Scala analysis: 361_D1
Diatonic tetrachord 156/149 * 149/135 * 15/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 156/149 79.480438 2: 52/45 250.303946 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 15/13 247.7411 tridecimal 5/4-tone 1: 156/149 79.4804 2: 149/135 170.8235 3: 15/13 247.7411 tridecimal 5/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 156/149 79.480 cents 1: 1 149/135 170.824 cents 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 1 180/149 327.221 cents 2: 1 149/117 418.565 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 : 79.5 250.3 498.0 79.5 : 170.8 418.6 498.0 250.3: 247.7 327.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 79.4804 .. 247.7411 cents 745/676, 168.2606 cents 156/149, 79.4804 cents 2: 250.3039 .. 418.5646 cents 745/676, 168.2606 cents 676/675, 2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 156/149, 79.4804 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 15/13, 247.7411 cents Average / Smallest step : 2.088753 Largest / Average step : 1.492281 Largest / Smallest step : 3.117007 Median interval of one step : 149/135, 170.8235 cents, amount: 1 Least squares average step : 148.15881 cents, oct.: 444.47643 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1554-tone equal temperament with octave 4/3 degrees: 248 781 1554 Least number of segments generator : 779 of 249.663 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 839 of 268.893 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 2.56289 cents Scale diversity : 1.033138 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.324316 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 minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 149 Odd number limit : 149 (O: 149 U: 149) Highest odd numerator or denominator: 149 Scale harmonicity : 0.025938 Fundamental : 1/6705, -12.7110 octaves, 0.0390 Hz. Guide tone : 156, 7.2854 octaves, 40813.588 Hz. Exponens Consonantiae : 1.045980E+06, 19.99642 octaves Euler's gradus suavitatis : 173 Sum of Mann's harmonic distance : 204.5, average 68.16667 Mersenne's string divisions : 207095 Sum of van Prooijen's expressibility: 4.30352, average 1.43451 Sum of Tenney's harmonic distance : 8.81471, average 2.93824 Vogel's harmonic complexity : 117.33333 Wille's k value : 1117 Wilson's harmonic complexity : 176 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 14.97823, average 2.49637 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 2.00000 6 3: -2 .. 1 -0.66667 4 1 5: -1 .. 0 -0.33333 1 13: 0 .. 1 0.66667 2 1 149: -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 53| Scale is weakly epimorphic with val: <6 10 16 27 51| Scale is weakly epimorphic with val: <6 10 17 28 52| Scale is weakly epimorphic with val: <6 10 18 29 53| Scale is weakly epimorphic with val: <6 10 19 30 51| Scale is weakly epimorphic with val: <6 11 15 28 52| Scale is weakly epimorphic with val: <6 11 16 29 53| Scale is weakly epimorphic with val: <6 11 17 30 51| Scale is weakly epimorphic with val: <7 10 16 25 53| Scale is weakly epimorphic with val: <7 10 16 30 51| Scale is weakly epimorphic with val: <7 10 17 26 51| Scale is weakly epimorphic with val: <7 10 18 27 52| Scale is weakly epimorphic with val: <7 10 19 28 53| Scale is weakly epimorphic with val: <7 10 19 30 51| Scale is weakly epimorphic with val: <7 11 15 25 52| Scale is weakly epimorphic with val: <7 11 15 27 53| Scale is weakly epimorphic with val: <7 11 15 28 52| Scale is weakly epimorphic with val: <7 11 15 30 53| Scale is weakly epimorphic with val: <7 11 16 25 51| Scale is weakly epimorphic with val: <7 11 16 26 53| Scale is weakly epimorphic with val: <7 11 16 28 51| Scale is weakly epimorphic with val: <7 11 16 29 53| Scale is weakly epimorphic with val: <7 11 17 26 52| Scale is JI-epimorphic with val: <7 11 17 27 51| Scale is weakly epimorphic with val: <7 11 17 29 52| Scale is weakly epimorphic with val: <7 11 17 30 51| Scale is weakly epimorphic with val: <7 11 18 25 52| Scale is weakly epimorphic with val: <7 11 18 27 53| Scale is