Scala analysis: 315_C24
Chromatic tetrachord 40/39 * 39/35 * 7/6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/39 43.831051 tridecimal minor diesis 2: 8/7 231.174094 septimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 40/39 43.8311 tridecimal minor diesis 2: 39/35 187.3430 3: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 39/35 187.343 cents 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 140/117 310.702 cents 2: 1 13/10 454.214 cents tridecimal semi-diminished fourth 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 : 43.8 231.2 498.0 43.8 : 187.3 454.2 498.0 231.2: 266.9 310.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 266.8709 cents 91/80, 223.0399 cents 40/39, 43.8311 cents 2: 231.1741 .. 454.2139 cents 91/80, 223.0399 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 3.787612 Largest / Average step : 1.607511 Largest / Smallest step : 6.088627 Median interval of one step : 39/35, 187.3430 cents, amount: 1 Least squares average step : 142.87959 cents, oct.: 428.63876 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1284-tone equal temperament with octave 4/3 degrees: 113 596 1284 Least number of segments generator : 643 of 249.410 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1171 of 454.214 cents and inv. generated superset size: 29 = 26 more = 966.667% Number of contiguous 1-step segments: 0 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 35.69681 cents Scale diversity : 0.744398 Lumma stability : 0.176012 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 : 49/48, 35.6968 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 : 13 Odd number limit : 117 (O: 39 U: 117) Highest odd numerator or denominator: 39 Scale harmonicity : 0.022469 Average absolute harmonicity : 0.106258 Specific harmonicity : 0.116630 Fundamental : 1/273, -8.0928 octaves, 0.9583 Hz. Guide tone : 40, 5.3219 octaves, 10465.023 Hz. Exponens Consonantiae : 1.092000E+04, 13.41469 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 50.5, average 16.83333 Mersenne's string divisions : 8295 Sum of van Prooijen's expressibility: 2.91328, average 0.97109 Sum of Tenney's harmonic distance : 6.02049, average 2.00683 Vogel's harmonic complexity : 18.66667 Wille's k value : 45 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 14.32655, average 2.38776 Lattice compactness (without 2's) : 8.56048, average 1.42675 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -1 .. 0 -0.66667 2 1 5: 0 .. 1 0.33333 1 7: -1 .. 0 -0.33333 1 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <7 10 15 18 27| Scale is weakly epimorphic with val: <7 10 15 18 30| Scale is weakly epimorphic with val: <7 10 16 18 25| Scale is weakly epimorphic with val: <7 10 16 18 28| Scale is weakly epimorphic with val: <7 10 17 18 26| Scale is weakly epimorphic with val: <7 10 17 18 29| Scale is weakly epimorphic with val: <7 10 17 19 25| Scale is weakly epimorphic with val: <7 10 17 22 25| Scale is weakly epimorphic with val: <7 10 18 18 27| Scale is weakly epimorphic with val: <7 10 18 18 30| Scale is weakly