Scala analysis: 075_E8
Enharmonic tetrachord 512/499 * 499/486 * 81/64, Boethius
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 512/499 44.524794 2: 256/243 90.224996 limma, Pythagorean minor second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 81/64 407.8200 Pythagorean major third 1: 512/499 44.5248 2: 499/486 45.7002 3: 81/64 407.8200 Pythagorean major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 512/499 44.525 cents 1: 1 499/486 45.700 cents 1: 1 81/64 407.820 cents Pythagorean major third 2: 1 256/243 90.225 cents limma, Pythagorean minor second 2: 1 648/499 452.345 cents 2: 1 499/384 453.520 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 : 44.5 90.2 498.0 44.5 : 45.7 453.5 498.0 90.2 : 407.8 452.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.5248 .. 407.8200 cents 40419/32768, 363.2952 cents 512/499, 44.5248 cents 2: 90.2250 .. 453.5202 cents 40419/32768, 363.2952 cents 16384/19683,-317.5950 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 512/499, 44.5248 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 81/64, 407.8200 cents Average / Smallest step : 3.728597 Largest / Average step : 2.456525 Largest / Smallest step : 9.159391 Median interval of one step : 499/486, 45.7002 cents, amount: 1 Least squares average step : 122.79356 cents, oct.: 368.38067 cents Scale is not proper Scale has trivalence property Scale is a mode of a 839-tone equal temperament with octave 4/3 degrees: 75 152 839 Least number of segments generator : 420 of 249.319 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 610 of 362.107 cents and inv. generated superset size: 8 = 5 more = 266.667% 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 44.52479 cents Scale diversity : 0.356131 Lumma stability : 0.178798 Lumma impropriety factor : 0.637683 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 : 249001/248832, 1.1754 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 362.1198 cents: 2 -- Rational properties -- Prime limit : 499 Odd number limit : 499 (O: 499 U: 499) Highest odd numerator or denominator: 499 Scale harmonicity : 0.044776 Fundamental : 1/121257, -16.8877 octaves, 0.0022 Hz. Guide tone : 512, 9.0000 octaves, 133952.289 Hz. Exponens Consonantiae : 6.208358E+07, 25.88771 octaves Euler's gradus suavitatis : 518 Sum of Mann's harmonic distance : 758.5, average 252.83333 Mersenne's string divisions : 3531423 Sum of van Prooijen's expressibility: 5.56083, average 1.85361 Sum of Tenney's harmonic distance : 11.28040, average 3.76013 Vogel's harmonic complexity : 348.00000 Wille's k value : 20209 Wilson's harmonic complexity : 514 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 40.05124, average 6.67521 Lattice compactness (without 2's) : 16.00000, average 2.66667 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 9 6.33333 19 3: -5 .. 0 -2.00000 6 2 499: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-7 / 3 =-2.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 11 64|
FIT/MODE