JI-epimorphic with val: <7 11 18 28 52| Scale is weakly epimorphic with val: <7 11 18 30 53| Scale is weakly epimorphic with val: <7 11 19 25 51| Scale is weakly epimorphic with val: <7 11 19 26 53| Scale is weakly epimorphic with val: <7 11 19 28 51| Scale is JI-epimorphic with val: <7 11 19 29 53| Scale is weakly epimorphic with val: <7 12 15 28 53| Scale is weakly epimorphic with val: <7 12 15 29 52| Scale is weakly epimorphic with val: <7 12 16 29 51| Scale is weakly epimorphic with val: <7 12 16 30 53| Scale is weakly epimorphic with val: <7 12 17 28 51| Scale is weakly epimorphic with val: <7 12 17 30 52| Scale is weakly epimorphic with val: <7 12 18 29 52| Scale is weakly epimorphic with val: <7 12 19 30 53| Scale is weakly epimorphic with val: <8 11 15 28 52| Scale is weakly epimorphic with val: <8 11 16 25 51| Scale is weakly epimorphic with val: <8 11 16 29 53| Scale is weakly epimorphic with val: <8 11 17 26 52| Scale is weakly epimorphic with val: <8 11 17 27 51| Scale is weakly epimorphic with val: <8 11 18 27 53| Scale is weakly epimorphic with val: <8 11 18 28 52| Scale is weakly epimorphic with val: <8 11 19 28 51| Scale is weakly epimorphic with val: <8 11 19 29 53| Scale is weakly epimorphic with val: <8 12 15 26 52| Scale is weakly epimorphic with val: <8 12 15 28 53| Scale is weakly epimorphic with val: <8 12 16 26 51| Scale is weakly epimorphic with val: <8 12 16 27 53| Scale is weakly epimorphic with val: <8 12 17 27 52| Scale is weakly epimorphic with val: <8 12 17 28 51| Scale is weakly epimorphic with val: <8 12 18 28 53| Scale is weakly epimorphic with val: <8 12 18 29 52| Scale is weakly epimorphic with val: <8 12 19 26 51| Scale is weakly epimorphic with val: <8 12 19 30 53|
FIT/MODE
3: 0 1 2 N G T3 SD: 66.8874 c. M: 84.2889 c. 4: 1 1 2 P M ME S SD: 26.0091 c. M:-45.0308 c. 5: 1 2 2 SP M ME S SD: 30.3296 c. M:-48.5231 c. 6: 1 2 3 P T3 SD: 2.1666 c. M:-3.5271 c. 26: 4 9 13 P T3 SD: 1.8084 c. M: 2.8581 c. 32: 5 11 16 P T3 SD: 1.2112 c. M: 1.6609 c. 38: 6 13 19 P T3 SD: 0.8852 c. M: 1.2814 c. 44: 7 15 22 P T3 SD: 0.7534 c. M: 1.2814 c. 50: 8 17 25 P T3 SD: 0.7494 c. M: 1.2814 c. 82: 13 28 41 P T3 SD: 0.7989 c. M: 1.2814 c. 94: 15 32 47 P T3 SD: 0.7398 c. M: 1.2814 c. 99: 16 34 49 SP T3 SD: 0.9212 c. M:-1.2339 c. 101: 16 35 50 SP T3 SD: 0.7618 c. M:-1.1841 c. 105: 17 36 52 SP T3 SD: 0.9172 c. M:-1.1554 c. 106: 17 36 53 P T3 SD: 0.7741 c. M: 1.2814 c. 107: 17 37 53 SP T3 SD: 0.6371 c. M:-1.0459 c. 113: 18 39 56 SP T3 SD: 0.5391 c. M:-0.9223 c. 119: 19 41 59 SP T3 SD: 0.4689 c. M:-0.8112 c. 125: 20 43 62 SP T3 SD: 0.4274 c. M:-0.7107 c. 131: 21 45 65 SP T3 SD: 0.4133 c. M:-0.6195 c. 137: 22 47 68 SP T3 SD: 0.4224 c. M:-0.5362 c. 145: 23 50 72 SP T3 SD: 0.3745 c. M: 0.4802 c. 151: 24 52 75 SP T3 SD: 0.2818 c. M:-0.3677 c. 157: 25 54 78 SP T3 SD: 0.2025 c. M:-0.3047 c. 163: 26 56 81 SP T3 SD: 0.1439 c. M:-0.2463 c. 169: 27 58 84 SP T3 SD: 0.1222 c. M:-0.1921 c. 201: 32 69 100 SP T3 SD: 0.1122 c. M: 0.1897 c. 207: 33 71 103 SP T3 SD: 0.0655 c. M: 0.0820 c. 370: 59 127 184 SP T3 SD: 0.0519 c. M:-0.0646 c. 376: 60 129 187 SP T3 SD: 0.0251 c. M:-0.0431 c. 583: 93 200 290 SP T3 SD: 0.0187 c. M: 0.0324 c. 589: 94 202 293 SP T3 SD: 0.0079 c. M: 0.0131 c. 965: 154 331 480 SP T3 SD: 0.0051 c. M:-0.0088 c. 1554: 248 533 773 SP T3 SD: 0.0010 c. M:-0.0016 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 x 9:11 SD: 35.3214 cents 9 x 10:12 S SD: 33.9501 cents 10 x 12:13 S SD: 39.3387 cents 11:12:13:15 SD: 29.9826 cents 12:13:14:16 S SD: 20.4569 cents 13:14:15:17 SD: 19.7762 cents 14:15:16:19 SD: 17.9564 cents 15:16:17:20 SD: 15.5286 cents 17:18:20:23 SD: 14.8413 cents 18:19:21:24 SD: 7.2565 cents 21:22:24:28 S SD: 6.3863 cents 24:25:28:32 SD: 6.2543 cents 38:40:44:51 SD: 5.0332 cents 39:41:45:52 SD: 2.5159 cents 45:47:52:60 SD: 1.3992 cents 84:88:97:112 SD: 0.5303 cents 129:135:149:172 SD: 0.3651 cents 192:201:222:256 SD: 0.3515 cents 213:223:246:284 SD: 0.3132 cents 276:289:319:368 SD: 0.1380 cents 360:377:416:480 SD: 0.1336 cents 405:424:468:540 SD: 0.0365 cents