Scala analysis: 647_T54
Aristoxenian style tetrachord 4.5 + 13.5 + 12, Aristoxenos
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 75.000 cents 75.000000 2: 300.000 cents 300.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 200.0000 cents 200.0000 1: 75.0000 cents 75.0000 2: 225.0000 cents 225.0000 3: 200.0000 cents 200.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 75.00000 cents 1: 1 200.00000 cents 1: 1 225.00000 cents 2: 1 275.00000 cents 2: 1 300.00000 cents 2: 1 425.00000 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 : 75.0 300.0 500.0 75.0 : 225.0 425.0 500.0 300.0: 200.0 275.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 75.0000 .. 225.0000 cents 150.00000 cents 75.00000 cents 2: 275.0000 .. 425.0000 cents 150.00000 cents 50.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 75.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 225.00000 cents Average / Smallest step : 2.222222 Largest / Average step : 1.350000 Largest / Smallest step : 3.000000 Median interval of one step : 200.00000 cents, amount: 1 Least squares average step : 155.35714 cents, oct.: 466.07143 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 20-tone equal temperament with octave 500.000 cents degrees: 3 12 20 Least number of segments generator : 11 of 275.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 17 of 425.000 cents and inv. generated superset size: 5 = 2 more = 166.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Interval vector is [ 0 0 1 0 0 0 0 1 1 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 50.00000 cents Scale diversity : 0.954867 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.400000 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 : 25.00000 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 150.0000 cents: 1 -- Rational properties --
FIT/MODE
3: 0 2 1 N G T3 SD: 47.3853 c. M: 75.0000 c. 4: 0 2 2 P M DE S SD: 52.0416 c. M: 75.0000 c. 5: 1 2 2 SP M ME S SD: 14.4338 c. M:-25.0000 c. 7: 1 3 3 SP M DE S SD: 8.5017 c. M: 14.2857 c. 8: 1 4 3 P T3 SD: 10.2062 c. M:-12.5000 c. 12: 2 5 5 SP M DE S SD: 6.8041 c. M:-8.3333 c. 13: 2 6 5 SP T3 SD: 4.5778 c. M:-7.6923 c. 20: 3 9 8 SP 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 5 x S SD: 86.3137 cents 5 x 6:7 S SD: 41.9908 cents 6 x 7:8 S SD: 16.5934 cents 7 x 8:9 S SD: 47.3051 cents 8 x 10:11 S SD: 50.2085 cents 9:10:11:12 H SD: 39.1392 cents 10:11:12:13 H SD: 34.0617 cents 11:12:13:15 SD: 28.2897 cents 12:13:14:16 S SD: 23.9045 cents 14:15:17:19 SD: 21.3527 cents 15:16:18:20 S SD: 13.3236 cents 17:18:20:23 SD: 12.7589 cents 18:19:21:24 SD: 12.6817 cents 20:21:24:27 S SD: 8.9227 cents 21:22:25:28 SD: 2.0518 cents 48:50:57:64 SD: 1.7868 cents 68:71:81:91 SD: 1.7517 cents 69:72:82:92 SD: 0.8771 cents 90:94:107:120 SD: 0.6763 cents 137:143:163:183 SD: 0.5547 cents 158:165:188:211 SD: 0.4156 cents 206:215:245:275 SD: 0.3312 cents 227:237:270:303 SD: 0.1631 cents 475:496:565:634 SD: 0.1412 cents