Scala analysis: 024_H7
Hyperenharmonic tetrachord 45/44 * 88/87 * 58/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 45/44 38.905773 1/5-tone 2: 30/29 58.691521 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 58/45 439.3535 1: 45/44 38.9058 1/5-tone 2: 88/87 19.7857 3: 58/45 439.3535
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 88/87 19.786 cents 1: 1 45/44 38.906 cents 1/5-tone 1: 1 58/45 439.353 cents 2: 1 30/29 58.692 cents 2: 1 176/135 459.139 cents 2: 1 29/22 478.259 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 : 38.9 58.7 498.0 38.9 : 19.8 459.1 498.0 58.7 : 439.4 478.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 19.7857 .. 439.3535 cents 841/660, 419.5677 cents 88/87, 19.7857 cents 2: 58.6915 .. 478.2593 cents 841/660, 419.5677 cents 675/841,-380.6620 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 88/87, 19.7857 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 58/45, 439.3535 cents Average / Smallest step : 8.390636 Largest / Average step : 2.646469 Largest / Smallest step : 22.205554 Median interval of one step : 45/44, 38.9058 cents, amount: 1 Least squares average step : 117.88742 cents, oct.: 353.66225 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1485-tone equal temperament with octave 4/3 degrees: 116 175 1485 Least number of segments generator : 743 of 249.190 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1181 of 396.088 cents and inv. generated superset size: 60 = 57 more = 2000.000% 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 19.78575 cents Scale diversity : 0.106956 Lumma stability : 0.079454 Lumma impropriety factor : 0.764312 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 : 3915/3872, 19.1200 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 Limited inverse transpositions with margin 419.5677 cents: 2 -- Rational properties -- Prime limit : 29 Odd number limit : 135 (O: 45 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.011031 Average absolute harmonicity : 0.087070 Specific harmonicity : 0.056733 Fundamental : 1/3828, -11.9024 octaves, 0.0683 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 6.890400E+05, 19.39423 octaves Euler's gradus suavitatis : 53 Sum of Mann's harmonic distance : 77.5, average 25.83333 Mersenne's string divisions : 36757 Sum of van Prooijen's expressibility: 3.59273, average 1.19758 Sum of Tenney's harmonic distance : 7.31537, average 2.43846 Vogel's harmonic complexity : 37.33333 Wille's k value : 1957 Wilson's harmonic complexity : 54 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 18.70435, average 3.11739 Lattice compactness (without 2's) : 12.67971, average 2.11328 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.33333 5 3: -1 .. 2 0.66667 4 1 5: 0 .. 1 0.66667 2 11: -1 .. 0 -0.33333 1 1 29: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 18 23 33| Scale is weakly epimorphic with val: <6 10 18 23 36| Scale is weakly epimorphic with val: <6 10 19 23 32| Scale is weakly epimorphic with val: <6 10 19 24 34| Scale is weakly epimorphic with val: <6 10 19 24 37| Scale is weakly epimorphic with val: <6 10 19 26 32| Scale is weakly epimorphic with val: <6 11 16 23 34| Scale is weakly epimorphic with val: <6 11 16 23 37| Scale is weakly epimorphic with val: <6 11 17 24 32| Scale is weakly epimorphic with val: <6 11 17 24 35| Scale is weakly epimorphic with val: <6 11 17 24 38| Scale is weakly epimorphic with val: <6 11 18 23 32| Scale is weakly epimorphic with val: <6 11 18 25 33| Scale is weakly epimorphic with val: <6 11 18 25 36| Scale is weakly epimorphic with val: <6 11 18 26 32| Scale is weakly epimorphic with val: <6 11 19 24 33| Scale is weakly epimorphic with val: <6 11 19 26 34| Scale is weakly epimorphic with val: <6 11 19 26 37| Scale is weakly epimorphic with val: <6 11 19 27 33| Scale