Scala analysis: 083_E9
Enharmonic tetrachord 38/37 * 37/36 * 24/19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 38/37 46.168977 2: 19/18 93.603014 undevicesimal semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 24/19 404.4420 smaller undevicesimal major third 1: 38/37 46.1690 2: 37/36 47.4340 3: 24/19 404.4420 smaller undevicesimal major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 38/37 46.169 cents 1: 1 37/36 47.434 cents 1: 1 24/19 404.442 cents smaller undevicesimal major third 2: 1 19/18 93.603 cents undevicesimal semitone 2: 1 48/37 450.611 cents 2: 1 74/57 451.876 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 : 46.2 93.6 498.0 46.2 : 47.4 451.9 498.0 93.6 : 404.4 450.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 46.1690 .. 404.4420 cents 444/361, 358.2730 cents 38/37, 46.1690 cents 2: 93.6030 .. 451.8760 cents 444/361, 358.2730 cents 361/432,-310.8390 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 38/37, 46.1690 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 24/19, 404.4420 cents Average / Smallest step : 3.595813 Largest / Average step : 2.436177 Largest / Smallest step : 8.760038 Median interval of one step : 37/36, 47.4340 cents, amount: 1 Least squares average step : 123.39357 cents, oct.: 370.18072 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1575-tone equal temperament with octave 4/3 degrees: 146 296 1575 Least number of segments generator : 788 of 249.181 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 989 of 312.741 cents and inv. generated superset size: 76 = 73 more = 2533.333% 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 46.16898 cents Scale diversity : 0.381481 Lumma stability : 0.185401 Lumma impropriety factor : 0.624118 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 : 1369/1368, 1.2651 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 : 2 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 Limited inverse transpositions with margin 357.0079 cents: 2 -- Rational properties -- Prime limit : 37 Odd number limit : 57 (O: 37 U: 57) Highest odd numerator or denominator: 37 Scale harmonicity : 0.023563 Fundamental : 1/666, -9.3794 octaves, 0.3928 Hz. Guide tone : 76, 6.2479 octaves, 19883.543 Hz. Exponens Consonantiae : 5.061600E+04, 15.62731 octaves Euler's gradus suavitatis : 62 Sum of Mann's harmonic distance : 59.5, average 19.83333 Mersenne's string divisions : 19425 Sum of van Prooijen's expressibility: 3.32408, average 1.10803 Sum of Tenney's harmonic distance : 6.76119, average 2.25373 Vogel's harmonic complexity : 42.00000 Wille's k value : 351 Wilson's harmonic complexity : 62 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.97687, average 2.32948 Lattice compactness (without 2's) : 9.06450, average 1.51075 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -2 .. 0 -1.00000 3 1 19: 0 .. 1 0.66667 2 1 37: -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 29 37| Scale is weakly epimorphic with val: <6 10 29 40| Scale is weakly epimorphic with val: <6 10 33 36| Scale is weakly epimorphic with val: <6 11 31 35| Scale is weakly epimorphic with val: <6 11 31 38| Scale is weakly epimorphic with val: <6 11 31 41| Scale is weakly epimorphic with val: <6 11 33 36| Scale is weakly epimorphic with val: <7 10 30 35| Scale is weakly epimorphic with val: <7 10 30 38| Scale is weakly epimorphic with val: <7 10 30 41| Scale is weakly epimorphic with val: <7 10 32 36| Scale is weakly epimorphic with val: <7 11 28 37| Scale is weakly epimorphic with val: <7 11 28 40| Scale is weakly epimorphic with val: <7 11 30 35| Scale is weakly epimorphic with val: <7 11 30 38| Scale is weakly epimorphic with val: <7 11 30 41| Scale is JI-epimorphic with val: <7 11 31 37| Scale is weakly epimorphic with