Scala analysis: 600_T7
Aristoxenian style tetrachord 7/3 + 14/3 + 23, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 38.889 cents 38.888890 2: 116.667 cents 116.666670 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 383.3333 cents 383.3333 1: 38.8889 cents 38.8889 2: 77.7778 cents 77.7778 3: 383.3333 cents 383.3333
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 38.88889 cents 1: 1 77.77778 cents 1: 1 383.33333 cents 2: 1 116.66667 cents 2: 1 422.22222 cents 2: 1 461.11111 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 : 38.9 116.7 500.0 38.9 : 77.8 461.1 500.0 116.7: 383.3 422.2 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.8889 .. 383.3333 cents 344.44444 cents 38.88889 cents 2: 116.6667 .. 461.1111 cents 344.44444 cents -266.66666 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 38.88889 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 383.33333 cents Average / Smallest step : 4.285714 Largest / Average step : 2.300000 Largest / Smallest step : 9.857142 Median interval of one step : 77.77778 cents, amount: 1 Least squares average step : 126.58730 cents, oct.: 379.76191 cents Scale is not proper Scale has trivalence property Scale is a mode of a 90-tone equal temperament with octave 500.000 cents degrees: 7 21 90 Least number of segments generator : 47 of 261.111 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 83 of 461.111 cents and inv. generated superset size: 4 = 1 more = 133.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 0 0 0 0 0 0 1 0 0 0 0 0 0 1 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 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 38.88889 cents Scale diversity : 0.511219 Lumma stability : 0.155556 Lumma impropriety factor : 0.533333 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 : 38.88889 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 1 2 N G T3 SD: 36.5711 c. M:-50.0000 c. 4: 0 1 3 N G T3 SD: 22.9622 c. M: 38.8889 c. 5: 0 1 4 N G T3 SD: 24.4276 c. M: 38.8889 c. 8: 1 1 6 N M DE S SD: 14.4560 c. M:-23.6111 c. 9: 1 1 7 N M DE S SD: 10.1430 c. M:-16.6667 c. 11: 1 2 8 N T3 SD: 11.9872 c. M:-19.6970 c. 12: 1 2 9 N T3 SD: 5.0715 c. M:-8.3333 c. 13: 1 2 10 N T3 SD: 0.7802 c. M: 1.2821 c. 51: 4 8 39 N T3 SD: 0.5966 c. M:-0.9804 c. 64: 5 10 49 N T3 SD: 0.3170 c. M:-0.5208 c. 77: 6 12 59 N T3 SD: 0.1317 c. M:-0.2164 c. 90: 7 14 69 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: 75.1085 cents 7 x 8:9 S SD: 65.8142 cents 8 x 9:11 SD: 50.6086 cents 9 x 10:12 S SD: 32.8831 cents 10 x 11:13 SD: 33.2899 cents 11 x 12:15 S SD: 25.0965 cents 12 x 13:16 SD: 10.9965 cents 13 x 14:17 SD: 18.7128 cents 14 x 15:19 SD: 14.4106 cents 15 x 16:20 S SD: 2.6542 cents 16 x 17:21 SD: 15.7394 cents 17 x 18:23 SD: 14.6415 cents 18 x 19:24 SD: 11.5732 cents 19 x 20:25 S SD: 18.6802 cents 20 x 21:27 SD: 18.8352 cents 21 x 22:28 SD: 18.0912 cents 23:24:25:31 SD: 15.8393 cents 24:25:26:32 SD: 12.8836 cents 25:26:27:33 SD: 12.8705 cents 26:27:28:35 S SD: 10.7926 cents 27:28:29:36 SD: 8.3860 cents 29:30:31:39 SD: 7.8892 cents 30:31:32:40 S SD: 6.2165 cents 38:39:41:51 SD: 6.2074 cents 39:40:42:52 SD: 4.2628 cents 41:42:44:55 S SD: 3.5383 cents 42:43:45:56 SD: 1.2886 cents 86:88:92:115 S SD: 1.0680 cents 87:89:93:116 SD: 0.7812 cents 128:131:137:171 SD: 0.7035 cents 170:174:182:227 SD: 0.6868 cents 173:177:185:231 SD: 0.3466 cents 215:220:230:287 SD: 0.3058 cents 358:366:383:478 SD: 0.2677 cents 400:409:428:534 SD: 0.2097 cents 445:455:476:594 SD: 0.1410 cents 487:498:521:650 SD: 0.1097 cents