Scala analysis: 081_E8
Enharmonic tetrachord 282429536481/274877906944 * 70368744177664/68630377364883 * 81/64
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46.920 cents 46.920021 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: 46.9200 cents 46.9200 2: 43.3050 cents 43.3050 3: 81/64 407.8200 Pythagorean major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 43.30497 cents 1: 1 46.92002 cents 1: 1 81/64 407.820 cents Pythagorean major third 2: 1 256/243 90.225 cents limma, Pythagorean minor second 2: 1 451.12498 cents 2: 1 454.74002 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 : 46.9 90.2 498.0 46.9 : 43.3 451.1 498.0 90.2 : 407.8 454.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.3050 .. 407.8200 cents 364.51503 cents 43.30497 cents 2: 90.2250 .. 454.7400 cents 364.51503 cents 16384/19683,-317.5950 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 43.30497 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 81/64, 407.8200 cents Average / Smallest step : 3.833624 Largest / Average step : 2.456525 Largest / Smallest step : 9.417394 Median interval of one step : 46.92002 cents, amount: 1 Least squares average step : 122.96464 cents, oct.: 368.89393 cents Scale is not proper Scale has trivalence property Scale is a mode of a 138-tone equal temperament with octave 4/3 degrees: 13 25 138 Least number of segments generator : 71 of 256.241 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 113 of 407.819 cents and inv. generated superset size: 7 = 4 more = 233.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Interval vector is [ 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 43.30497 cents Scale diversity : 0.354475 Lumma stability : 0.173900 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 : 3.61505 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% Limited inverse transpositions with margin 364.5150 cents: 2 -- Rational properties -- Prime limit : 3 (not all pitches rational)
FIT/MODE
3: 0 0 3 N M DE S SD: 58.7141 c. M: 90.2250 c. 4: 0 1 3 N G T3 SD: 33.5511 c. M: 46.9200 c. 5: 0 1 4 N G T3 SD: 27.6258 c. M: 46.9200 c. 6: 0 1 5 N G T3 SD: 27.4079 c. M: 46.9200 c. 7: 1 0 6 N G T3 SD: 17.8039 c. M:-24.2293 c. 9: 1 1 7 N M DE S SD: 12.7690 c. M:-20.4517 c. 10: 1 1 8 N M DE S SD: 5.6680 c. M:-9.3840 c. 11: 1 1 9 N M DE S SD: 0.9675 c. M: 1.6432 c. 72: 7 6 59 N T3 SD: 0.8838 c. M:-1.5010 c. 83: 8 7 68 N T3 SD: 0.6384 c. M:-1.0843 c. 94: 9 8 77 N T3 SD: 0.4505 c. M:-0.7651 c. 105: 10 9 86 N T3 SD: 0.3019 c. M:-0.5128 c. 116: 11 10 95 N T3 SD: 0.1816 c. M:-0.3084 c. 127: 12 11 104 N T3 SD: 0.0820 c. M:-0.1393 c. 138: 13 12 113 N T3 SD: 0.0016 c. M: 0.0027 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 25:26 x 33 SD: 13.6282 cents 26:27 x 35 SD: 12.3861 cents 27:28 x 36 SD: 8.0204 cents 30:31:32:40 S SD: 7.8844 cents 32:33:34:43 SD: 6.9830 cents 33:34:35:44 SD: 4.1927 cents 36:37:38:48 SD: 1.1390 cents 75:77:79:100 SD: 0.4618 cents 111:114:117:148 SD: 0.3942 cents 186:191:196:248 SD: 0.3624 cents 357:367:376:476 SD: 0.3382 cents 393:404:414:524 SD: 0.2924 cents 429:441:452:572 SD: 0.2874 cents 432:444:455:576 SD: 0.2218 cents 468:481:493:624 SD: 0.1767 cents 504:518:531:672 SD: 0.1760 cents 507:521:534:676 SD: 0.1551 cents 543:558:572:724 SD: 0.0987 cents 579:595:610:772 SD: 0.0935 cents