Scala analysis: 151_C4
Chromatic tetrachord 51/50 * 18/17 * 100/81
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 51/50 34.282983 17th-partial chroma 2: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 100/81 364.8074 grave major third 1: 51/50 34.2830 17th-partial chroma 2: 18/17 98.9546 Arabic lute index finger 3: 100/81 364.8074 grave major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 51/50 34.283 cents 17th-partial chroma 1: 1 18/17 98.955 cents Arabic lute index finger 1: 1 100/81 364.807 cents grave major third 2: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 1 34/27 399.090 cents septendecimal major third 2: 1 200/153 463.762 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 : 34.3 133.2 498.0 34.3 : 99.0 463.8 498.0 133.2: 364.8 399.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.2830 .. 364.8074 cents 5000/4131, 330.5244 cents 51/50, 34.2830 cents 2: 133.2376 .. 463.7620 cents 5000/4131, 330.5244 cents 2187/2500,-231.5698 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 51/50, 34.2830 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 100/81, 364.8074 cents Average / Smallest step : 4.842490 Largest / Average step : 2.197437 Largest / Smallest step : 10.641064 Median interval of one step : 18/17, 98.9546 cents, amount: 1 Least squares average step : 128.20665 cents, oct.: 384.61996 cents Scale is not proper Scale has trivalence property Scale is a mode of a 770-tone equal temperament with octave 4/3 degrees: 53 206 770 Least number of segments generator : 387 of 250.316 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 529 of 342.163 cents and inv. generated superset size: 37 = 34 more = 1233.333% 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 34.28298 cents Scale diversity : 0.577015 Lumma stability : 0.137670 Lumma impropriety factor : 0.464958 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 : 51/50, 34.2830 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 17 Odd number limit : 153 (O: 51 U: 153) Highest odd numerator or denominator: 51 Scale harmonicity : 0.017673 Average absolute harmonicity : 0.094609 Specific harmonicity : 0.086383 Fundamental : 1/150, -7.2288 octaves, 1.7442 Hz. Guide tone : 1836, 10.8424 octaves, 480344.538 Hz. Exponens Consonantiae : 2.754000E+05, 18.07117 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 80.0, average 26.66667 Mersenne's string divisions : 36764 Sum of van Prooijen's expressibility: 3.61606, average 1.20535 Sum of Tenney's harmonic distance : 7.31503, average 2.43834 Vogel's harmonic complexity : 16.33333 Wille's k value : 76 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 20.07848, average 3.34641 Lattice compactness (without 2's) : 16.76324, average 2.79387 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 3 1.00000 5 1 5: -2 .. 0 -1.33333 4 1 17: 0 .. 