val: <7 11 31 40| Scale is weakly epimorphic with val: <7 11 33 35| Scale is weakly epimorphic with val: <7 11 33 38| Scale is weakly epimorphic with val: <7 11 33 41| Scale is weakly epimorphic with val: <7 11 34 37| Scale is weakly epimorphic with val: <7 11 34 40| Scale is weakly epimorphic with val: <7 12 32 36| Scale is weakly epimorphic with val: <7 12 34 37| Scale is weakly epimorphic with val: <7 12 34 40| Scale is weakly epimorphic with val: <8 11 31 36| Scale is weakly epimorphic with val: <8 11 33 37| Scale is weakly epimorphic with val: <8 11 33 40| Scale is weakly epimorphic with val: <8 11 34 39| Scale is weakly epimorphic with val: <8 12 31 36| Scale is weakly epimorphic with val: <8 12 34 39|
FIT/MODE
3: 0 0 3 N M DE S SD: 60.2581 c. M: 93.6030 c. 4: 0 1 3 N G T3 SD: 32.0775 c. M: 46.1690 c. 5: 0 1 4 N G T3 SD: 26.8803 c. M: 46.1690 c. 6: 0 1 5 N G T3 SD: 27.3486 c. M: 46.1690 c. 7: 0 1 6 N G T3 SD: 29.6409 c. M: 46.1690 c. 9: 1 1 7 N M DE S SD: 11.1891 c. M:-17.0737 c. 10: 1 1 8 N M DE S SD: 4.0533 c. M:-6.0060 c. 11: 1 1 9 N M DE S SD: 1.8344 c. M: 3.0494 c. 21: 2 2 17 N M DE S SD: 1.0315 c. M:-1.2639 c. 32: 3 3 26 N M DE S SD: 0.3273 c. M:-0.5227 c. 107: 10 10 87 N M DE S SD: 0.3665 c. M: 0.5105 c. 117: 11 11 95 N M DE S SD: 0.3796 c. M:-0.6558 c. 139: 13 13 113 N M DE S SD: 0.3490 c. M: 0.4435 c. 149: 14 14 121 N M DE S SD: 0.3622 c. M:-0.6272 c. 171: 16 16 139 N M DE S SD: 0.3404 c. M:-0.4317 c. 196: 18 19 159 N T3 SD: 0.3454 c. M: 0.4302 c. 203: 19 19 165 N M DE S SD: 0.3357 c. M:-0.4461 c. 207: 19 20 168 N T3 SD: 0.2946 c. M: 0.4547 c. 218: 20 21 177 N T3 SD: 0.2779 c. M: 0.4768 c. 228: 21 22 185 N T3 SD: 0.2546 c. M:-0.3265 c. 229: 21 22 186 N T3 SD: 0.2908 c. M: 0.4967 c. 239: 22 23 194 N T3 SD: 0.2115 c. M: 0.3238 c. 250: 23 24 203 N T3 SD: 0.2021 c. M: 0.3488 c. 260: 24 25 211 N T3 SD: 0.1875 c. M:-0.2593 c. 261: 24 25 212 N T3 SD: 0.2223 c. M: 0.3717 c. 271: 25 26 220 N T3 SD: 0.1480 c. M: 0.2239 c. 282: 26 27 229 N T3 SD: 0.1443 c. M: 0.2499 c. 292: 27 28 237 N T3 SD: 0.1372 c. M:-0.2068 c. 303: 28 29 246 N T3 SD: 0.0981 c. M: 0.1450 c. 314: 29 30 255 N T3 SD: 0.0996 c. M: 0.1712 c. 335: 31 32 272 N T3 SD: 0.0580 c. M: 0.0812 c. 346: 32 33 281 N T3 SD: 0.0659 c. M: 0.1070 c. 367: 34 35 298 N T3 SD: 0.0260 c. M:-0.0349 c. 399: 37 38 324 N T3 SD: 0.0123 c. M:-0.0156 c. 1165: 108 111 946 N T3 SD: 0.0121 c. M:-0.0209 c. 1176: 109 112 955 N T3 SD: 0.0059 c. M: 0.0078 c. 1575: 146 150 1279 N T3 SD: 0.0014 c. M: 0.0022 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: 86.6339 cents 7 x 8:9 S SD: 75.6470 cents 8 x 9:11 SD: 61.2488 cents 9 x 10:12 S SD: 44.4003 cents 10 x 11:13 SD: 41.8906 cents 11 x 12:15 S SD: 34.5201 cents 12 x 13:16 SD: 22.4848 cents 13 x 14:17 SD: 24.1551 cents 14 x 15:19 SD: 20.0414 cents 15 x 16:20 S SD: 9.0641 cents 16 x 17:21 SD: 14.7666 cents 17 x 18:23 SD: 12.9172 cents 18 x 19:24 SD: 0.0000 cents 19 x 20:25 S SD: 11.7140 cents 20 x 21:27 SD: 11.6831 cents 21 x 22:28 SD: 6.5330 cents 22 x 23:29 SD: 12.9285 cents 23 x 24:31 SD: 13.6675 cents 24 x 25:32 SD: 11.4653 cents 25:26 x 33 SD: 13.9193 cents 26:27 x 35 SD: 12.6678 cents 27:28:29:36 SD: 11.4917 cents 28:29:30:37 SD: 11.1625 cents 29:30:31:39 SD: 9.7485 cents 30:31:32:40 S SD: 6.9996 cents 32:33:34:43 SD: 6.3321 cents 33:34:35:44 SD: 3.3114 cents 36:37:38:48 SD: 0.4217 cents 291:299:307:388 SD: 0.4076 cents 327:336:345:436 SD: 0.3941 cents 339:348:358:452 SD: 0.3801 cents 375:385:396:500 SD: 0.3163 cents 411:422:434:548 SD: 0.2664 cents 414:425:437:552 SD: 0.2568 cents 447:459:472:596 SD: 0.2279 cents 450:462:475:600 SD: 0.2025 cents 483:496:510:644 SD: 0.1988 cents 486:499:513:648 SD: 0.1563 cents 522:536:551:696 SD: 0.1164 cents 558:573:589:744 SD: 0.0817 cents 594:610:627:792 SD: 0.0511 cents