Scala analysis: 345_C28
Chromatic tetrachord 40/39 * 247/220 * 22/19
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: 38/33 244.240073 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 22/19 253.8049 Godzilla third 1: 40/39 43.8311 tridecimal minor diesis 2: 247/220 200.4090 3: 22/19 253.8049 Godzilla third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 247/220 200.409 cents 1: 1 22/19 253.805 cents Godzilla third 2: 1 38/33 244.240 cents 2: 1 880/741 297.636 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 : 43.8 244.2 498.0 43.8 : 200.4 454.2 498.0 244.2: 253.8 297.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 253.8049 cents 429/380, 209.9739 cents 40/39, 43.8311 cents 2: 244.2401 .. 454.2139 cents 429/380, 209.9739 cents 361/363,-9.5649 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 : 22/19, 253.8049 cents Average / Smallest step : 3.787612 Largest / Average step : 1.528807 Largest / Smallest step : 5.790528 Median interval of one step : 247/220, 200.4090 cents, amount: 1 Least squares average step : 144.74616 cents, oct.: 434.23847 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1250-tone equal temperament with octave 4/3 degrees: 110 613 1250 Least number of segments generator : 627 of 249.819 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 739 of 294.444 cents and inv. generated superset size: 34 = 31 more = 1133.333% 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 9.56485 cents Scale diversity : 0.690655 Lumma stability : 0.176012 Lumma impropriety factor : 0.019205 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 : 363/361, 9.5649 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% -- Rational properties -- Prime limit : 19 Odd number limit : 741 (O: 247 U: 741) Highest odd numerator or denominator: 39 Scale harmonicity : 0.011560 Average absolute harmonicity : 0.087126 Specific harmonicity : 0.061415 Fundamental : 1/429, -8.7448 octaves, 0.6098 Hz. Guide tone : 760, 9.5699 octaves, 198835.430 Hz. Exponens Consonantiae : 3.260400E+05, 18.31469 octaves Euler's gradus suavitatis : 50 Sum of Mann's harmonic distance : 78.5, average 26.16667 Mersenne's string divisions : 39263 Sum of van Prooijen's expressibility: 3.58670, average 1.19557 Sum of Tenney's harmonic distance : 7.37060, average 2.45687 Vogel's harmonic complexity : 26.00000 Wille's k value : 123 Wilson's harmonic complexity : 51 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 13.99270, average 2.33212 Lattice compactness (without 2's) : 9.29253, average 1.54875 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -1 ..-1 -1.00000 3 1 5: 0 .. 1 0.33333 1 11: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 1 19: 0 .. 