epimorphic with val: <7 10 18 19 26| Scale is weakly epimorphic with val: <7 10 18 22 26| Scale is weakly epimorphic with val: <7 10 19 19 27| Scale is weakly epimorphic with val: <7 10 19 22 27| Scale is weakly epimorphic with val: <7 11 15 19 27| Scale is weakly epimorphic with val: <7 11 15 19 30| Scale is weakly epimorphic with val: <7 11 15 20 26| Scale is weakly epimorphic with val: <7 11 15 20 29| Scale is weakly epimorphic with val: <7 11 15 22 27| Scale is weakly epimorphic with val: <7 11 15 22 30| Scale is JI-epimorphic with val: <7 11 16 19 25| Scale is weakly epimorphic with val: <7 11 16 19 28| Scale is weakly epimorphic with val: <7 11 16 20 27| Scale is weakly epimorphic with val: <7 11 16 20 30| Scale is weakly epimorphic with val: <7 11 16 22 25| Scale is weakly epimorphic with val: <7 11 16 22 28| Scale is JI-epimorphic with val: <7 11 17 19 26| Scale is weakly epimorphic with val: <7 11 17 19 29| Scale is weakly epimorphic with val: <7 11 17 20 25| Scale is weakly epimorphic with val: <7 11 17 20 28| Scale is weakly epimorphic with val: <7 11 17 22 26| Scale is weakly epimorphic with val: <7 11 17 22 29| Scale is JI-epimorphic with val: <7 11 18 19 27| Scale is weakly epimorphic with val: <7 11 18 19 30| Scale is weakly epimorphic with val: <7 11 18 20 26| Scale is weakly epimorphic with val: <7 11 18 20 29| Scale is weakly epimorphic with val: <7 11 18 22 27| Scale is weakly epimorphic with val: <7 11 18 22 30| Scale is weakly epimorphic with val: <7 11 19 19 25| Scale is JI-epimorphic with val: <7 11 19 19 28| Scale is weakly epimorphic with val: <7 11 19 20 27| Scale is weakly epimorphic with val: <7 11 19 20 30| Scale is weakly epimorphic with val: <7 11 19 22 25| Scale is weakly epimorphic with val: <7 11 19 22 28| Scale is weakly epimorphic with val: <7 12 15 18 26| Scale is weakly epimorphic with val: <7 12 15 18 29| Scale is weakly epimorphic with val: <7 12 16 18 27| Scale is weakly epimorphic with val: <7 12 16 18 30| Scale is weakly epimorphic with val: <7 12 17 18 25| Scale is weakly epimorphic with val: <7 12 17 18 28| Scale is weakly epimorphic with val: <7 12 18 18 26| Scale is weakly epimorphic with val: <7 12 18 18 29| Scale is weakly epimorphic with val: <7 12 19 20 25| Scale is weakly epimorphic with val: <8 11 15 20 25| Scale is weakly epimorphic with val: <8 11 15 21 27| Scale is weakly epimorphic with val: <8 11 15 21 30| Scale is weakly epimorphic with val: <8 11 16 20 26| Scale is weakly epimorphic with val: <8 11 16 21 25| Scale is weakly epimorphic with val: <8 11 16 21 28| Scale is weakly epimorphic with val: <8 11 17 20 27| Scale is weakly epimorphic with val: <8 11 17 21 26| Scale is weakly epimorphic with val: <8 11 17 21 29| Scale is weakly epimorphic with val: <8 11 18 20 28| Scale is weakly epimorphic with val: <8 11 18 21 27| Scale is weakly epimorphic with val: <8 11 18 21 30| Scale is weakly epimorphic with val: <8 11 19 20 29| Scale is weakly epimorphic with val: <8 11 19 21 25| Scale is weakly epimorphic with val: <8 11 19 21 28| Scale is weakly epimorphic with