Scala analysis: 624_T31
Aristoxenian style tetrachord 6 + 6 + 18, Aristoxenos
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 100.000 cents 100.000000 2: 200.000 cents 200.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 300.0000 cents 300.0000 1: 100.0000 cents 100.0000 2: 100.0000 cents 100.0000 3: 300.0000 cents 300.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 100.00000 cents 1: 1 300.00000 cents 2: 1 200.00000 cents 2: 2 400.00000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 100.0 200.0 500.0 100.0: 100.0 400.0 500.0 200.0: 300.0 400.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 100.0000 .. 300.0000 cents 200.00000 cents 100.00000 cents 2: 200.0000 .. 400.0000 cents 200.00000 cents -100.00000 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 : 300.00000 cents Average / Smallest step : 1.666667 Largest / Average step : 1.800000 Largest / Smallest step : 3.000000 Median interval of one step : 100.00000 cents, amount: 2 Most common interval of one step : 100.00000 cents, amount: 2 Least squares average step : 142.85714 cents, oct.: 428.57143 cents Scale is not proper Scale has Myhill's property chromas: 200.00000 cents and 100.00000 cents, ratio: 2.000000 generators: 1 of 100.00000 cents and 400.00000 cents ET pair of linear temperament : 10&10 Scale is distributional even Scale is a mode of a 5-tone equal temperament with octave 500.000 cents degrees: 1 2 5 generators: 1 and 4 Number of contiguous 1-step segments: 1 Scale is a Winograd/Gamer deep scale Step pattern alph. order: AAB Step pattern size order : SSL Interval vector is [ 2 1 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 100.00000 cents Scale diversity : 1.075073 Lumma stability : 0.400000 Lumma impropriety factor : 0.200000 Rothenberg efficiency : 0.888889 redundancy: 0.111111 Efficiency x scale size : 2.666667 Number of different interval sizes : 4 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 100.00000 cents Most common intervals : 100.00000 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties --
FIT/MODE
3: 0 1 2 N G T3 SD: 60.8581 c. M: 100.0000 c. 4: 1 1 2 P M ME S SD: 32.2749 c. M:-50.0000 c. 5: 1 1 3 N M DE S 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 6:7 S SD: 71.0302 cents 6 x 7:8 S SD: 33.4497 cents 7 x 8:9 S SD: 36.0066 cents 8 x 9:11 SD: 25.7333 cents 9 x 10:12 S SD: 8.8523 cents 10 x 11:13 SD: 28.8143 cents 11 x 12:15 S SD: 30.8304 cents 12:13 x 16 SD: 19.3111 cents 14:15:16:19 SD: 15.5378 cents 15:16:17:20 SD: 6.8304 cents 18:19:20:24 S SD: 6.2749 cents 32:34:36:43 SD: 4.3780 cents 33:35:37:44 SD: 1.1069 cents 131:139:147:175 SD: 0.9964 cents 155:164:174:207 SD: 0.8138 cents 170:180:191:227 SD: 0.6788 cents 188:199:211:251 SD: 0.5353 cents 203:215:228:271 SD: 0.4071 cents 221:234:248:295 SD: 0.3791 cents 236:250:265:315 SD: 0.2324 cents 269:285:302:359 SD: 0.1600 cents 523:554:587:698 SD: 0.1514 cents 555:588:623:741 SD: 0.1314 cents 588:623:660:785 SD: 0.0905 cents