Scala analysis: 425_D10
Diatonic tetrachord 201/181 * 181/171 * 76/67
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 201/181 181.446965 2: 67/57 279.839012 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 76/67 218.2060 1: 201/181 181.4470 2: 181/171 98.3920 3: 76/67 218.2060
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 181/171 98.392 cents 1: 1 201/181 181.447 cents 1: 1 76/67 218.206 cents 2: 1 67/57 279.839 cents 2: 1 724/603 316.598 cents 2: 1 228/181 399.653 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 : 181.4 279.8 498.0 181.4: 98.4 316.6 498.0 279.8: 218.2 399.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 98.3920 .. 218.2060 cents 12996/12127, 119.8139 cents 181/171, 98.3920 cents 2: 279.8390 .. 399.6530 cents 12996/12127, 119.8139 cents 4489/4332, 61.6330 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 181/171, 98.3920 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 76/67, 218.2060 cents Average / Smallest step : 1.687281 Largest / Average step : 1.314375 Largest / Smallest step : 2.217720 Median interval of one step : 201/181, 181.4470 cents, amount: 1 Least squares average step : 159.66143 cents, oct.: 478.98428 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1721-tone equal temperament with octave 4/3 degrees: 627 967 1721 Least number of segments generator : 861 of 249.167 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 903 of 261.322 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 : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 61.63302 cents Scale diversity : 1.188643 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.518863 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 : 13756/13467, 36.7590 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 : 181 Odd number limit : 603 (O: 201 U: 603) Highest odd numerator or denominator: 201 Scale harmonicity : 0.024132 Fundamental : 1/10317, -13.3327 octaves, 0.0254 Hz. Guide tone : 804, 9.6511 octaves, 210346.955 Hz. Exponens Consonantiae : 8.294868E+06, 22.98379 octaves Euler's gradus suavitatis : 271 Sum of Mann's harmonic distance : 256.5, average 85.50000 Mersenne's string divisions : 165788 Sum of van Prooijen's expressibility: 4.60639, average 1.53546 Sum of Tenney's harmonic distance : 9.22201, average 3.07400 Vogel's harmonic complexity : 180.66667 Wille's k value : 6063 Wilson's harmonic complexity : 273 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 11.95084, average 1.99181 Lattice compactness (without 2's) : 8.65028, average 1.44171 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -1 .. 1 -0.33333 3 1 19: -1 .. 0 -0.33333 1 67: 0 .. 1 0.66667 2 1 181: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 30 43 55| Scale is weakly epimorphic with val: <6 10 31 44 53| Scale is weakly epimorphic with val: <6 10 32 45 54| Scale is weakly epimorphic with val: <6 11 29 43 55| Scale is weakly epimorphic with val: <6 11 29 45 53| Scale is weakly epimorphic with val: <6 11 30 44 53| Scale is weakly epimorphic with val: <6 11 31 45 54| Scale is weakly epimorphic with val: <6 11 32 45 53| Scale is weakly epimorphic with val: <7 10 30 43 54| Scale is weakly epimorphic with val: <7 10 31 44 55| Scale is weakly epimorphic with val: <7 10 32 45 53| Scale is weakly epimorphic with val: <7 11 28 43 55| Scale is weakly epimorphic with val: <7 11 28 44 54| Scale is weakly epimorphic with val: <7 11 29 44 53| Scale is weakly epimorphic with val: <7 11 29 45 55| Scale is JI-epimorphic