Scala analysis: 226_C14
Chromatic tetrachord 46/45 * 6/5 * 25/23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46/45 38.050632 23rd-partial chroma 2: 92/75 353.691919 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 25/23 144.3531 1: 46/45 38.0506 23rd-partial chroma 2: 6/5 315.6413 minor third 3: 25/23 144.3531
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 46/45 38.051 cents 23rd-partial chroma 1: 1 25/23 144.353 cents 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 92/75 353.692 cents 2: 1 30/23 459.994 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 : 38.1 353.7 498.0 38.1 : 315.6 460.0 498.0 353.7: 144.4 182.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.0506 .. 315.6413 cents 27/23, 277.5907 cents 46/45, 38.0506 cents 2: 182.4037 .. 459.9944 cents 27/23, 277.5907 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 46/45, 38.0506 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 4.363002 Largest / Average step : 1.901282 Largest / Smallest step : 8.295297 Median interval of one step : 25/23, 144.3531 cents, amount: 1 Least squares average step : 159.96925 cents, oct.: 479.90774 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 38.05063 cents Scale diversity : 0.749718 Lumma stability : 0.152800 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 : 46/45, 38.0506 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 class 1 -- Rational properties -- Prime limit : 23 Odd number limit : 75 (O: 25 U: 75) Highest odd numerator or denominator: 75 Scale harmonicity : 0.016072 Average absolute harmonicity : 0.083106 Specific harmonicity : 0.067754 Fundamental : 1/225, -7.8138 octaves, 1.1628 Hz. Guide tone : 92, 6.5236 octaves, 24069.552 Hz. Exponens Consonantiae : 2.070000E+04, 14.33734 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 132.5, average 44.16667 Mersenne's string divisions : 15197 Sum of van Prooijen's expressibility: 4.00540, average 1.33513 Sum of Tenney's harmonic distance : 8.23400, average 2.74467 Vogel's harmonic complexity : 24.00000 Wille's k value : 57 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 14.01222, average 2.33537 Lattice compactness (without 2's) : 11.28131, average 1.88022 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -2 ..-1 -1.33333 4 1 5: -2 .. 0 -1.00000 3 23: 0 .. 1 0.66667 2 2 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 15 32| Scale is weakly epimorphic with val: <6 10 17 35| Scale is weakly epimorphic with val: <6 10 18 35| Scale is weakly epimorphic with val: <6 11 15 34| Scale is weakly epimorphic with val: <6 11 16 34| Scale is weakly epimorphic with val: <7 10 15 31| Scale is weakly epimorphic with val: <7 10 16 31| Scale is weakly epimorphic with val: <7 10 18 34| Scale is weakly epimorphic with val: <7 11 16 30| Scale is weakly epimorphic with val: <7 11 16 33| Scale is weakly epimorphic with val: <7 11 16 36| Scale is weakly epimorphic with val: <7 11 17 30| Scale is JI-epimorphic with val: <7 11 17 33| = patent Scale is weakly epimorphic with val: <7 11 17 36| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <7 11 19 33| Scale is weakly epimorphic with val: <7 11 19 36| Scale is weakly epimorphic with val: <7 12 15 35| Scale is weakly epimorphic with val: <7 12 17 35| Scale is weakly epimorphic with val: <8 11 15 32| Scale is weakly epimorphic with val: <8 11 17 32| Scale is weakly epimorphic with val: <8 11 18 35| Scale is weakly epimorphic with val: <8 12 15 34| Scale is weakly epimorphic with val: <8 12 16 31|
FIT/MODE
3: 0 2 1 N G T3 SD: 25.2790 c. M: 38.0506 c. 4: 0 3 1 N G T3 SD: 24.7760 c. M: 38.0506 c. 7: 1 4 2 N T3 SD: 19.1463 c. M:-33.0987 c. 8: 1 5 2 N T3 SD: 18.0700 c. M:-24.2050 c. 9: 1 5 3 N T3 SD: 16.0011 c. M: 21.6619 c. 10: 1 6 3 N T3 SD: 7.3883 c. M:-11.7539 c. 11: 1 7 3 N T3 SD: 6.4512 c. M:-8.5226 c. 13: 1 8 4 N T3 SD: 5.1357 c. M: 8.8915 c. 14: 1 9 4 N T3 SD: 1.8576 c. M: 2.4760 c. 27: 2 17 8 N T3 SD: 1.9734 c. M: 3.2158 c. 38: 3 24 11 N T3 SD: 0.7400 c. M:-1.2687 c. 52: 4 33 15 N T3 SD: 0.4238 c. M:-0.6863 c. 79: 6 50 23 N T3 SD: 0.3956 c. M: 0.6474 c. 93: 7 59 27 N T3 SD: 0.3537 c. M: 0.5634 c. 117: 9 74 34 N T3 SD: 0.2650 c. M: 0.3779 c. 131: 10 83 38 N T3 SD: 0.0706 c. M: 0.1180 c. 183: 14 116 53 N T3 SD: 0.0703 c. M:-0.1105 c. 314: 24 199 91 N T3 SD: 0.0130 c. M:-0.0165 c. 759: 58 481 220 N T3 SD: 0.0065 c. M:-0.0081 c. 1073: 82 680 311 N T3 SD: 0.0061 c. M:-0.0106 c. 1387: 106 879 402 N T3 SD: 0.0071 c. M:-0.0119 c. 1832: 140 1161 531 N T3 SD: 0.0060 c. M:-0.0096 c. 2291: 175 1452 664 N T3 SD: 0.0049 c. M: 0.0070 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: 32.6218 cents 5 x 6:7 S SD: 46.3210 cents 6 x 7:8 S SD: 43.4105 cents 7 x x 9 SD: 62.9609 cents 8 x 10:11 S SD: 31.2337 cents 14:15:17:19 SD: 29.5749 cents 15:16:18:20 S SD: 27.6419 cents 16:17:20:21 SD: 26.4234 cents 17:18:21:23 SD: 22.3490 cents 18:19:22:24 SD: 18.6356 cents 21:22:26:28 SD: 15.1395 cents 22:23:27:29 SD: 14.5521 cents 23:24:28:31 SD: 14.1125 cents 24:25:29:32 SD: 13.9197 cents 25:26:31:33 SD: 13.0981 cents 26:27:32:35 SD: 10.8138 cents 27:28:33:36 SD: 8.5636 cents 30:31:37:40 SD: 6.9789 cents 35:36:43:47 SD: 5.5172 cents 36:37:44:48 SD: 3.7644 cents 39:40:48:52 S SD: 2.7249 cents 45:46:55:60 SD: 2.0947 cents 48:49:59:64 SD: 1.4128 cents 84:86:103:112 SD: 0.9230 cents 93:95:114:124 SD: 0.5725 cents 132:135:162:176 SD: 0.4031 cents 177:181:217:236 SD: 0.3834 cents 225:230:276:300 SD: 0.0000 cents