Scala analysis: 374_D2
Diatonic tetrachord 22/21 * 21/19 * 38/33
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22/21 80.537035 undecimal minor semitone 2: 22/19 253.804926 Godzilla third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 38/33 244.2401 1: 22/21 80.5370 undecimal minor semitone 2: 21/19 173.2679 3: 38/33 244.2401
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 21/19 173.268 cents 1: 1 38/33 244.240 cents 2: 1 22/19 253.805 cents Godzilla third 2: 1 76/63 324.777 cents 2: 1 14/11 417.508 cents undecimal diminished fourth or major 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 : 80.5 253.8 498.0 80.5 : 173.3 417.5 498.0 253.8: 244.2 324.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 244.2401 cents 133/121, 163.7030 cents 22/21, 80.5370 cents 2: 253.8049 .. 417.5080 cents 133/121, 163.7030 cents 363/361, 9.5649 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 38/33, 244.2401 cents Average / Smallest step : 2.061350 Largest / Average step : 1.471193 Largest / Smallest step : 3.032643 Median interval of one step : 21/19, 173.2679 cents, amount: 1 Least squares average step : 148.73442 cents, oct.: 446.20326 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1509-tone equal temperament with octave 4/3 degrees: 244 769 1509 Least number of segments generator : 755 of 249.188 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 893 of 294.734 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 : 1.049731 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.342617 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 minor thirds form a closed circle 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 : 63 (O: 21 U: 63) Highest odd numerator or denominator: 21 Scale harmonicity : 0.014872 Average absolute harmonicity : 0.088057 Specific harmonicity : 0.071888 Fundamental : 1/399, -8.6402 octaves, 0.6557 Hz. Guide tone : 44, 5.4594 octaves, 11511.525 Hz. Exponens Consonantiae : 1.755600E+04, 14.09968 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 45.5, average 15.16667 Mersenne's string divisions : 12341 Sum of van Prooijen's expressibility: 3.07809, average 1.02603 Sum of Tenney's harmonic distance : 6.36500, average 2.12167 Vogel's harmonic complexity : 27.00000 Wille's k value : 115 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 11.43222, average 1.90537 Lattice compactness (without 2's) : 9.02458, average 1.50410 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -1 .. 0 -0.66667 2 1 7: -1 .. 0 -0.33333 1 11: 0 .. 1 0.66667 2 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 18 25 30| Scale is weakly epimorphic with val: <6 10 18 25 33| Scale is weakly epimorphic with val: <6 10 18 26 29| Scale is weakly epimorphic with val: <6 10 19 26 28| Scale is weakly epimorphic with val: <6 10 19 26 31| Scale is weakly epimorphic with val: <6 10 19 26 34| Scale is weakly epimorphic with val: <6 10 19 27 30| Scale is weakly epimorphic with val: <6 10 20 25 28| Scale is weakly epimorphic with val: <6 10 20 27 29| Scale is weakly epimorphic with val: <6 10 20 27 32| Scale is weakly epimorphic with val: <6 10 21 26 29| Scale is weakly epimorphic with val: <6 10 22 27 30| Scale is weakly epimorphic with val: <6 11 18 25 28| Scale is weakly epimorphic with val: <6 11 18 26 30| Scale is weakly epimorphic with val: <6 11 18 26 33| Scale is weakly epimorphic with val: <6 11 19 26 29| Scale is weakly epimorphic with val: <6 11 19 27 