Scala analysis: 476_D17
Diatonic tetrachord 10/9 * 13/12 * 72/65, Avicenna
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 65/54 320.976373 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 72/65 177.0686 1: 10/9 182.4037 minor whole tone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 72/65 177.0686
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 72/65 177.069 cents 1: 1 10/9 182.404 cents minor whole tone 2: 1 6/5 315.641 cents minor third 2: 1 65/54 320.976 cents 2: 1 16/13 359.472 cents tridecimal neutral third 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 : 182.4 321.0 498.0 182.4: 138.6 315.6 498.0 321.0: 177.1 359.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.5727 .. 182.4037 cents 40/39, 43.8311 cents 13/12, 138.5727 cents 2: 315.6413 .. 359.4723 cents 40/39, 43.8311 cents 27/25, 133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 13/12, 138.5727 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 1.198036 Largest / Average step : 1.098718 Largest / Smallest step : 1.316304 Median interval of one step : 72/65, 177.0686 cents, amount: 1 Least squares average step : 165.60653 cents, oct.: 496.81960 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 841-tone equal temperament with octave 4/3 degrees: 308 542 841 Least number of segments generator : 421 of 249.319 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 459 of 271.822 cents and inv. generated superset size: 26 = 23 more = 866.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LSM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 133.23757 cents Scale diversity : 1.242969 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.823988 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 : 325/324, 5.3351 cents 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 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 n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 13 Odd number limit : 65 (O: 65 U: 65) Highest odd numerator or denominator: 65 Scale harmonicity : 0.025282 Average absolute harmonicity : 0.106482 Specific harmonicity : 0.124292 Fundamental : 1/54, -5.7549 octaves, 4.8449 Hz. Guide tone : 260, 8.0224 octaves, 68022.647 Hz. Exponens Consonantiae : 1.404000E+04, 13.77726 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 72.5, average 24.16667 Mersenne's string divisions : 2261 Sum of van Prooijen's expressibility: 3.24428, average 1.08143 Sum of Tenney's harmonic distance : 6.57873, average 2.19291 Vogel's harmonic complexity : 12.33333 Wille's k value : 32 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 16.20418, average 2.70070 Lattice compactness (without 2's) : 11.83061, average 1.97177 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -3 ..-1 -2.00000 6 1 5: 0 .. 1 0.66667 2 1 13: 0 .. 1 0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 17 26| Scale is weakly epimorphic with val: <6 10 17 29| Scale is weakly epimorphic with val: <6 11 15 27| Scale is weakly epimorphic with val: <6 11 19 25| Scale is weakly epimorphic with val: <6 11 19 28| Scale is weakly epimorphic with val: <7 10 15 25| Scale is weakly epimorphic with val: <7 10 16 26| Scale is weakly epimorphic with val: <7 10 16 29| Scale is JI-epimorphic with val: <7 11 16 26| Scale is weakly epimorphic with val: <7 11 16 29| Scale is weakly epimorphic with val: <7 11 17 27| = patent Scale is weakly epimorphic with val: <7 11 17 30| Scale is weakly epimorphic with val: <7 11 19 26| Scale is weakly epimorphic with val: <7 11 19 29| Scale is weakly epimorphic with val: <7 12 18 28| Scale is weakly epimorphic with val: <8 11 15 29| Scale is weakly epimorphic with val: <8 11 17 25| Scale is weakly epimorphic with val: <8 11 17 28| Scale is weakly epimorphic with val: <8 11 18 26| Scale is weakly epimorphic with val: <8 12 18 29| Scale is weakly epimorphic with val: <8 12 19 27| Scale is weakly epimorphic with val: <8 12 19 30|
FIT/MODE
3: 1 1 1 SP B ME I SD: 11.4130 c. M: 16.3887 c. 8: 3 2 3 SP M ME I SD: 6.1398 c. M: 9.6982 c. 11: 4 3 4 SP M ME I SD: 2.4489 c. M: 4.0386 c. 25: 9 7 9 SP M DE I SD: 2.2075 c. M: 3.1075 c. 36: 13 10 13 SP M DE I SD: 2.1800 c. M: 2.7810 c. 51: 19 14 18 SP T3 SD: 1.9608 c. M:-3.1425 c. 54: 20 15 19 SP T3 SD: 1.5900 c. M:-2.0574 c. 57: 21 16 20 SP T3 SD: 1.4770 c. M:-2.3160 c. 62: 23 17 22 SP T3 SD: 1.3740 c. M:-2.3549 c. 65: 24 18 23 SP T3 SD: 0.9867 c. M:-1.4898 c. 68: 25 19 24 SP T3 SD: 0.8467 c. M:-1.2880 c. 76: 28 21 27 SP T3 SD: 0.6319 c. M:-1.0866 c. 79: 29 22 28 SP T3 SD: 0.3989 c. M:-0.5463 c. 90: 33 25 32 SP T3 SD: 0.1231 c. M:-0.2128 c. 183: 67 51 65 SP T3 SD: 0.1025 c. M:-0.1674 c. 194: 71 54 69 SP T3 SD: 0.0853 c. M: 0.1295 c. 273: 100 76 97 SP T3 SD: 0.0645 c. M:-0.1076 c. 284: 104 79 101 SP T3 SD: 0.0329 c. M: 0.0530 c. 374: 137 104 133 SP T3 SD: 0.0324 c. M: 0.0436 c. 467: 171 130 166 SP T3 SD: 0.0284 c. M: 0.0361 c. 557: 204 155 198 SP T3 SD: 0.0150 c. M:-0.0257 c. 841: 308 234 299 SP T3 SD: 0.0026 c. M: 0.0044 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 5 x S SD: 65.3373 cents 5 x 6:7 S SD: 42.3178 cents 6 x 7:8 S SD: 27.0527 cents 7:8 x 9 S SD: 39.8203 cents 8:9:10:11 H SD: 29.0009 cents 9:10:11:12 H SD: 8.8105 cents 24:27:29:32 SD: 7.5032 cents 29:32:35:39 SD: 6.5439 cents 30:33:36:40 S SD: 6.0663 cents 34:38:41:45 SD: 5.5392 cents 35:39:42:47 SD: 4.7690 cents 36:40:43:48 SD: 4.4562 cents 44:49:53:59 SD: 3.5453 cents 45:50:54:60 SD: 1.7784 cents 54:60:65:72 SD: 0.0000 cents