Scala analysis: 224_C14
Chromatic tetrachord 24/23 * 115/108 * 6/5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 24/23 73.680654 vicesimotertial minor semitone 2: 10/9 182.403712 minor whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 24/23 73.6807 vicesimotertial minor semitone 2: 115/108 108.7231 3: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 24/23 73.681 cents vicesimotertial minor semitone 1: 1 115/108 108.723 cents 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 144/115 389.322 cents 2: 1 23/18 424.364 cents vicesimotertial major 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 : 73.7 182.4 498.0 73.7 : 108.7 424.4 498.0 182.4: 315.6 389.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.6807 .. 315.6413 cents 23/20, 241.9606 cents 24/23, 73.6807 cents 2: 182.4037 .. 424.3643 cents 23/20, 241.9606 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 24/23, 73.6807 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 2.253169 Largest / Average step : 1.901282 Largest / Smallest step : 4.283910 Median interval of one step : 115/108, 108.7231 cents, amount: 1 Least squares average step : 138.04451 cents, oct.: 414.13352 cents Scale is not proper Scale has trivalence property 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 73.68065 cents Scale diversity : 0.987033 Lumma stability : 0.295880 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 : 2645/2592, 35.0424 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 23 Odd number limit : 115 (O: 115 U: 115) Highest odd numerator or denominator: 23 Scale harmonicity : 0.016810 Average absolute harmonicity : 0.104586 Specific harmonicity : 0.087850 Fundamental : 1/207, -7.6935 octaves, 1.2639 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 2.484000E+04, 14.60038 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 36.5, average 12.16667 Mersenne's string divisions : 6251 Sum of van Prooijen's expressibility: 2.79309, average 0.93103 Sum of Tenney's harmonic distance : 5.77536, average 1.92512 Vogel's harmonic complexity : 23.00000 Wille's k value : 57 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 16.05671, average 2.67612 Lattice compactness (without 2's) : 11.61719, average 1.93620 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -2 .. 1 -0.66667 4 1 5: 0 .. 1 0.33333 1 1 23: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 17 30| Scale is weakly epimorphic with val: <6 10 17 33| Scale is weakly epimorphic with val: <6 10 17 36| Scale is weakly epimorphic with val: <6 11 19 30| Scale is weakly epimorphic with val: <6 11 19 33| Scale is weakly epimorphic with val: <6 11 19 36| Scale is weakly epimorphic with val: <7 10 16 32| Scale is weakly epimorphic with val: <7 10 16 35| 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 JI-epimorphic with val: <7 11 17 31| Scale is weakly epimorphic with val: <7 11 17 34| 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 30| Scale is weakly epimorphic with val: <7 12 18 30| Scale is weakly epimorphic with val: <8 11 15 32| Scale is weakly epimorphic with val: <8 11 17 31| Scale is weakly epimorphic with val: <8 11 17 34| Scale is weakly epimorphic with val: <8 11 18 32| Scale is weakly epimorphic with val: <8 12 15 33| Scale is weakly epimorphic with val: <8 12 18 33| Scale is weakly epimorphic with val: <8 12 19 31| Scale is weakly epimorphic with val: <8 12 19 34|
FIT/MODE
3: 0 1 2 N G T3 SD: 43.5792 c. M: 73.6807 c. 5: 1 1 3 N M DE S SD: 17.8419 c. M:-25.9283 c. 6: 1 1 4 N M DE S SD: 10.8870 c. M: 16.3887 c. 8: 1 2 5 N T3 SD: 7.0609 c. M: 11.4250 c. 13: 2 3 8 N T3 SD: 5.5502 c. M:-9.1521 c. 14: 2 3 9 N T3 SD: 2.9963 c. M: 4.5305 c. 19: 3 4 12 N T3 SD: 2.9305 c. M:-4.9580 c. 27: 4 6 17 N T3 SD: 1.1894 c. M:-2.0574 c. 33: 5 7 21 N T3 SD: 1.2717 c. M:-1.7807 c. 41: 6 9 26 N T3 SD: 0.4728 c. M: 0.7960 c. 68: 10 15 43 N T3 SD: 0.4775 c. M:-0.7011 c. 74: 11 16 47 N T3 SD: 0.4447 c. M: 0.6846 c. 101: 15 22 64 N T3 SD: 0.1677 c. M:-0.2864 c. 142: 21 31 90 N T3 SD: 0.0194 c. M: 0.0261 c. 669: 99 146 424 N T3 SD: 0.0136 c. M:-0.0211 c. 811: 120 177 514 N T3 SD: 0.0103 c. M:-0.0128 c. 953: 141 208 604 N T3 SD: 0.0089 c. M: 0.0137 c. 1095: 162 239 694 N T3 SD: 0.0086 c. M: 0.0146 c. 1237: 183 270 784 N T3 SD: 0.0089 c. M: 0.0154 c. 1379: 204 301 874 N T3 SD: 0.0094 c. M: 0.0159 c. 1521: 225 332 964 N T3 SD: 0.0100 c. M: 0.0164 c. 1690: 250 369 1071 N T3 SD: 0.0099 c. M:-0.0163 c. 1764: 261 385 1118 N T3 SD: 0.0094 c. M: 0.0131 c. 1832: 271 400 1161 N T3 SD: 0.0087 c. M:-0.0134 c. 1933: 286 422 1225 N T3 SD: 0.0100 c. M:-0.0153 c. 1974: 292 431 1251 N T3 SD: 0.0079 c. M:-0.0109 c. 2075: 307 453 1315 N T3 SD: 0.0081 c. M:-0.0128 c. 2116: 313 462 1341 N T3 SD: 0.0075 c. M: 0.0095 c. 2217: 328 484 1405 N T3 SD: 0.0065 c. M:-0.0106 c. 2359: 349 515 1495 N T3 SD: 0.0052 c. M:-0.0087 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: 78.8780 cents 6 x 7:8 S SD: 42.2336 cents 7 x 8:9 S SD: 39.8203 cents 8 x 9:11 SD: 28.7251 cents 9 x 10:12 S SD: 0.0000 cents 10 x 11:13 SD: 23.5791 cents 11 x 12:15 S SD: 25.1136 cents 12 x 13:16 SD: 21.9155 cents 13 x 14:17 SD: 31.8493 cents 14:15:16:19 SD: 24.5213 cents 15:16:17:20 SD: 17.0723 cents 16:17:18:21 S SD: 15.5776 cents 17:18:19:23 SD: 12.3857 cents 18:19:20:24 S SD: 6.6408 cents 26:27:29:35 SD: 6.5680 cents 27:28:30:36 S SD: 3.5732 cents 45:47:50:60 SD: 0.5341 cents 117:122:130:156 SD: 0.4112 cents 162:169:180:216 SD: 0.1484 cents 207:216:230:276 SD: 0.0000 cents