Scala analysis: 394_D6
Diatonic tetrachord 49/48 * 8/7 * 8/7, Al-Farabi
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 49/48 35.696812 slendro diesis, septimal 1/6-tone 2: 7/6 266.870906 septimal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 49/48 35.6968 slendro diesis, septimal 1/6-tone 2: 8/7 231.1741 septimal whole tone 3: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 1 64/49 462.348 cents 2 septatones or septatonic major third 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 : 35.7 266.9 498.0 35.7 : 231.2 462.3 498.0 266.9: 231.2 266.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 231.1741 cents 384/343, 195.4773 cents 49/48, 35.6968 cents 2: 266.8709 .. 462.3482 cents 384/343, 195.4773 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 4.650695 Largest / Average step : 1.392489 Largest / Smallest step : 6.476043 Median interval of one step : 8/7, 231.1741 cents, amount: 2 Most common interval of one step : 8/7, 231.1741 cents, amount: 2 Least squares average step : 147.39812 cents, oct.: 442.19435 cents Scale is strictly proper Scale has Myhill's property chromas: 384/343, 195.4773 cents and 18432/16807, 159.7805 cents, ratio: 1.223412 generators: 231.17409 cents and 2 of 266.87091 cents ET pair of linear temperament : 26&56 Scale is distributional even Scale is a mode of a 293-tone equal temperament with octave 4/3 degrees: 21 157 293 generators: 136 and 157 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABB Step pattern size order : SLL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 0.492957 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.215022 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 : 49/48, 35.6968 cents Most common intervals : 8/7, 231.1741 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 All steps are superparticular (epimoric) Steps are increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Limited inverse transpositions : 1 Inversional symmetry on degrees : 2 Inversional symmetry on intervals : 0-1 -- Rational properties -- Prime limit : 7 Odd number limit : 49 (O: 49 U: 49) Highest odd numerator or denominator: 49 Scale harmonicity : 0.034202 Average absolute harmonicity : 0.107557 Specific harmonicity : 0.161616 Fundamental : 1/48, -5.5850 octaves, 5.4505 Hz. Guide tone : 196, 7.6147 octaves, 51278.611 Hz. Exponens Consonantiae : 9.408000E+03, 13.19967 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 58.5, average 19.50000 Mersenne's string divisions : 8827 Sum of van Prooijen's expressibility: 3.01242, average 1.00414 Sum of Tenney's harmonic distance : 6.07387, average 2.02462 Vogel's harmonic complexity : 10.00000 Wille's k value : 24 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 21.19981, average 3.53330 Lattice compactness (without 2's) : 8.65028, average 1.44171 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.00000 7 3: -1 ..-1 -1.00000 3 1 7: 0 .. 2 1.00000 3 2 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 19| Scale is weakly epimorphic with val: <6 11 19| Scale is weakly epimorphic with val: <6 11 20| Scale is weakly epimorphic with val: <7 10 20| Scale is weakly epimorphic with val: <7 11 19| Scale is JI-epimorphic with val: <7 11 20| = patent Scale is weakly epimorphic with val: <7 11 22| Scale is weakly epimorphic with val: <7 12 22| Scale is weakly epimorphic with val: <8 11 22|
FIT/MODE
3: 0 1 2 N G T3 SD: 61.7689 c. M: 100.8559 c. 4: 0 2 2 P M DE S SD: 23.0422 c. M: 35.6968 c. 6: 0 3 3 P M DE S SD: 23.0422 c. M: 35.6968 c. 9: 1 4 4 SP M DE S SD: 12.6785 c. M:-19.6415 c. 10: 1 4 5 P T3 SD: 13.1351 c. M: 17.8484 c. 11: 1 5 5 SP M DE S SD: 6.1839 c. M:-9.5800 c. 13: 1 6 6 SP M DE S SD: 1.6876 c. M:-2.6143 c. 15: 1 7 7 SP M DE S SD: 1.6097 c. M: 2.4938 c. 28: 2 13 13 SP M DE S SD: 0.0789 c. M: 0.1222 c. 153: 11 71 71 SP M DE S SD: 0.0712 c. M:-0.1103 c. 181: 13 84 84 SP M DE S SD: 0.0480 c. M:-0.0744 c. 209: 15 97 97 SP M DE S SD: 0.0310 c. M:-0.0480 c. 237: 17 110 110 SP M DE S SD: 0.0180 c. M:-0.0279 c. 265: 19 123 123 SP M DE S SD: 0.0078 c. M:-0.0121 c. 293: 21 136 136 SP M DE S SD: 0.0005 c. M: 0.0008 c. 2316: 166 1075 1075 SP M DE S SD: 0.0005 c. M:-0.0007 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 48.7680 cents 6 x 7:8 S SD: 0.0000 cents 7 x 8:9 S SD: 36.1882 cents 8 x 9:11 SD: 41.2374 cents 9 x 11:12 SD: 40.2685 cents 10 x 12:13 S SD: 32.7861 cents 14:15:16:19 SD: 32.0184 cents 15:16:18:20 S SD: 30.1105 cents 16:17:19:21 SD: 26.8308 cents 17:18:20:23 SD: 23.2145 cents 18:19:21:24 SD: 19.3021 cents 21:22:25:28 SD: 18.9559 cents 22:23:26:29 SD: 16.9734 cents 23:24:27:31 SD: 14.5602 cents 24:25:28:32 SD: 11.6585 cents 28:29:33:37 SD: 11.4394 cents 29:30:34:39 SD: 9.5566 cents 30:31:35:40 SD: 7.0233 cents 35:36:41:47 SD: 6.4332 cents 36:37:42:48 SD: 3.9124 cents 42:43:49:56 SD: 1.6800 cents 48:49:56:64 S SD: 0.0000 cents