Scala analysis: 373_D2
Diatonic tetrachord 11/10 * 20/19 * 38/33
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 22/19 253.804926 Godzilla third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 38/33 244.2401 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 20/19 88.8007 small undevicesimal semitone 3: 38/33 244.2401
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 20/19 88.801 cents small undevicesimal semitone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 38/33 244.240 cents 2: 1 22/19 253.805 cents Godzilla third 2: 1 40/33 333.041 cents 2: 1 19/15 409.244 cents undevicesimal ditone 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 : 165.0 253.8 498.0 165.0: 88.8 333.0 498.0 253.8: 244.2 409.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.8007 .. 244.2401 cents 361/330, 155.4394 cents 20/19, 88.8007 cents 2: 253.8049 .. 409.2443 cents 361/330, 155.4394 cents 363/361, 9.5649 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 20/19, 88.8007 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 38/33, 244.2401 cents Average / Smallest step : 1.869524 Largest / Average step : 1.471193 Largest / Smallest step : 2.750430 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 154.76779 cents, oct.: 464.30337 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1980-tone equal temperament with octave 4/3 degrees: 656 1009 1980 Least number of segments generator : 991 of 249.274 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1753 of 440.946 cents and inv. generated superset size: 33 = 30 more = 1100.000% 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 9.56485 cents Scale diversity : 1.111271 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.375802 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 Best fifths form a closed circle 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 : 19 Odd number limit : 33 (O: 19 U: 33) Highest odd numerator or denominator: 19 Scale harmonicity : 0.015539 Average absolute harmonicity : 0.090714 Specific harmonicity : 0.075385 Fundamental : 1/570, -9.1548 octaves, 0.4590 Hz. Guide tone : 44, 5.4594 octaves, 11511.525 Hz. Exponens Consonantiae : 2.508000E+04, 14.61425 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 34.5, average 11.50000 Mersenne's string divisions : 861 Sum of van Prooijen's expressibility: 2.79727, average 0.93242 Sum of Tenney's harmonic distance : 5.74175, average 1.91392 Vogel's harmonic complexity : 27.00000 Wille's k value : 313 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.61376, average 2.26896 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 0.66667 4 3: -1 .. 0 -0.33333 1 1 5: -1 .. 0 -0.33333 1 11: 0 .. 1 0.66667 2 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 15 24 29| Scale is weakly epimorphic with val: <6 10 15 24 32| Scale is weakly epimorphic with val: <6 10 15 25 28| Scale is weakly epimorphic with val: <6 10 16 25 30| Scale is weakly epimorphic with val: <6 10 16 25 33| Scale is weakly epimorphic with val: <6 10 16 26 29| Scale is weakly epimorphic with val: <6 10 17 26 28| Scale is weakly epimorphic with val: <6 10 17 26 31| Scale is weakly epimorphic with val: <6 10 17 26 34| Scale is weakly epimorphic with val: <6 10 17 27 30| Scale is weakly epimorphic with val: <6 10 18 25 28| Scale is weakly epimorphic with val: <6 10 18 27 29| Scale is weakly epimorphic with val: <6 10 18 27 32| Scale is weakly epimorphic with val: <6 10 19 26 29| Scale is weakly epimorphic with val: <6 11 15 24 28| Scale is weakly epimorphic with val: <6 11 15 24 31| Scale is weakly epimorphic with val: <6 11 15 24 34| Scale is weakly epimorphic with val: <6 11 15 26 29| Scale is weakly epimorphic with val: <6 