: <7 11 19 29 41| Scale is weakly epimorphic with val: <7 11 19 31 36| Scale is JI-epimorphic with val: <7 11 19 31 39| Scale is weakly epimorphic with val: <7 11 19 32 35| Scale is weakly epimorphic with val: <7 11 19 32 38| Scale is weakly epimorphic with val: <7 11 19 32 41| Scale is weakly epimorphic with val: <7 12 16 27 36| Scale is weakly epimorphic with val: <7 12 16 27 39| Scale is weakly epimorphic with val: <7 12 17 27 35| Scale is weakly epimorphic with val: <7 12 17 28 37| Scale is weakly epimorphic with val: <7 12 17 28 40| Scale is weakly epimorphic with val: <7 12 17 30 35| Scale is weakly epimorphic with val: <7 12 17 33 35| Scale is weakly epimorphic with val: <7 12 18 28 36| Scale is weakly epimorphic with val: <7 12 18 29 35| Scale is weakly epimorphic with val: <7 12 18 29 38| Scale is weakly epimorphic with val: <7 12 18 29 41| Scale is weakly epimorphic with val: <7 12 18 31 36| Scale is weakly epimorphic with val: <7 12 19 29 37| Scale is weakly epimorphic with val: <7 12 19 30 36| Scale is weakly epimorphic with val: <7 12 19 30 39| Scale is weakly epimorphic with val: <7 12 19 32 37| Scale is weakly epimorphic with val: <8 11 15 27 36| Scale is weakly epimorphic with val: <8 11 15 28 35| Scale is weakly epimorphic with val: <8 11 15 28 38| Scale is weakly epimorphic with val: <8 11 15 28 41| Scale is weakly epimorphic with val: <8 11 15 30 36| Scale is weakly epimorphic with val: <8 11 15 33 36| Scale is weakly epimorphic with val: <8 11 16 28 37| Scale is weakly epimorphic with val: <8 11 16 29 36| Scale is weakly epimorphic with val: <8 11 16 29 39| Scale is weakly epimorphic with val: <8 11 16 31 37| Scale is weakly epimorphic with val: <8 11 17 29 38| Scale is weakly epimorphic with val: <8 11 17 30 37| Scale is weakly epimorphic with val: <8 11 17 30 40| Scale is weakly epimorphic with val: <8 11 17 32 38| Scale is weakly epimorphic with val: <8 11 18 27 39| Scale is weakly epimorphic with val: <8 11 18 30 39| Scale is weakly epimorphic with val: <8 11 18 31 35| Scale is weakly epimorphic with val: <8 11 18 31 38| Scale is weakly epimorphic with val: <8 11 18 31 41| Scale is weakly epimorphic with val: <8 11 18 33 39| Scale is weakly epimorphic with val: <8 11 19 28 40| Scale is weakly epimorphic with val: <8 11 19 31 40| Scale is weakly epimorphic with val: <8 11 19 32 36| Scale is weakly epimorphic with val: <8 11 19 32 39| Scale is weakly epimorphic with val: <8 12 15 28 37| Scale is weakly epimorphic with val: <8 12 15 28 40| Scale is weakly epimorphic with val: <8 12 15 29 36| Scale is weakly epimorphic with val: <8 12 15 32 36| Scale is weakly epimorphic with val: <8 12 16 27 37| Scale is weakly epimorphic with val: <8 12 16 29 35| Scale is weakly epimorphic with val: <8 12 16 29 38| Scale is weakly epimorphic with val: <8 12 16 29 41| Scale is weakly epimorphic with val: <8 12 16 30 37| Scale is weakly epimorphic with val: <8 12 16 33 37| Scale is weakly epimorphic with val: <8 12 17 28 38| Scale is weakly epimorphic with val: <8 12 17 30 36| Scale is weakly epimorphic with val: <8 12 17 30 39| Scale is weakly epimorphic with val: <8 12 17 31 38| Scale is weakly epimorphic with val: <8 12 18 29 39| Scale is weakly epimorphic with val: <8 12 18 31 37| Scale is weakly epimorphic with val: <8 12 18 31 40| Scale is weakly epimorphic with val: <8 12 18 32 39| Scale is weakly epimorphic with val: <8 12 19 27 40| Scale is weakly epimorphic with val: <8 12 19 30 40| Scale is weakly epimorphic with val: <8 12 19 32 35| Scale is weakly epimorphic with val: <8 12 19 32 38| Scale is weakly epimorphic with val: <8 12 19 32 41| Scale is weakly epimorphic with val: <8 12 19 33 40|
FIT/MODE
3: 1 1 1 SP B ME I SD: 34.3095 c. M:-50.6717 c. 4: 1 1 2 P M ME S SD: 19.6213 c. M: 32.3358 c. 6: 2 1 3 P T3 SD: 25.8806 c. M: 32.3358 c. 7: 2 2 3 SP M ME S SD: 4.6261 c. M:-7.3289 c. 18: 5 5 8 SP M DE S SD: 3.3255 c. M: 4.6666 c. 23: 6 7 10 SP T3 SD: 2.9139 c. M: 5.0449 c. 25: 7 7 11 SP M DE S SD: 2.9504 c. M:-4.4829 c. 30: 8 9 13 SP T3 SD: 1.3426 c. M: 2.1577 c. 37: 10 11 16 SP T3 SD: 0.7881 c. M:-1.3159 c. 48: 13 14 21 SP T3 SD: 0.6991 c. M: 1.2080 c. 55: 15 16 24 SP T3 SD: 0.6200 c. M:-0.8608 c. 78: 21 23 34 SP T3 SD: 0.5608 c. M: 0.8806 c. 85: 23 25 37 SP T3 SD: 0.1339 c. M: 0.2046 c. 177: 48 52 77 SP T3 SD: 0.0555 c. M:-0.0934 c. 262: 71 77 114 SP T3 SD: 0.0116 c. M: 0.0199 c. 963: 261 283 419 SP T3 SD: 0.0109 c. M:-0.0145 c. 1225: 332 360 533 SP T3 SD: 0.0100 c. M: 0.0137 c. 1487: 403 437 647 SP T3 SD: 0.0098 c. M: 0.0148 c. 1524: 413 448 663 SP T3 SD: 0.0101 c. M:-0.0175 c. 1609: 436 473 700 SP T3 SD: 0.0091 c. M: 0.0116 c. 1786: 484 525 777 SP T3 SD: 0.0070 c. M:-0.0120 c. 1871: 507 550 814 SP T3 SD: 0.0071 c. M: 0.0104 c. 2048: 555 602 891 SP T3 SD: 0.0047 c. M:-0.0079 c. 2310: 626 679 1005 SP T3 SD: 0.0029 c. M:-0.0048 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: 43.5625 cents 9:10:11:12 H SD: 27.1058 cents 10:11:12:13 H SD: 21.0781 cents 11:12:13:15 SD: 14.2235 cents 12:13:14:16 S SD: 4.9762 cents 39:42:46:52 SD: 2.6701 cents 51:55:60:68 SD: 1.4161 cents 63:68:74:84 SD: 1.2964 cents 96:104:113:128 SD: 1.2380 cents 108:117:127:144 SD: 1.2304 cents 123:133:145:164 SD: 1.1776 cents 135:146:159:180 SD: 0.6755 cents 147:159:173:196 SD: 0.3538 cents 198:214:233:264 SD: 0.2061 cents 210:227:247:280 SD: 0.1536 cents 357:386:420:476 SD: 0.0808 cents 555:600:653:740 SD: 0.0520 cents