Scala analysis: 365_D1
Diatonic tetrachord 20/19 * 247/225 * 15/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 20/19 88.800698 small undevicesimal semitone 2: 52/45 250.303946 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 15/13 247.7411 tridecimal 5/4-tone 1: 20/19 88.8007 small undevicesimal semitone 2: 247/225 161.5032 3: 15/13 247.7411 tridecimal 5/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 20/19 88.801 cents small undevicesimal semitone 1: 1 247/225 161.503 cents 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 1 300/247 336.542 cents 2: 1 19/15 409.244 cents undevicesimal ditone 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 : 88.8 250.3 498.0 88.8 : 161.5 409.2 498.0 250.3: 247.7 336.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.8007 .. 247.7411 cents 57/52, 158.9404 cents 20/19, 88.8007 cents 2: 250.3039 .. 409.2443 cents 57/52, 158.9404 cents 676/675, 2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 20/19, 88.8007 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 15/13, 247.7411 cents Average / Smallest step : 1.869524 Largest / Average step : 1.492281 Largest / Smallest step : 2.789855 Median interval of one step : 247/225, 161.5032 cents, amount: 1 Least squares average step : 148.82454 cents, oct.: 446.47363 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 774-tone equal temperament with octave 4/3 degrees: 138 389 774 Least number of segments generator : 389 of 250.309 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 569 of 366.134 cents and inv. generated superset size: 18 = 15 more = 600.000% 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 : 1.096589 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.361743 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 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% -- Rational properties -- Prime limit : 19 Odd number limit : 247 (O: 247 U: 247) Highest odd numerator or denominator: 45 Scale harmonicity : 0.013090 Average absolute harmonicity : 0.088559 Specific harmonicity : 0.069011 Fundamental : 1/855, -9.7398 octaves, 0.3060 Hz. Guide tone : 260, 8.0224 octaves, 68022.647 Hz. Exponens Consonantiae : 2.223000E+05, 17.76215 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 71.5, average 23.83333 Mersenne's string divisions : 26481 Sum of van Prooijen's expressibility: 3.40909, average 1.13636 Sum of Tenney's harmonic distance : 7.02818, average 2.34273 Vogel's harmonic complexity : 27.00000 Wille's k value : 142 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 14.47421, average 2.41237 Lattice compactness (without 2's) : 11.49008, average 1.91501 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -2 .. 0 -1.00000 3 1 5: -1 .. 1 0.00000 2 13: 0 .. 1 0.33333 1 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 15 26 29| Scale is weakly epimorphic with val: <6 10 15 26 32| Scale is weakly epimorphic with val: <6 10 16 27 30| Scale is weakly epimorphic with val: <6 10 16 27 33| Scale is weakly epimorphic with val: <6 10 17 28 28| Scale is weakly epimorphic with val: <6 10 17 28 31| Scale is weakly epimorphic with val: <6 10 17 28 34| Scale is weakly epimorphic with val: <6 10 18 29 29| Scale is weakly epimorphic with val: <6 10 18 29 32| Scale is weakly epimorphic with val: <6 10 19 25 28| Scale is weakly epimorphic with val: <6 10 19 28 28| Scale is weakly epimorphic with val: <6 10 19 30 30| Scale is weakly epimorphic with val: <6 10 19 30 33| Scale is weakly epimorphic with val: <6 11 15 28 28| Scale is weakly epimorphic with val: <6 11 15 28 31| Scale is weakly epimorphic with val: <6 11 15 28 34| Scale is weakly epimorphic with val: <6 11 16 29 29| Scale is weakly epimorphic with val: <6 11 16 29 32| Scale is weakly epimorphic with val: <6 11 17 30 30| Scale is weakly epimorphic with val: <6 11 17 30 33| Scale is weakly epimorphic with val: <6 11 19 25 28| Scale is weakly epimorphic with val: <6 11 19 28 28| Scale is weakly epimorphic with val: <7 10 16 25 28| Scale is weakly epimorphic with val: <7 10 16 25 31| Scale is weakly epimorphic with val: <7 10 16 25 34| Scale is weakly epimorphic