Scala analysis: 038_H10
Hyperenharmonic tetrachord 52/51 * 51/50 * 50/39
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 52/51 33.617251 2: 26/25 67.900234 tridecimal 1/3-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 50/39 430.1448 1: 52/51 33.6173 2: 51/50 34.2830 17th-partial chroma 3: 50/39 430.1448
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 52/51 33.617 cents 1: 1 51/50 34.283 cents 17th-partial chroma 1: 1 50/39 430.145 cents 2: 1 26/25 67.900 cents tridecimal 1/3-tone 2: 1 200/153 463.762 cents 2: 1 17/13 464.428 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 : 33.6 67.9 498.0 33.6 : 34.3 464.4 498.0 67.9 : 430.1 463.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.6173 .. 430.1448 cents 425/338, 396.5275 cents 52/51, 33.6173 cents 2: 67.9002 .. 464.4277 cents 425/338, 396.5275 cents 507/625,-362.2445 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 52/51, 33.6173 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 50/39, 430.1448 cents Average / Smallest step : 4.938387 Largest / Average step : 2.590999 Largest / Smallest step : 12.795358 Median interval of one step : 51/50, 34.2830 cents, amount: 1 Least squares average step : 118.82519 cents, oct.: 356.47558 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1511-tone equal temperament with octave 4/3 degrees: 102 206 1511 Least number of segments generator : 756 of 249.187 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1042 of 343.457 cents and inv. generated superset size: 36 = 33 more = 1200.000% 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 33.61725 cents Scale diversity : 0.191297 Lumma stability : 0.134997 Lumma impropriety factor : 0.727333 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 : 2601/2600, 0.6657 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 395.8618 cents: 2 -- Rational properties -- Prime limit : 17 Odd number limit : 153 (O: 51 U: 153) Highest odd numerator or denominator: 51 Scale harmonicity : 0.014339 Average absolute harmonicity : 0.086554 Specific harmonicity : 0.068075 Fundamental : 1/1275, -10.3163 octaves, 0.2052 Hz. Guide tone : 52, 5.7004 octaves, 13604.529 Hz. Exponens Consonantiae : 6.630000E+04, 16.01672 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 80.5, average 26.83333 Mersenne's string divisions : 36771 Sum of van Prooijen's expressibility: 3.58263, average 1.19421 Sum of Tenney's harmonic distance : 7.31567, average 2.43856 Vogel's harmonic complexity : 29.33333 Wille's k value : 331 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 14.03703, average 2.33950 Lattice compactness (without 2's) : 11.28131, average 1.88022 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 0 -0.66667 2 1 5: -2 .. 0 -0.66667 2 13: 0 .. 1 0.66667 2 1 17: -1 .. 0 -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 15 27 28| Scale is weakly epimorphic with val: <6 10 15 27 31| Scale is weakly epimorphic with val: <6 10 16 29 30| Scale is weakly epimorphic with val: <6 10 16 29 33| Scale is weakly epimorphic with val: <6 11 15 27 29| Scale is weakly epimorphic with val: <6 11 15 27 32| Scale is weakly epimorphic with val: <6 11 16 29 31| Scale is weakly epimorphic with val: <7 10 15 26 28| Scale is weakly epimorphic with val: <7 10 15 26 31| Scale is weakly epimorphic with val: <7 10 15 28 29| Scale is weakly epimorphic with val: <7 10 16 27 28| Scale is weakly epimorphic with val: <7 10 16 28 30| Scale is weakly epimorphic with val: <7 10 16 28 33| Scale is weakly epimorphic with val: <7 10 16 30 31| Scale is weakly epimorphic with val: <7 10 17 26 27| Scale is weakly epimorphic with val: <7 10 17 29 30| Scale is weakly epimorphic with val: <7 10 17 30 32| Scale is weakly epimorphic with val: <7 10 18 