Scala analysis: 562_M70
Miscellaneous tetrachord 81/70 * 2240/2187 * 9/8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 81/70 252.680383 Al-Hwarizmi's lute middle finger 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 81/70 252.6804 Al-Hwarizmi's lute middle finger 2: 2240/2187 41.4546 3: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 2240/2187 41.455 cents 1: 1 9/8 203.910 cents major whole tone 1: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 280/243 245.365 cents 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 729/560 456.590 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 : 252.7 294.1 498.0 252.7: 41.5 245.4 498.0 294.1: 203.9 456.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.4546 .. 252.6804 cents 177147/156800, 211.2258 cents 2240/2187, 41.4546 cents 2: 245.3646 .. 456.5904 cents 177147/156800, 211.2258 cents 19600/19683,-7.3158 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 2240/2187, 41.4546 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 81/70, 252.6804 cents Average / Smallest step : 4.004741 Largest / Average step : 1.522033 Largest / Smallest step : 6.095350 Median interval of one step : 9/8, 203.9100 cents, amount: 1 Least squares average step : 166.79181 cents, oct.: 500.37544 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1634-tone equal temperament with octave 4/3 degrees: 829 965 1634 Least number of segments generator : 819 of 249.632 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 821 of 250.242 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 : LSM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 0.657669 Lumma stability : 0.166469 Lumma impropriety factor : 0.014689 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 : 19683/19600, 7.3158 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 7 Odd number limit : 2187 (O: 729 U: 2187) Highest odd numerator or denominator: 81 Scale harmonicity : 0.024182 Average absolute harmonicity : 0.108826 Specific harmonicity : 0.124297 Fundamental : 1/1890, -10.8842 octaves, 0.1384 Hz. Guide tone : 2592, 11.3399 octaves, 678133.465 Hz. Exponens Consonantiae : 4.898880E+06, 22.22402 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 108.5, average 36.16667 Mersenne's string divisions : 62363 Sum of van Prooijen's expressibility: 3.81697, average 1.27232 Sum of Tenney's harmonic distance : 7.76928, average 2.58976 Vogel's harmonic complexity : 20.00000 Wille's k value : 1093 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 9 Triangular lattice diameter : 7 Lattice compactness : 31.35885, average 5.22647 Lattice compactness (without 2's) : 22.58022, average 3.76337 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 5 2.00000 8 3: -3 .. 4 0.00000 8 2 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <7 11 15 18| Scale is JI-epimorphic with val: <7 11 15 21| Scale is JI-epimorphic with val: <7 11 16 20| Scale is JI-epimorphic with val: <7 11 17 19| Scale is weakly epimorphic with val: <7 11 17 22| Scale is JI-epimorphic with val: <7 11 18 18| Scale is weakly epimorphic with val: <7 11 18 21| Scale is weakly epimorphic with val: <7 11 19 20| Scale is weakly epimorphic with val: <8 11 15 18|
FIT/MODE
3: 2 0 1 N G T3 SD: 50.7687 c. M:-79.3496 c. 4: 2 0 2 P M DE I SD: 26.1312 c. M: 45.1125 c. 6: 3 0 3 P M DE I SD: 26.1312 c. M: 45.1125 c. 7: 3 1 3 SP M DE I SD: 23.3107 c. M: 39.2325 c. 8: 4 1 3 P T3 SD: 10.1204 c. M:-17.1431 c. 10: 5 1 4 P T3 SD: 3.4349 c. M:-4.6920 c. 12: 6 1 5 P T3 SD: 2.9667 c. M: 3.6579 c. Raga Ongkari 22: 11 2 9 P T3 SD: 2.1140 c. M: 3.6579 c. 34: 17 3 14 P T3 SD: 2.2168 c. M: 3.6579 c. 37: 19 3 15 N T3 SD: 2.1166 c. M:-3.0725 c. 39: 20 3 16 N T3 SD: 1.5928 c. M:-2.7273 c. 41: 21 3 17 N T3 SD: 2.0476 c. M: 2.5965 c. 47: 24 4 19 N T3 SD: 1.7616 c. M:-2.5727 c. 49: 25 4 20 N T3 SD: 0.8983 c. M:-1.4242 c. 51: 26 4 21 N T3 SD: 0.9769 c. M:-1.2249 c. 59: 30 5 24 N T3 SD: 0.8261 c. M:-1.3154 c. 61: 31 5 25 N T3 SD: 0.2726 c. M:-0.4245 c. 132: 67 11 54 N T3 SD: 0.1159 c. M:-0.1643 c. 205: 104 17 84 N T3 SD: 0.0967 c. M: 0.1670 c. 276: 140 23 113 N T3 SD: 0.0282 c. M: 0.0489 c. 337: 171 28 138 N T3 SD: 0.0302 c. M: 0.0372 c. 613: 311 51 251 N T3 SD: 0.0118 c. M: 0.0203 c. 745: 378 62 305 N T3 SD: 0.0131 c. M:-0.0190 c. 889: 451 74 364 N T3 SD: 0.0124 c. M: 0.0164 c. 1021: 518 85 418 N T3 SD: 0.0053 c. M:-0.0091 c. 1634: 829 136 669 N T3 SD: 0.0011 c. M: 0.0019 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: 92.1787 cents 5 x 6:7 S SD: 43.5810 cents 6:7 x 8 S SD: 7.0953 cents 7:8 x 9 S SD: 33.2663 cents 8:9 x 11 SD: 36.1129 cents 9:10:11:12 H SD: 29.3954 cents 10 x 12:13 S SD: 24.4115 cents 11 x 13:15 SD: 19.6081 cents 12:14 x 16 S SD: 7.0953 cents 13:15 x 17 SD: 16.9891 cents 15:17:18:20 SD: 13.9764 cents 16 x 19:21 SD: 13.7363 cents 17 x 20:23 SD: 14.1599 cents 18:21 x 24 S SD: 7.0953 cents 23 x 27:31 SD: 12.4901 cents 24:28 x 32 S SD: 7.0953 cents 26:30:31:35 SD: 6.7203 cents 27:31:32:36 SD: 4.5033 cents 29 x 34:39 SD: 11.9651 cents 30:35:36:40 S SD: 8.5887 cents 31:36:37:41 SD: 6.5240 cents 32:37:38:43 SD: 4.6513 cents 33:38:39:44 SD: 3.2574 cents 35 x 41:47 SD: 11.8360 cents 36:42:43:48 SD: 6.5225 cents 37:43:44:49 SD: 5.0333 cents 38:44:45:51 SD: 3.8322 cents 39:45:46:52 SD: 3.2319 cents 63:73:75:84 SD: 2.6895 cents 64:74:76:85 SD: 2.5628 cents 69:80:82:92 SD: 1.9339 cents 75:87:89:100 SD: 1.5953 cents 96:111:114:128 SD: 1.2109 cents 102:118:121:136 SD: 0.5483 cents 108:125:128:144 SD: 0.1319 cents 534:618:633:712 SD: 0.1291 cents 567:656:672:756 SD: 0.0880 cents