Scala analysis: 156_C5
Chromatic tetrachord 80/77 * 77/74 * 37/30, Ptolemy
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 80/77 66.169865 2: 40/37 134.969675 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 37/30 363.0753 1: 80/77 66.1699 2: 77/74 68.7998 3: 37/30 363.0753
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 80/77 66.170 cents 1: 1 77/74 68.800 cents 1: 1 37/30 363.075 cents 2: 1 40/37 134.970 cents 2: 1 296/231 429.245 cents 2: 1 77/60 431.875 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 : 66.2 135.0 498.0 66.2 : 68.8 431.9 498.0 135.0: 363.1 429.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.1699 .. 363.0753 cents 2849/2400, 296.9055 cents 80/77, 66.1699 cents 2: 134.9697 .. 431.8751 cents 2849/2400, 296.9055 cents 1200/1369,-228.1056 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 80/77, 66.1699 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 37/30, 363.0753 cents Average / Smallest step : 2.508922 Largest / Average step : 2.187003 Largest / Smallest step : 5.487019 Median interval of one step : 77/74, 68.7998 cents, amount: 1 Least squares average step : 130.73173 cents, oct.: 392.19519 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2273-tone equal temperament with octave 4/3 degrees: 302 616 2273 Least number of segments generator : 1137 of 249.132 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1212 of 265.566 cents and inv. generated superset size: 42 = 39 more = 1400.000% 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 66.16987 cents Scale diversity : 0.692741 Lumma stability : 0.265718 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 : 5929/5920, 2.6299 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 294.2755 cents: 2 -- Rational properties -- Prime limit : 37 Odd number limit : 231 (O: 77 U: 231) Highest odd numerator or denominator: 77 Scale harmonicity : 0.024077 Fundamental : 1/8547, -13.0612 octaves, 0.0306 Hz. Guide tone : 80, 6.3219 octaves, 20930.045 Hz. Exponens Consonantiae : 6.837600E+05, 19.38313 octaves Euler's gradus suavitatis : 63 Sum of Mann's harmonic distance : 120.5, average 40.16667 Mersenne's string divisions : 12089 Sum of van Prooijen's expressibility: 3.93181, average 1.31060 Sum of Tenney's harmonic distance : 8.03902, average 2.67967 Vogel's harmonic complexity : 45.00000 Wille's k value : 1424 Wilson's harmonic complexity : 63 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 16.04977, average 2.67496 Lattice compactness (without 2's) : 8.56048, average 1.42675 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -1 .. 0 -0.33333 1 1 5: 0 .. 1 0.66667 2 7: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 1 37: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 11 16 19 24 38| Scale is weakly epimorphic with val: <7 11 16 19 26 36| Scale is weakly epimorphic with val: <7 11 16 19 26 39| Scale is weakly epimorphic with val: <7 11 16 20 25 36| Scale is weakly epimorphic with val: <7 11 16 20 25 39| Scale is weakly epimorphic with val: <7 11 16 20 26 38| Scale is weakly epimorphic with val: <7 11 16 21 24 36| Scale is weakly epimorphic with val: <7 11 16 21 24 39| Scale is weakly epimorphic with val: <7 11 16 21 25 38| Scale is weakly epimorphic with val: <7 11 17 19 24 37| Scale is weakly