Scala analysis: 117_E14
Enharmonic tetrachord 4374/4235 * 4235/4096 * 8192/6561
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 4374/4235 55.909501 2: 2187/2048 113.685006 apotome 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 8192/6561 384.3600 Pythagorean diminished fourth 1: 4374/4235 55.9095 2: 4235/4096 57.7755 3: 8192/6561 384.3600 Pythagorean diminished fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 4374/4235 55.910 cents 1: 1 4235/4096 57.776 cents 1: 1 8192/6561 384.360 cents Pythagorean diminished fourth 2: 1 2187/2048 113.685 cents apotome 2: 1 16384/12705 440.269 cents 2: 1 8470/6561 442.135 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 : 55.9 113.7 498.0 55.9 : 57.8 442.1 498.0 113.7: 384.4 440.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 55.9095 .. 384.3600 cents 17346560/14348907, 328.4505 cents 4374/4235, 55.9095 cents 2: 113.6850 .. 442.1355 cents 17346560/14348907, 328.4505 cents 14348907/16777216,-270.6750 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 4374/4235, 55.9095 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 8192/6561, 384.3600 cents Average / Smallest step : 2.969352 Largest / Average step : 2.315212 Largest / Smallest step : 6.874681 Median interval of one step : 4235/4096, 57.7755 cents, amount: 1 Least squares average step : 126.95818 cents, oct.: 380.87454 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1069-tone equal temperament with octave 4/3 degrees: 120 244 1069 Least number of segments generator : 535 of 249.255 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 794 of 369.923 cents and inv. generated superset size: 20 = 17 more = 666.667% 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 55.90950 cents Scale diversity : 0.533238 Lumma stability : 0.224516 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 : 17935225/17915904, 1.8660 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 326.5845 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 12705 (O: 4235 U: 12705) Highest odd numerator or denominator: 4235 Scale harmonicity : 0.011444 Average absolute harmonicity : 0.087248 Specific harmonicity : 0.056774 Fundamental : 1/26019840, -24.6331 octaves, 0.0000 Hz. Guide tone : 8748, 13.0947 octaves, 2288700.445 Hz. Exponens Consonantiae : 2.276216E+11, 37.72785 octaves Euler's gradus suavitatis : 60 Sum of Mann's harmonic distance : 6425.5, average 2141.83333 Mersenne's string divisions : 36459115 Sum of van Prooijen's expressibility: 7.44382, average 2.48127 Sum of Tenney's harmonic distance : 14.99809, average 4.99936 Vogel's harmonic complexity : 47.00000 Wille's k value : 13892917 Wilson's harmonic complexity : 58 Rectangular lattice diameter : 12 Triangular lattice diameter : 8 Lattice compactness : 58.69572, average 9.78262 Lattice compactness (without 2's) : 34.23229, average 5.70538 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -11 .. 2 -2.66667 14 3: -1 .. 7 4.33333 15 2 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 11: -2 .. 0 -0.66667 2 1 Average exponent except 2's : 9 / 3 = 3.00000 Average absolute exponent except 2's: 19 / 3 = 6.33333 Scale is weakly epimorphic with val: <6 11 15 19 23| Scale is weakly epimorphic with val: <6 11 16 18 23| Scale is weakly epimorphic with val: <7 12 15 19 27| Scale is weakly epimorphic with val: <7 12 15 21 26| Scale is weakly epimorphic with val: <7 12 16 18 27| Scale is weakly epimorphic with val: <7 12 16 20 26| Scale is weakly epimorphic with val: <7 12 16 22 25| Scale is weakly epimorphic with val: <7 12 17 19 26| Scale is weakly epimorphic with val: <7 12 