Scala analysis: 529_M37
Miscellaneous tetrachord 16/15 * 2240/2187 * 2187/1792
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 7168/6561 153.185900 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 2187/1792 344.8591 1: 16/15 111.7313 minor diatonic semitone 2: 2240/2187 41.4546 3: 2187/1792 344.8591
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 2240/2187 41.455 cents 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 2187/1792 344.859 cents 2: 1 7168/6561 153.186 cents 2: 1 5/4 386.314 cents major third 2: 1 729/560 456.590 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 : 111.7 153.2 498.0 111.7: 41.5 386.3 498.0 153.2: 344.9 456.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.4546 .. 344.8591 cents 4782969/4014080, 303.4045 cents 2240/2187, 41.4546 cents 2: 153.1859 .. 456.5904 cents 4782969/4014080, 303.4045 cents 12845056/14348907,-191.6732 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 2240/2187, 41.4546 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 2187/1792, 344.8591 cents Average / Smallest step : 4.004741 Largest / Average step : 2.077277 Largest / Smallest step : 8.318956 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 136.58843 cents, oct.: 409.76530 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2162-tone equal temperament with octave 4/3 degrees: 485 665 2162 Least number of segments generator : 1083 of 249.483 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1703 of 392.308 cents and inv. generated superset size: 68 = 65 more = 2266.667% 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 41.45461 cents Scale diversity : 0.705944 Lumma stability : 0.166469 Lumma impropriety factor : 0.384851 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 : 2240/2187, 41.4546 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 classes 1 and 2 combined -- Rational properties -- Prime limit : 7 Odd number limit : 6561 (O: 2187 U: 6561) Highest odd numerator or denominator: 6561 Scale harmonicity : 0.020825 Average absolute harmonicity : 0.104947 Specific harmonicity : 0.109546 Fundamental : 1/32805, -15.0016 octaves, 0.0080 Hz. Guide tone : 7168, 12.8074 octaves, 1875332.052 Hz. Exponens Consonantiae : 2.351462E+08, 27.80898 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 6883.5, average 2294.50000 Mersenne's string divisions : 2979193 Sum of van Prooijen's expressibility: 5.47018, average 1.82339 Sum of Tenney's harmonic distance : 11.13176, average 3.71059 Vogel's harmonic complexity : 25.00000 Wille's k value : 5467 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 10 Triangular lattice diameter : 7 Lattice compactness : 41.56447, average 6.92741 Lattice compactness (without 2's) : 25.68897, average 4.28149 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 10 5.33333 16 3: -8 ..-1 -3.33333 10 1 5: -1 .. 0 -0.33333 1 1 7: 0 .. 1 0.33333 1 1 Average exponent except 2's :-10 / 3 =-3.33333 Average absolute exponent except 2's: 12 / 3 = 4.00000 Scale is weakly epimorphic with val: <7 10 15 18| Scale is weakly epimorphic with val: <7 10 15 21| Scale is weakly epimorphic with val: <7 11 15 19| Scale is weakly epimorphic with val: <7 11 15 22| Scale is JI-epimorphic with val: <7 11 16 20| Scale is weakly epimorphic with val: <7 11 18 19| Scale is weakly epimorphic with val: <7 11 18 22| Scale is weakly epimorphic with val: <7 11 19 20| Scale is weakly epimorphic with val: <8 11 18 18| Scale is weakly epimorphic with val: <8 11 18 21| Scale is weakly epimorphic with val: <8 12 15 19| Scale is weakly epimorphic with val: <8 12 17 18| Scale is weakly epimorphic with val: <8 12 17 21| Scale is weakly epimorphic with val: <8 12 18 19|
FIT/MODE
3: 1 0 2 N G T3 SD: 32.2041 c. M:-54.2837 c. 4: 1 0 3 N G T3 SD: 18.1251 c. M: 28.6746 c. 9: 2 1 6 N T3 SD: 7.4319 c. M:-12.8291 c. 10: 2 1 7 N T3 SD: 7.3299 c. M: 12.1223 c. 13: 3 1 9 N T3 SD: 1.8491 c. M:-3.2022 c. 23: 5 2 16 N T3 SD: 2.2029 c. M: 3.4606 c. 32: 7 3 22 N T3 SD: 2.1423 c. M: 2.7839 c. 35: 8 3 24 N T3 SD: 2.2814 c. M:-3.3425 c. 36: 8 3 25 N T3 SD: 0.8413 c. M: 1.0546 c. 49: 11 4 34 N T3 SD: 0.4197 c. M: 0.7231 c. 94: 21 8 65 N T3 SD: 0.3806 c. M:-0.4663 c. 107: 24 9 74 N T3 SD: 0.2409 c. M:-0.4168 c. 120: 27 10 83 N T3 SD: 0.2893 c. M:-0.3780 c. 143: 32 12 99 N T3 SD: 0.1655 c. M: 0.2807 c. 156: 35 13 108 N T3 SD: 0.0343 c. M:-0.0587 c. 361: 81 30 250 N T3 SD: 0.0294 c. M: 0.0474 c. 517: 116 43 358 N T3 SD: 0.0127 c. M:-0.0158 c. 673: 151 56 466 N T3 SD: 0.0083 c. M:-0.0143 c. 829: 186 69 574 N T3 SD: 0.0106 c. M:-0.0134 c. 1190: 267 99 824 N T3 SD: 0.0092 c. M:-0.0149 c. 1489: 334 124 1031 N T3 SD: 0.0091 c. M: 0.0140 c. 1502: 337 125 1040 N T3 SD: 0.0091 c. M:-0.0138 c. 1645: 369 137 1139 N T3 SD: 0.0098 c. M:-0.0121 c. 1694: 380 141 1173 N T3 SD: 0.0075 c. M: 0.0093 c. 1850: 415 154 1281 N T3 SD: 0.0049 c. M: 0.0077 c. 2006: 450 167 1389 N T3 SD: 0.0037 c. M: 0.0063 c. 2162: 485 180 1497 N T3 SD: 0.0044 c. M:-0.0056 c. 2367: 531 197 1639 N T3 SD: 0.0038 c. M: 0.0060 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: 91.5512 cents 6 x 7:8 S SD: 56.8425 cents 7 x 8:9 S SD: 50.1155 cents 8 x 9:11 SD: 36.7795 cents 9 x 10:12 S SD: 14.6089 cents 10 x 11:13 SD: 22.6982 cents 11 x 12:15 S SD: 19.4946 cents 12 x 13:16 SD: 7.3066 cents 13:14 x 17 SD: 18.7389 cents 14:15 x 19 SD: 15.7988 cents 15:16 x 20 S SD: 0.0000 cents 16:17 x 21 SD: 14.0467 cents 18:19:20:24 S SD: 11.4616 cents 21:22:23:28 SD: 10.4968 cents 23 x 25:31 SD: 10.3479 cents 24 x 26:32 SD: 7.3066 cents 25 x 27:33 SD: 13.2352 cents 26:28 x 35 S SD: 11.7146 cents 27:29:30:36 SD: 10.5263 cents 28:30:31:37 SD: 9.6070 cents 29:31:32:39 SD: 7.6872 cents 30:32:33:40 SD: 3.9394 cents 33:35:36:44 SD: 3.3962 cents 42:45:46:56 SD: 2.9443 cents 45:48:49:60 SD: 1.9193 cents 75:80:82:100 SD: 0.4314 cents 195:208:213:260 SD: 0.1102 cents 270:288:295:360 SD: 0.0403 cents 465:496:508:620 SD: 0.0229 cents