Scala analysis: 344_C28
Chromatic tetrachord 34/33 * 19/17 * 22/19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 34/33 51.682466 2: 38/33 244.240073 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 22/19 253.8049 Godzilla third 1: 34/33 51.6825 2: 19/17 192.5576 quasi-meantone 3: 22/19 253.8049 Godzilla third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 34/33 51.682 cents 1: 1 19/17 192.558 cents quasi-meantone 1: 1 22/19 253.805 cents Godzilla third 2: 1 38/33 244.240 cents 2: 1 68/57 305.487 cents 2: 1 22/17 446.363 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 : 51.7 244.2 498.0 51.7 : 192.6 446.4 498.0 244.2: 253.8 305.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.6825 .. 253.8049 cents 363/323, 202.1225 cents 34/33, 51.6825 cents 2: 244.2401 .. 446.3625 cents 363/323, 202.1225 cents 361/363,-9.5649 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 34/33, 51.6825 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 22/19, 253.8049 cents Average / Smallest step : 3.212211 Largest / Average step : 1.528807 Largest / Smallest step : 4.910852 Median interval of one step : 19/17, 192.5576 cents, amount: 1 Least squares average step : 145.30697 cents, oct.: 435.92092 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1301-tone equal temperament with octave 4/3 degrees: 135 638 1301 Least number of segments generator : 651 of 249.214 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1166 of 446.365 cents and inv. generated superset size: 25 = 22 more = 833.333% 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 : 0.780501 Lumma stability : 0.207541 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 : 57 (O: 19 U: 57) Highest odd numerator or denominator: 33 Scale harmonicity : 0.011485 Average absolute harmonicity : 0.083800 Specific harmonicity : 0.057266 Fundamental : 1/33, -5.0444 octaves, 7.9280 Hz. Guide tone : 1292, 10.3354 octaves, 338020.230 Hz. Exponens Consonantiae : 4.263600E+04, 15.37978 octaves Euler's gradus suavitatis : 49 Sum of Mann's harmonic distance : 72.5, average 24.16667 Mersenne's string divisions : 33299 Sum of van Prooijen's expressibility: 3.51415, average 1.17138 Sum of Tenney's harmonic distance : 7.22747, average 2.40916 Vogel's harmonic complexity : 17.00000 Wille's k value : 9 Wilson's harmonic complexity : 50 Rectangular lattice diameter : 4 Triangular lattice diameter : 1 Lattice compactness : 11.11438, average 1.85240 Lattice compactness (without 2's) : 8.70674, average 1.45112 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -1 ..-1 -1.00000 3 1 11: -1 .. 0 -0.66667 2 17: 0 .. 1 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: <6 10 23 28 30| Scale is weakly epimorphic with val: <6 10 23 30 31| Scale is weakly epimorphic with val: <6 10 23 30 34| Scale is weakly epimorphic with val: <6 10 24 29 31| Scale is weakly epimorphic with val: <6 10 24 31 32| Scale is weakly epimorphic with val: <6 10 25 27 32| Scale is weakly epimorphic with val: <6 10 25 30 32| Scale is weakly epimorphic with val: <6 10 25 32 33| Scale is weakly epimorphic with val: <6 10 26 28 33| Scale is weakly epimorphic with val: <6 10 26 31 33| Scale is weakly epimorphic with val: <6 10 26 33 34| Scale is weakly epimorphic with val: <6 10 27 29 34| Scale is weakly epimorphic with val: <6 10 27 32 34| Scale is weakly epimorphic with val: <6 11 23 27 31| Scale is weakly epimorphic with val: <6 11 23 30 31| Scale is weakly epimorphic with val: <6 11 23 31 33| Scale is weakly epimorphic with val: <6 11 24 28 32| Scale is weakly epimorphic with val: <6 11 24 31 32| Scale is weakly epimorphic with val: <6 11 24 32 34| Scale is weakly epimorphic with val: <6 11 25 29 33| Scale is weakly epimorphic with val: <6 11 25 32 33| Scale is weakly epimorphic with val: <6 11 26 27 34| Scale is weakly epimorphic with val: <6 11 26 30 34| Scale is weakly epimorphic with val: <6 11 26 33 34| Scale is weakly epimorphic with val: <7 10 23 28 29| Scale is weakly epimorphic with val: <7 10 23 29 31| Scale is weakly epimorphic with val: <7 10 23 29 34| Scale is weakly epimorphic with val: <7 10 24 29 30| Scale is weakly epimorphic with val: <7 10 24 30 32| Scale is weakly epimorphic with val: <7 10 25 27 31| Scale is weakly epimorphic with val: <7 10 25 30 31| Scale is weakly epimorphic with val: <7 10 25 31 33| Scale is weakly epimorphic with val: <7 10 26 28 32| Scale is weakly epimorphic with val: <7 10 26 31 32| Scale is weakly epimorphic with val: <7 10 26 32 34| Scale is weakly epimorphic with val: <7 10 27 29 33| Scale is weakly epimorphic with val: <7 10 27 32 33| Scale is JI-epimorphic with val: <7 11 23 28 29| Scale is weakly epimorphic with val: <7 11 23 28 32| Scale is weakly epimorphic with val: <7 11 23 29 31| Scale is weakly epimorphic with val: <7 11 23 29 34| Scale is weakly epimorphic with val: <7 11 23 31 32| Scale is weakly epimorphic with val: <7 11 23 32 34| Scale is weakly epimorphic with val: <7 11 24 27 29| Scale is weakly epimorphic with val: <7 11 24 27 32| Scale is JI-epimorphic with val: <7 11 24 29 30| Scale is weakly epimorphic with val: <7 11 24 29 33| Scale is weakly epimorphic with val: <7 11 24 30 32| Scale is weakly epimorphic with val: <7 11 24 32 33| Scale is weakly epimorphic with val: <7 11 25 27 28| Scale is weakly epimorphic with val: <7 11 25 27 31| Scale is weakly epimorphic with val: <7 11 25 27 34| Scale is weakly epimorphic with val: <7 11 25 28 30| Scale is weakly epimorphic with val: <7 11 25 28 33| Scale is JI-epimorphic with val: <7 11 25 30 31| = patent Scale is weakly epimorphic with val: <7 11 25 30 34| Scale is weakly epimorphic with val: <7 11 25 31 33| Scale is weakly epimorphic with val: <7 11 25 33 34| Scale is weakly epimorphic with val: <7 11 26 28 29| Scale is weakly epimorphic with val: <7 11 26 28 32| Scale is weakly epimorphic with val: <7 11 26 29 31| Scale is weakly epimorphic with val: <7 11 26 29 34| Scale is JI-epimorphic with val: <7 11 26 31 32| Scale is weakly epimorphic with val: <7 11 26 32 34| Scale is weakly epimorphic with val: <7 11 27 27 29| Scale is weakly epimorphic with val: <7 11 27 27 32| Scale is weakly epimorphic with val: <7 11 27 29 30| Scale is weakly epimorphic with val: <7 11 27 29 33| Scale is weakly epimorphic with val: <7 11 27 30 32| Scale is JI-epimorphic with val: <7 11 27 32 33| Scale is weakly epimorphic with val: <7 12 23 29 31| Scale is weakly epimorphic with val: <7 12 23 31 32| Scale is weakly epimorphic with val: <7 12 24 27 32| Scale is weakly epimorphic with val: <7 12 24 30 32| Scale is weakly epimorphic with val: <7 12 24 32 33| Scale is weakly epimorphic with val: <7 12 25 28 33| Scale is weakly epimorphic with val: <7 12 25 31 33| Scale is