1 0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <6 10 16 31| Scale is weakly epimorphic with val: <6 11 15 27| Scale is weakly epimorphic with val: <6 11 15 30| Scale is weakly epimorphic with val: <6 11 15 33| Scale is weakly epimorphic with val: <6 11 17 32| Scale is weakly epimorphic with val: <7 11 16 27| Scale is weakly epimorphic with val: <7 11 16 30| Scale is weakly epimorphic with val: <7 11 16 33| Scale is weakly epimorphic with val: <7 11 17 28| Scale is weakly epimorphic with val: <7 11 17 31| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <7 11 19 33| Scale is weakly epimorphic with val: <7 12 16 30| Scale is weakly epimorphic with val: <8 11 15 28| Scale is weakly epimorphic with val: <8 11 15 31| Scale is weakly epimorphic with val: <8 11 16 32| Scale is weakly epimorphic with val: <8 12 17 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 27.3842 c. M: 34.2830 c. 4: 0 1 3 N G T3 SD: 20.4244 c. M: 34.2830 c. 9: 1 1 7 N M DE S SD: 17.8169 c. M: 22.5609 c. 10: 1 2 7 N T3 SD: 12.9432 c. M:-16.1759 c. 11: 1 2 8 N T3 SD: 6.5214 c. M:-10.9938 c. 12: 1 2 9 N T3 SD: 6.5393 c. M: 8.7263 c. 14: 1 3 10 N T3 SD: 5.2843 c. M:-9.0610 c. 15: 1 3 11 N T3 SD: 0.6702 c. M: 1.0800 c. 71: 5 14 52 N T3 SD: 0.4571 c. M:-0.7906 c. 86: 6 17 63 N T3 SD: 0.2691 c. M:-0.4643 c. 101: 7 20 74 N T3 SD: 0.1467 c. M:-0.2350 c. 116: 8 23 85 N T3 SD: 0.0888 c. M: 0.1393 c. 131: 9 26 96 N T3 SD: 0.1065 c. M: 0.1721 c. 247: 17 49 181 N T3 SD: 0.0905 c. M: 0.1567 c. 333: 23 66 244 N T3 SD: 0.0993 c. M: 0.1264 c. 363: 25 72 266 N T3 SD: 0.0879 c. M: 0.1512 c. 407: 28 81 298 N T3 SD: 0.0847 c. M:-0.1455 c. 422: 29 84 309 N T3 SD: 0.0794 c. M:-0.1252 c. 437: 30 87 320 N T3 SD: 0.0813 c. M:-0.1063 c. 478: 33 95 350 N T3 SD: 0.0951 c. M:-0.1301 c. 479: 33 95 351 N T3 SD: 0.0873 c. M: 0.1483 c. 493: 34 98 361 N T3 SD: 0.0754 c. M:-0.1132 c. 508: 35 101 372 N T3 SD: 0.0590 c. M:-0.0973 c. 523: 36 104 383 N T3 SD: 0.0475 c. M:-0.0823 c. 538: 37 107 394 N T3 SD: 0.0432 c. M:-0.0681 c. 553: 38 110 405 N T3 SD: 0.0466 c. M: 0.0593 c. 609: 42 121 446 N T3 SD: 0.0531 c. M:-0.0651 c. 624: 43 124 457 N T3 SD: 0.0376 c. M:-0.0533 c. 639: 44 127 468 N T3 SD: 0.0251 c. M:-0.0421 c. 654: 45 130 479 N T3 SD: 0.0198 c. M:-0.0313 c. 755: 52 150 553 N T3 SD: 0.0139 c. M:-0.0195 c. 770: 53 153 564 N T3 SD: 0.0034 c. M:-0.0056 c. 1656: 114 329 1213 N T3 SD: 0.0030 c. M: 0.0045 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: 100.5060 cents 6 x 7:8 S SD: 66.8167 cents 7 x 8:9 S SD: 58.2143 cents 8 x 9:11 SD: 44.2510 cents 9 x 10:12 S SD: 24.5831 cents 10 x 11:13 SD: 27.0660 cents 11 x 12:15 S SD: 21.3096 cents 12 x 13:16 SD: 2.6675 cents 13 x 14:17 SD: 16.9891 cents 14 x 15:19 SD: 16.8020 cents 15 x 16:20 S SD: 10.7531 cents 16 x 17:21 SD: 19.6419 cents 17 x 18:23 SD: 21.2961 cents 18 x 19:24 SD: 19.8173 cents 19 x 21:25 SD: 23.0664 cents 20 x 22:27 SD: 19.1810 cents 21:22:23:28 SD: 17.4094 cents 22:23:24:29 SD: 16.7174 cents 23:24:25:31 SD: 15.0038 cents 24:25:26:32 SD: 12.2595 cents 26:27:28:35 S SD: 11.8473 cents 27:28:29:36 SD: 10.0728 cents 33:34:36:44 SD: 8.2022 cents 34:35:37:45 SD: 8.0901 cents 35:36:38:47 SD: 7.0331 cents 36:37:39:48 SD: 4.7307 cents 39:40:42:52 SD: 3.5833 cents 48:49:52:64 SD: 1.8397 cents 51:52:55:68 SD: 0.8676 cents 99:101:107:132 SD: 0.4465 cents 150:153:162:200 SD: 0.0000 cents