Scala analysis: 597_T4
Aristoxenian style tetrachord 3 + 3 + 24, Aristoxenos
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 50.000 cents 50.000000 2: 100.000 cents 100.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 400.0000 cents 400.0000 1: 50.0000 cents 50.0000 2: 50.0000 cents 50.0000 3: 400.0000 cents 400.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 50.00000 cents 1: 1 400.00000 cents 2: 1 100.00000 cents 2: 2 450.00000 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 : 50.0 100.0 500.0 50.0 : 50.0 450.0 500.0 100.0: 400.0 450.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 50.0000 .. 400.0000 cents 350.00000 cents 50.00000 cents 2: 100.0000 .. 450.0000 cents 350.00000 cents -300.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 50.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 400.00000 cents Average / Smallest step : 3.333333 Largest / Average step : 2.400000 Largest / Smallest step : 8.000000 Median interval of one step : 50.00000 cents, amount: 2 Most common interval of one step : 50.00000 cents, amount: 2 Least squares average step : 125.00000 cents, oct.: 375.00000 cents Scale is not proper Scale has Myhill's property chromas: 350.00000 cents and 300.00000 cents, ratio: 1.166667 generators: 1 of 50.00000 cents and 450.00000 cents ET pair of linear temperament : 20&20 Scale is distributional even Scale is a mode of a 10-tone equal temperament with octave 500.000 cents degrees: 1 2 10 generators: 1 and 9 Number of contiguous 1-step segments: 1 Step pattern alph. order: AAB Step pattern size order : SSL Interval vector is [ 2 1 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 50.00000 cents Scale diversity : 0.429841 Lumma stability : 0.200000 Lumma impropriety factor : 0.600000 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 : 50.00000 cents Most common intervals : 50.00000 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 0 3 N M DE S SD: 64.5497 c. M: 100.0000 c. 4: 0 1 3 N G T3 SD: 32.2749 c. M: 50.0000 c. 5: 0 1 4 N G T3 SD: 28.8675 c. M: 50.0000 c. 6: 0 1 5 N G T3 SD: 30.4290 c. M: 50.0000 c. 7: 1 0 6 N G T3 SD: 20.6197 c. M: 28.5714 c. 8: 1 1 6 N M DE S SD: 16.1374 c. M:-25.0000 c. 9: 1 1 7 N M DE S SD: 7.1722 c. M:-11.1111 c. 10: 1 1 8 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 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 23:24 x 31 SD: 14.5061 cents 24:25 x 32 SD: 10.3823 cents 25:26 x 33 SD: 13.1816 cents 26:27:28:35 S SD: 11.7829 cents 27:28:29:36 SD: 9.0313 cents 29:30:31:39 SD: 7.3110 cents 30:31:32:40 S SD: 4.5611 cents 32:33:34:43 SD: 4.3195 cents 33:34:35:44 SD: 1.0613 cents 69:71:73:92 SD: 1.0572 cents 101:104:107:135 SD: 0.8075 cents 102:105:108:136 SD: 0.7415 cents 134:138:142:179 SD: 0.5396 cents 167:172:177:223 SD: 0.4735 cents 170:175:180:227 SD: 0.4047 cents 203:209:215:271 SD: 0.2451 cents 236:243:250:315 SD: 0.2191 cents 439:452:465:586 SD: 0.2170 cents