with val: <7 11 30 43 53| Scale is weakly epimorphic with val: <7 11 30 45 54| Scale is weakly epimorphic with val: <7 11 31 43 55| Scale is JI-epimorphic with val: <7 11 31 44 54| = patent Scale is weakly epimorphic with val: <7 11 32 44 53| Scale is JI-epimorphic with val: <7 11 32 45 55| Scale is weakly epimorphic with val: <7 11 33 43 53| Scale is weakly epimorphic with val: <7 11 33 45 54| Scale is weakly epimorphic with val: <7 11 34 43 55| Scale is weakly epimorphic with val: <7 11 34 44 54| Scale is weakly epimorphic with val: <7 12 28 43 54| Scale is weakly epimorphic with val: <7 12 28 44 53| Scale is weakly epimorphic with val: <7 12 29 44 55| Scale is weakly epimorphic with val: <7 12 29 45 54| Scale is weakly epimorphic with val: <7 12 30 45 53| Scale is weakly epimorphic with val: <7 12 31 44 53| Scale is weakly epimorphic with val: <7 12 32 45 54| Scale is weakly epimorphic with val: <7 12 34 44 53| Scale is weakly epimorphic with val: <8 11 29 43 53| Scale is weakly epimorphic with val: <8 11 30 44 54| Scale is weakly epimorphic with val: <8 11 30 45 53| Scale is weakly epimorphic with val: <8 11 31 45 55| Scale is weakly epimorphic with val: <8 11 33 45 53| Scale is weakly epimorphic with val: <8 12 28 43 53| Scale is weakly epimorphic with val: <8 12 28 45 54| Scale is weakly epimorphic with val: <8 12 29 44 54| Scale is weakly epimorphic with val: <8 12 30 44 53| Scale is weakly epimorphic with val: <8 12 30 45 55| Scale is weakly epimorphic with val: <8 12 31 45 54| Scale is weakly epimorphic with val: <8 12 33 44 53| Scale is weakly epimorphic with val: <8 12 34 45 54|
FIT/MODE
3: 1 1 1 SP B ME I SD: 31.4221 c. M:-52.1910 c. 4: 1 1 2 P M ME S SD: 37.3779 c. M: 56.9357 c. 5: 2 1 2 SP M ME I SD: 15.0150 c. M:-18.9880 c. 9: 3 2 4 SP T3 SD: 9.0931 c. M: 15.4320 c. 11: 4 2 5 SP T3 SD: 4.7257 c. M: 8.1781 c. 14: 5 3 6 SP T3 SD: 3.4357 c. M:-4.7581 c. 16: 6 3 7 SP T3 SD: 3.0767 c. M:-5.3199 c. 25: 9 5 11 SP T3 SD: 1.3537 c. M: 2.1508 c. 41: 15 8 18 SP T3 SD: 0.5116 c. M:-0.7646 c. 66: 24 13 29 SP T3 SD: 0.4142 c. M: 0.6320 c. 96: 35 19 42 SP T3 SD: 0.1952 c. M:-0.3113 c. 137: 50 27 60 SP T3 SD: 0.1917 c. M:-0.3213 c. 162: 59 32 71 SP T3 SD: 0.0546 c. M: 0.0730 c. 258: 94 51 113 SP T3 SD: 0.0409 c. M:-0.0700 c. 420: 153 83 184 SP T3 SD: 0.0127 c. M: 0.0163 c. 881: 321 174 386 SP T3 SD: 0.0122 c. M:-0.0201 c. 1002: 365 198 439 SP T3 SD: 0.0135 c. M: 0.0234 c. 1043: 380 206 457 SP T3 SD: 0.0107 c. M: 0.0170 c. 1139: 415 225 499 SP T3 SD: 0.0121 c. M:-0.0181 c. 1301: 474 257 570 SP T3 SD: 0.0048 c. M:-0.0083 c. 1463: 533 289 641 SP T3 SD: 0.0046 c. M: 0.0079 c. 1721: 627 340 754 SP T3 SD: 0.0026 c. M:-0.0038 c. 1883: 686 372 825 SP T3 SD: 0.0024 c. M: 0.0031 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: 106.4747 cents 5 x 6:7 S SD: 45.8708 cents 6 x 7:8 S SD: 6.4841 cents 7 x 8:9 S SD: 39.7880 cents 8:9 x 11 SD: 28.9076 cents 9:10:11:12 H SD: 22.5252 cents 10:11:12:13 H SD: 19.6450 cents 11:12:13:15 SD: 16.8349 cents 12:13:14:16 S SD: 14.9309 cents 14 x 16:19 SD: 28.7542 cents 15:17:18:20 SD: 16.7453 cents 16:18:19:21 SD: 13.1668 cents 17:19:20:23 SD: 9.2167 cents 18:20:21:24 S SD: 4.3345 cents 45:50:53:60 SD: 1.1908 cents 63:70:74:84 SD: 0.5197 cents 108:120:127:144 SD: 0.3987 cents 171:190:201:228 SD: 0.3189 cents 291:323:342:388 SD: 0.2902 cents 336:373:395:448 SD: 0.2111 cents 399:443:469:532 SD: 0.1151 cents 462:513:543:616 SD: 0.0791 cents 507:563:596:676 SD: 0.0558 cents 570:633:670:760 SD: 0.0151 cents