17 21 25| Scale is weakly epimorphic with val: <7 12 18 18 26| Scale is weakly epimorphic with val: <7 12 18 20 25| Scale is weakly epimorphic with val: <7 12 18 22 24| Scale is weakly epimorphic with val: <7 12 19 19 25| Scale is weakly epimorphic with val: <7 12 19 21 24| Scale is weakly epimorphic with val: <8 11 15 19 24| Scale is weakly epimorphic with val: <8 11 15 21 23| Scale is weakly epimorphic with val: <8 11 16 18 24| Scale is weakly epimorphic with val: <8 11 16 20 23| Scale is weakly epimorphic with val: <8 11 17 19 23| Scale is weakly epimorphic with val: <8 11 18 18 23| Scale is weakly epimorphic with val: <8 12 15 20 27| Scale is weakly epimorphic with val: <8 12 15 22 26| Scale is weakly epimorphic with val: <8 12 16 19 27| Scale is weakly epimorphic with val: <8 12 16 21 26| Scale is weakly epimorphic with val: <8 12 17 18 27| Scale is weakly epimorphic with val: <8 12 17 20 26| Scale is weakly epimorphic with val: <8 12 17 22 25| Scale is weakly epimorphic with val: <8 12 18 19 26| Scale is weakly epimorphic with val: <8 12 18 21 25| Scale is weakly epimorphic with val: <8 12 19 20 25| Scale is weakly epimorphic with val: <8 12 19 22 24|
FIT/MODE
3: 0 1 2 N G T3 SD: 44.2127 c. M: 55.9095 c. 4: 0 1 3 N G T3 SD: 32.8790 c. M: 55.9095 c. 5: 0 1 4 N G T3 SD: 33.2867 c. M: 55.9095 c. 6: 0 1 5 N G T3 SD: 36.8193 c. M: 55.9095 c. 7: 1 1 5 N M DE S SD: 18.7171 c. M:-28.6136 c. 8: 1 1 6 N M DE S SD: 7.2452 c. M:-10.8262 c. 9: 1 1 7 N M DE S SD: 1.7679 c. M: 3.0083 c. 26: 3 3 20 N M DE S SD: 1.1523 c. M:-1.5572 c. 35: 4 4 27 N M DE S SD: 0.5898 c. M:-1.0099 c. 44: 5 5 34 N M DE S SD: 0.4880 c. M:-0.6865 c. 114: 13 13 88 N M DE S SD: 0.5140 c. M:-0.8851 c. 123: 14 14 95 N M DE S SD: 0.4836 c. M:-0.7785 c. 135: 15 16 104 N T3 SD: 0.5131 c. M:-0.6809 c. 136: 15 16 105 N T3 SD: 0.5722 c. M: 0.9781 c. 141: 16 16 109 N M DE S SD: 0.5147 c. M: 0.6535 c. 144: 16 17 111 N T3 SD: 0.4199 c. M: 0.5712 c. 153: 17 18 118 N T3 SD: 0.3592 c. M: 0.5712 c. 162: 18 19 125 N T3 SD: 0.3320 c. M: 0.5712 c. 171: 19 20 132 N T3 SD: 0.3344 c. M: 0.5712 c. 179: 20 21 138 N T3 SD: 0.2724 c. M:-0.3923 c. 188: 21 22 145 N T3 SD: 0.2076 c. M: 0.2768 c. 197: 22 23 152 N T3 SD: 0.1741 c. M: 0.2903 c. 206: 23 24 159 N T3 SD: 0.1774 c. M: 0.3025 c. 215: 24 25 166 N T3 SD: 0.2080 c. M: 0.3138 c. 223: 25 26 172 N T3 SD: 0.1329 c. M:-0.2177 c. 232: 26 27 179 N T3 SD: 0.0762 c. M: 0.0941 c. 241: 27 28 186 N T3 SD: 0.0660 c. M: 0.1119 c. 267: 30 31 206 N T3 SD: 0.0650 c. M:-0.1006 c. 276: 31 32 213 N T3 SD: 0.0175 c. M:-0.0303 c. 784: 88 91 605 N T3 SD: 0.0159 c. M:-0.0268 c. 793: 89 92 612 N T3 SD: 0.0087 c. M: 0.0129 c. 1069: 120 124 825 N T3 SD: 0.0035 c. M: 0.0059 c. 1345: 151 156 1038 N T3 SD: 0.0040 c. M: 0.0048 c. 2129: 239 247 1643 N T3 SD: 0.0039 c. M:-0.0068 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 x 19:24 SD: 10.0410 cents 19 x 20:25 S SD: 16.9192 cents 20:21 x 27 SD: 17.8750 cents 21:22 x 28 SD: 12.3138 cents 22:23 x 29 SD: 14.4434 cents 23:24:25:31 SD: 13.3610 cents 24:25:26:32 SD: 9.6456 cents 25:26:27:33 SD: 9.5964 cents 26:27:28:35 S SD: 8.0062 cents 27:28:29:36 SD: 4.0861 cents 30:31:32:40 S SD: 0.7112 cents 147:152:157:196 SD: 0.6709 cents 177:183:189:236 SD: 0.6026 cents 207:214:221:276 SD: 0.5702 cents 237:245:253:316 SD: 0.5566 cents 249:257:266:332 SD: 0.4442 cents 279:288:298:372 SD: 0.3385 cents 309:319:330:412 SD: 0.2612 cents 339:350:362:452 SD: 0.2091 cents 369:381:394:492 SD: 0.1806 cents 396:409:423:528 SD: 0.1679 cents 426:440:455:568 SD: 0.1127 cents 456:471:487:608 SD: 0.0727 cents 486:502:519:648 SD: 0.0582 cents