epimorphic with val: <7 11 17 19 24 40| Scale is JI-epimorphic with val: <7 11 17 19 25 36| Scale is weakly epimorphic with val: <7 11 17 19 25 39| Scale is JI-epimorphic with val: <7 11 17 20 24 36| Scale is weakly epimorphic with val: <7 11 17 20 24 39| Scale is weakly epimorphic with val: <7 11 17 20 26 37| Scale is weakly epimorphic with val: <7 11 17 20 26 40| Scale is weakly epimorphic with val: <7 11 17 21 25 37| Scale is weakly epimorphic with val: <7 11 17 21 25 40| Scale is weakly epimorphic with val: <7 11 17 21 26 36| Scale is weakly epimorphic with val: <7 11 17 21 26 39| Scale is weakly epimorphic with val: <7 11 18 19 25 38| Scale is JI-epimorphic with val: <7 11 18 19 26 37| Scale is weakly epimorphic with val: <7 11 18 19 26 40| Scale is weakly epimorphic with val: <7 11 18 20 24 38| Scale is JI-epimorphic with val: <7 11 18 20 25 37| Scale is weakly epimorphic with val: <7 11 18 20 25 40| Scale is JI-epimorphic with val: <7 11 18 21 24 37| Scale is weakly epimorphic with val: <7 11 18 21 24 40| Scale is weakly epimorphic with val: <7 11 18 21 26 38| Scale is weakly epimorphic with val: <7 12 18 19 24 38| Scale is weakly epimorphic with val: <7 12 18 19 26 36| Scale is weakly epimorphic with val: <7 12 18 20 25 36| Scale is weakly epimorphic with val: <7 12 18 21 24 36|
FIT/MODE
3: 0 1 2 N G T3 SD: 42.1990 c. M: 66.1699 c. 4: 0 1 3 N G T3 SD: 38.6774 c. M: 66.1699 c. 5: 1 0 4 N G T3 SD: 28.0984 c. M: 35.3607 c. 6: 1 1 4 N M DE S SD: 20.3905 c. M:-31.0453 c. 7: 1 1 5 N M DE S SD: 5.1156 c. M:-7.3289 c. 15: 2 2 11 N M DE S SD: 1.2532 c. M: 2.1577 c. 22: 3 3 16 N M DE S SD: 1.1236 c. M:-1.7454 c. 37: 5 5 27 N M DE S SD: 0.6872 c. M:-1.1335 c. 52: 7 7 38 N M DE S SD: 0.7166 c. M: 0.8806 c. 59: 8 8 43 N M DE S SD: 0.7880 c. M:-1.3617 c. 89: 12 12 65 N M DE S SD: 0.6850 c. M:-0.9823 c. 96: 13 13 70 N M DE S SD: 0.7369 c. M:-1.2737 c. 99: 13 14 72 N T3 SD: 0.6668 c. M:-0.8608 c. 107: 14 15 78 N T3 SD: 0.5804 c. M: 1.0051 c. 114: 15 16 83 N T3 SD: 0.4552 c. M: 0.6376 c. 122: 16 17 89 N T3 SD: 0.5133 c. M: 0.8525 c. 129: 17 18 94 N T3 SD: 0.3228 c. M: 0.5360 c. 136: 18 19 99 N T3 SD: 0.3377 c. M:-0.5279 c. 144: 19 20 105 N T3 SD: 0.2673 c. M: 0.4556 c. 151: 20 21 110 N T3 SD: 0.1912 c. M:-0.2611 c. 166: 22 23 121 N T3 SD: 0.0978 c. M: 0.1639 c. 181: 24 25 132 N T3 SD: 0.1105 c. M: 0.1398 c. 188: 25 26 137 N T3 SD: 0.0869 c. M:-0.1383 c. 203: 27 28 148 N T3 SD: 0.0456 c. M:-0.0726 c. 369: 49 51 269 N T3 SD: 0.0195 c. M: 0.0338 c. 572: 76 79 417 N T3 SD: 0.0062 c. M: 0.0099 c. 941: 125 130 686 N T3 SD: 0.0070 c. M: 0.0109 c. 1513: 201 209 1103 N T3 SD: 0.0051 c. M: 0.0071 c. 2085: 277 288 1520 N T3 SD: 0.0048 c. M: 0.0078 c. 2273: 302 314 1657 N T3 SD: 0.0028 c. M:-0.0042 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 17:18 x 23 SD: 20.6979 cents 18:19 x 24 SD: 13.7166 cents 21:22:23:28 SD: 8.9053 cents 23:24:25:31 SD: 7.4144 cents 24:25:26:32 SD: 1.9222 cents 51:53:55:68 SD: 1.4232 cents 75:78:81:100 SD: 0.8161 cents 99:103:107:132 SD: 0.8141 cents 159:165:172:212 SD: 0.7716 cents 183:190:198:244 SD: 0.6157 cents 207:215:224:276 SD: 0.5839 cents 210:218:227:280 SD: 0.4860 cents 234:243:253:312 SD: 0.2843 cents 258:268:279:344 SD: 0.2016 cents 309:321:334:412 SD: 0.1167 cents 333:346:360:444 SD: 0.0433 cents