Scala analysis: 269_C18
Chromatic tetrachord 38/35 * 28/27 * 45/38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 38/35 142.373396 2: 152/135 205.334300 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 45/38 292.7107 1: 38/35 142.3734 2: 28/27 62.9609 Archytas' 1/3-tone 3: 45/38 292.7107
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 38/35 142.373 cents 1: 1 45/38 292.711 cents 2: 1 152/135 205.334 cents 2: 1 70/57 355.672 cents 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 : 142.4 205.3 498.0 142.4: 63.0 355.7 498.0 205.3: 292.7 435.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 292.7107 cents 1215/1064, 229.7498 cents 28/27, 62.9609 cents 2: 205.3343 .. 435.0841 cents 1215/1064, 229.7498 cents 5776/6075,-87.3764 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 : 45/38, 292.7107 cents Average / Smallest step : 2.636795 Largest / Average step : 1.763158 Largest / Smallest step : 4.649087 Median interval of one step : 38/35, 142.3734 cents, amount: 1 Least squares average step : 146.22693 cents, oct.: 438.68078 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1938-tone equal temperament with octave 4/3 degrees: 554 799 1938 Least number of segments generator : 971 of 249.536 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1529 of 392.936 cents and inv. generated superset size: 62 = 59 more = 2066.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 62.96090 cents Scale diversity : 0.982419 Lumma stability : 0.252832 Lumma impropriety factor : 0.175439 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 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 19 Odd number limit : 135 (O: 45 U: 135) Highest odd numerator or denominator: 135 Scale harmonicity : 0.016184 Average absolute harmonicity : 0.084336 Specific harmonicity : 0.069703 Fundamental : 1/945, -9.8842 octaves, 0.2769 Hz. Guide tone : 152, 7.2479 octaves, 39767.086 Hz. Exponens Consonantiae : 1.436400E+05, 17.13210 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 183.5, average 61.16667 Mersenne's string divisions : 20951 Sum of van Prooijen's expressibility: 4.15152, average 1.38384 Sum of Tenney's harmonic distance : 8.51521, average 2.83840 Vogel's harmonic complexity : 26.00000 Wille's k value : 256 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 17.33168, average 2.88861 Lattice compactness (without 2's) : 13.66044, average 2.27674 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -3 .. 0 -1.33333 4 1 5: -1 .. 0 -0.66667 2 7: -1 .. 0 -0.33333 1 19: 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 19 31| Scale is weakly epimorphic with val: <6 10 15 20 30| Scale is weakly epimorphic with val: <6 10 15 22 34| Scale is weakly epimorphic with val: <6 10 16 19 32| Scale is weakly epimorphic with val: <6 10 16 20 31| Scale is weakly epimorphic with val: <6 10 17 19 33| Scale is weakly epimorphic with val: <6 10 17 20 32| Scale is weakly epimorphic with val: <6 10 18 19 34| Scale is weakly epimorphic with val: <6 10 18 20 33| Scale is weakly epimorphic with val: <6 10 19 20 34| Scale is weakly epimorphic with val: <6 11 15 19 33| Scale is weakly epimorphic with val: <6 11 15 20 32| Scale is weakly epimorphic with val: <6 11 15 22 33| Scale is weakly epimorphic with val: <6 11 16 19 34| Scale is weakly epimorphic with val: <6 11 16 20 33| Scale is weakly