val: <8 12 15 21 25| Scale is weakly epimorphic with val: <8 12 15 21 28| Scale is weakly epimorphic with val: <8 12 16 19 25| Scale is weakly epimorphic with val: <8 12 16 21 26| Scale is weakly epimorphic with val: <8 12 16 21 29| Scale is weakly epimorphic with val: <8 12 16 22 25| Scale is weakly epimorphic with val: <8 12 17 19 26| Scale is weakly epimorphic with val: <8 12 17 21 27| Scale is weakly epimorphic with val: <8 12 17 21 30| Scale is weakly epimorphic with val: <8 12 17 22 26| Scale is weakly epimorphic with val: <8 12 18 19 27| Scale is weakly epimorphic with val: <8 12 18 21 25| Scale is weakly epimorphic with val: <8 12 18 21 28| Scale is weakly epimorphic with val: <8 12 18 22 27| Scale is weakly epimorphic with val: <8 12 19 19 28| Scale is weakly epimorphic with val: <8 12 19 21 26| Scale is weakly epimorphic with val: <8 12 19 21 29| Scale is weakly epimorphic with val: <8 12 19 22 28|
FIT/MODE
3: 0 1 2 N G T3 SD: 45.3390 c. M: 65.1591 c. 4: 0 2 2 P M DE S SD: 27.3235 c. M: 43.8311 c. 5: 0 2 3 N G T3 SD: 31.3175 c. M: 43.8311 c. 6: 1 2 3 P T3 SD: 24.8553 c. M:-39.1764 c. 8: 1 3 4 P T3 SD: 14.8102 c. M:-18.4246 c. 9: 1 3 5 N T3 SD: 8.7343 c. M:-11.5073 c. 11: 1 4 6 N T3 SD: 2.8887 c. M: 4.7900 c. 13: 1 5 7 N T3 SD: 3.2751 c. M: 5.5199 c. 24: 2 9 13 N T3 SD: 2.1484 c. M: 2.9035 c. 32: 3 12 17 N T3 SD: 2.1136 c. M:-2.8607 c. 34: 3 13 18 N T3 SD: 1.8487 c. M:-3.2000 c. 43: 4 16 23 N T3 SD: 1.4684 c. M:-2.4987 c. 45: 4 17 24 N T3 SD: 0.7633 c. M:-1.2469 c. 56: 5 21 30 N T3 SD: 0.3696 c. M:-0.6373 c. 69: 6 26 37 N T3 SD: 0.3225 c. M: 0.5228 c. 114: 10 43 61 N T3 SD: 0.2307 c. M:-0.3731 c. 125: 11 47 67 N T3 SD: 0.0469 c. M: 0.0812 c. 364: 32 137 195 N T3 SD: 0.0445 c. M:-0.0611 c. 420: 37 158 225 N T3 SD: 0.0436 c. M:-0.0611 c. 489: 43 184 262 N T3 SD: 0.0251 c. M: 0.0357 c. 545: 48 205 292 N T3 SD: 0.0254 c. M:-0.0335 c. 614: 54 231 329 N T3 SD: 0.0169 c. M: 0.0290 c. 670: 59 252 359 N T3 SD: 0.0161 c. M:-0.0266 c. 739: 65 278 396 N T3 SD: 0.0156 c. M: 0.0247 c. 795: 70 299 426 N T3 SD: 0.0132 c. M:-0.0220 c. 864: 76 325 463 N T3 SD: 0.0175 c. M: 0.0215 c. 920: 81 346 493 N T3 SD: 0.0142 c. M:-0.0186 c. 1159: 102 436 621 N T3 SD: 0.0087 c. M:-0.0150 c. 1284: 113 483 688 N T3 SD: 0.0033 c. M:-0.0057 c. 1409: 124 530 755 N T3 SD: 0.0012 c. M: 0.0020 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: 59.7273 cents 6 x 7:8 S SD: 17.8484 cents 7 x 8:9 S SD: 31.4805 cents 8 x 9:11 SD: 29.9221 cents 9 x 10:12 S SD: 24.3852 cents 10 x 11:13 SD: 39.6850 cents 11 x 13:15 SD: 34.9349 cents 12 x 14:16 S SD: 17.8484 cents 20:21:23:27 SD: 15.7415 cents 21:22:24:28 S SD: 12.2353 cents 26:27:30:35 S SD: 10.6011 cents 27:28:31:36 SD: 6.9113 cents 30:31:34:40 SD: 6.4740 cents 33:34:38:44 SD: 5.0812 cents 35:36:40:47 SD: 4.4250 cents 36:37:41:48 SD: 2.3391 cents 42:43:48:56 SD: 1.0314 cents 78:80:89:104 SD: 0.9255 cents 120:123:137:160 SD: 0.7014 cents 153:157:175:204 SD: 0.5496 cents 189:194:216:252 SD: 0.4578 cents 195:200:223:260 SD: 0.3698 cents 231:237:264:308 SD: 0.1873 cents 273:280:312:364 SD: 0.0000 cents