is weakly epimorphic with val: <7 10 18 25 32| Scale is weakly epimorphic with val: <7 10 19 23 33| Scale is weakly epimorphic with val: <7 10 19 26 33| Scale is weakly epimorphic with val: <7 11 15 24 32| Scale is weakly epimorphic with val: <7 11 15 24 35| Scale is weakly epimorphic with val: <7 11 15 24 38| Scale is weakly epimorphic with val: <7 11 15 25 34| Scale is weakly epimorphic with val: <7 11 15 25 37| Scale is weakly epimorphic with val: <7 11 15 27 32| Scale is weakly epimorphic with val: <7 11 15 27 35| Scale is weakly epimorphic with val: <7 11 15 27 38| Scale is JI-epimorphic with val: <7 11 16 23 32| Scale is weakly epimorphic with val: <7 11 16 23 35| Scale is weakly epimorphic with val: <7 11 16 23 38| Scale is weakly epimorphic with val: <7 11 16 25 33| Scale is weakly epimorphic with val: <7 11 16 25 36| Scale is weakly epimorphic with val: <7 11 16 26 32| Scale is weakly epimorphic with val: <7 11 16 26 35| Scale is weakly epimorphic with val: <7 11 16 26 38| Scale is weakly epimorphic with val: <7 11 17 23 34| Scale is weakly epimorphic with val: <7 11 17 23 37| Scale is JI-epimorphic with val: <7 11 17 24 33| Scale is weakly epimorphic with val: <7 11 17 24 36| Scale is weakly epimorphic with val: <7 11 17 26 34| Scale is weakly epimorphic with val: <7 11 17 26 37| Scale is weakly epimorphic with val: <7 11 17 27 33| Scale is weakly epimorphic with val: <7 11 17 27 36| Scale is weakly epimorphic with val: <7 11 18 24 32| Scale is weakly epimorphic with val: <7 11 18 24 35| Scale is weakly epimorphic with val: <7 11 18 24 38| Scale is JI-epimorphic with val: <7 11 18 25 34| Scale is weakly epimorphic with val: <7 11 18 25 37| Scale is weakly epimorphic with val: <7 11 18 27 32| Scale is weakly epimorphic with val: <7 11 18 27 35| Scale is weakly epimorphic with val: <7 11 18 27 38| Scale is weakly epimorphic with val: <7 11 19 23 32| Scale is weakly epimorphic with val: <7 11 19 23 35| Scale is weakly epimorphic with val: <7 11 19 23 38| Scale is weakly epimorphic with val: <7 11 19 25 33| Scale is weakly epimorphic with val: <7 11 19 25 36| Scale is weakly epimorphic with val: <7 11 19 26 32| Scale is JI-epimorphic with val: <7 11 19 26 35| Scale is weakly epimorphic with val: <7 11 19 26 38| Scale is weakly epimorphic with val: <7 12 16 23 34| Scale is weakly epimorphic with val: <7 12 16 23 37| Scale is weakly epimorphic with val: <7 12 16 25 32| Scale is weakly epimorphic with val: <7 12 17 23 33| Scale is weakly epimorphic with val: <7 12 17 24 32| Scale is weakly epimorphic with val: <7 12 17 24 35| Scale is weakly epimorphic with val: <7 12 17 24 38| Scale is weakly epimorphic with val: <7 12 17 26 33| Scale is weakly epimorphic with val: <7 12 18 24 34| Scale is weakly epimorphic with val: <7 12 18 25 33| Scale is weakly epimorphic with val: <7 12 18 25 36| Scale is weakly epimorphic with val: <7 12 18 27 34| Scale is weakly epimorphic with val: <7 12 19 25 35| Scale is weakly epimorphic with val: <7 12 19 26 34| Scale is weakly epimorphic with val: <7 12 19 26 37| Scale is weakly epimorphic with val: <8 11 16 24 32| Scale is weakly epimorphic with val: <8 11 16 27 32| Scale is weakly epimorphic with val: <8 11 17 25 33| Scale is weakly epimorphic with val: <8 11 18 23 34| Scale is weakly epimorphic with val: <8 11 18 26 34| Scale is weakly epimorphic with val: <8 11 19 24 35| Scale is weakly epimorphic with val: <8 11 19 27 35| Scale is weakly epimorphic with val: <8 12 15 24 32| Scale is weakly epimorphic with val: <8 12 15 27 32| Scale is weakly epimorphic with val: <8 12 16 25 33| Scale is weakly epimorphic with val: <8 12 17 23 34| Scale is weakly epimorphic with val: <8 12 17 26 34| Scale is weakly epimorphic with val: <8 12 18 23 33| Scale is weakly epimorphic with val: <8 12 18 23 36| Scale is weakly epimorphic with val: <8 12 18 24 35| Scale is weakly epimorphic with val: <8 12 18 27 35| Scale is weakly epimorphic with val: <8 12 19 24 34| Scale is weakly epimorphic with val: <8 12 19 24 37| Scale is weakly epimorphic with val: <8 12 19 25 36|
