Scala analysis: 390_D6
Diatonic tetrachord 14/13 * 13/12 * 8/7, Avicenna
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-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: 14/13 128.2982 2/3-tone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 14/13 128.298 cents 2/3-tone 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 16/13 359.472 cents tridecimal neutral third 2: 1 26/21 369.747 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 128.3 266.9 498.0 128.3: 138.6 369.7 498.0 266.9: 231.2 359.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 128.2982 .. 231.1741 cents 52/49, 102.8758 cents 14/13, 128.2982 cents 2: 266.8709 .. 369.7468 cents 52/49, 102.8758 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 14/13, 128.2982 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 1.293977 Largest / Average step : 1.392489 Largest / Smallest step : 1.801849 Median interval of one step : 13/12, 138.5727 cents, amount: 1 Least squares average step : 154.01250 cents, oct.: 462.03751 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 823-tone equal temperament with octave 4/3 degrees: 212 441 823 Least number of segments generator : 412 of 249.325 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 543 of 328.601 cents and inv. generated superset size: 20 = 17 more = 666.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.266782 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.586881 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 169/168, 10.2744 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle All steps are superparticular (epimoric) Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 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 Limited inverse transpositions with margin 92.6014 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 21 (O: 13 U: 21) Highest odd numerator or denominator: 13 Scale harmonicity : 0.026242 Average absolute harmonicity : 0.105287 Specific harmonicity : 0.124735 Fundamental : 1/78, -6.2854 octaves, 3.3542 Hz. Guide tone : 28, 4.8074 octaves, 7325.516 Hz. Exponens Consonantiae : 2.184000E+03, 11.09276 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 23.5, average 7.83333 Mersenne's string divisions : 2457 Sum of van Prooijen's expressibility: 2.43616, average 0.81205 Sum of Tenney's harmonic distance : 4.96250, average 1.65417 Vogel's harmonic complexity : 16.00000 Wille's k value : 45 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 13.31194, average 2.21866 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 0 -0.66667 2 1 7: 0 .. 1 0.66667 2 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 19 27| Scale is weakly epimorphic with val: <6 10 19 30| Scale is weakly epimorphic with val: <6 11 20 27| Scale is weakly epimorphic with val: <6 11 20 30| Scale is weakly epimorphic with val: <6 11 22 25| Scale is weakly epimorphic with val: <7 10 20 25| Scale is weakly epimorphic with val: <7 10 20 28| Scale is weakly epimorphic with val: <7 10 22 26| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 11 19 30| Scale is JI-epimorphic with val: <7 11 20 26| Scale is weakly epimorphic with val: <7 11 20 29| Scale is weakly epimorphic with val: <7 11 22 27| Scale is weakly epimorphic with val: <7 11 22 30| Scale is weakly epimorphic with val: <7 12 22 25| Scale is weakly epimorphic with val: <7 12 22 28| Scale is weakly epimorphic with val: <8 11 20 25| Scale is weakly epimorphic with val: <8 11 22 26| Scale is weakly epimorphic with val: <8 11 22 29| Scale is weakly epimorphic with val: <8 12 22 27|
FIT/MODE
3: 1 1 1 SP B ME I SD: 43.4675 c. M:-65.1591 c. 4: 1 1 2 P M ME S SD: 10.5342 c. M: 17.8484 c. 7: 2 2 3 SP M ME S SD: 13.0413 c. M:-17.7262 c. 9: 2 3 4 SP T3 SD: 11.6471 c. M: 17.6216 c. 11: 3 3 5 SP M DE S SD: 5.1536 c. M:-7.5322 c. 15: 4 4 7 SP M DE S SD: 2.7036 c. M:-4.5138 c. 24: 6 7 11 SP T3 SD: 2.7551 c. M: 3.7870 c. 28: 7 8 13 SP T3 SD: 2.1867 c. M: 3.7870 c. 32: 8 9 15 SP T3 SD: 2.5534 c. M: 3.7870 c. 34: 9 9 16 SP M DE S SD: 2.7539 c. M:-3.5372 c. 35: 9 10 16 SP T3 SD: 2.0230 c. M:-3.4964 c. 39: 10 11 18 SP T3 SD: 0.8291 c. M:-1.3072 c. 43: 11 12 20 SP T3 SD: 0.5831 c. M: 0.8914 c. 54: 14 15 25 SP T3 SD: 0.5880 c. M:-0.8245 c. 58: 15 16 27 SP T3 SD: 0.4870 c. M: 0.6744 c. 82: 21 23 38 SP T3 SD: 0.4836 c. M: 0.7501 c. 97: 25 27 45 SP T3 SD: 0.0797 c. M:-0.1223 c. 237: 61 66 110 SP T3 SD: 0.0637 c. M: 0.1094 c. 334: 86 93 155 SP T3 SD: 0.0430 c. M: 0.0591 c. 392: 101 109 182 SP T3 SD: 0.0380 c. M: 0.0611 c. 489: 126 136 227 SP T3 SD: 0.0235 c. M:-0.0324 c. 586: 151 163 272 SP T3 SD: 0.0217 c. M:-0.0376 c. 629: 162 175 292 SP T3 SD: 0.0241 c. M: 0.0328 c. 726: 187 202 337 SP T3 SD: 0.0106 c. M: 0.0139 c. 823: 212 229 382 SP T3 SD: 0.0035 c. M: 0.0048 c. 2135: 550 594 991 SP T3 SD: 0.0027 c. M:-0.0037 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 9:10:11:12 H SD: 32.3413 cents 10:11:12:13 H SD: 25.0489 cents 11:12:13:15 SD: 16.7056 cents 12:13:14:16 S SD: 3.4248 cents 42:45:49:56 SD: 2.9518 cents 54:58:63:72 SD: 1.5287 cents 66:71:77:88 SD: 0.6249 cents 78:84:91:104 S SD: 0.0000 cents