28 29| Scale is weakly epimorphic with val: <7 10 19 27 28| Scale is weakly epimorphic with val: <7 10 19 30 31| Scale is JI-epimorphic with val: <7 11 15 25 27| Scale is weakly epimorphic with val: <7 11 15 25 30| Scale is weakly epimorphic with val: <7 11 15 25 33| Scale is weakly epimorphic with val: <7 11 15 27 28| Scale is weakly epimorphic with val: <7 11 15 27 31| Scale is weakly epimorphic with val: <7 11 15 28 30| Scale is weakly epimorphic with val: <7 11 15 28 33| Scale is weakly epimorphic with val: <7 11 15 30 31| Scale is weakly epimorphic with val: <7 11 16 26 27| Scale is weakly epimorphic with val: <7 11 16 26 30| Scale is weakly epimorphic with val: <7 11 16 26 33| Scale is JI-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 16 29 30| Scale is weakly epimorphic with val: <7 11 16 29 33| Scale is weakly epimorphic with val: <7 11 16 30 32| Scale is weakly epimorphic with val: <7 11 17 25 29| Scale is weakly epimorphic with val: <7 11 17 25 32| Scale is weakly epimorphic with val: <7 11 17 26 28| Scale is weakly epimorphic with val: <7 11 17 26 31| Scale is weakly epimorphic with val: <7 11 17 28 29| Scale is weakly epimorphic with val: <7 11 17 28 32| Scale is JI-epimorphic with val: <7 11 17 29 31| Scale is weakly epimorphic with val: <7 11 18 25 27| Scale is weakly epimorphic with val: <7 11 18 25 30| Scale is weakly epimorphic with val: <7 11 18 25 33| Scale is weakly epimorphic with val: <7 11 18 27 28| Scale is weakly epimorphic with val: <7 11 18 27 31| Scale is weakly epimorphic with val: <7 11 18 28 30| Scale is weakly epimorphic with val: <7 11 18 28 33| Scale is weakly epimorphic with val: <7 11 18 30 31| Scale is weakly epimorphic with val: <7 11 19 26 27| Scale is weakly epimorphic with val: <7 11 19 26 30| Scale is weakly epimorphic with val: <7 11 19 26 33| 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 19 29 30| Scale is weakly epimorphic with val: <7 11 19 29 33| Scale is weakly epimorphic with val: <7 11 19 30 32| Scale is weakly epimorphic with val: <7 12 15 26 27| Scale is weakly epimorphic with val: <7 12 15 26 30| Scale is weakly epimorphic with val: <7 12 15 26 33| Scale is weakly epimorphic with val: <7 12 16 28 29| Scale is weakly epimorphic with val: <7 12 16 28 32| Scale is weakly epimorphic with val: <7 12 17 30 31| Scale is weakly epimorphic with val: <8 11 15 25 29| Scale is weakly epimorphic with val: <8 11 15 25 32| Scale is weakly epimorphic with val: <8 11 15 26 28| Scale is weakly epimorphic with val: <8 11 15 29 31| Scale is weakly epimorphic with val: <8 11 16 25 27| 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 28 30| Scale is weakly epimorphic with val: <8 11 17 27 29| Scale is weakly epimorphic with val: <8 11 17 29 30| Scale is weakly epimorphic with val: <8 11 17 29 33| Scale is weakly epimorphic with val: <8 11 17 30 32| Scale is weakly epimorphic with val: <8 11 18 26 28| Scale is weakly epimorphic with val: <8 11 18 29 31| Scale is weakly epimorphic with val: <8 11 19 25 27| Scale is weakly epimorphic with val: <8 11 19 28 30| Scale is weakly epimorphic with val: <8 12 15 25 27| Scale is weakly epimorphic with val: <8 12 15 25 30| Scale is weakly epimorphic with val: <8 12 15 25 33| Scale is weakly epimorphic with val: <8 12 15 27 28| Scale is weakly epimorphic with val: <8 12 15 30 31| Scale is weakly epimorphic with val: <8 12 16 26 27| Scale is weakly epimorphic with val: <8 12 16 27 29| Scale is weakly epimorphic with val: <8 12 16 27 32| Scale is weakly epimorphic with val: <8 12 16 29 30| Scale is weakly epimorphic with val: <8 12 17 28 29| Scale is weakly epimorphic with val: <8 12 17 29 31| Scale is weakly epimorphic with val: <8 12 18 27 28| Scale is weakly epimorphic with val: <8 12 18 30 31| Scale is weakly epimorphic with val: <8 12 19 26 27| Scale is weakly epimorphic with val: <8 12 19 29 30|