epimorphic with val: <6 11 16 22 34| Scale is weakly epimorphic with val: <6 11 17 20 34| Scale is weakly epimorphic with val: <7 10 15 18 29| Scale is weakly epimorphic with val: <7 10 15 21 32| Scale is weakly epimorphic with val: <7 10 16 18 30| Scale is weakly epimorphic with val: <7 10 16 20 28| Scale is weakly epimorphic with val: <7 10 16 21 33| Scale is weakly epimorphic with val: <7 10 17 18 31| Scale is weakly epimorphic with val: <7 10 17 20 29| Scale is weakly epimorphic with val: <7 10 17 21 34| Scale is weakly epimorphic with val: <7 10 18 18 32| Scale is weakly epimorphic with val: <7 10 18 20 30| Scale is weakly epimorphic with val: <7 10 19 20 31| Scale is weakly epimorphic with val: <7 11 15 18 28| Scale is weakly epimorphic with val: <7 11 15 18 31| Scale is weakly epimorphic with val: <7 11 15 18 34| Scale is JI-epimorphic with val: <7 11 15 20 29| Scale is weakly epimorphic with val: <7 11 15 20 32| Scale is weakly epimorphic with val: <7 11 15 21 28| Scale is weakly epimorphic with val: <7 11 15 21 31| Scale is weakly epimorphic with val: <7 11 15 21 34| Scale is weakly epimorphic with val: <7 11 16 18 29| Scale is weakly epimorphic with val: <7 11 16 18 32| Scale is JI-epimorphic with val: <7 11 16 20 30| Scale is weakly epimorphic with val: <7 11 16 20 33| Scale is weakly epimorphic with val: <7 11 16 21 29| Scale is weakly epimorphic with val: <7 11 16 21 32| Scale is weakly epimorphic with val: <7 11 17 18 30| Scale is weakly epimorphic with val: <7 11 17 18 33| Scale is weakly epimorphic with val: <7 11 17 20 28| Scale is JI-epimorphic with val: <7 11 17 20 31| = patent Scale is weakly epimorphic with val: <7 11 17 20 34| Scale is weakly epimorphic with val: <7 11 17 21 30| Scale is weakly epimorphic with val: <7 11 17 21 33| Scale is weakly epimorphic with val: <7 11 18 18 28| Scale is weakly epimorphic with val: <7 11 18 18 31| Scale is weakly epimorphic with val: <7 11 18 18 34| Scale is weakly epimorphic with val: <7 11 18 20 29| Scale is JI-epimorphic with val: <7 11 18 20 32| Scale is weakly epimorphic with val: <7 11 18 21 28| Scale is weakly epimorphic with val: <7 11 18 21 31| Scale is weakly epimorphic with val: <7 11 18 21 34| Scale is weakly epimorphic with val: <7 11 19 20 30| Scale is JI-epimorphic with val: <7 11 19 20 33| Scale is weakly epimorphic with val: <7 11 19 21 29| Scale is weakly epimorphic with val: <7 11 19 21 32| Scale is weakly epimorphic with val: <7 12 15 18 33| Scale is weakly epimorphic with val: <7 12 15 20 31| Scale is weakly epimorphic with val: <7 12 15 21 33| Scale is weakly epimorphic with val: <7 12 16 18 34| Scale is weakly epimorphic with val: <7 12 16 20 32| Scale is weakly epimorphic with val: <7 12 16 21 34| Scale is weakly epimorphic with val: <7 12 17 20 33| Scale is weakly epimorphic with val: <7 12 18 20 34| Scale is weakly epimorphic with val: <8 11 15 18 28| Scale is weakly epimorphic with val: <8 11 15 21 31| Scale is weakly epimorphic with val: <8 11 16 18 29| Scale is weakly epimorphic with val: <8 11 16 19 28| Scale is weakly epimorphic with val: <8 11 16 21 32| Scale is weakly epimorphic with val: <8 11 16 22 28| Scale is weakly epimorphic with val: <8 11 17 18 30| Scale is weakly epimorphic with val: <8 11 17 19 29| Scale is weakly epimorphic with val: <8 11 17 21 33| Scale is weakly epimorphic with val: <8 