weakly epimorphic with val: <7 12 25 33 34| Scale is weakly epimorphic with val: <7 12 26 29 34| Scale is weakly epimorphic with val: <7 12 26 32 34| Scale is weakly epimorphic with val: <8 11 23 27 29| Scale is weakly epimorphic with val: <8 11 23 29 30| Scale is weakly epimorphic with val: <8 11 23 29 33| Scale is weakly epimorphic with val: <8 11 24 28 30| Scale is weakly epimorphic with val: <8 11 24 30 31| Scale is weakly epimorphic with val: <8 11 24 30 34| Scale is weakly epimorphic with val: <8 11 25 29 31| Scale is weakly epimorphic with val: <8 11 25 31 32| Scale is weakly epimorphic with val: <8 11 26 27 32| Scale is weakly epimorphic with val: <8 11 26 30 32| Scale is weakly epimorphic with val: <8 11 26 32 33| Scale is weakly epimorphic with val: <8 11 27 28 33| Scale is weakly epimorphic with val: <8 11 27 31 33| Scale is weakly epimorphic with val: <8 11 27 33 34| Scale is weakly epimorphic with val: <8 12 23 29 30| Scale is weakly epimorphic with val: <8 12 23 30 32| Scale is weakly epimorphic with val: <8 12 24 27 31| Scale is weakly epimorphic with val: <8 12 24 30 31| Scale is weakly epimorphic with val: <8 12 24 31 33| Scale is weakly epimorphic with val: <8 12 25 28 32| Scale is weakly epimorphic with val: <8 12 25 31 32| Scale is weakly epimorphic with val: <8 12 25 32 34| Scale is weakly epimorphic with val: <8 12 26 29 33| Scale is weakly epimorphic with val: <8 12 26 32 33| Scale is weakly epimorphic with val: <8 12 27 27 34| Scale is weakly epimorphic with val: <8 12 27 30 34| Scale is weakly epimorphic with val: <8 12 27 33 34|
FIT/MODE
3: 0 1 2 N G T3 SD: 54.1302 c. M: 78.2251 c. 4: 0 2 2 P M DE S SD: 29.9664 c. M: 51.6825 c. 6: 1 2 3 P T3 SD: 18.2951 c. M:-31.3250 c. 7: 1 2 4 N T3 SD: 21.0327 c. M: 30.7922 c. 8: 1 3 4 P T3 SD: 6.6998 c. M:-10.5732 c. 10: 1 4 5 P T3 SD: 2.9664 c. M:-4.7824 c. 18: 2 7 9 P T3 SD: 3.4755 c. M:-4.7824 c. 27: 3 10 14 N T3 SD: 3.3209 c. M: 4.4406 c. 28: 3 11 14 P T3 SD: 2.9264 c. M:-4.7824 c. 29: 3 11 15 N T3 SD: 2.1985 c. M: 3.8046 c. 31: 3 12 16 N T3 SD: 2.7513 c. M: 3.4846 c. 37: 4 14 19 N T3 SD: 1.6794 c. M:-2.1602 c. 39: 4 15 20 N T3 SD: 0.9883 c. M: 1.6028 c. 47: 5 18 24 N T3 SD: 0.8081 c. M:-1.3010 c. 49: 5 19 25 N T3 SD: 0.5266 c. M: 0.8615 c. 57: 6 22 29 N T3 SD: 0.4911 c. M:-0.7433 c. 96: 10 37 49 N T3 SD: 0.2604 c. M: 0.4055 c. 106: 11 41 54 N T3 SD: 0.0484 c. M:-0.0839 c. 308: 32 119 157 N T3 SD: 0.0536 c. M: 0.0687 c. 414: 43 160 211 N T3 SD: 0.0320 c. M:-0.0468 c. 520: 54 201 265 N T3 SD: 0.0220 c. M:-0.0376 c. 626: 65 242 319 N T3 SD: 0.0189 c. M:-0.0315 c. 732: 76 283 373 N T3 SD: 0.0194 c. M:-0.0271 c. 781: 81 302 398 N T3 SD: 0.0165 c. M: 0.0286 c. 887: 92 343 452 N T3 SD: 0.0155 c. M: 0.0250 c. 993: 103 384 506 N T3 SD: 0.0164 c. M: 0.0222 c. 1089: 113 421 555 N T3 SD: 0.0115 c. M: 0.0197 c. 1195: 124 462 609 N T3 SD: 0.0062 c. M: 0.0105 c. 1301: 135 503 663 N T3 SD: 0.0020 c. M: 0.0028 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 13:14:15:17 SD: 27.9133 cents 14:15:16:19 SD: 25.1686 cents 15:16:17:20 SD: 22.0228 cents 17:18:20:23 SD: 21.7337 cents 18:19:21:24 SD: 15.8797 cents 19:20:22:25 SD: 14.8887 cents 20:21:23:27 SD: 13.0918 cents 21:22:24:28 S SD: 10.5583 cents 24:25:28:32 SD: 9.8476 cents 25:26:29:33 SD: 8.9895 cents 26:27:30:35 S SD: 7.2509 cents 27:28:31:36 SD: 4.1218 cents 33:34:38:44 SD: 0.0000 cents