Scala analysis: 127_E15
Enharmonic tetrachord 40/39 * 117/112 * 56/45
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: 15/14 119.442808 major diatonic semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 56/45 378.6022 septimal narrow major third 1: 40/39 43.8311 tridecimal minor diesis 2: 117/112 75.6118 3: 56/45 378.6022 septimal narrow major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 117/112 75.612 cents 1: 1 56/45 378.602 cents septimal narrow major third 2: 1 15/14 119.443 cents major diatonic semitone 2: 1 448/351 422.433 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 : 43.8 119.4 498.0 43.8 : 75.6 454.2 498.0 119.4: 378.6 422.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 378.6022 cents 91/75, 334.7711 cents 40/39, 43.8311 cents 2: 119.4428 .. 454.2139 cents 91/75, 334.7711 cents 675/784,-259.1594 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 : 56/45, 378.6022 cents Average / Smallest step : 3.787612 Largest / Average step : 2.280530 Largest / Smallest step : 8.637762 Median interval of one step : 117/112, 75.6118 cents, amount: 1 Least squares average step : 126.91798 cents, oct.: 380.75393 cents Scale is not proper Scale has trivalence property Scale is a mode of a 909-tone equal temperament with octave 4/3 degrees: 80 218 909 Least number of segments generator : 455 of 249.296 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 829 of 454.213 cents and inv. generated superset size: 22 = 19 more = 733.333% 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 43.83105 cents Scale diversity : 0.545645 Lumma stability : 0.176012 Lumma impropriety factor : 0.520353 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 : 4563/4480, 31.7807 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 : 13 Odd number limit : 351 (O: 117 U: 351) Highest odd numerator or denominator: 39 Scale harmonicity : 0.020759 Average absolute harmonicity : 0.097547 Specific harmonicity : 0.102837 Fundamental : 1/546, -9.0928 octaves, 0.4792 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 6.552000E+04, 15.99965 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 57.5, average 19.16667 Mersenne's string divisions : 16037 Sum of van Prooijen's expressibility: 3.24428, average 1.08143 Sum of Tenney's harmonic distance : 6.59453, average 2.19818 Vogel's harmonic complexity : 21.00000 Wille's k value : 292 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 17.99562, average 2.99927 Lattice compactness (without 2's) : 10.77729, average 1.79622 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.33333 6 3: -1 .. 1 -0.33333 3 1 5: 0 .. 1 0.66667 2 7: -1 .. 0 -0.33333 1 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 17 18 27| Scale is weakly epimorphic with val: <6 10 17 18 30| Scale is weakly epimorphic with val: <6 10 18 19 25| Scale is weakly epimorphic with val: <6 10 18 19 28| Scale is weakly epimorphic with val: <6 10 19 20 26| Scale is weakly epimorphic with val: <6 10 19 20 29| Scale is weakly epimorphic with val: <6 11 16 18 27| Scale is weakly epimorphic with val: <6 11 16 18 30| Scale is weakly epimorphic with val: <6 11 17 19 25| Scale is weakly epimorphic with val: <6 11 17 19 28| Scale is weakly epimorphic with val: <6 11 18 20 26| Scale is weakly epimorphic with val: <6 11 18 20 29| Scale is weakly epimorphic with val: <6 11 19 21 27| Scale is weakly epimorphic with val: <6 11 19 21 30| Scale is weakly epimorphic with val: <7 10 17 18 25| Scale is weakly epimorphic with val: <7 10 17 21 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 25| Scale is weakly epimorphic with val: <7 10 19 19 28| Scale is weakly epimorphic with val: <7 10 19 20 27| Scale is weakly epimorphic with val: <7 11 15 18 26| Scale is weakly epimorphic with val: <7 11 15 18 29| Scale is weakly epimorphic with val: <7 11 15 20 27| Scale is weakly epimorphic with val: <7 11 15 20 30| Scale is weakly epimorphic with val: <7 11 15 21 26| Scale is weakly epimorphic with val: <7 11 15 21 29| Scale is JI-epimorphic with val: <7 11 16 18 25| Scale is weakly epimorphic with val: <7 11 16 18 28| Scale is weakly epimorphic with val: <7 11 16 19 27| Scale is weakly epimorphic with val: <7 11 16 19 30| Scale is weakly epimorphic with val: <7 11 16 21 25| Scale is weakly epimorphic with val: <7 11 16 21 28| Scale is weakly epimorphic with val: <7 11 16 22 27| Scale is weakly epimorphic with val: <7 11 16 22 30| 