Scala analysis: 598_T5
Aristoxenian style tetrachord 2 + 4 + 24, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33.333 cents 33.333330 2: 100.000 cents 100.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 400.0000 cents 400.0000 1: 33.3333 cents 33.3333 2: 66.6667 cents 66.6667 3: 400.0000 cents 400.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33.33333 cents 1: 1 66.66667 cents 1: 1 400.00000 cents 2: 1 100.00000 cents 2: 1 433.33333 cents 2: 1 466.66667 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 : 33.3 100.0 500.0 33.3 : 66.7 466.7 500.0 100.0: 400.0 433.3 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3333 .. 400.0000 cents 366.66667 cents 33.33333 cents 2: 100.0000 .. 466.6667 cents 366.66667 cents -300.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 33.33333 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 400.00000 cents Average / Smallest step : 5.000001 Largest / Average step : 2.400000 Largest / Smallest step : 12.000001 Median interval of one step : 66.66667 cents, amount: 1 Least squares average step : 123.80952 cents, oct.: 371.42857 cents Scale is not proper Scale has trivalence property Scale is a mode of a 15-tone equal temperament with octave 500.000 cents degrees: 1 3 15 Least number of segments generator : 11 of 366.667 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 14 of 466.667 cents and inv. generated superset size: 4 = 1 more = 133.333% Number of contiguous 1-step segments: 1 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 1 1 1 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 33.33333 cents Scale diversity : 0.393283 Lumma stability : 0.133333 Lumma impropriety factor : 0.600000 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 : 33.33333 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% -- Rational properties --
FIT/MODE
3: 0 0 3 N M DE S SD: 60.8581 c. M: 100.0000 c. 4: 0 1 3 N G T3 SD: 24.0563 c. M: 33.3333 c. 5: 0 1 4 N G T3 SD: 19.2450 c. M: 33.3333 c. 6: 0 1 5 N G T3 SD: 21.5166 c. M: 33.3333 c. 9: 1 1 7 N M DE S SD: 14.3444 c. M:-22.2222 c. 10: 1 1 8 N M DE S SD: 9.6225 c. M:-16.6667 c. 11: 1 1 9 N M DE S SD: 8.7477 c. M:-12.1212 c. 13: 1 2 10 N T3 SD: 9.3628 c. M:-15.3846 c. 14: 1 2 11 N T3 SD: 4.3470 c. M:-7.1429 c. 15: 1 2 12 N T3 SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x 2 S SD: 700.0000 cents 2 x x 3 S SD: 201.9550 cents 3 x x 4 S SD: 1.9550 cents 4 x x 5 S SD: 113.6863 cents 5 x x 7 SD: 82.5122 cents 6 x 7:8 S SD: 83.4412 cents 7 x 8:9 S SD: 73.1791 cents 8 x 9:11 SD: 57.9457 cents 9 x 10:12 S SD: 41.2134 cents 10 x 11:13 SD: 39.7552 cents 11 x 12:15 S SD: 31.3427 cents 12 x 13:16 SD: 19.3111 cents 13 x 14:17 SD: 22.7276 cents 14 x 15:19 SD: 17.3275 cents 15 x 16:20 S SD: 5.9465 cents 16 x 17:21 SD: 14.8182 cents 17 x 18:23 SD: 11.6712 cents 18 x 19:24 SD: 3.3445 cents 19 x 20:25 S SD: 13.6448 cents 20 x 21:27 SD: 12.4852 cents 21 x 22:28 SD: 9.7805 cents 22 x 23:29 SD: 15.8404 cents 23 x 24:31 SD: 15.6017 cents 24 x 25:32 SD: 14.6963 cents 25 x 26:33 SD: 18.7416 cents 26:27:28:35 S SD: 15.0501 cents 27:28:29:36 SD: 12.6662 cents 28:29:30:37 SD: 12.6288 cents 29:30:31:39 SD: 10.7938 cents 30:31:32:40 S SD: 8.7596 cents 32:33:34:43 SD: 7.8514 cents 33:34:35:44 SD: 6.1824 cents 36:37:38:48 SD: 5.2023 cents 45:46:48:60 S SD: 4.2648 cents 47:48:50:63 SD: 3.5382 cents 48:49:51:64 SD: 1.9426 cents 51:52:54:68 SD: 0.7450 cents 149:152:158:199 SD: 0.7179 cents 152:155:161:203 SD: 0.3675 cents 203:207:215:271 SD: 0.2491 cents 403:411:427:538 SD: 0.2459 cents 454:463:481:606 SD: 0.2175 cents 469:478:497:626 SD: 0.1959 cents 520:530:551:694 SD: 0.1744 cents 570:581:604:761 SD: 0.1681 cents