Scala analysis: 440_D12
Diatonic tetrachord 99/89 * 89/84 * 112/99
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 99/89 184.347827 2: 33/28 284.447037 undecimal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 112/99 213.5980 1: 99/89 184.3478 2: 89/84 100.0992 quasi-equal semitone 3: 112/99 213.5980
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 89/84 100.099 cents quasi-equal semitone 1: 1 99/89 184.348 cents 1: 1 112/99 213.598 cents 2: 1 33/28 284.447 cents undecimal minor third 2: 1 356/297 313.697 cents 2: 1 112/89 397.946 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 : 184.3 284.4 498.0 184.3: 100.1 313.7 498.0 284.4: 213.6 397.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 100.0992 .. 213.5980 cents 3136/2937, 113.4988 cents 89/84, 100.0992 cents 2: 284.4470 .. 397.9458 cents 3136/2937, 113.4988 cents 3267/3136, 70.8491 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 89/84, 100.0992 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 112/99, 213.5980 cents Average / Smallest step : 1.658505 Largest / Average step : 1.286618 Largest / Smallest step : 2.133863 Median interval of one step : 99/89, 184.3478 cents, amount: 1 Least squares average step : 160.52692 cents, oct.: 481.58076 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1413-tone equal temperament with octave 4/3 degrees: 523 807 1413 Least number of segments generator : 707 of 249.199 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1228 of 432.837 cents and inv. generated superset size: 56 = 53 more = 1866.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 70.84907 cents Scale diversity : 1.184427 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.544223 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 : 9968/9801, 29.2501 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 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 89 Odd number limit : 297 (O: 99 U: 297) Highest odd numerator or denominator: 99 Scale harmonicity : 0.024711 Fundamental : 1/7476, -12.8681 octaves, 0.0350 Hz. Guide tone : 396, 8.6294 octaves, 103603.724 Hz. Exponens Consonantiae : 2.960496E+06, 21.49741 octaves Euler's gradus suavitatis : 115 Sum of Mann's harmonic distance : 128.0, average 42.66667 Mersenne's string divisions : 80276 Sum of van Prooijen's expressibility: 3.99127, average 1.33042 Sum of Tenney's harmonic distance : 7.98988, average 2.66329 Vogel's harmonic complexity : 78.33333 Wille's k value : 4405 Wilson's harmonic complexity : 116 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 17.99945, average 2.99991 Lattice compactness (without 2's) : 11.99410, average 1.99902 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.00000 4 3: -1 .. 2 0.66667 4 1 7: -1 .. 0 -0.33333 1 11: 0 .. 1 0.66667 2 1 89: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 18 23 48| Scale is weakly epimorphic with val: <6 10 19 24 46| Scale is weakly epimorphic with val: <6 10 20 25 47| Scale is weakly epimorphic with val: <6 10 21 26 48| Scale is weakly epimorphic with val: <6 10 22 27 46| Scale is weakly epimorphic with val: <6 11 18 27 46| Scale is weakly epimorphic with val: <6 11 19 23 46| Scale is weakly epimorphic with val: <6 11 20 24 47| Scale is weakly epimorphic with val: <6 11 21 25 48| Scale is weakly epimorphic with val: <6 11 21 27 46| Scale is weakly epimorphic with val: <6 11 22 26 46| Scale is weakly epimorphic with val: <7 10 18 25 46| Scale is weakly epimorphic with val: <7 10 19 26 47| Scale is weakly epimorphic with val: <7 10 20 27 48| Scale is weakly epimorphic with val: <7 11 18 23 47| Scale is weakly epimorphic with val: <7 11 18 25 48| Scale is weakly epimorphic with val: <7 11 