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 weakly epimorphic with val: <7 11 18 18 26| Scale is weakly epimorphic with val: <7 11 18 18 29| Scale is JI-epimorphic with val: <7 11 18 20 27| Scale is weakly epimorphic with val: <7 11 18 20 30| Scale is weakly epimorphic with val: <7 11 18 21 26| Scale is weakly epimorphic with val: <7 11 18 21 29| Scale is weakly epimorphic with val: <7 11 19 19 27| Scale is weakly epimorphic with val: <7 11 19 19 30| Scale is weakly epimorphic with val: <7 11 19 21 25| Scale is JI-epimorphic with val: <7 11 19 21 28| Scale is weakly epimorphic with val: <7 11 19 22 27| Scale is weakly epimorphic with val: <7 11 19 22 30| 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 19 25| Scale is weakly epimorphic with val: <7 12 17 19 28| Scale is weakly epimorphic with val: <7 12 18 20 26| Scale is weakly epimorphic with val: <7 12 18 20 29| Scale is weakly epimorphic with val: <7 12 19 20 25| Scale is weakly epimorphic with val: <7 12 19 21 27| Scale is weakly epimorphic with val: <7 12 19 21 30| Scale is weakly epimorphic with val: <8 11 15 20 25| Scale is weakly epimorphic with val: <8 11 16 18 26| Scale is weakly epimorphic with val: <8 11 16 21 26| Scale is weakly epimorphic with val: <8 11 17 19 27| Scale is weakly epimorphic with val: <8 11 17 22 27| Scale is weakly epimorphic with val: <8 11 18 18 27| Scale is weakly epimorphic with val: <8 11 18 18 30| Scale is weakly epimorphic with val: <8 11 18 20 28| Scale is weakly epimorphic with val: <8 11 19 19 25| Scale is weakly epimorphic with val: <8 11 19 19 28| Scale is weakly epimorphic with val: <8 11 19 21 29| Scale is weakly epimorphic with val: <8 12 16 18 25| Scale is weakly epimorphic with val: <8 12 16 21 25| Scale is weakly epimorphic with val: <8 12 17 18 27| Scale is weakly epimorphic with val: <8 12 17 18 30| Scale is weakly epimorphic with val: <8 12 17 19 26| Scale is weakly epimorphic with val: <8 12 17 22 26| Scale is weakly epimorphic with val: <8 12 18 19 25| Scale is weakly epimorphic with val: <8 12 18 19 28| Scale is weakly epimorphic with val: <8 12 18 20 27| Scale is weakly epimorphic with val: <8 12 19 20 26| Scale is weakly epimorphic with val: <8 12 19 20 29| Scale is weakly epimorphic with val: <8 12 19 21 28|
FIT/MODE
3: 0 1 2 N G T3 SD: 36.9239 c. M:-46.5722 c. 4: 0 1 3 N G T3 SD: 25.4745 c. M: 43.8311 c. 5: 0 1 4 N G T3 SD: 27.7761 c. M: 43.8311 c. 7: 1 1 5 N M DE S SD: 20.5643 c. M:-27.3182 c. 8: 1 1 6 N M DE S SD: 11.0326 c. M:-18.4246 c. 9: 1 1 7 N M DE S SD: 8.3519 c. M:-11.5073 c. 11: 1 2 8 N T3 SD: 9.4982 c. M:-16.3876 c. 12: 1 2 9 N T3 SD: 3.2200 c. M:-5.0684 c. 21: 2 3 16 N T3 SD: 2.1380 c. M:-3.6018 c. 25: 2 4 19 N T3 SD: 2.3027 c. M: 3.9875 c. 33: 3 5 25 N T3 SD: 1.1207 c. M:-1.4458 c. 46: 4 7 35 N T3 SD: 0.3617 c. M: 0.5228 c. 79: 7 12 60 N T3 SD: 0.2617 c. M:-0.3402 c. 125: 11 19 95 N T3 SD: 0.0508 c. M:-0.0880 c. 296: 26 45 225 N T3 SD: 0.0499 c. M: 0.0839 c. 363: 32 55 276 N T3 SD: 0.0614 c. M: 0.0767 c. 421: 37 64 320 N T3 SD: 0.0418 c. M: 0.0599 c. 488: 43 74 371 N T3 SD: 0.0370 c. M:-0.0541 c. 534: 47 81 406 N T3 SD: 0.0354 c. M: 0.0612 c. 546: 48 83 415 N T3 SD: 0.0402 c. M:-0.0515 c. 613: 54 93 466 N T3 SD: 0.0251 c. M:-0.0424 c. 659: 58 100 501 N T3 SD: 0.0191 c. M: 0.0329 c. 738: 65 112 561 N T3 SD: 0.0204 c. M:-0.0347 c. 784: 69 119 596 N T3 SD: 0.0080 c. M: 0.0137 c. 909: 80 138 691 N T3 SD: 0.0008 c. M:-0.0013 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 73.7140 cents 7 x 8:9 S SD: 64.1248 cents 8 x 9:11 SD: 49.9317 cents 9 x 10:12 S SD: 31.4805 cents 10 x 11:13 SD: 31.6109 cents 11 x 12:15 S SD: 24.9336 cents 12 x 13:16 SD: 9.5649 cents 13 x 14:17 SD: 17.3820 cents 14 x 15:19 SD: 15.3211 cents 15 x 16:20 S SD: 3.8558 cents 16 x 17:21 SD: 15.4371 cents 17 x 18:23 SD: 16.2676 cents 18 x 19:24 SD: 12.9199 cents 19 x 20:25 S SD: 19.1360 cents 20 x 21:27 SD: 20.5293 cents 21:22:23:28 SD: 17.6232 cents 22:23:24:29 SD: 16.5390 cents 23:24:25:31 SD: 14.3829 cents 24:25:26:32 SD: 10.9869 cents 25:26:27:33 SD: 10.9157 cents 26:27:28:35 S SD: 9.5184 cents 27:28:29:36 SD: 6.5335 cents 30:31:32:40 S SD: 5.0200 cents 39:40:42:52 SD: 2.9518 cents 42:43:45:56 SD: 1.0314 cents 111:114:119:148 SD: 0.8529 cents 114:117:122:152 SD: 0.7747 cents 153:157:164:204 SD: 0.3784 cents 195:200:209:260 SD: 0.1973 cents 309:317:331:412 SD: 0.1874 cents 351:360:376:468 SD: 0.1096 cents 504:517:540:672 SD: 0.0859 cents 546:560:585:728 SD: 0.0000 cents