Scala analysis: 317_C24
Chromatic tetrachord 50/49 * 7/6 * 28/25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 50/49 34.975615 Erlich's decatonic comma, tritonic diesis 2: 25/21 301.846520 BP second, quasi-equal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 28/25 196.1985 middle second 1: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 2: 7/6 266.8709 septimal minor third 3: 28/25 196.1985 middle second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 1 28/25 196.198 cents middle second 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 25/21 301.847 cents BP second, quasi-equal minor third 2: 1 98/75 463.069 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 : 35.0 301.8 498.0 35.0 : 266.9 463.1 498.0 301.8: 196.2 231.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.9756 .. 266.8709 cents 343/300, 231.8953 cents 50/49, 34.9756 cents 2: 231.1741 .. 463.0694 cents 343/300, 231.8953 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 50/49, 34.9756 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 4.746593 Largest / Average step : 1.607511 Largest / Smallest step : 7.630199 Median interval of one step : 28/25, 196.1985 cents, amount: 1 Least squares average step : 152.34312 cents, oct.: 457.02935 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1353-tone equal temperament with octave 4/3 degrees: 95 820 1353 Least number of segments generator : 677 of 249.207 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 944 of 347.490 cents and inv. generated superset size: 42 = 39 more = 1400.000% Number of contiguous 1-step segments: 0 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 34.97561 cents Scale diversity : 0.641064 Lumma stability : 0.140452 Lumma impropriety factor : 0.071674 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 : 50/49, 34.9756 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 : 7 Odd number limit : 75 (O: 49 U: 75) Highest odd numerator or denominator: 49 Scale harmonicity : 0.026289 Average absolute harmonicity : 0.094070 Specific harmonicity : 0.113582 Fundamental : 1/147, -7.1997 octaves, 1.7798 Hz. Guide tone : 100, 6.6439 octaves, 26162.557 Hz. Exponens Consonantiae : 1.470000E+04, 13.84353 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 76.0, average 25.33333 Mersenne's string divisions : 31878 Sum of van Prooijen's expressibility: 3.56526, average 1.18842 Sum of Tenney's harmonic distance : 7.18851, average 2.39617 Vogel's harmonic complexity : 15.66667 Wille's k value : 87 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 15.57989, average 2.59665 Lattice compactness (without 2's) : 12.92820, average 2.15470 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.00000 3 3: -1 .. 0 -0.66667 2 1 5: 0 .. 2 1.33333 4 7: -2 .. 0 -1.00000 3 2 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 17 21| Scale is weakly epimorphic with val: <6 11 16 18| Scale is weakly epimorphic with val: <7 10 17 19| Scale is weakly epimorphic with val: <7 10 17 21| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 16 20| Scale is weakly epimorphic with val: <7 11 16 22| Scale is weakly epimorphic with val: <7 11 19 19| Scale is weakly epimorphic with val: <7 11 19 20| Scale is weakly epimorphic with val: <7 11 19 22| Scale is weakly epimorphic with val: <7 12 18 20| Scale is weakly epimorphic with val: <7 12 18 21| Scale is weakly epimorphic with val: <8 11 16 18| Scale is weakly epimorphic with val: <8 12 18 21|
FIT/MODE
3: 0 2 1 N G T3 SD: 26.6729 c. M: 34.9756 c. 5: 0 3 2 N G T3 SD: 20.2683 c. M: 34.9756 c. 7: 0 4 3 N G T3 SD: 22.5154 c. M: 34.9756 c. 8: 1 4 3 P T3 SD: 16.6649 c. M:-27.2800 c. 10: 1 5 4 P T3 SD: 8.7371 c. M:-14.8289 c. 12: 1 6 5 P T3 SD: 7.5446 c. M: 11.3203 c. 13: 1 7 5 N T3 SD: 3.3005 c. M:-4.6427 c. 15: 1 8 6 N T3 SD: 2.0215 c. M: 3.0195 c. 28: 2 15 11 N T3 SD: 0.4648 c. M:-0.5990 c. 43: 3 23 17 N T3 SD: 0.4268 c. M: 0.7030 c. 71: 5 38 28 N T3 SD: 0.1357 c. M: 0.2136 c. 99: 7 53 39 N T3 SD: 0.1384 c. M:-0.2397 c. 170: 12 91 67 N T3 SD: 0.1164 c. M:-0.1805 c. 241: 17 129 95 N T3 SD: 0.1160 c. M:-0.1562 c. 269: 19 144 106 N T3 SD: 0.1214 c. M:-0.2023 c. 312: 22 167 123 N T3 SD: 0.1180 c. M: 0.1462 c. 358: 25 192 141 N T3 SD: 0.1156 c. M: 0.1959 c. 386: 27 207 152 N T3 SD: 0.0914 c. M: 0.1383 c. 414: 29 222 163 N T3 SD: 0.0807 c. M:-0.1083 c. 429: 30 230 169 N T3 SD: 0.0850 c. M: 0.1473 c. 442: 31 237 174 N T3 SD: 0.0824 c. M:-0.1355 c. 457: 32 245 180 N T3 SD: 0.0615 c. M: 0.1016 c. 485: 34 260 191 N T3 SD: 0.0499 c. M:-0.0612 c. 528: 37 283 208 N T3 SD: 0.0432 c. M: 0.0747 c. 556: 39 298 219 N T3 SD: 0.0280 c. M: 0.0408 c. 584: 41 313 230 N T3 SD: 0.0298 c. M:-0.0506 c. 599: 42 321 236 N T3 SD: 0.0348 c. M: 0.0543 c. 627: 44 336 247 N T3 SD: 0.0145 c. M: 0.0251 c. 655: 46 351 258 N T3 SD: 0.0127 c. M:-0.0220 c. 698: 49 374 275 N T3 SD: 0.0150 c. M: 0.0227 c. 726: 51 389 286 N T3 SD: 0.0064 c. M:-0.0110 c. 1353: 95 725 533 N T3 SD: 0.0034 c. M: 0.0057 c. 2079: 146 1114 819 N T3 SD: 0.0006 c. M: 0.0011 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: 84.4672 cents 5 x 6:7 S SD: 42.7931 cents 6 x 7:8 S SD: 17.4878 cents 7 x 8:9 S SD: 47.3251 cents 8 x 10:11 S SD: 49.9317 cents 9 x 11:12 SD: 22.7807 cents 18:19:21:24 SD: 22.7559 cents 19:20:23:25 SD: 21.7537 cents 20:21:24:27 S SD: 18.5659 cents 21:22:25:28 SD: 15.1871 cents 24:25:29:32 SD: 14.6767 cents 25:26:30:33 SD: 13.2374 cents 26:27:31:35 SD: 11.5633 cents 27:28:32:36 S SD: 9.6761 cents 30:31:36:40 SD: 8.5969 cents 31:32:37:41 SD: 8.2729 cents 32:33:38:43 SD: 7.7106 cents 33:34:39:44 SD: 6.9826 cents 36:37:43:48 SD: 4.5753 cents 42:43:50:56 SD: 1.9204 cents 48:49:57:64 SD: 1.4644 cents 90:92:107:120 SD: 1.2820 cents 99:101:118:132 SD: 0.7087 cents 141:144:168:188 SD: 0.6943 cents 147:150:175:196 SD: 0.0000 cents