with val: <7 10 17 25 28| Scale is weakly epimorphic with val: <7 10 17 26 29| Scale is weakly epimorphic with val: <7 10 17 26 32| Scale is weakly epimorphic with val: <7 10 17 28 28| Scale is weakly epimorphic with val: <7 10 18 26 29| Scale is weakly epimorphic with val: <7 10 18 27 30| Scale is weakly epimorphic with val: <7 10 18 27 33| Scale is weakly epimorphic with val: <7 10 18 29 29| Scale is weakly epimorphic with val: <7 10 19 27 30| Scale is weakly epimorphic with val: <7 10 19 28 28| Scale is weakly epimorphic with val: <7 10 19 28 31| Scale is weakly epimorphic with val: <7 10 19 28 34| Scale is weakly epimorphic with val: <7 10 19 30 30| Scale is JI-epimorphic with val: <7 11 15 25 28| Scale is weakly epimorphic with val: <7 11 15 25 31| Scale is weakly epimorphic with val: <7 11 15 25 34| Scale is weakly epimorphic with val: <7 11 15 27 30| Scale is weakly epimorphic with val: <7 11 15 27 33| Scale is weakly epimorphic with val: <7 11 15 28 28| Scale is weakly epimorphic with val: <7 11 15 28 31| Scale is weakly epimorphic with val: <7 11 15 28 34| Scale is weakly epimorphic with val: <7 11 15 30 30| Scale is weakly epimorphic with val: <7 11 15 30 33| Scale is weakly epimorphic with val: <7 11 16 25 28| Scale is weakly epimorphic with val: <7 11 16 25 31| Scale is weakly epimorphic with val: <7 11 16 25 34| Scale is JI-epimorphic with val: <7 11 16 26 29| Scale is weakly epimorphic with val: <7 11 16 26 32| Scale is weakly epimorphic with val: <7 11 16 28 28| Scale is weakly epimorphic with val: <7 11 16 28 31| Scale is weakly epimorphic with val: <7 11 16 28 34| Scale is weakly epimorphic with val: <7 11 16 29 29| Scale is weakly epimorphic with val: <7 11 16 29 32| Scale is weakly epimorphic with val: <7 11 17 26 29| Scale is weakly epimorphic with val: <7 11 17 26 32| Scale is JI-epimorphic with val: <7 11 17 27 30| Scale is weakly epimorphic with val: <7 11 17 27 33| Scale is weakly epimorphic with val: <7 11 17 29 29| Scale is weakly epimorphic with val: <7 11 17 29 32| Scale is weakly epimorphic with val: <7 11 17 30 30| Scale is weakly epimorphic with val: <7 11 17 30 33| Scale is weakly epimorphic with val: <7 11 18 25 28| Scale is weakly epimorphic with val: <7 11 18 25 31| Scale is weakly epimorphic with val: <7 11 18 25 34| Scale is weakly epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 18 27 33| Scale is weakly epimorphic with val: <7 11 18 28 28| Scale is JI-epimorphic with val: <7 11 18 28 31| Scale is weakly epimorphic with val: <7 11 18 28 34| Scale is weakly epimorphic with val: <7 11 18 30 30| Scale is weakly epimorphic with val: <7 11 18 30 33| Scale is weakly epimorphic with val: <7 11 19 25 28| Scale is weakly epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 25 34| Scale is weakly epimorphic with val: <7 11 19 26 29| Scale is weakly epimorphic with val: <7 11 19 26 32| Scale is weakly epimorphic with val: <7 11 19 28 28| Scale is weakly epimorphic with val: <7 11 19 28 31| Scale is weakly epimorphic with val: <7 11 19 28 34| Scale is weakly epimorphic with val: <7 11 19 29 29| Scale is JI-epimorphic with val: <7 11 19 29 32| Scale is weakly epimorphic with val: <7 12 15 28 28| Scale is weakly epimorphic with val: <7 12 15 28 31| Scale is weakly epimorphic with val: <7 12 15 28 34| Scale is weakly epimorphic with val: <7 12 16 29 29| Scale is weakly epimorphic with val: <7 12 16 29 32| Scale is weakly epimorphic with val: <7 12 17 25 28| Scale is weakly epimorphic with val: <7 12 17 28 28| Scale is weakly epimorphic with val: <7 12 17 30 30| Scale is weakly epimorphic with val: <7 12 17 30 33| Scale is weakly epimorphic with val: <7 12 18 26 29| Scale is weakly epimorphic with val: <7 12 18 29 29| Scale is weakly epimorphic with val: <7 12 19 27 30| Scale is weakly epimorphic with val: <7 12 19 30 30| Scale is weakly epimorphic with val: <8 11 15 25 28| Scale is weakly epimorphic with val: <8 11 15 28 28| Scale is weakly epimorphic with val: <8 11 16 25 28| Scale is weakly epimorphic with val: <8 11 16 25 31| Scale is weakly epimorphic with val: <8 11 16 25 34| Scale is weakly epimorphic