Scala analysis: 360_D1
Diatonic tetrachord 78/71 * 142/135 * 15/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 78/71 162.786119 porcupine neutral second 2: 52/45 250.303946 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 15/13 247.7411 tridecimal 5/4-tone 1: 78/71 162.7861 porcupine neutral second 2: 142/135 87.5178 3: 15/13 247.7411 tridecimal 5/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 142/135 87.518 cents 1: 1 78/71 162.786 cents porcupine neutral second 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 1 142/117 335.259 cents 2: 1 90/71 410.527 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 : 162.8 250.3 498.0 162.8: 87.5 335.3 498.0 250.3: 247.7 410.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 87.5178 .. 247.7411 cents 2025/1846, 160.2232 cents 142/135, 87.5178 cents 2: 250.3039 .. 410.5272 cents 2025/1846, 160.2232 cents 676/675, 2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 142/135, 87.5178 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 15/13, 247.7411 cents Average / Smallest step : 1.896928 Largest / Average step : 1.492281 Largest / Smallest step : 2.830750 Median interval of one step : 78/71, 162.7861 cents, amount: 1 Least squares average step : 154.10921 cents, oct.: 462.32764 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1747-tone equal temperament with octave 4/3 degrees: 571 878 1747 Least number of segments generator : 874 of 249.165 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1668 of 475.523 cents and inv. generated superset size: 38 = 35 more = 1266.667% 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 2.56289 cents Scale diversity : 1.089090 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.356591 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 : 676/675, 2.5629 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 71 Odd number limit : 135 (O: 71 U: 135) Highest odd numerator or denominator: 71 Scale harmonicity : 0.025938 Fundamental : 1/3195, -11.6416 octaves, 0.0819 Hz. Guide tone : 156, 7.2854 octaves, 40813.588 Hz. Exponens Consonantiae : 4.984200E+05, 18.92700 octaves Euler's gradus suavitatis : 95 Sum of Mann's harmonic distance : 126.5, average 42.16667 Mersenne's string divisions : 101171 Sum of van Prooijen's expressibility: 3.98159, average 1.32720 Sum of Tenney's harmonic distance : 8.19175, average 2.73058 Vogel's harmonic complexity : 65.00000 Wille's k value : 877 Wilson's harmonic complexity : 98 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 14.62856, average 2.43809 Lattice compactness (without 2's) : 11.99410, average 1.99902 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -2 .. 1 -0.66667 4 1 5: -1 .. 0 -0.33333 1 13: 0 .. 1 0.66667 2 1 71: -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 15 26 44| Scale is weakly epimorphic with val: <6 10 15 30 43| Scale is weakly epimorphic with val: <6 10 16 27 45| Scale is weakly epimorphic with val: <6 10 17 28 43| Scale is weakly epimorphic with val: <6 10 18 29 44| Scale is weakly epimorphic with val: <6 10 18 30 43| Scale is weakly epimorphic with val: <6 10 19 30 45| Scale is weakly epimorphic with val: <6 11 15 28 43| Scale is weakly epimorphic with val: <6 11 15 30 44| Scale is weakly epimorphic with val: <6 11 16 29 44| Scale is weakly epimorphic with val: <6 11 17 29 43| Scale is weakly epimorphic with val: <6 11 17 30 45| Scale is weakly epimorphic with val: <6 11 18 30 44| Scale is weakly epimorphic with val: <7 10 15 29 43| Scale is weakly epimorphic with val: <7 10 16 25 43| Scale is weakly epimorphic with val: <7 10 16 30 44| Scale is weakly epimorphic with val: <7 10 17 26 44| Scale is weakly epimorphic with val: <7 10 18 27 45| Scale is weakly epimorphic with val: <7 10 18 29 43| Scale is weakly epimorphic with val: <7 10 19 28 43| Scale is weakly epimorphic with val: <7 10 19 30 44| Scale is weakly epimorphic with val: <7 11 15 25 45| Scale is weakly epimorphic with val: <7 11 15 27 43| Scale is weakly epimorphic with val: <7 11 15 28 45| Scale is weakly epimorphic with val: <7 11 15 30 43| Scale is weakly epimorphic with val: <7 11 16 25 44| Scale is JI-epimorphic with val: <7 11 16 26 43| Scale is weakly epimorphic with val: <7 11 16 28 44| Scale is weakly epimorphic with val: <7 11 16 29 43| Scale is weakly epimorphic with val: <7 11 17 26 45| Scale is JI-epimorphic with val: <7 11 