18 26 47| Scale is weakly epimorphic with val: <7 11 19 23 46| Scale is weakly epimorphic with val: <7 11 19 24 48| Scale is weakly epimorphic with val: <7 11 19 26 46| Scale is weakly epimorphic with val: <7 11 19 27 48| Scale is weakly epimorphic with val: <7 11 20 24 47| Scale is JI-epimorphic with val: <7 11 20 25 46| Scale is weakly epimorphic with val: <7 11 20 27 47| Scale is weakly epimorphic with val: <7 11 21 23 47| Scale is weakly epimorphic with val: <7 11 21 25 48| Scale is JI-epimorphic with val: <7 11 21 26 47| Scale is weakly epimorphic with val: <7 11 22 23 46| Scale is weakly epimorphic with val: <7 11 22 24 48| Scale is weakly epimorphic with val: <7 11 22 26 46| Scale is JI-epimorphic with val: <7 11 22 27 48| Scale is weakly epimorphic with val: <7 12 18 23 46| Scale is weakly epimorphic with val: <7 12 18 27 48| Scale is weakly epimorphic with val: <7 12 19 24 47| Scale is weakly epimorphic with val: <7 12 19 25 46| Scale is weakly epimorphic with val: <7 12 20 25 48| Scale is weakly epimorphic with val: <7 12 20 26 47| Scale is weakly epimorphic with val: <7 12 21 26 46| Scale is weakly epimorphic with val: <7 12 21 27 48| Scale is weakly epimorphic with val: <7 12 22 25 46| Scale is weakly epimorphic with val: <7 12 22 27 47| Scale is weakly epimorphic with val: <8 11 18 26 47| Scale is weakly epimorphic with val: <8 11 18 27 46| Scale is weakly epimorphic with val: <8 11 19 27 48| Scale is weakly epimorphic with val: <8 11 21 27 46| Scale is weakly epimorphic with val: <8 12 18 25 47| Scale is weakly epimorphic with val: <8 12 18 27 48| Scale is weakly epimorphic with val: <8 12 19 25 46| Scale is weakly epimorphic with val: <8 12 19 26 48| Scale is weakly epimorphic with val: <8 12 20 26 47| Scale is weakly epimorphic with val: <8 12 20 27 46| Scale is weakly epimorphic with val: <8 12 21 27 48| Scale is weakly epimorphic with val: <8 12 22 25 46|
FIT/MODE
3: 1 1 1 SP B ME I SD: 29.4405 c. M:-47.5830 c. 5: 2 1 2 SP M ME I SD: 11.9430 c. M:-14.8702 c. 9: 3 2 4 SP T3 SD: 11.4926 c. M: 18.3328 c. 11: 4 2 5 SP T3 SD: 7.6155 c. M: 12.7861 c. 14: 5 3 6 SP T3 SD: 3.7391 c. M: 6.4746 c. 16: 6 3 7 SP T3 SD: 2.8468 c. M: 4.2967 c. 19: 7 4 8 SP T3 SD: 2.3025 c. M:-3.8948 c. 30: 11 6 13 SP T3 SD: 1.6261 c. M: 2.2215 c. 35: 13 7 15 SP T3 SD: 0.3797 c. M:-0.6403 c. 84: 31 17 36 SP T3 SD: 0.3267 c. M: 0.5455 c. 100: 37 20 43 SP T3 SD: 0.3267 c. M: 0.5614 c. 119: 44 24 51 SP T3 SD: 0.1429 c. M: 0.1967 c. 154: 57 31 66 SP T3 SD: 0.0867 c. M:-0.1501 c. 254: 94 51 109 SP T3 SD: 0.0773 c. M: 0.1300 c. 289: 107 58 124 SP T3 SD: 0.0624 c. M: 0.0961 c. 373: 138 75 160 SP T3 SD: 0.0542 c. M: 0.0845 c. 408: 151 82 175 SP T3 SD: 0.0191 c. M: 0.0243 c. 443: 164 89 190 SP T3 SD: 0.0184 c. M:-0.0300 c. 562: 208 113 241 SP T3 SD: 0.0171 c. M:-0.0235 c. 851: 315 171 365 SP T3 SD: 0.0103 c. M: 0.0171 c. 1005: 372 202 431 SP T3 SD: 0.0052 c. M:-0.0085 c. 1413: 523 284 606 SP T3 SD: 0.0025 c. M: 0.0042 c. 1856: 687 373 796 SP T3 SD: 0.0030 c. M:-0.0040 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: 101.8667 cents 5 x 6:7 S SD: 45.0216 cents 6 x 7:8 S SD: 8.7881 cents 7:8 x 9 S SD: 39.2326 cents 8:9 x 11 SD: 28.3755 cents 9:10:11:12 H SD: 20.9970 cents 10:11:12:13 H SD: 19.0567 cents 11:12:13:15 SD: 17.2329 cents 12:13:14:16 S SD: 16.3445 cents 15:17:18:20 SD: 14.9773 cents 16:18:19:21 SD: 12.0034 cents 17:19:20:23 SD: 8.9176 cents 18:20:21:24 S SD: 5.8944 cents 27:30:32:36 S SD: 3.2937 cents 45:50:53:60 SD: 0.7557 cents 162:180:191:216 SD: 0.6830 cents 168:187:198:224 SD: 0.3815 cents 213:237:251:284 SD: 0.1836 cents 258:287:304:344 SD: 0.1374 cents 498:554:587:664 SD: 0.0844 cents 543:604:640:724 SD: 0.0339 cents