Scala analysis: 234_C15
Chromatic tetrachord 28/27 * 27/25 * 25/21
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 28/25 196.198479 middle second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 25/21 301.8465 BP second, quasi-equal minor third 1: 28/27 62.9609 Archytas' 1/3-tone 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 25/21 301.8465 BP second, quasi-equal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 1 25/21 301.847 cents BP second, quasi-equal minor third 2: 1 28/25 196.198 cents middle second 2: 1 100/81 364.807 cents grave major third 2: 1 9/7 435.084 cents septimal major third, BP third 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 : 63.0 196.2 498.0 63.0 : 133.2 435.1 498.0 196.2: 301.8 364.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 301.8465 cents 225/196, 238.8856 cents 28/27, 62.9609 cents 2: 196.1985 .. 435.0841 cents 225/196, 238.8856 cents 588/625,-105.6480 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 25/21, 301.8465 cents Average / Smallest step : 2.636795 Largest / Average step : 1.818188 Largest / Smallest step : 4.794190 Median interval of one step : 27/25, 133.2376 cents, amount: 1 Least squares average step : 139.24949 cents, oct.: 417.74847 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1155-tone equal temperament with octave 4/3 degrees: 146 455 1155 Least number of segments generator : 578 of 249.238 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 911 of 392.830 cents and inv. generated superset size: 36 = 33 more = 1200.000% 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 62.96090 cents Scale diversity : 0.973909 Lumma stability : 0.252832 Lumma impropriety factor : 0.212125 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 : 28/27, 62.9609 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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% -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 27 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.030225 Average absolute harmonicity : 0.101148 Specific harmonicity : 0.142590 Fundamental : 1/675, -9.3987 octaves, 0.3876 Hz. Guide tone : 28, 4.8074 octaves, 7325.516 Hz. Exponens Consonantiae : 1.890000E+04, 14.20610 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 57.5, average 19.16667 Mersenne's string divisions : 20405 Sum of van Prooijen's expressibility: 3.30643, average 1.10214 Sum of Tenney's harmonic distance : 6.80280, average 2.26760 Vogel's harmonic complexity : 18.33333 Wille's k value : 112 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 17.26883, average 2.87814 Lattice compactness (without 2's) : 14.68945, average 2.44824 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -3 .. 0 -1.33333 4 1 5: -2 .. 0 -0.66667 2 7: 0 .. 1 0.66667 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 16 21| Scale is weakly epimorphic with val: <6 10 19 21| Scale is weakly epimorphic with val: <7 10 16 21| Scale is weakly epimorphic with val: <7 10 17 19| Scale is JI-epimorphic with val: <7 11 16 20| Scale is weakly epimorphic with val: <7 11 17 18| Scale is weakly epimorphic with val: <7 11 17 21| Scale is weakly epimorphic with val: <7 11 19 20| Scale is weakly epimorphic with val: <8 11 16 20| Scale is weakly epimorphic with val: <8 11 17 21| Scale is weakly epimorphic with val: <8 11 19 20| Scale is weakly epimorphic with val: <8 12 16 19|
FIT/MODE
3: 0 1 2 N G T3 SD: 40.3118 c. M: 62.9609 c. 5: 1 1 3 N M DE S SD: 21.2305 c. M:-36.6481 c. 6: 1 1 4 N M DE S SD: 20.9198 c. M: 30.1835 c. 7: 1 2 4 N T3 SD: 11.0241 c. M:-17.2494 c. 8: 1 2 5 N T3 SD: 5.4605 c. M: 9.4316 c. 15: 2 4 9 N T3 SD: 2.6449 c. M:-3.4451 c. 23: 3 6 14 N T3 SD: 1.3815 c. M:-2.0015 c. 33: 4 9 20 N T3 SD: 1.4964 c. M: 2.5918 c. 38: 5 10 23 N T3 SD: 1.5023 c. M:-2.5713 c. 41: 5 11 25 N T3 SD: 1.6662 c. M: 2.2237 c. 48: 6 13 29 N T3 SD: 0.6805 c. M:-0.9443 c. 56: 7 15 34 N T3 SD: 0.5121 c. M: 0.7053 c. 71: 9 19 43 N T3 SD: 0.1582 c. M:-0.2136 c. 127: 16 34 77 N T3 SD: 0.1416 c. M: 0.2151 c. 198: 25 53 120 N T3 SD: 0.0441 c. M: 0.0764 c. 269: 34 72 163 N T3 SD: 0.0336 c. M:-0.0572 c. 467: 59 125 283 N T3 SD: 0.0295 c. M: 0.0387 c. 617: 78 165 374 N T3 SD: 0.0276 c. M: 0.0479 c. 688: 87 184 417 N T3 SD: 0.0161 c. M: 0.0209 c. 759: 96 203 460 N T3 SD: 0.0190 c. M:-0.0329 c. 886: 112 237 537 N T3 SD: 0.0093 c. M: 0.0160 c. 957: 121 256 580 N T3 SD: 0.0060 c. M:-0.0103 c. 1155: 146 309 700 N T3 SD: 0.0027 c. M: 0.0046 c. 2112: 267 565 1280 N T3 SD: 0.0014 c. M:-0.0022 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 x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 73.1459 cents 6 x 7:8 S SD: 35.3362 cents 7 x 8:9 S SD: 36.0117 cents 8 x 9:11 SD: 26.9141 cents 9 x 10:12 S SD: 6.8974 cents 10 x 11:13 SD: 26.8991 cents 11 x 12:15 S SD: 29.9562 cents 12 x 13:16 SD: 28.8129 cents 14:15:16:19 SD: 24.3868 cents 15:16:17:20 SD: 17.6330 cents 16:17:18:21 S SD: 16.8863 cents 17:18:19:23 SD: 14.7104 cents 18:19:20:24 S SD: 11.2014 cents 23:24:26:31 SD: 8.9627 cents 24:25:27:32 SD: 3.6352 cents 50:52:56:67 SD: 3.3158 cents 51:53:57:68 SD: 1.7145 cents 75:78:84:100 SD: 1.6464 cents 84:87:94:112 SD: 0.8852 cents 108:112:121:144 SD: 0.1908 cents 351:364:393:468 SD: 0.1762 cents 375:389:420:500 SD: 0.1649 cents 408:423:457:544 SD: 0.1598 cents 459:476:514:612 SD: 0.0898 cents 567:588:635:756 SD: 0.0364 cents