Scala analysis: 160_C5
Chromatic tetrachord 60/59 * 118/111 * 37/30
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 60/59 29.097055 2: 40/37 134.969675 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 37/30 363.0753 1: 60/59 29.0971 2: 118/111 105.8726 3: 37/30 363.0753
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 60/59 29.097 cents 1: 1 118/111 105.873 cents 1: 1 37/30 363.075 cents 2: 1 40/37 134.970 cents 2: 1 74/59 392.172 cents 2: 1 59/45 468.948 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 : 29.1 135.0 498.0 29.1 : 105.9 468.9 498.0 135.0: 363.1 392.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.0971 .. 363.0753 cents 2183/1800, 333.9783 cents 60/59, 29.0971 cents 2: 134.9697 .. 468.9479 cents 2183/1800, 333.9783 cents 1200/1369,-228.1056 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 60/59, 29.0971 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 37/30, 363.0753 cents Average / Smallest step : 5.705560 Largest / Average step : 2.187003 Largest / Smallest step : 12.478078 Median interval of one step : 118/111, 105.8726 cents, amount: 1 Least squares average step : 128.08367 cents, oct.: 384.25101 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1797-tone equal temperament with octave 4/3 degrees: 105 487 1797 Least number of segments generator : 899 of 249.161 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1205 of 333.970 cents and inv. generated superset size: 32 = 29 more = 1066.667% 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 29.09706 cents Scale diversity : 0.552861 Lumma stability : 0.116845 Lumma impropriety factor : 0.458002 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 : 60/59, 29.0971 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% -- Rational properties -- Prime limit : 59 Odd number limit : 111 (O: 59 U: 111) Highest odd numerator or denominator: 59 Scale harmonicity : 0.067873 Fundamental : 1/6549, -12.6771 octaves, 0.0399 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 7.858800E+05, 19.58395 octaves Euler's gradus suavitatis : 106 Sum of Mann's harmonic distance : 101.5, average 33.83333 Mersenne's string divisions : 1309 Sum of van Prooijen's expressibility: 3.81617, average 1.27206 Sum of Tenney's harmonic distance : 7.79845, average 2.59948 Vogel's harmonic complexity : 72.66667 Wille's k value : 1091 Wilson's harmonic complexity : 107 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.23017, average 2.20503 Lattice compactness (without 2's) : 8.06450, average 1.34408 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.66667 2 37: -1 .. 0 -0.33333 1 1 59: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 10 17 35 42| Scale is weakly epimorphic with val: <7 10 18 36 43| Scale is weakly epimorphic with val: <7 10 19 37 44| Scale is weakly epimorphic with val: <7 11 15 35 44| Scale is weakly epimorphic with val: <7 11 15 37 42| Scale is weakly epimorphic with val: <7 11 15 38 44| Scale is weakly epimorphic with val: <7 11 15 40 42| Scale is weakly epimorphic with val: <7 11 15 41 44| Scale is weakly epimorphic with val: <7 11 16 35 43| Scale is weakly epimorphic with val: <7 11 16 36 42| Scale is weakly epimorphic with val: <7 11 16 38 43| Scale is weakly epimorphic with val: <7 11 16 39 42| Scale is weakly epimorphic with val: <7 11 16 41 43| Scale is weakly epimorphic with val: <7 11 17 36 44| Scale is weakly epimorphic with val: <7 11 17 37 43| Scale is weakly epimorphic with val: <7 11 17 39 44| Scale is weakly epimorphic with val: <7 11 17 40 43| Scale is weakly epimorphic with val: <7 11 18 35 44| Scale is JI-epimorphic with val: <7 11 18 37 42| Scale is weakly epimorphic with val: <7 11 18 38 44| Scale is weakly epimorphic with val: <7 11 18 40 42| Scale is weakly epimorphic with val: <7 11 18 41 44| Scale is weakly epimorphic with val: <7 11 19 35 43| Scale is weakly epimorphic with val: <7 11 19 36 42| Scale is JI-epimorphic with val: <7 11 19 38 43| Scale is weakly epimorphic with val: <7 11 19 39 42| Scale is weakly epimorphic with val: <7 11 19 41 43| Scale is weakly epimorphic with val: <7 12 17 35 42| Scale is weakly epimorphic with val: <7 12 18 36 43| Scale is weakly epimorphic with val: <7 12 19 36 42| Scale is weakly epimorphic with val: <7 12 19 37 44| Scale is weakly epimorphic with val: <7 12 19 39 42| Scale is weakly epimorphic with val: <8 11 15 36 44| Scale is weakly epimorphic with val: <8 11 16 37 42| Scale is weakly epimorphic with val: <8 11 17 38 43| Scale is weakly epimorphic with val: <8 11 18 35 42| Scale is weakly epimorphic with val: <8 11 18 38 42| Scale is weakly epimorphic with val: <8 11 18 39 44| Scale is weakly epimorphic with val: <8 11 18 41 42| Scale is weakly epimorphic with val: <8 11 19 36 43| Scale is weakly epimorphic with val: <8 11 19 39 43| Scale is weakly epimorphic with val: <8 11 19 40 42| Scale is weakly epimorphic with val: <8 12 15 36 44| Scale is weakly epimorphic with val: <8 12 16 37 42| Scale is weakly epimorphic with val: <8 12 17 36 42| Scale is weakly epimorphic with val: <8 12 17 38 43| Scale is weakly epimorphic with val: <8 12 17 39 42| Scale is weakly epimorphic with val: <8 12 18 37 43| Scale is weakly epimorphic with val: <8 12 18 39 44| Scale is weakly epimorphic with val: <8 12 18 40 43| Scale is weakly epimorphic with val: <8 12 19 35 44| Scale is weakly epimorphic with val: <8 12 19 38 44| Scale is weakly epimorphic with val: <8 12 19 40 42| Scale is weakly epimorphic with val: <8 12 19 41 44|
FIT/MODE
3: 0 1 2 N G T3 SD: 24.5659 c. M:-31.0453 c. 4: 0 1 3 N G T3 SD: 17.8514 c. M: 29.0971 c. 7: 0 2 5 N G T3 SD: 17.3239 c. M: 29.0971 c. 10: 1 2 7 N T3 SD: 14.5765 c. M:-20.7074 c. 11: 1 2 8 N T3 SD: 9.3546 c. M:-16.1798 c. 12: 1 2 9 N T3 SD: 9.3685 c. M:-12.4067 c. 14: 1 3 10 N T3 SD: 5.6472 c. M:-7.3289 c. 15: 1 3 11 N T3 SD: 2.6780 c. M:-4.1059 c. 18: 1 4 13 N T3 SD: 2.1164 c. M:-3.3762 c. 33: 2 7 24 N T3 SD: 0.8007 c. M:-1.0875 c. 52: 3 11 38 N T3 SD: 0.5501 c. M: 0.8806 c. 70: 4 15 51 N T3 SD: 0.3882 c. M: 0.6373 c. 85: 5 18 62 N T3 SD: 0.1651 c. M: 0.2046 c. 155: 9 33 113 N T3 SD: 0.1033 c. M: 0.1783 c. 188: 11 40 137 N T3 SD: 0.0838 c. M:-0.1383 c. 240: 14 51 175 N T3 SD: 0.0541 c. M: 0.0825 c. 343: 20 73 250 N T3 SD: 0.0514 c. M:-0.0688 c. 428: 25 91 312 N T3 SD: 0.0090 c. M:-0.0145 c. 941: 55 200 686 N T3 SD: 0.0081 c. M:-0.0129 c. 1096: 64 233 799 N T3 SD: 0.0090 c. M: 0.0141 c. 1369: 80 291 998 N T3 SD: 0.0041 c. M:-0.0071 c. 1797: 105 382 1310 N T3 SD: 0.0033 c. M:-0.0041 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: 99.7208 cents 6 x 7:8 S SD: 65.9506 cents 7 x 8:9 S SD: 57.4877 cents 8 x 9:11 SD: 43.5625 cents 9 x 10:12 S SD: 23.7170 cents 10 x 11:13 SD: 26.5671 cents 11 x 12:15 S SD: 20.9710 cents 12 x 13:16 SD: 1.8015 cents 13 x 14:17 SD: 17.1364 cents 14 x 15:19 SD: 17.1757 cents 15 x 16:20 S SD: 11.6192 cents 16 x 17:21 SD: 20.2743 cents 17 x 18:23 SD: 21.9992 cents 18 x 19:24 SD: 20.6833 cents 19 x 21:25 SD: 22.3191 cents 20 x 22:27 SD: 18.4702 cents 22:23:24:29 SD: 18.0353 cents 23:24:25:31 SD: 16.4183 cents 24:25:26:32 SD: 13.9104 cents 26:27:28:35 S SD: 13.4674 cents 27:28:29:36 SD: 11.8953 cents 32:33:35:43 SD: 11.4155 cents 33:34:36:44 SD: 9.1625 cents 34:35:37:45 SD: 9.0573 cents 35:36:38:47 SD: 8.1219 cents 36:37:39:48 SD: 6.2292 cents 39:40:42:52 SD: 5.3913 cents 45:46:49:60 SD: 5.1140 cents 47:48:51:63 SD: 4.4695 cents 48:49:52:64 SD: 2.5064 cents 51:52:55:68 SD: 2.0678 cents 60:61:65:80 SD: 1.2116 cents 63:64:68:84 SD: 1.1017 cents 111:113:120:148 SD: 0.6062 cents 123:125:133:164 SD: 0.4083 cents 174:177:188:232 SD: 0.3709 cents 234:238:253:312 SD: 0.1027 cents 531:540:574:708 SD: 0.0543 cents