11 16 25 29| Scale is weakly epimorphic with val: <6 11 16 25 32| Scale is weakly epimorphic with val: <6 11 16 27 30| Scale is weakly epimorphic with val: <6 11 17 25 28| Scale is weakly epimorphic with val: <6 11 17 26 30| Scale is weakly epimorphic with val: <6 11 17 26 33| Scale is weakly epimorphic with val: <6 11 18 26 29| Scale is weakly epimorphic with val: <6 11 18 27 28| Scale is weakly epimorphic with val: <6 11 18 27 31| Scale is weakly epimorphic with val: <6 11 18 27 34| Scale is weakly epimorphic with val: <6 11 19 27 30| Scale is weakly epimorphic with val: <7 10 15 24 28| Scale is weakly epimorphic with val: <7 10 15 25 30| Scale is weakly epimorphic with val: <7 10 15 25 33| Scale is weakly epimorphic with val: <7 10 15 27 31| Scale is weakly epimorphic with val: <7 10 16 25 29| Scale is weakly epimorphic with val: <7 10 16 26 28| Scale is weakly epimorphic with val: <7 10 16 26 31| Scale is weakly epimorphic with val: <7 10 16 26 34| Scale is weakly epimorphic with val: <7 10 17 26 30| Scale is weakly epimorphic with val: <7 10 17 27 29| Scale is weakly epimorphic with val: <7 10 17 27 32| Scale is weakly epimorphic with val: <7 10 18 24 28| Scale is weakly epimorphic with val: <7 10 18 27 31| Scale is weakly epimorphic with val: <7 10 19 25 29| Scale is JI-epimorphic with val: <7 11 15 23 28| Scale is weakly epimorphic with val: <7 11 15 23 31| Scale is weakly epimorphic with val: <7 11 15 23 34| Scale is weakly epimorphic with val: <7 11 15 24 30| Scale is weakly epimorphic with val: <7 11 15 24 33| Scale is weakly epimorphic with val: <7 11 15 26 28| Scale is weakly epimorphic with val: <7 11 15 26 31| Scale is weakly epimorphic with val: <7 11 15 26 34| Scale is weakly epimorphic with val: <7 11 15 27 30| Scale is weakly epimorphic with val: <7 11 15 27 33| Scale is JI-epimorphic with val: <7 11 16 24 29| Scale is weakly epimorphic with val: <7 11 16 24 32| Scale is weakly epimorphic with val: <7 11 16 25 28| Scale is weakly epimorphic with val: <7 11 16 25 31| Scale is weakly epimorphic with val: <7 11 16 25 34| Scale is weakly epimorphic with val: <7 11 16 27 29| Scale is weakly epimorphic with val: <7 11 16 27 32| Scale is weakly epimorphic with val: <7 11 17 23 29| Scale is weakly epimorphic with val: <7 11 17 23 32| Scale is JI-epimorphic with val: <7 11 17 25 30| Scale is weakly epimorphic with val: <7 11 17 25 33| Scale is weakly epimorphic with val: <7 11 17 26 29| Scale is weakly epimorphic with val: <7 11 17 26 32| Scale is weakly epimorphic with val: <7 11 18 23 28| Scale is weakly epimorphic with val: <7 11 18 23 31| Scale is weakly epimorphic with val: <7 11 18 23 34| Scale is weakly epimorphic with val: <7 11 18 24 30| Scale is weakly epimorphic with val: <7 11 18 24 33| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is JI-epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 26 34| Scale is weakly epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 18 27 33| Scale is weakly epimorphic with val: <7 11 19 24 29| Scale is weakly epimorphic with val: <7 11 19 24 32| Scale is weakly epimorphic with val: <7 11 19 25 28| Scale is weakly epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 25 34| Scale is weakly epimorphic with val: <7 11 19 27 29| Scale is JI-epimorphic with val: <7 11 19 27 32| Scale is weakly epimorphic with val: <7 12 15 25 28| Scale is weakly epimorphic with val: <7 12 15 25 31| Scale is weakly epimorphic with val: <7 12 15 25 34| Scale is weakly epimorphic with val: <7 12 15 26 30| Scale is weakly epimorphic with val: <7 12 16 24 28| Scale is weakly epimorphic with val: <7 12 16 26 29| Scale is weakly epimorphic with val: <7 12 16 26 32| Scale is weakly epimorphic