11 17 22 29| Scale is weakly epimorphic with val: <8 11 18 18 31| Scale is weakly epimorphic with val: <8 11 18 19 30| Scale is weakly epimorphic with val: <8 11 18 21 34| Scale is weakly epimorphic with val: <8 11 18 22 30| Scale is weakly epimorphic with val: <8 11 19 19 31| Scale is weakly epimorphic with val: <8 11 19 22 31| Scale is weakly epimorphic with val: <8 12 15 18 30| Scale is weakly epimorphic with val: <8 12 15 19 29| Scale is weakly epimorphic with val: <8 12 15 21 30| Scale is weakly epimorphic with val: <8 12 15 22 32| Scale is weakly epimorphic with val: <8 12 16 18 31| Scale is weakly epimorphic with val: <8 12 16 19 30| Scale is weakly epimorphic with val: <8 12 16 21 31| Scale is weakly epimorphic with val: <8 12 16 22 33| Scale is weakly epimorphic with val: <8 12 17 18 32| Scale is weakly epimorphic with val: <8 12 17 19 31| Scale is weakly epimorphic with val: <8 12 17 21 32| Scale is weakly epimorphic with val: <8 12 17 22 34| Scale is weakly epimorphic with val: <8 12 18 18 33| Scale is weakly epimorphic with val: <8 12 18 19 32| Scale is weakly epimorphic with val: <8 12 18 21 33| Scale is weakly epimorphic with val: <8 12 19 19 33| Scale is weakly epimorphic with val: <8 12 19 21 34|
FIT/MODE
3: 1 0 2 N G T3 SD: 26.4886 c. M: 39.3193 c. 4: 1 1 2 P M ME S SD: 27.2502 c. M:-43.6882 c. 5: 1 1 3 N M DE S SD: 24.9413 c. M: 42.7644 c. 7: 2 1 4 N T3 SD: 4.6846 c. M:-8.1136 c. 10: 3 1 6 N T3 SD: 5.3843 c. M:-7.0401 c. 17: 5 2 10 N T3 SD: 2.3778 c. M:-4.1104 c. 24: 7 3 14 N T3 SD: 2.0914 c. M:-2.8897 c. 39: 11 5 23 N T3 SD: 1.2414 c. M: 1.8992 c. 46: 13 6 27 N T3 SD: 0.9616 c. M: 1.6215 c. 53: 15 7 31 N T3 SD: 1.1507 c. M: 1.4173 c. 56: 16 7 33 N T3 SD: 0.4525 c. M: 0.7801 c. 63: 18 8 37 N T3 SD: 0.1277 c. M:-0.2081 c. 182: 52 23 107 N T3 SD: 0.0703 c. M: 0.0960 c. 245: 70 31 144 N T3 SD: 0.0444 c. M: 0.0748 c. 371: 106 47 218 N T3 SD: 0.0550 c. M: 0.0748 c. 427: 122 54 251 N T3 SD: 0.0523 c. M: 0.0748 c. 507: 145 64 298 N T3 SD: 0.0407 c. M:-0.0655 c. 570: 163 72 335 N T3 SD: 0.0289 c. M:-0.0500 c. 633: 181 80 372 N T3 SD: 0.0248 c. M:-0.0376 c. 752: 215 95 442 N T3 SD: 0.0176 c. M: 0.0232 c. 815: 233 103 479 N T3 SD: 0.0078 c. M:-0.0125 c. 878: 251 111 516 N T3 SD: 0.0068 c. M:-0.0100 c. 1060: 303 134 623 N T3 SD: 0.0065 c. M: 0.0082 c. 1693: 484 214 995 N T3 SD: 0.0055 c. M:-0.0092 c. 1875: 536 237 1102 N T3 SD: 0.0041 c. M: 0.0069 c. 1938: 554 245 1139 N T3 SD: 0.0008 c. M: 0.0014 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: 69.4664 cents 6 x 7:8 S SD: 30.7683 cents 7 x 8:9 S SD: 34.0286 cents 8 x 9:11 SD: 26.6460 cents 9 x 10:12 S SD: 11.4653 cents 10:11 x 13 SD: 24.6643 cents 11:12 x 15 S SD: 19.8869 cents 13:14:15:17 SD: 18.6386 cents 14:15:16:19 SD: 15.3928 cents 15:16:17:20 SD: 10.8925 cents 18 x 20:24 S SD: 11.4653 cents 19:21 x 25 SD: 19.2372 cents 20:22:23:27 SD: 16.0422 cents 21:23:24:28 SD: 9.9795 cents 22:24:25:29 SD: 8.9130 cents 23:25:26:31 SD: 6.6841 cents 24:26:27:32 SD: 1.3529 cents 81:88:91:108 SD: 1.3212 cents 105:114:118:140 SD: 1.0858 cents 126:137:142:168 SD: 1.0023 cents 129:140:145:172 SD: 1.0002 cents 141:153:159:188 SD: 0.9449 cents 150:163:169:200 SD: 0.6325 cents 174:189:196:232 SD: 0.3702 cents 198:215:223:264 SD: 0.1888 cents 222:241:250:296 SD: 0.1233 cents 501:544:564:668 SD: 0.1093 cents 525:570:591:700 SD: 0.1085 cents