1 0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 11 16 24 27 32| Scale is weakly epimorphic with val: <7 11 16 24 28 30| Scale is weakly epimorphic with val: <7 11 16 25 27 30| Scale is weakly epimorphic with val: <7 11 16 25 28 31| Scale is weakly epimorphic with val: <7 11 16 26 27 31| Scale is weakly epimorphic with val: <7 11 16 26 28 32| Scale is JI-epimorphic with val: <7 11 17 24 26 30| Scale is weakly epimorphic with val: <7 11 17 24 28 32| Scale is JI-epimorphic with val: <7 11 17 25 26 31| Scale is weakly epimorphic with val: <7 11 17 25 28 30| Scale is JI-epimorphic with val: <7 11 17 26 26 32| Scale is weakly epimorphic with val: <7 11 17 26 28 31| Scale is weakly epimorphic with val: <7 11 18 24 26 32| Scale is JI-epimorphic with val: <7 11 18 24 27 30| Scale is weakly epimorphic with val: <7 11 18 25 26 30| Scale is JI-epimorphic with val: <7 11 18 25 27 31| Scale is weakly epimorphic with val: <7 11 18 26 26 31| Scale is JI-epimorphic with val: <7 11 18 26 27 32| Scale is weakly epimorphic with val: <7 12 16 24 27 32| Scale is weakly epimorphic with val: <7 12 17 24 28 32| Scale is weakly epimorphic with val: <7 12 18 24 26 32|
FIT/MODE
3: 0 1 2 N G T3 SD: 51.7698 c. M: 78.2251 c. 4: 0 2 2 P M DE S SD: 25.4561 c. M: 43.8311 c. 6: 1 2 3 P T3 SD: 22.7864 c. M:-39.1764 c. 7: 1 2 4 N T3 SD: 23.7658 c. M: 30.7922 c. 8: 1 3 4 P T3 SD: 10.9899 c. M:-18.4246 c. 10: 1 4 5 P T3 SD: 4.4179 c. M:-5.9734 c. 12: 1 5 6 P T3 SD: 3.0707 c. M:-4.7824 c. 22: 2 9 11 P T3 SD: 2.8845 c. M:-4.7824 c. 31: 3 12 16 N T3 SD: 3.1430 c. M:-4.3669 c. 32: 3 13 16 P T3 SD: 3.2174 c. M:-4.7824 c. 33: 3 13 17 N T3 SD: 1.8008 c. M: 2.7637 c. 35: 3 14 18 N T3 SD: 1.4993 c. M: 2.3325 c. 45: 4 18 23 N T3 SD: 0.5026 c. M: 0.7514 c. 57: 5 23 29 N T3 SD: 0.2526 c. M:-0.4136 c. 102: 9 41 52 N T3 SD: 0.0877 c. M:-0.1141 c. 159: 14 64 81 N T3 SD: 0.0501 c. M:-0.0839 c. 261: 23 105 133 N T3 SD: 0.0342 c. M:-0.0580 c. 420: 37 169 214 N T3 SD: 0.0341 c. M:-0.0443 c. 671: 59 270 342 N T3 SD: 0.0330 c. M: 0.0422 c. 728: 64 293 371 N T3 SD: 0.0273 c. M: 0.0469 c. 830: 73 334 423 N T3 SD: 0.0188 c. M: 0.0271 c. 932: 82 375 475 N T3 SD: 0.0170 c. M: 0.0270 c. 989: 87 398 504 N T3 SD: 0.0111 c. M: 0.0192 c. 1091: 96 439 556 N T3 SD: 0.0074 c. M: 0.0109 c. 1250: 110 503 637 N T3 SD: 0.0019 c. M: 0.0031 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: 55.3011 cents 6 x 7:8 S SD: 11.3154 cents 7 x 8:9 S SD: 32.1512 cents 8 x 9:11 SD: 33.4085 cents 9 x 10:12 S SD: 30.9182 cents 10 x 12:13 S SD: 41.8906 cents 11 x 13:15 SD: 29.7318 cents 14:15:16:19 SD: 27.5415 cents 15:16:17:20 SD: 24.4259 cents 17:18:20:23 SD: 23.6998 cents 18:19:21:24 SD: 18.2251 cents 19:20:22:25 SD: 17.1256 cents 20:21:23:27 SD: 15.3442 cents 21:22:24:28 S SD: 12.9874 cents 24:25:28:32 SD: 11.7029 cents 25:26:29:33 SD: 10.7683 cents 26:27:30:35 S SD: 9.1241 cents 27:28:31:36 SD: 6.5967 cents 32:33:37:43 SD: 5.9734 cents 33:34:38:44 SD: 2.6171 cents 39:40:45:52 SD: 1.1670 cents 111:114:128:148 SD: 1.1315 cents 120:123:138:160 SD: 0.8411 cents 153:157:176:204 SD: 0.6596 cents 159:163:183:212 SD: 0.3953 cents 192:197:221:256 SD: 0.3273 cents 198:203:228:264 SD: 0.2186 cents 231:237:266:308 SD: 0.1873 cents 390:400:449:520 SD: 0.1168 cents 429:440:494:572 SD: 0.0000 cents