with val: <7 12 16 27 31| Scale is weakly epimorphic with val: <7 12 17 25 29| Scale is weakly epimorphic with val: <7 12 17 27 30| Scale is weakly epimorphic with val: <7 12 17 27 33| Scale is weakly epimorphic with val: <7 12 18 26 30| Scale is weakly epimorphic with val: <7 12 19 24 28| Scale is weakly epimorphic with val: <7 12 19 27 31| Scale is weakly epimorphic with val: <8 11 15 24 29| Scale is weakly epimorphic with val: <8 11 15 26 30| Scale is weakly epimorphic with val: <8 11 15 26 33| Scale is weakly epimorphic with val: <8 11 15 27 32| Scale is weakly epimorphic with val: <8 11 16 25 30| Scale is weakly epimorphic with val: <8 11 16 27 28| Scale is weakly epimorphic with val: <8 11 16 27 31| Scale is weakly epimorphic with val: <8 11 16 27 34| Scale is weakly epimorphic with val: <8 11 17 23 28| Scale is weakly epimorphic with val: <8 11 17 26 31| Scale is weakly epimorphic with val: <8 11 18 24 29| Scale is weakly epimorphic with val: <8 11 18 27 32| Scale is weakly epimorphic with val: <8 11 19 25 30| Scale is weakly epimorphic with val: <8 12 15 25 30| Scale is weakly epimorphic with val: <8 12 15 26 29| Scale is weakly epimorphic with val: <8 12 15 26 32| Scale is weakly epimorphic with val: <8 12 16 23 28| Scale is weakly epimorphic with val: <8 12 16 26 31| Scale is weakly epimorphic with val: <8 12 16 27 30| Scale is weakly epimorphic with val: <8 12 16 27 33| Scale is weakly epimorphic with val: <8 12 17 24 29| Scale is weakly epimorphic with val: <8 12 17 27 32| Scale is weakly epimorphic with val: <8 12 18 25 30| Scale is weakly epimorphic with val: <8 12 19 23 28| Scale is weakly epimorphic with val: <8 12 19 26 31|
FIT/MODE
3: 1 1 1 SP B ME I SD: 45.1670 c. M:-78.2251 c. 4: 1 1 2 P M ME S SD: 23.5411 c. M: 40.4930 c. 6: 2 1 3 P T3 SD: 2.8221 c. M: 4.7824 c. 27: 9 5 13 SP T3 SD: 2.6294 c. M:-4.4406 c. 31: 10 6 15 SP T3 SD: 3.1327 c. M: 4.3446 c. 33: 11 6 16 SP T3 SD: 1.6990 c. M:-2.7637 c. 39: 13 7 19 SP T3 SD: 1.0940 c. M:-1.6028 c. 45: 15 8 22 SP T3 SD: 0.7272 c. M:-1.0108 c. 51: 17 9 25 SP T3 SD: 0.5864 c. M:-1.0108 c. 88: 29 16 43 SP T3 SD: 0.7156 c. M:-0.8772 c. 94: 31 17 46 SP T3 SD: 0.5281 c. M: 0.7553 c. 96: 32 17 47 SP T3 SD: 0.6288 c. M:-1.0108 c. 100: 33 18 49 SP T3 SD: 0.3920 c. M: 0.6494 c. 106: 35 19 52 SP T3 SD: 0.3243 c. M: 0.5554 c. 112: 37 20 55 SP T3 SD: 0.3341 c. M: 0.4715 c. 145: 48 26 71 SP T3 SD: 0.2271 c. M:-0.3698 c. 151: 50 27 74 SP T3 SD: 0.1082 c. M:-0.1650 c. 157: 52 28 77 SP T3 SD: 0.0303 c. M: 0.0466 c. 516: 171 92 253 SP T3 SD: 0.0364 c. M:-0.0456 c. 522: 173 93 256 SP T3 SD: 0.0334 c. M:-0.0567 c. 673: 223 120 330 SP T3 SD: 0.0212 c. M:-0.0278 c. 679: 225 121 333 SP T3 SD: 0.0207 c. M:-0.0328 c. 830: 275 148 407 SP T3 SD: 0.0121 c. M:-0.0180 c. 836: 277 149 410 SP T3 SD: 0.0140 c. M:-0.0179 c. 987: 327 176 484 SP T3 SD: 0.0066 c. M:-0.0113 c. 1144: 379 204 561 SP T3 SD: 0.0047 c. M:-0.0065 c. 1823: 604 325 894 SP T3 SD: 0.0053 c. M:-0.0090 c. 1980: 656 353 971 SP T3 SD: 0.0032 c. M:-0.0046 c. 2137: 708 381 1048 SP T3 SD: 0.0028 c. M: 0.0047 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: 52.3413 cents 6 x 7:8 S SD: 6.5330 cents 7 x 8:9 S SD: 33.4523 cents 8:9 x 11 SD: 32.9836 cents 9:10 x 12 S SD: 8.6997 cents 15 x 17:20 SD: 18.5591 cents 17:19:20:23 SD: 15.4817 cents 18:20:21:24 S SD: 7.2531 cents 30:33:35:40 SD: 4.3553 cents 39:43:45:52 SD: 2.4271 cents 51:56:59:68 SD: 1.1510 cents 69:76:80:92 SD: 1.0745 cents 108:119:125:144 SD: 1.0006 cents 120:132:139:160 SD: 0.2185 cents 279:307:323:372 SD: 0.2102 cents 291:320:337:388 SD: 0.2016 cents 330:363:382:440 SD: 0.1590 cents 399:439:462:532 SD: 0.1315 cents 450:495:521:600 SD: 0.0583 cents 570:627:660:760 SD: 0.0000 cents