3: 0 0 3 N M DE S SD: 58.0890 c. M: 90.2250 c. 4: 0 1 3 N G T3 SD: 32.4448 c. M: 44.5248 c. 5: 0 1 4 N G T3 SD: 26.2711 c. M: 44.5248 c. 6: 0 1 5 N G T3 SD: 26.0420 c. M: 44.5248 c. 7: 0 1 6 N G T3 SD: 27.9663 c. M: 44.5248 c. 8: 1 0 7 N G T3 SD: 19.1195 c. M: 27.9694 c. 9: 1 1 7 N M DE S SD: 13.3567 c. M:-20.4517 c. 10: 1 1 8 N M DE S SD: 6.2165 c. M:-9.3840 c. 11: 1 1 9 N M DE S SD: 0.4738 c. M:-0.7520 c. 89: 8 8 73 N M DE S SD: 0.4218 c. M: 0.6888 c. 100: 9 9 82 N M DE S SD: 0.3752 c. M: 0.5769 c. 111: 10 10 91 N M DE S SD: 0.3444 c. M: 0.4872 c. 122: 11 11 100 N M DE S SD: 0.3246 c. M: 0.4136 c. 133: 12 12 109 N M DE S SD: 0.3128 c. M:-0.4116 c. 144: 13 13 118 N M DE S SD: 0.3064 c. M:-0.4376 c. 155: 14 14 127 N M DE S SD: 0.3038 c. M:-0.4599 c. 166: 15 15 136 N M DE S SD: 0.3037 c. M:-0.4793 c. 177: 16 16 145 N M DE S SD: 0.3053 c. M:-0.4962 c. 188: 17 17 154 N M DE S SD: 0.3081 c. M:-0.5112 c. 199: 18 18 163 N M DE S SD: 0.3115 c. M:-0.5245 c. 210: 19 19 172 N M DE S SD: 0.3153 c. M:-0.5364 c. 215: 19 20 176 N T3 SD: 0.3031 c. M: 0.5115 c. 226: 20 21 185 N T3 SD: 0.2702 c. M: 0.4500 c. 237: 21 22 194 N T3 SD: 0.2411 c. M: 0.3942 c. 248: 22 23 203 N T3 SD: 0.2154 c. M: 0.3434 c. 259: 23 24 212 N T3 SD: 0.1930 c. M: 0.2969 c. 270: 24 25 221 N T3 SD: 0.1737 c. M: 0.2541 c. 281: 25 26 230 N T3 SD: 0.1572 c. M: 0.2147 c. 292: 26 27 239 N T3 SD: 0.1437 c. M: 0.1783 c. 303: 27 28 248 N T3 SD: 0.1329 c. M:-0.1792 c. 314: 28 29 257 N T3 SD: 0.1249 c. M:-0.1844 c. 325: 29 30 266 N T3 SD: 0.1195 c. M:-0.1893 c. 326: 29 30 267 N T3 SD: 0.1369 c. M: 0.2202 c. 336: 30 31 275 N T3 SD: 0.1166 c. M:-0.1939 c. 337: 30 31 276 N T3 SD: 0.1170 c. M: 0.1884 c. 347: 31 32 284 N T3 SD: 0.1158 c. M:-0.1982 c. 348: 31 32 285 N T3 SD: 0.0983 c. M: 0.1587 c. 359: 32 33 294 N T3 SD: 0.0808 c. M: 0.1308 c. 370: 33 34 303 N T3 SD: 0.0643 c. M: 0.1046 c. 381: 34 35 312 N T3 SD: 0.0488 c. M: 0.0798 c. 392: 35 36 321 N T3 SD: 0.0342 c. M: 0.0565 c. 403: 36 37 330 N T3 SD: 0.0205 c. M: 0.0344 c. 414: 37 38 339 N T3 SD: 0.0078 c. M: 0.0135 c. 425: 38 39 348 N T3 SD: 0.0064 c. M:-0.0090 c. 839: 75 77 687 N T3 SD: 0.0034 c. M:-0.0048 c. 1264: 113 116 1035 N T3 SD: 0.0036 c. M:-0.0063 c. 2103: 188 193 1722 N T3 SD: 0.0034 c. M:-0.0057 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: 88.3230 cents 7 x 8:9 S SD: 77.1860 cents 8 x 9:11 SD: 62.7740 cents 9 x 10:12 S SD: 46.0894 cents 10 x 11:13 SD: 43.3391 cents 11 x 12:15 S SD: 35.9280 cents 12 x 13:16 SD: 24.1738 cents 13 x 14:17 SD: 25.3953 cents 14 x 15:19 SD: 21.1697 cents 15 x 16:20 S SD: 10.7531 cents 16 x 17:21 SD: 15.4945 cents 17 x 18:23 SD: 13.3695 cents 18 x 19:24 SD: 1.6890 cents 19 x 20:25 S SD: 11.4874 cents 20 x 21:27 SD: 11.1319 cents 21 x 22:28 SD: 4.8440 cents 22 x 23:29 SD: 11.9115 cents 23 x 24:31 SD: 12.4901 cents 24 x 25:32 SD: 9.7763 cents 25 x 26:33 SD: 14.1522 cents 26:27 x 35 SD: 13.3006 cents 27:28 x 36 SD: 9.2181 cents 30:31:32:40 S SD: 8.2488 cents 32:33:34:43 SD: 7.2651 cents 33:34:35:44 SD: 4.5554 cents 36:37:38:48 SD: 1.4860 cents 39:40:41:52 SD: 1.2369 cents 75:77:79:100 SD: 0.3571 cents 339:348:357:452 SD: 0.3552 cents 390:400:411:520 SD: 0.2997 cents 426:437:449:568 SD: 0.2993 cents 429:440:452:572 SD: 0.2397 cents 465:477:490:620 SD: 0.2006 cents 504:517:531:672 SD: 0.1508 cents 540:554:569:720 SD: 0.1332 cents 579:594:610:772 SD: 0.0850 cents