Scala analysis: 231_C14
Chromatic tetrachord 6/5 * 2240/2187 * 243/224
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 6/5 315.641287 minor third 2: 896/729 357.095901 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 243/224 140.9491 Archytas' 2/3-tone 1: 6/5 315.6413 minor third 2: 2240/2187 41.4546 3: 243/224 140.9491 Archytas' 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 2240/2187 41.455 cents 1: 1 243/224 140.949 cents Archytas' 2/3-tone 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 896/729 357.096 cents 2: 1 729/560 456.590 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 : 315.6 357.1 498.0 315.6: 41.5 182.4 498.0 357.1: 140.9 456.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.4546 .. 315.6413 cents 6561/5600, 274.1867 cents 2240/2187, 41.4546 cents 2: 182.4037 .. 456.5904 cents 6561/5600, 274.1867 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 2240/2187, 41.4546 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 4.004741 Largest / Average step : 1.901282 Largest / Smallest step : 7.614141 Median interval of one step : 243/224, 140.9491 cents, amount: 1 Least squares average step : 180.28343 cents, oct.: 540.85030 cents Scale is not proper Scale has trivalence property Scale is a mode of a 841-tone equal temperament with octave 4/3 degrees: 533 603 841 Least number of segments generator : 421 of 249.319 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 827 of 489.754 cents and inv. generated superset size: 23 = 20 more = 766.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LSM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 41.45461 cents Scale diversity : 0.781223 Lumma stability : 0.166469 Lumma impropriety factor : 0.267521 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 : 2240/2187, 41.4546 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 7 Odd number limit : 2187 (O: 729 U: 2187) Highest odd numerator or denominator: 729 Scale harmonicity : 0.023611 Average absolute harmonicity : 0.114555 Specific harmonicity : 0.122395 Fundamental : 1/3645, -11.8317 octaves, 0.0718 Hz. Guide tone : 2688, 11.3923 octaves, 703249.520 Hz. Exponens Consonantiae : 9.797760E+06, 23.22402 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 821.5, average 273.83333 Mersenne's string divisions : 125125 Sum of van Prooijen's expressibility: 4.03882, average 1.34627 Sum of Tenney's harmonic distance : 8.37134, average 2.79045 Vogel's harmonic complexity : 21.00000 Wille's k value : 1093 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 9 Triangular lattice diameter : 7 Lattice compactness : 32.16003, average 5.36001 Lattice compactness (without 2's) : 22.97349, average 3.82892 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 7 3.33333 10 3: -6 .. 1 -2.00000 8 1 5: -1 .. 0 -0.33333 1 1 7: 0 .. 1 0.33333 1 1 Average exponent except 2's :-6 / 3 =-2.00000 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <6 10 15 21| Scale is weakly epimorphic with val: <6 10 18 21| Scale is weakly epimorphic with val: <7 11 16 18| Scale is weakly epimorphic with val: <7 11 16 21| Scale is JI-epimorphic with val: <7 11 17 19| Scale is weakly epimorphic with val: <7 11 17 22| Scale is weakly epimorphic with val: <7 11 19 21| Scale is weakly epimorphic with val: <7 12 16 18| Scale is weakly epimorphic with val: <7 12 16 21| Scale is weakly epimorphic with val: <8 11 16 20| Scale is weakly epimorphic with val: <8 12 15 19| Scale is weakly epimorphic with val: <8 12 17 18| Scale is weakly epimorphic with val: <8 12 17 21| Scale is weakly epimorphic with val: <8 12 18 19|
FIT/MODE
3: 2 0 1 N G T3 SD: 17.2905 c. M: 25.0659 c. 7: 4 1 2 N T3 SD: 17.9403 c. M: 31.0441 c. 8: 5 1 2 N T3 SD: 9.8190 c. M:-16.4378 c. 10: 6 1 3 N T3 SD: 10.8684 c. M: 16.8143 c. 11: 7 1 3 N T3 SD: 3.0486 c. M:-5.1186 c. 14: 9 1 4 N T3 SD: 2.7293 c. M:-4.5305 c. 24: 15 2 7 N T3 SD: 3.5425 c. M: 4.3632 c. 25: 16 2 7 N T3 SD: 1.9913 c. M:-3.1075 c. 35: 22 3 10 N T3 SD: 1.6833 c. M: 2.5844 c. 46: 29 4 13 N T3 SD: 0.9631 c. M: 1.6564 c. 49: 31 4 14 N T3 SD: 0.8417 c. M: 1.3495 c. 57: 36 5 16 N T3 SD: 0.9122 c. M:-1.1470 c. 60: 38 5 17 N T3 SD: 0.1550 c. M: 0.2128 c. 191: 121 16 54 N T3 SD: 0.1089 c. M:-0.1406 c. 205: 130 17 58 N T3 SD: 0.1132 c. M:-0.1921 c. 251: 159 21 71 N T3 SD: 0.0933 c. M: 0.1466 c. 265: 168 22 75 N T3 SD: 0.0581 c. M:-0.1004 c. 325: 206 27 92 N T3 SD: 0.0322 c. M:-0.0426 c. 385: 244 32 109 N T3 SD: 0.0323 c. M: 0.0558 c. 456: 289 38 129 N T3 SD: 0.0318 c. M:-0.0548 c. 516: 327 43 146 N T3 SD: 0.0204 c. M:-0.0294 c. 781: 495 65 221 N T3 SD: 0.0156 c. M:-0.0210 c. 841: 533 70 238 N T3 SD: 0.0035 c. M:-0.0044 c. 1742: 1104 145 493 N T3 SD: 0.0020 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: 29.2178 cents 5:6 x 7 S SD: 42.2336 cents 6:7 x 8 S SD: 24.3852 cents 7:8 x 9 S SD: 52.6754 cents 8 x 10:11 S SD: 30.3796 cents 9 x 11:12 SD: 4.8440 cents 10:12 x 13 S SD: 21.9155 cents 12:14:15:16 S SD: 18.9509 cents 13 x 16:17 SD: 16.8506 cents 14:17 x 19 SD: 18.4303 cents 15:18 x 20 S SD: 0.0000 cents 18 x 22:24 SD: 4.8440 cents 19:23 x 25 SD: 13.7334 cents 20:24:25:27 SD: 12.0932 cents 21:25:26:28 SD: 6.2391 cents 23 x 28:31 SD: 12.4901 cents 24:29:30:32 SD: 10.5263 cents 25:30:31:33 SD: 7.7259 cents 26:31:32:35 SD: 6.7004 cents 28:34 x 37 SD: 12.8535 cents 29:35:36:39 SD: 8.2756 cents 30:36:37:40 SD: 1.9931 cents 66:79:81:88 SD: 1.6884 cents 75:90:92:100 SD: 1.1347 cents 96:115:118:128 SD: 1.0035 cents 105:126:129:140 SD: 0.2393 cents 240:288:295:320 SD: 0.0403 cents 585:702:719:780 SD: 0.0099 cents