Scala analysis: 678_T85
Tempered tetrachord in cents 125 + 125 + 250, Chapter 5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 125.000 cents 125.000000 2: 250.000 cents 250.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 250.0000 cents 250.0000 1: 125.0000 cents 125.0000 2: 125.0000 cents 125.0000 3: 250.0000 cents 250.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 125.00000 cents 1: 1 250.00000 cents 2: 1 250.00000 cents 2: 2 375.00000 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 : 125.0 250.0 500.0 125.0: 125.0 375.0 500.0 250.0: 250.0 375.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 125.0000 .. 250.0000 cents 125.00000 cents 125.00000 cents 2: 250.0000 .. 375.0000 cents 125.00000 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 125.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 250.00000 cents Average / Smallest step : 1.333333 Largest / Average step : 1.500000 Largest / Smallest step : 2.000000 Median interval of one step : 125.00000 cents, amount: 2 Most common interval of one step : 125.00000 cents, amount: 2 Least squares average step : 151.78571 cents, oct.: 455.35714 cents Scale is proper Scale has Myhill's property chromas: 125.00000 cents and 1/1, 0.0000 cents generators: 1 of 125.00000 cents and 375.00000 cents Scale is maximally even in 4-tone equal temperament Scale is equal temperament minus one tone ET pair of linear temperament : 8&8 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 4-tone equal temperament with octave 500.000 cents degrees: 1 2 4 generators: 1 and 3 Number of contiguous 1-step segments: 1 Scale is a Winograd/Gamer deep scale Scale is an Agmon diatonic system Step pattern alph. order: AAB Step pattern size order : SSL Interval vector is [ 2 1 ] Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.100127 Rothenberg stability : 0.666667 = 2/3 Lumma stability : 0.500000 Rothenberg efficiency : 1.000000 redundancy: 0.000000 Efficiency x scale size : 3.000000 Number of different interval sizes : 3 = 1.50000 / 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 : 125.00000 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are increasing Formal octave complements present : 2 = 66.6667% 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: 1 1 1 SP B ME I SD: 53.7914 c. M:-83.3333 c. 4: 1 1 2 P 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 x 5 S SD: 113.6863 cents 5 x 6:7 S SD: 52.7187 cents 6 x 7:8 S SD: 8.4919 cents 7 x 8:9 S SD: 33.7953 cents 8 x 9:11 SD: 34.4885 cents 9:10 x 12 S SD: 28.7185 cents 11:12:13:15 SD: 19.8886 cents 12:13:14:16 S SD: 7.2470 cents 26:28:30:35 S SD: 5.0496 cents 27:29:31:36 SD: 3.6932 cents 39:42:45:52 SD: 1.4834 cents 96:103:111:128 SD: 1.3157 cents 108:116:125:144 SD: 1.2885 cents 122:131:141:163 SD: 0.8176 cents 134:144:155:179 SD: 0.8128 cents 135:145:156:180 SD: 0.7869 cents 161:173:186:215 SD: 0.3064 cents 200:215:231:267 SD: 0.2011 cents 361:388:417:482 SD: 0.1910 cents 373:401:431:498 SD: 0.1751 cents 496:533:573:662 SD: 0.1733 cents 508:546:587:678 SD: 0.1216 cents