28| Scale is weakly epimorphic with val: <6 11 19 27 31| Scale is weakly epimorphic with val: <6 11 19 27 34| Scale is weakly epimorphic with val: <6 11 20 27 30| Scale is weakly epimorphic with val: <6 11 21 25 28| Scale is weakly epimorphic with val: <6 11 22 26 29| Scale is weakly epimorphic with val: <7 10 18 24 29| Scale is weakly epimorphic with val: <7 10 18 24 32| Scale is weakly epimorphic with val: <7 10 18 26 30| Scale is weakly epimorphic with val: <7 10 19 24 28| Scale is weakly epimorphic with val: <7 10 19 25 30| Scale is weakly epimorphic with val: <7 10 19 25 33| Scale is weakly epimorphic with val: <7 10 19 27 31| Scale is weakly epimorphic with val: <7 10 20 25 29| Scale is weakly epimorphic with val: <7 10 20 26 28| Scale is weakly epimorphic with val: <7 10 20 26 31| Scale is weakly epimorphic with val: <7 10 20 26 34| Scale is weakly epimorphic with val: <7 10 21 26 30| Scale is weakly epimorphic with val: <7 10 21 27 29| Scale is weakly epimorphic with val: <7 10 21 27 32| Scale is weakly epimorphic with val: <7 10 22 24 28| Scale is weakly epimorphic with val: <7 10 22 27 31| Scale is JI-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 weakly 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 JI-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 weakly epimorphic with val: <7 11 19 27 32| Scale is weakly epimorphic with val: <7 11 20 23 29| Scale is weakly epimorphic with val: <7 11 20 23 32| Scale is JI-epimorphic with val: <7 11 20 25 30| Scale is weakly epimorphic with val: <7 11 20 25 33| Scale is weakly epimorphic with val: <7 11 20 26 29| Scale is weakly epimorphic with val: <7 11 20 26 32| Scale is weakly epimorphic with val: <7 11 21 23 28| Scale is weakly epimorphic with val: <7 11 21 23 31| Scale is weakly epimorphic with val: <7 11 21 23 34| Scale is weakly epimorphic with val: <7 11 21 24 30| Scale is weakly epimorphic with val: <7 11 21 24 33| Scale is weakly epimorphic with val: <7 11 21 26 28| Scale is JI-epimorphic with val: <7 11 21 26 31| Scale is weakly epimorphic with val: <7 11 21 26 34| Scale is weakly epimorphic with val: <7 11 21 27 30| Scale is weakly epimorphic with val: <7 11 21 27 33| Scale is weakly epimorphic with val: <7 11 22 24 29| Scale is weakly epimorphic with val: <7 11 22 24 32| Scale is weakly epimorphic with val: <7 11 22 25 28| Scale is weakly epimorphic with val: <7 11 22 25 31| Scale is weakly epimorphic with val: <7 11 22 25 34| Scale is weakly epimorphic with val: <7 11 22 27 29| Scale is JI-epimorphic with val: <7 11 22 27 32| Scale is weakly epimorphic with val: <7 12 18 24 28| Scale is weakly epimorphic with val: <7 12 18 26 29| Scale is weakly epimorphic with val: <7 12 18 26 32| Scale is weakly epimorphic with val: <7 12 18 27 31| Scale is weakly epimorphic with val: <7 12 19 25 29| Scale is weakly epimorphic with val: <7 12 19 27 30| Scale is weakly epimorphic with val: <7 12 19 27 33| Scale is weakly epimorphic with val: <7 12 20 26 30| Scale is weakly epimorphic with val: <7 12 21 24 28| Scale is weakly epimorphic with val: <7 12 21 27 31| Scale is weakly epimorphic with val: <7 12 22 25 29| Scale is weakly epimorphic with val: <8 11 18 24 28| Scale is weakly epimorphic with val: <8 11 18 24 31| Scale is weakly epimorphic with val: <8 11 18 24 34| Scale is weakly epimorphic with val: <8 11 18 25 30| Scale is weakly epimorphic with val: <8 11 19 23 28| Scale is weakly epimorphic with val: <8 11 