Scala analysis: 641_T48
Aristoxenian style tetrachord 9 + 15 + 6, Athanasopoulos
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 150.000 cents 150.000000 2: 400.000 cents 400.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 100.0000 cents 100.0000 1: 150.0000 cents 150.0000 2: 250.0000 cents 250.0000 3: 100.0000 cents 100.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 100.00000 cents 1: 1 150.00000 cents 1: 1 250.00000 cents 2: 1 250.00000 cents 2: 1 350.00000 cents 2: 1 400.00000 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 : 150.0 400.0 500.0 150.0: 250.0 350.0 500.0 400.0: 100.0 250.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 100.0000 .. 250.0000 cents 150.00000 cents 100.00000 cents 2: 250.0000 .. 400.0000 cents 150.00000 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 100.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 250.00000 cents Average / Smallest step : 1.666667 Largest / Average step : 1.500000 Largest / Smallest step : 2.500000 Median interval of one step : 150.00000 cents, amount: 1 Least squares average step : 175.00000 cents, oct.: 525.00000 cents Scale is proper Scale has trivalence property Scale is a mode of a 10-tone equal temperament with octave 500.000 cents degrees: 3 8 10 Least number of segments generator : 7 of 350.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 7 of 350.000 cents and inv. generated superset size: 6 = 3 more = 200.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MLS Interval vector is [ 0 1 1 0 1 ] Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.136403 Rothenberg stability : 0.666667 = 2/3 Lumma stability : 0.400000 Rothenberg efficiency : 0.777778 redundancy: 0.222222 Efficiency x scale size : 2.333333 Number of different interval sizes : 5 = 2.50000 / 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 : 50.00000 cents Most common intervals : 250.00000 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 1 1 1 SP B ME I SD: 39.6746 c. M: 66.6667 c. 4: 1 2 1 P M ME I SD: 20.4124 c. M: 25.0000 c. 6: 2 3 1 P T3 SD: 13.6083 c. M:-16.6667 c. 9: 3 4 2 SP T3 SD: 11.5648 c. M:-16.6667 c. 10: 3 5 2 P 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: 13.6863 cents 5 x 6:7 S SD: 59.0014 cents 6:7 x 8 S SD: 58.4436 cents 7:8:9 x S SD: 44.2157 cents 8:9:10:11 H SD: 25.2259 cents 9:10:11:12 H SD: 20.6014 cents 10:11 x 13 SD: 24.0909 cents 11:12:14:15 S SD: 13.6312 cents 12:13:15:16 SD: 5.9789 cents 23:25:29:31 SD: 5.9116 cents 30:33:38:40 SD: 5.9105 cents 33:36:42:44 S SD: 5.8761 cents 34:37:43:45 SD: 5.5089 cents 35:38:44:47 SD: 4.4752 cents 42:46:53:56 SD: 2.7364 cents 54:59:68:72 SD: 1.3159 cents 66:72:83:88 SD: 1.2751 cents 77:84:97:103 SD: 1.2401 cents 89:97:112:119 SD: 1.2296 cents 111:121:140:148 SD: 0.9219 cents 123:134:155:164 SD: 0.8729 cents 131:143:165:175 SD: 0.7530 cents 143:156:180:191 SD: 0.6814 cents 177:193:223:236 SD: 0.6546 cents 188:205:237:251 SD: 0.3508 cents 200:218:252:267 SD: 0.2799 cents 254:277:320:339 SD: 0.0942 cents