with val: <8 11 16 26 29| Scale is weakly epimorphic with val: <8 11 16 29 29| Scale is weakly epimorphic with val: <8 11 17 26 29| Scale is weakly epimorphic with val: <8 11 17 26 32| Scale is weakly epimorphic with val: <8 11 17 27 30| Scale is weakly epimorphic with val: <8 11 17 30 30| Scale is weakly epimorphic with val: <8 11 18 25 31| Scale is weakly epimorphic with val: <8 11 18 27 30| Scale is weakly epimorphic with val: <8 11 18 27 33| Scale is weakly epimorphic with val: <8 11 18 28 31| Scale is weakly epimorphic with val: <8 11 19 26 32| Scale is weakly epimorphic with val: <8 11 19 28 28| Scale is weakly epimorphic with val: <8 11 19 28 31| Scale is weakly epimorphic with val: <8 11 19 28 34| Scale is weakly epimorphic with val: <8 11 19 29 32| Scale is weakly epimorphic with val: <8 12 15 25 28| Scale is weakly epimorphic with val: <8 12 15 26 29| Scale is weakly epimorphic with val: <8 12 15 26 32| Scale is weakly epimorphic with val: <8 12 15 28 28| Scale is weakly epimorphic with val: <8 12 16 26 29| Scale is weakly epimorphic with val: <8 12 16 27 30| Scale is weakly epimorphic with val: <8 12 16 27 33| Scale is weakly epimorphic with val: <8 12 16 29 29| Scale is weakly epimorphic with val: <8 12 17 27 30| Scale is weakly epimorphic with val: <8 12 17 28 28| Scale is weakly epimorphic with val: <8 12 17 28 31| Scale is weakly epimorphic with val: <8 12 17 28 34| Scale is weakly epimorphic with val: <8 12 17 30 30| Scale is weakly epimorphic with val: <8 12 18 25 31| Scale is weakly epimorphic with val: <8 12 18 28 31| Scale is weakly epimorphic with val: <8 12 18 29 29| Scale is weakly epimorphic with val: <8 12 18 29 32| Scale is weakly epimorphic with val: <8 12 19 26 32| Scale is weakly epimorphic with val: <8 12 19 29 32| Scale is weakly epimorphic with val: <8 12 19 30 30| Scale is weakly epimorphic with val: <8 12 19 30 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 70.6876 c. M: 88.8007 c. 4: 1 1 2 P M ME S SD: 20.6308 c. M:-35.7106 c. 6: 1 2 3 P T3 SD: 3.4256 c. M: 5.7932 c. 16: 3 5 8 P T3 SD: 2.7473 c. M:-4.5827 c. 22: 4 7 11 P T3 SD: 1.2536 c. M:-1.7529 c. 28: 5 9 14 P T3 SD: 0.7440 c. M: 1.2814 c. 62: 11 20 31 P T3 SD: 0.7818 c. M: 1.2814 c. 72: 13 23 36 P T3 SD: 0.9842 c. M: 1.2814 c. 78: 14 25 39 P T3 SD: 0.8150 c. M: 1.2814 c. 90: 16 29 45 P T3 SD: 0.7548 c. M: 1.2814 c. 96: 17 31 48 P T3 SD: 0.8182 c. M: 1.2814 c. 101: 18 33 50 SP T3 SD: 0.6840 c. M:-1.1841 c. 107: 19 35 53 SP T3 SD: 0.6391 c. M:-1.0459 c. 111: 20 36 55 SP T3 SD: 0.7754 c. M:-0.9620 c. 113: 20 37 56 SP T3 SD: 0.6518 c. M:-0.9223 c. 117: 21 38 58 SP T3 SD: 0.5966 c. M:-0.8470 c. 123: 22 40 61 SP T3 SD: 0.4586 c. M:-0.7431 c. 129: 23 42 64 SP T3 SD: 0.3747 c. M:-0.6490 c. 135: 24 44 67 SP T3 SD: 0.3580 c. M:-0.5632 c. 141: 25 46 70 SP T3 SD: 0.3999 c. M: 0.4948 c. 145: 26 47 72 SP T3 SD: 0.3847 c. M:-0.5039 c. 151: 27 49 75 SP T3 SD: 0.2579 c. M:-0.3677 c. 157: 28 51 78 SP T3 SD: 0.1764 c. M:-0.3047 c. 163: 29 53 81 SP T3 SD: 0.1801 c. M:-0.2463 c. 179: 32 58 89 SP T3 SD: 0.1499 c. M:-0.2353 c. 185: 33 60 92 SP T3 SD: 0.0438 c. M:-0.0646 c. 376: 67 122 187 SP T3 SD: 0.0396 c. M: 0.0533 c. 398: 71 129 198 SP T3 SD: 0.0320 c. M:-0.0465 c. 404: 72 131 201 SP T3 SD: 0.0364 c. M: 0.0487 c. 561: 100 182 279 SP T3 SD: 0.0318 c. M:-0.0502 c. 583: 104 189 290 SP T3 SD: 0.0256 c. M:-0.0444 c. 589: 105 191 293 SP T3 SD: 0.0115 c. M: 0.0151 c. 774: 138 251 385 SP T3 SD: 0.0034 c. M:-0.0055 c. 2137: 381 693 1063 SP T3 SD: 0.0032 c. M: 0.0056 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 11:12:13:15 SD: 27.5904 cents 12:13:14:16 S SD: 17.4856 cents 13:14:15:17 SD: 17.3101 cents 14:15:16:19 SD: 15.7897 cents 15:16:17:20 SD: 13.5644 cents 18:19:21:24 SD: 5.7497 cents 33:35:38:44 SD: 4.8015 cents 38:40:44:51 SD: 3.9600 cents 39:41:45:52 SD: 1.1304 cents 96:101:111:128 SD: 0.4589 cents 135:142:156:180 SD: 0.4276 cents 225:237:260:300 SD: 0.3846 cents 264:278:305:352 SD: 0.2523 cents 303:319:350:404 SD: 0.2395 cents 321:338:371:428 SD: 0.2075 cents 360:379:416:480 SD: 0.0801 cents 456:480:527:608 SD: 0.0730 cents 495:521:572:660 SD: 0.0583 cents