19 25 29| Scale is weakly epimorphic with val: <8 11 19 25 32| Scale is weakly epimorphic with val: <8 11 19 26 31| Scale is weakly epimorphic with val: <8 11 20 24 29| Scale is weakly epimorphic with val: <8 11 20 26 30| Scale is weakly epimorphic with val: <8 11 20 26 33| Scale is weakly epimorphic with val: <8 11 20 27 32| Scale is weakly epimorphic with val: <8 11 21 25 30| Scale is weakly epimorphic with val: <8 11 21 27 28| Scale is weakly epimorphic with val: <8 11 21 27 31| Scale is weakly epimorphic with val: <8 11 21 27 34| Scale is weakly epimorphic with val: <8 11 22 23 28| Scale is weakly epimorphic with val: <8 11 22 26 31| Scale is weakly epimorphic with val: <8 12 18 24 29| Scale is weakly epimorphic with val: <8 12 18 25 28| Scale is weakly epimorphic with val: <8 12 18 25 31| Scale is weakly epimorphic with val: <8 12 18 25 34| Scale is weakly epimorphic with val: <8 12 18 27 32| Scale is weakly epimorphic with val: <8 12 19 25 30| Scale is weakly epimorphic with val: <8 12 19 26 29| Scale is weakly epimorphic with val: <8 12 19 26 32| Scale is weakly epimorphic with val: <8 12 20 23 28| Scale is weakly epimorphic with val: <8 12 20 26 31| Scale is weakly epimorphic with val: <8 12 20 27 30| Scale is weakly epimorphic with val: <8 12 20 27 33| Scale is weakly epimorphic with val: <8 12 21 24 29| Scale is weakly epimorphic with val: <8 12 21 27 32| Scale is weakly epimorphic with val: <8 12 22 25 30|
FIT/MODE
3: 0 1 2 N G T3 SD: 68.7830 c. M: 87.7899 c. 4: 1 1 2 P M ME S SD: 25.5382 c. M:-43.9742 c. 5: 1 2 2 SP M ME S SD: 28.2296 c. M:-45.0221 c. 6: 1 2 3 P T3 SD: 3.1078 c. M: 4.7824 c. 25: 4 9 12 SP T3 SD: 3.0298 c. M:-5.1785 c. 26: 4 9 13 P T3 SD: 3.5682 c. M: 4.7824 c. 31: 5 11 15 SP T3 SD: 1.8805 c. M:-3.2506 c. 37: 6 13 18 SP T3 SD: 1.1322 c. M:-1.9479 c. 43: 7 15 21 SP T3 SD: 0.6606 c. M:-1.0088 c. 49: 8 17 24 SP T3 SD: 0.4805 c. M:-0.7764 c. 92: 15 32 45 SP T3 SD: 0.5297 c. M:-0.6660 c. 100: 16 35 49 SP T3 SD: 0.5038 c. M: 0.8498 c. 106: 17 37 52 SP T3 SD: 0.3852 c. M: 0.6619 c. 112: 18 39 55 SP T3 SD: 0.3448 c. M: 0.4941 c. 143: 23 50 70 SP T3 SD: 0.3567 c. M:-0.4418 c. 149: 24 52 73 SP T3 SD: 0.2257 c. M: 0.3150 c. 155: 25 54 76 SP T3 SD: 0.1216 c. M: 0.2072 c. 161: 26 56 79 SP T3 SD: 0.1029 c. M: 0.1423 c. 204: 33 71 100 SP T3 SD: 0.0603 c. M:-0.1004 c. 210: 34 73 103 SP T3 SD: 0.0614 c. M:-0.0988 c. 359: 58 125 176 SP T3 SD: 0.0596 c. M:-0.0732 c. 365: 59 127 179 SP T3 SD: 0.0184 c. M: 0.0311 c. 575: 93 200 282 SP T3 SD: 0.0143 c. M: 0.0185 c. 779: 126 271 382 SP T3 SD: 0.0135 c. M:-0.0197 c. 934: 151 325 458 SP T3 SD: 0.0142 c. M: 0.0180 c. 940: 152 327 461 SP T3 SD: 0.0081 c. M: 0.0139 c. 1144: 185 398 561 SP T3 SD: 0.0042 c. M:-0.0065 c. 1509: 244 525 740 SP T3 SD: 0.0034 c. M: 0.0049 c. 2084: 337 725 1022 SP T3 SD: 0.0017 c. M: 0.0027 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 x 9:11 SD: 36.4949 cents 9 x 10:12 S SD: 35.7006 cents 11:12:13:15 SD: 29.2141 cents 12:13:14:16 S SD: 19.8294 cents 13:14:15:17 SD: 19.5733 cents 14:15:16:19 SD: 18.1498 cents 15:16:17:20 SD: 16.1618 cents 17:18:20:23 SD: 13.8931 cents 18:19:21:24 SD: 6.1594 cents 24:25:28:32 SD: 5.4572 cents 38:40:44:51 SD: 4.6805 cents 39:41:45:52 SD: 2.8536 cents 45:47:52:60 SD: 2.1046 cents 63:66:73:84 SD: 0.4162 cents 210:220:243:280 SD: 0.3748 cents 228:239:264:304 SD: 0.3450 cents 273:286:316:364 SD: 0.1922 cents 336:352:389:448 SD: 0.0781 cents 399:418:462:532 SD: 0.0000 cents