Scala analysis: 118_E14
Enharmonic tetrachord 6561/6283 * 6283/6144 * 8192/6561
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 6561/6283 74.954569 2: 2187/2048 113.685006 apotome 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 8192/6561 384.3600 Pythagorean diminished fourth 1: 6561/6283 74.9546 2: 6283/6144 38.7304 3: 8192/6561 384.3600 Pythagorean diminished fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 6283/6144 38.730 cents 1: 1 6561/6283 74.955 cents 1: 1 8192/6561 384.360 cents Pythagorean diminished fourth 2: 1 2187/2048 113.685 cents apotome 2: 1 25132/19683 423.090 cents 2: 1 8192/6283 459.315 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 : 75.0 113.7 498.0 75.0 : 38.7 423.1 498.0 113.7: 384.4 459.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.7304 .. 384.3600 cents 16777216/13740921, 345.6296 cents 6283/6144, 38.7304 cents 2: 113.6850 .. 459.3146 cents 16777216/13740921, 345.6296 cents 14348907/16777216,-270.6750 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 6283/6144, 38.7304 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 8192/6561, 384.3600 cents Average / Smallest step : 4.286422 Largest / Average step : 2.315212 Largest / Smallest step : 9.923978 Median interval of one step : 6561/6283, 74.9546 cents, amount: 1 Least squares average step : 128.31854 cents, oct.: 384.95562 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1196-tone equal temperament with octave 4/3 degrees: 180 273 1196 Least number of segments generator : 599 of 249.439 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1125 of 468.479 cents and inv. generated superset size: 49 = 46 more = 1633.333% 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 38.73044 cents Scale diversity : 0.493737 Lumma stability : 0.155530 Lumma impropriety factor : 0.543475 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 : 40310784/39476089, 36.2241 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 103 Odd number limit : 19683 (O: 6561 U: 19683) Highest odd numerator or denominator: 6561 Scale harmonicity : 0.027027 Fundamental : 1/38602752, -25.2022 octaves, 0.0000 Hz. Guide tone : 26244, 14.6797 octaves, 6866101.336 Hz. Exponens Consonantiae : 1.013091E+12, 39.88190 octaves Euler's gradus suavitatis : 194 Sum of Mann's harmonic distance : 8543.0, average 2847.66667 Mersenne's string divisions : 54394340 Sum of van Prooijen's expressibility: 7.63394, average 2.54465 Sum of Tenney's harmonic distance : 15.34550, average 5.11517 Vogel's harmonic complexity : 134.33333 Wille's k value : 20611381 Wilson's harmonic complexity : 191 Rectangular lattice diameter : 11 Triangular lattice diameter : 9 Lattice compactness : 58.80372, average 9.80062 Lattice compactness (without 2's) : 34.00000, average 5.66667 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -11 .. 2 -3.00000 13 3: -1 .. 8 4.66667 16 2 61: -1 .. 0 -0.33333 1 103: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 12 / 3 = 4.00000 Average absolute exponent except 2's: 18 / 3 = 6.00000 Scale is weakly epimorphic with val: <7 12 44 49| Scale is weakly epimorphic with val: <8 12 44 49|
FIT/MODE
3: 0 1 2 N G T3 SD: 52.7782 c. M: 74.9546 c. 4: 1 0 3 N G T3 SD: 29.2864 c. M:-49.5567 c. 5: 1 0 4 N G T3 SD: 16.3908 c. M:-24.6544 c. 7: 1 1 5 N M DE S SD: 16.6655 c. M:-28.6136 c. 8: 1 1 6 N M DE S SD: 9.6345 c. M: 12.6989 c. 9: 1 1 7 N M DE S SD: 11.4578 c. M: 19.6162 c. 12: 2 1 9 N T3 SD: 7.7901 c. M:-10.8262 c. 13: 2 1 10 N T3 SD: 1.2028 c. M:-1.6677 c. 40: 6 3 31 N T3 SD: 0.9490 c. M: 1.6249 c. 53: 8 4 41 N T3 SD: 0.5465 c. M: 0.9201 c. 66: 10 5 51 N T3 SD: 0.4082 c. M:-0.5068 c. 79: 12 6 61 N T3 SD: 0.4201 c. M:-0.6978 c. 114: 17 9 88 N T3 SD: 0.3992 c. M: 0.6847 c. 127: 19 10 98 N T3 SD: 0.2574 c. M: 0.4439 c. 140: 21 11 108 N T3 SD: 0.1684 c. M: 0.2478 c. 153: 23 12 118 N T3 SD: 0.1507 c. M:-0.2469 c. 193: 29 15 149 N T3 SD: 0.1065 c. M: 0.1411 c. 206: 31 16 159 N T3 SD: 0.0310 c. M: 0.0534 c. 425: 64 33 328 N T3 SD: 0.0272 c. M:-0.0451 c. 565: 85 44 436 N T3 SD: 0.0226 c. M:-0.0279 c. 631: 95 49 487 N T3 SD: 0.0225 c. M:-0.0284 c. 771: 116 60 595 N T3 SD: 0.0130 c. M: 0.0217 c. 977: 147 76 754 N T3 SD: 0.0113 c. M: 0.0184 c. 990: 149 77 764 N T3 SD: 0.0062 c. M:-0.0101 c. 1196: 180 93 923 N T3 SD: 0.0013 c. M:-0.0020 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: 76.5929 cents 7 x 8:9 S SD: 66.6479 cents 8 x 9:11 SD: 52.3893 cents 9 x 10:12 S SD: 34.3594 cents 10 x 11:13 SD: 33.7447 cents 11 x 12:15 S SD: 26.8287 cents 12 x 13:16 SD: 12.4438 cents 13 x 14:17 SD: 18.3280 cents 14 x 15:19 SD: 15.5892 cents 15 x 16:20 S SD: 0.9769 cents 16 x 17:21 SD: 14.3138 cents 17 x 18:23 SD: 14.6267 cents 18:19 x 24 SD: 9.3242 cents 19:20 x 25 S SD: 13.3933 cents 20:21 x 27 SD: 11.7581 cents 21:22 x 28 SD: 2.7912 cents 22:23 x 29 SD: 9.9434 cents 24:25:26:32 SD: 8.4178 cents 26:27:28:35 S SD: 8.0312 cents 27:28:29:36 SD: 5.2110 cents 34 x 36:45 S SD: 9.7497 cents 35 x 37:47 SD: 10.6935 cents 36:38 x 48 SD: 9.3242 cents 38:40:41:51 SD: 8.4310 cents 39:41:42:52 SD: 6.2244 cents 40:42:43:53 SD: 6.1553 cents 41:43:44:55 SD: 5.1691 cents 42:44:45:56 SD: 2.6732 cents 45:47:48:60 SD: 0.6604 cents 162:169:173:216 SD: 0.5733 cents 177:185:189:236 SD: 0.5270 cents 204:213:218:272 SD: 0.4147 cents 249:260:266:332 SD: 0.2206 cents 294:307:314:392 SD: 0.0858 cents 339:354:362:452 SD: 0.0133 cents