FIT/MODE
3: 0 0 3 N M DE S SD: 43.7438 c. M: 67.9002 c. 5: 0 1 4 N G T3 SD: 26.6806 c. M: 33.6173 c. 6: 0 1 5 N G T3 SD: 21.2787 c. M: 33.6173 c. 7: 0 1 6 N G T3 SD: 19.4994 c. M: 33.6173 c. 8: 0 1 7 N G T3 SD: 19.6806 c. M: 33.6173 c. 9: 0 1 8 N G T3 SD: 20.7197 c. M: 33.6173 c. 10: 0 1 9 N G T3 SD: 22.0422 c. M: 33.6173 c. 11: 1 1 9 N M DE S SD: 14.7097 c. M:-22.6534 c. 12: 1 1 10 N M DE S SD: 9.8391 c. M:-15.1073 c. 13: 1 1 11 N M DE S SD: 5.7186 c. M:-8.7221 c. 14: 1 1 12 N M DE S SD: 2.1900 c. M:-3.2491 c. 15: 1 1 13 N M DE S SD: 0.8952 c. M: 1.4942 c. 29: 2 2 25 N M DE S SD: 0.6237 c. M:-0.7956 c. 44: 3 3 38 N M DE S SD: 0.1967 c. M:-0.3404 c. 103: 7 7 89 N M DE S SD: 0.1780 c. M:-0.2305 c. 147: 10 10 127 N M DE S SD: 0.1719 c. M:-0.2634 c. 388: 26 27 335 N T3 SD: 0.1596 c. M: 0.2431 c. 389: 26 27 336 N T3 SD: 0.1915 c. M: 0.3289 c. 397: 27 27 343 N M DE S SD: 0.1725 c. M:-0.2548 c. 402: 27 28 347 N T3 SD: 0.1688 c. M:-0.2403 c. 403: 27 28 348 N T3 SD: 0.1498 c. M: 0.2495 c. 417: 28 29 360 N T3 SD: 0.1442 c. M:-0.1779 c. 418: 28 29 361 N T3 SD: 0.1477 c. M: 0.2554 c. 432: 29 30 373 N T3 SD: 0.1266 c. M: 0.1837 c. 447: 30 31 386 N T3 SD: 0.1168 c. M: 0.1914 c. 461: 31 32 398 N T3 SD: 0.1187 c. M:-0.1623 c. 462: 31 32 399 N T3 SD: 0.1150 c. M: 0.1986 c. 476: 32 33 411 N T3 SD: 0.1007 c. M: 0.1352 c. 477: 32 33 412 N T3 SD: 0.1201 c. M: 0.2054 c. 491: 33 34 424 N T3 SD: 0.0902 c. M: 0.1438 c. 506: 34 35 437 N T3 SD: 0.0881 c. M: 0.1518 c. 520: 35 36 449 N T3 SD: 0.0805 c. M:-0.1021 c. 521: 35 36 450 N T3 SD: 0.0934 c. M: 0.1593 c. 535: 36 37 462 N T3 SD: 0.0685 c. M: 0.1039 c. 550: 37 38 475 N T3 SD: 0.0655 c. M: 0.1124 c. 564: 38 39 487 N T3 SD: 0.0653 c. M:-0.0953 c. 565: 38 39 488 N T3 SD: 0.0710 c. M: 0.1204 c. 579: 39 40 500 N T3 SD: 0.0512 c. M: 0.0702 c. 594: 40 41 513 N T3 SD: 0.0463 c. M: 0.0789 c. 609: 41 42 526 N T3 SD: 0.0519 c. M: 0.0871 c. 623: 42 43 538 N T3 SD: 0.0380 c. M:-0.0513 c. 638: 43 44 551 N T3 SD: 0.0301 c. M: 0.0500 c. 653: 44 45 564 N T3 SD: 0.0355 c. M: 0.0583 c. 667: 45 46 576 N T3 SD: 0.0297 c. M:-0.0489 c. 682: 46 47 589 N T3 SD: 0.0167 c. M: 0.0248 c. 726: 49 50 627 N T3 SD: 0.0088 c. M:-0.0150 c. 785: 53 54 678 N T3 SD: 0.0094 c. M: 0.0138 c. 1467: 99 101 1267 N T3 SD: 0.0040 c. M: 0.0069 c. 1511: 102 104 1305 N T3 SD: 0.0019 c. M:-0.0033 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: 99.4853 cents 7 x 8:9 S SD: 87.4963 cents 8 x 9:11 SD: 73.0354 cents 9 x 10:12 S SD: 57.2517 cents 10 x 11:13 SD: 53.2690 cents 11 x 12:15 S SD: 45.7139 cents 12 x 13:16 SD: 35.3362 cents 13 x 14:17 SD: 34.5617 cents 14 x 15:19 SD: 29.9816 cents 15 x 16:20 S SD: 21.9155 cents 16 x 17:21 SD: 23.0023 cents 17 x 18:23 SD: 20.0196 cents 18 x 19:24 SD: 12.8514 cents 19 x 20:25 S SD: 15.5132 cents 20 x 21:27 SD: 13.5737 cents 21 x 22:28 SD: 6.3184 cents 22 x 23:29 SD: 10.8799 cents 23 x 24:31 SD: 9.7943 cents 24 x 25:32 SD: 1.3861 cents 25 x 26:33 SD: 8.6997 cents 26 x 27:35 SD: 8.3820 cents 27 x 28:36 SD: 2.4697 cents 28 x 29:37 SD: 8.5468 cents 29 x 30:39 SD: 8.7412 cents 30 x 31:40 SD: 5.5667 cents 31 x 32:41 SD: 9.5373 cents 32 x 33:43 SD: 9.9432 cents 33 x 34:44 SD: 8.1089 cents 34:35 x 45 SD: 10.4607 cents 35:36 x 47 SD: 9.7654 cents 36:37 x 48 SD: 6.9084 cents 37:38 x 49 SD: 8.5923 cents 39:40:41:52 SD: 7.0965 cents 41:42:43:55 SD: 6.5679 cents 42:43:44:56 SD: 4.8348 cents 44:45:46:59 SD: 4.7865 cents 45:46:47:60 SD: 2.8705 cents 48:49:50:64 SD: 1.1552 cents 51:52:53:68 SD: 0.4354 cents 99:101:103:132 SD: 0.4041 cents 150:153:156:200 SD: 0.2219 cents 201:205:209:268 SD: 0.1991 cents 552:563:574:736 SD: 0.1980 cents