FIT/MODE
3: 0 0 3 N M DE S SD: 40.6545 c. M: 58.6915 c. 6: 1 0 5 N G T3 SD: 29.0759 c. M:-44.1017 c. 7: 1 0 6 N G T3 SD: 19.9570 c. M:-32.2435 c. 8: 1 0 7 N G T3 SD: 13.6372 c. M:-23.3499 c. 9: 1 0 8 N G T3 SD: 9.6829 c. M:-16.4326 c. 10: 1 0 9 N G T3 SD: 8.1191 c. M:-10.8987 c. 14: 1 1 12 N M DE S SD: 7.4452 c. M:-12.4578 c. 15: 1 1 13 N M DE S SD: 5.5388 c. M:-7.7145 c. 16: 1 1 14 N M DE S SD: 4.9396 c. M: 7.7780 c. 17: 1 1 15 N M DE S SD: 5.5481 c. M: 9.6090 c. 22: 2 1 19 N T3 SD: 6.4722 c. M:-9.2237 c. 23: 2 1 20 N T3 SD: 4.4236 c. M:-6.2709 c. 24: 2 1 21 N T3 SD: 2.5464 c. M:-3.5641 c. 25: 2 1 22 N T3 SD: 0.8232 c. M:-1.0739 c. 26: 2 1 23 N T3 SD: 0.7861 c. M: 1.2248 c. 51: 4 2 45 N T3 SD: 0.1066 c. M:-0.1566 c. 331: 26 13 292 N T3 SD: 0.1246 c. M:-0.2156 c. 332: 26 13 293 N T3 SD: 0.1214 c. M: 0.1862 c. 347: 27 14 306 N T3 SD: 0.1259 c. M:-0.1553 c. 373: 29 15 329 N T3 SD: 0.1115 c. M: 0.1838 c. 382: 30 15 337 N T3 SD: 0.1205 c. M:-0.2077 c. 383: 30 15 338 N T3 SD: 0.1177 c. M: 0.1745 c. 398: 31 16 351 N T3 SD: 0.0965 c. M:-0.1228 c. 424: 33 17 374 N T3 SD: 0.0857 c. M: 0.1428 c. 449: 35 18 396 N T3 SD: 0.0739 c. M:-0.0978 c. 475: 37 19 419 N T3 SD: 0.0656 c. M: 0.1107 c. 500: 39 20 441 N T3 SD: 0.0561 c. M:-0.0778 c. 526: 41 21 464 N T3 SD: 0.0496 c. M: 0.0848 c. 551: 43 22 486 N T3 SD: 0.0419 c. M:-0.0615 c. 577: 45 23 509 N T3 SD: 0.0367 c. M: 0.0634 c. 602: 47 24 531 N T3 SD: 0.0305 c. M:-0.0480 c. 628: 49 25 554 N T3 SD: 0.0265 c. M: 0.0456 c. 653: 51 26 576 N T3 SD: 0.0216 c. M:-0.0366 c. 679: 53 27 599 N T3 SD: 0.0188 c. M: 0.0304 c. 704: 55 28 621 N T3 SD: 0.0157 c. M:-0.0269 c. 730: 57 29 644 N T3 SD: 0.0143 c. M: 0.0177 c. 755: 59 30 666 N T3 SD: 0.0135 c. M:-0.0184 c. 1332: 104 53 1175 N T3 SD: 0.0132 c. M: 0.0194 c. 1383: 108 55 1220 N T3 SD: 0.0087 c. M: 0.0129 c. 1434: 112 57 1265 N T3 SD: 0.0046 c. M: 0.0069 c. 1485: 116 59 1310 N T3 SD: 0.0008 c. M: 0.0012 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: 104.0897 cents 7 x 8:9 S SD: 91.8073 cents 8 x 9:11 SD: 77.3408 cents 9 x 10:12 S SD: 61.8561 cents 10 x 11:13 SD: 57.4969 cents 11 x 12:15 S SD: 49.9190 cents 12 x 13:16 SD: 39.9406 cents 13 x 14:17 SD: 38.6498 cents 14 x 15:19 SD: 34.0208 cents 15 x 16:20 S SD: 26.5199 cents 16 x 17:21 SD: 26.8499 cents 17 x 18:23 SD: 23.7691 cents 18 x 19:24 SD: 17.4557 cents 19 x 20:25 S SD: 18.9234 cents 20 x 21:27 SD: 16.7847 cents 21 x 22:28 SD: 10.9228 cents 22 x 23:29 SD: 13.4637 cents 23 x 24:31 SD: 11.9893 cents 24 x 25:32 SD: 5.9905 cents 25 x 26:33 SD: 9.8430 cents 26 x 27:35 SD: 8.9251 cents 27 x 28:36 SD: 2.1347 cents 28 x 29:37 SD: 7.8314 cents 29 x 30:39 SD: 7.4302 cents 30 x 31:40 SD: 0.9623 cents 31 x 32:41 SD: 7.2526 cents 32 x 33:43 SD: 7.2608 cents 33 x 34:44 SD: 3.5045 cents 34 x 35:45 SD: 7.6749 cents 35:36 x 47 SD: 7.8921 cents 36:37 x 48 SD: 4.2641 cents 37:38 x 49 SD: 6.9014 cents 38:39 x 51 SD: 6.4352 cents 39:40 x 52 SD: 2.4626 cents 40:41 x 53 SD: 5.7572 cents 41:42 x 55 SD: 5.4468 cents 42:43 x 56 SD: 0.9155 cents 43:44 x 57 SD: 5.0671 cents 48:49:50:64 SD: 4.1344 cents 51:52:53:68 SD: 3.1696 cents 54:55:56:72 SD: 2.7728 cents 66 x 68:88 SD: 3.5045 cents 67 x 69:89 SD: 5.0558 cents 68 x 70:91 SD: 5.3089 cents 69 x 71:92 SD: 4.6122 cents 70:72 x 93 SD: 5.8240 cents 71:73 x 95 SD: 5.5098 cents 72:74 x 96 SD: 4.2641 cents 75:77:78:100 SD: 3.7874 cents 77:79:80:103 SD: 3.6137 cents 78:80:81:104 SD: 2.7573 cents 81:83:84:108 SD: 1.8031 cents 84:86:87:112 SD: 0.9187 cents 87:89:90:116 SD: 0.1474 cents 438:448:453:584 SD: 0.1442 cents 525:537:543:700 SD: 0.1321 cents