Scala analysis: 655_T62
Aristoxenian style tetrachord 12 + 9 + 9, Al-Farabi; Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 200.000 cents 200.000000 2: 350.000 cents 350.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 150.0000 cents 150.0000 1: 200.0000 cents 200.0000 2: 150.0000 cents 150.0000 3: 150.0000 cents 150.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 150.00000 cents 1: 1 200.00000 cents 2: 1 300.00000 cents 2: 2 350.00000 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 : 200.0 350.0 500.0 200.0: 150.0 300.0 500.0 350.0: 150.0 350.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.0000 .. 200.0000 cents 50.00000 cents 150.00000 cents 2: 300.0000 .. 350.0000 cents 50.00000 cents 100.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 150.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 200.00000 cents Average / Smallest step : 1.111111 Largest / Average step : 1.200000 Largest / Smallest step : 1.333333 Median interval of one step : 150.00000 cents, amount: 2 Most common interval of one step : 150.00000 cents, amount: 2 Least squares average step : 171.42857 cents, oct.: 514.28571 cents Scale is strictly proper Scale has Myhill's property chromas: 50.00000 cents and 100.00000 cents, ratio: 2.000000 generators: 150.00000 cents and 2 of 350.00000 cents Scale is maximally even in 10-tone equal temperament ET pair of linear temperament : 20&20 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 10-tone equal temperament with octave 500.000 cents degrees: 4 7 10 generators: 3 and 7 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABB Step pattern size order : LSS Interval vector is [ 0 0 2 1 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 100.00000 cents Scale diversity : 1.336658 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.800000 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 : 150.00000 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Steps are decreasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 1 Inversional symmetry on degrees : 2 Inversional symmetry on intervals : 0-1 -- Rational properties --
FIT/MODE
3: 1 1 1 SP B ME I SD: 21.5166 c. M: 33.3333 c. 7: 3 2 2 SP M ME S SD: 9.2214 c. M:-14.2857 c. 10: 4 3 3 SP M ME 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 5 x S SD: 36.3137 cents 5 x 6:7 S SD: 44.6900 cents 6:7 x 8 S SD: 33.4497 cents 7:8 x 9 S SD: 36.0066 cents 8:9:10:11 H SD: 20.9960 cents 9:10:11:12 H SD: 5.9644 cents 32:36:39:43 SD: 4.7663 cents 39:44:48:52 SD: 4.3667 cents 41:46:50:55 SD: 3.5818 cents 48:54:59:64 SD: 2.8125 cents 57:64:70:76 SD: 2.0075 cents 66:74:81:88 SD: 1.7707 cents 72:81:88:96 SD: 1.6941 cents 81:91:99:108 SD: 1.1969 cents 89:100:109:119 SD: 1.1717 cents 90:101:110:120 SD: 1.0892 cents 98:110:120:131 SD: 0.8441 cents 138:155:169:184 SD: 0.7999 cents 147:165:180:196 SD: 0.6834 cents 170:191:208:227 SD: 0.6328 cents 179:201:219:239 SD: 0.3910 cents 188:211:230:251 SD: 0.3331 cents 236:265:289:315 SD: 0.3299 cents 245:275:300:327 SD: 0.2152 cents 424:476:519:566 SD: 0.0966 cents 433:486:530:578 SD: 0.0379 cents