Scala analysis: 463_D15
Diatonic tetrachord 9/8 * 18/17 * 272/243
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 81/68 302.864594 Persian wosta 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 272/243 195.1804 Persian whole tone 1: 9/8 203.9100 major whole tone 2: 18/17 98.9546 Arabic lute index finger 3: 272/243 195.1804 Persian whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 18/17 98.955 cents Arabic lute index finger 1: 1 272/243 195.180 cents Persian whole tone 1: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 81/68 302.865 cents Persian wosta 2: 1 34/27 399.090 cents septendecimal major 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 : 203.9 302.9 498.0 203.9: 99.0 294.1 498.0 302.9: 195.2 399.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 98.9546 .. 203.9100 cents 17/16, 104.9554 cents 18/17, 98.9546 cents 2: 294.1350 .. 399.0904 cents 17/16, 104.9554 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 18/17, 98.9546 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.677689 Largest / Average step : 1.228263 Largest / Smallest step : 2.060642 Median interval of one step : 272/243, 195.1804 cents, amount: 1 Least squares average step : 164.55530 cents, oct.: 493.66590 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1827-tone equal temperament with octave 4/3 degrees: 748 1111 1827 Least number of segments generator : 914 of 249.159 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1462 of 398.545 cents and inv. generated superset size: 44 = 41 more = 1466.667% 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 90.22500 cents Scale diversity : 1.105737 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.578530 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 : 2187/2176, 8.7296 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 : 17 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.020639 Average absolute harmonicity : 0.119219 Specific harmonicity : 0.104790 Fundamental : 1/408, -8.6724 octaves, 0.6412 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 1.321920E+05, 17.01228 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 86.5, average 28.83333 Mersenne's string divisions : 17731 Sum of van Prooijen's expressibility: 3.33985, average 1.11328 Sum of Tenney's harmonic distance : 6.67751, average 2.22584 Vogel's harmonic complexity : 21.33333 Wille's k value : 229 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 25.18538, average 4.19756 Lattice compactness (without 2's) : 17.45819, average 2.90970 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -1.00000 7 3: -1 .. 4 1.66667 7 2 17: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 4 / 3 = 1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is JI-epimorphic with val: <7 11 28| Scale is weakly epimorphic with val: <7 11 31| Scale is weakly epimorphic with val: <7 12 27| Scale is weakly epimorphic with val: <7 12 30| Scale is weakly epimorphic with val: <7 12 33|
FIT/MODE
3: 1 1 1 SP B ME I SD: 27.6083 c. M: 37.8950 c. 5: 2 1 2 SP M ME I SD: 3.5738 c. M: 4.6920 c. 31: 13 6 12 SP T3 SD: 3.1720 c. M:-4.9476 c. 34: 14 7 13 SP T3 SD: 2.8248 c. M:-4.7514 c. 36: 15 7 14 SP T3 SD: 2.2555 c. M:-3.6087 c. 39: 16 8 15 SP T3 SD: 2.1064 c. M:-3.6246 c. 41: 17 8 16 SP T3 SD: 1.5723 c. M:-2.5965 c. 46: 19 9 18 SP T3 SD: 1.0553 c. M:-1.8042 c. 51: 21 10 20 SP T3 SD: 0.6782 c. M:-1.1674 c. 56: 23 11 22 SP T3 SD: 0.4639 c. M:-0.6442 c. 61: 25 12 24 SP T3 SD: 0.4613 c. M: 0.7717 c. 105: 43 21 41 SP T3 SD: 0.4085 c. M:-0.7057 c. 110: 45 22 43 SP T3 SD: 0.2984 c. M:-0.4901 c. 115: 47 23 45 SP T3 SD: 0.2686 c. M: 0.3612 c. 161: 66 32 63 SP T3 SD: 0.2253 c. M:-0.2932 c. 166: 68 33 65 SP T3 SD: 0.1129 c. M:-0.1628 c. 171: 70 34 67 SP T3 SD: 0.0295 c. M:-0.0400 c. 569: 233 113 223 SP T3 SD: 0.0210 c. M:-0.0346 c. 740: 303 147 290 SP T3 SD: 0.0111 c. M:-0.0192 c. 911: 373 181 357 SP T3 SD: 0.0072 c. M:-0.0096 c. 1656: 678 329 649 SP T3 SD: 0.0043 c. M: 0.0075 c. 1827: 748 363 716 SP T3 SD: 0.0026 c. M: 0.0032 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: 83.4491 cents 5 x 6:7 S SD: 42.7140 cents 6 x 7:8 S SD: 17.9968 cents 7:8 x 9 S SD: 34.3053 cents 8:9:10:11 H SD: 33.0013 cents 9:10:11:12 H SD: 16.4878 cents 12 x 14:16 S SD: 17.9968 cents 13:15 x 17 SD: 27.6192 cents 14:16:17:19 SD: 17.6031 cents 15:17:18:20 SD: 6.0230 cents 31:35:37:41 SD: 5.2359 cents 32:36:38:43 SD: 4.8322 cents 41:46:49:55 SD: 4.2896 cents 42:47:50:56 SD: 3.0802 cents 48:54:57:64 SD: 1.7839 cents 57:64:68:76 SD: 1.4256 cents 63:71:75:84 SD: 1.0720 cents 105:118:125:140 SD: 0.6989 cents 120:135:143:160 SD: 0.2374 cents 288:324:343:384 SD: 0.0990 cents 408:459:486:544 SD: 0.0000 cents