17 27 44| = patent Scale is weakly epimorphic with val: <7 11 17 29 45| Scale is weakly epimorphic with val: <7 11 17 30 44| Scale is weakly epimorphic with val: <7 11 18 25 45| Scale is weakly epimorphic with val: <7 11 18 27 43| Scale is JI-epimorphic with val: <7 11 18 28 45| Scale is weakly epimorphic with val: <7 11 18 30 43| Scale is weakly epimorphic with val: <7 11 19 25 44| Scale is weakly epimorphic with val: <7 11 19 26 43| Scale is weakly epimorphic with val: <7 11 19 28 44| Scale is weakly epimorphic with val: <7 11 19 29 43| Scale is weakly epimorphic with val: <7 12 15 28 43| Scale is weakly epimorphic with val: <7 12 15 29 45| Scale is weakly epimorphic with val: <7 12 16 27 43| Scale is weakly epimorphic with val: <7 12 16 29 44| Scale is weakly epimorphic with val: <7 12 17 28 44| Scale is weakly epimorphic with val: <7 12 17 30 45| Scale is weakly epimorphic with val: <7 12 18 29 45| Scale is weakly epimorphic with val: <7 12 19 27 43| Scale is weakly epimorphic with val: <8 11 15 28 44| Scale is weakly epimorphic with val: <8 11 16 25 43| Scale is weakly epimorphic with val: <8 11 16 29 45| Scale is weakly epimorphic with val: <8 11 17 26 44| Scale is weakly epimorphic with val: <8 11 17 27 43| Scale is weakly epimorphic with val: <8 11 18 27 45| Scale is weakly epimorphic with val: <8 11 18 28 44| Scale is weakly epimorphic with val: <8 11 19 28 43| Scale is weakly epimorphic with val: <8 11 19 29 45| Scale is weakly epimorphic with val: <8 12 15 26 44| Scale is weakly epimorphic with val: <8 12 15 28 45| Scale is weakly epimorphic with val: <8 12 16 26 43| Scale is weakly epimorphic with val: <8 12 16 27 45| Scale is weakly epimorphic with val: <8 12 17 27 44| Scale is weakly epimorphic with val: <8 12 17 28 43| Scale is weakly epimorphic with val: <8 12 18 28 45| Scale is weakly epimorphic with val: <8 12 18 29 44| Scale is weakly epimorphic with val: <8 12 19 26 43| Scale is weakly epimorphic with val: <8 12 19 30 45|
FIT/MODE
3: 1 0 2 N G T3 SD: 48.6999 c. M: 84.2889 c. 4: 1 1 2 P M ME S SD: 22.1104 c. M: 38.2749 c. 6: 2 1 3 P T3 SD: 2.0056 c. M:-3.2289 c. 28: 9 5 14 P T3 SD: 1.7256 c. M: 2.7002 c. 34: 11 6 17 P T3 SD: 1.2080 c. M: 1.6539 c. 40: 13 7 20 P T3 SD: 0.9113 c. M: 1.2814 c. 46: 15 8 23 P T3 SD: 0.7717 c. M: 1.2814 c. 52: 17 9 26 P T3 SD: 0.7401 c. M: 1.2814 c. 86: 28 15 43 P T3 SD: 0.8249 c. M: 1.2814 c. 95: 31 17 47 SP T3 SD: 0.7887 c. M:-1.3398 c. 98: 32 17 49 P T3 SD: 0.7455 c. M: 1.2814 c. 101: 33 18 50 SP T3 SD: 0.6845 c. M:-1.1841 c. 107: 35 19 53 SP T3 SD: 0.6082 c. M:-1.0459 c. 113: 37 20 56 SP T3 SD: 0.5583 c. M:-0.9223 c. 119: 39 21 59 SP T3 SD: 0.5324 c. M:-0.8112 c. 125: 41 22 62 SP T3 SD: 0.5270 c. M:-0.7107 c. 129: 42 23 64 SP T3 SD: 0.5230 c. M:-0.6490 c. 135: 44 24 67 SP T3 SD: 0.4199 c. M:-0.5632 c. 141: 46 25 70 SP T3 SD: 0.3301 c. M:-0.4847 c. 147: 48 26 73 SP T3 SD: 0.2553 c. M:-0.4126 c. 153: 50 27 76 SP T3 SD: 0.2004 c. M:-0.3462 c. 159: 52 28 79 SP T3 SD: 0.1736 c. M:-0.2847 c. 165: 54 29 82 SP T3 SD: 0.1790 c. M:-0.2278 c. 193: 63 34 96 SP T3 SD: 0.1224 c. M: 0.2118 c. 199: 65 35 99 SP T3 SD: 0.0648 c. M: 0.1081 c. 205: 67 36 102 SP T3 SD: 0.0390 c. M: 0.0667 c. 404: 132 71 201 SP T3 SD: 0.0440 c. M: 0.0585 c. 563: 184 99 280 SP T3 SD: 0.0276 c. M:-0.0455 c. 569: 186 100 283 SP T3 SD: 0.0214 c. M:-0.0315 c. 768: 251 135 382 SP T3 SD: 0.0119 c. M:-0.0155 c. 774: 253 136 385 SP T3 SD: 0.0074 c. M:-0.0115 c. 979: 320 172 487 SP T3 SD: 0.0068 c. M: 0.0096 c. 1542: 504 271 767 SP T3 SD: 0.0061 c. M:-0.0105 c. 1747: 571 307 869 SP T3 SD: 0.0015 c. M: 0.0021 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: 53.3940 cents 6 x 7:8 S SD: 8.2835 cents 7 x 8:9 S SD: 32.9015 cents 8:9 x 11 SD: 33.6496 cents 9:10 x 12 S SD: 9.8088 cents 12:13:14:16 S SD: 9.7795 cents 16:18 x 21 S SD: 24.6703 cents 17:19:20:23 SD: 16.6316 cents 18:20:21:24 S SD: 8.5590 cents 19:21:22:25 SD: 8.4849 cents 20:22:23:27 SD: 7.7248 cents 21:23:24:28 SD: 6.6162 cents 30:33:35:40 SD: 5.5716 cents 31:34:36:41 SD: 5.5596 cents 32:35:37:43 SD: 5.1754 cents 33:36:38:44 SD: 4.5261 cents 39:43:45:52 SD: 2.2514 cents 51:56:59:68 SD: 0.7141 cents 141:155:163:188 SD: 0.4365 cents 192:211:222:256 SD: 0.3966 cents 213:234:246:284 SD: 0.3127 cents 264:290:305:352 SD: 0.1380 cents 315:346:364:420 SD: 0.0940 cents 405:445:468:540 SD: 0.0913 cents 456:501:527:608 SD: 0.0877 cents