Scala analysis: 564_M72
Miscellaneous tetrachord 135/128 * 7168/6561 * 81/70
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 135/128 92.178716 major chroma, major limma 2: 280/243 245.364616 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 81/70 252.6804 Al-Hwarizmi's lute middle finger 1: 135/128 92.1787 major chroma, major limma 2: 7168/6561 153.1859 3: 81/70 252.6804 Al-Hwarizmi's lute middle finger
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 135/128 92.179 cents major chroma, major limma 1: 1 7168/6561 153.186 cents 1: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 280/243 245.365 cents 2: 1 2187/1792 344.859 cents 2: 1 512/405 405.866 cents narrow diminished fourth 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 : 92.2 245.4 498.0 92.2 : 153.2 405.9 498.0 245.4: 252.7 344.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 252.6804 cents 192/175, 160.5017 cents 135/128, 92.1787 cents 2: 245.3646 .. 405.8663 cents 192/175, 160.5017 cents 19600/19683,-7.3158 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 135/128, 92.1787 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 81/70, 252.6804 cents Average / Smallest step : 1.801012 Largest / Average step : 1.522033 Largest / Smallest step : 2.741201 Median interval of one step : 7168/6561, 153.1859 cents, amount: 1 Least squares average step : 148.36021 cents, oct.: 445.08063 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1837-tone equal temperament with octave 4/3 degrees: 340 905 1837 Least number of segments generator : 919 of 249.158 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1338 of 362.757 cents and inv. generated superset size: 36 = 33 more = 1200.000% 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 7.31577 cents Scale diversity : 1.117720 Lumma stability : 0.370162 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 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 : 7 Odd number limit : 6561 (O: 2187 U: 6561) Highest odd numerator or denominator: 243 Scale harmonicity : 0.020825 Average absolute harmonicity : 0.097100 Specific harmonicity : 0.103143 Fundamental : 1/31104, -14.9248 octaves, 0.0084 Hz. Guide tone : 7560, 12.8842 octaves, 1977889.274 Hz. Exponens Consonantiae : 2.351462E+08, 27.80898 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 396.5, average 132.16667 Mersenne's string divisions : 962843 Sum of van Prooijen's expressibility: 4.99306, average 1.66435 Sum of Tenney's harmonic distance : 10.14949, average 3.38316 Vogel's harmonic complexity : 24.00000 Wille's k value : 16402 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 10 Triangular lattice diameter : 8 Lattice compactness : 43.02084, average 7.17014 Lattice compactness (without 2's) : 25.78643, average 4.29774 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -7 .. 3 -0.66667 12 3: -5 .. 3 -1.00000 9 1 5: 0 .. 1 0.66667 2 1 7: 0 .. 1 0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 12 / 3 = 4.00000 Scale is weakly epimorphic with val: <6 10 15 18| Scale is weakly epimorphic with val: <6 10 15 21| Scale is weakly epimorphic with val: <6 10 16 19| Scale is weakly epimorphic with val: <7 11 15 20| Scale is JI-epimorphic with val: <7 11 17 19| Scale is weakly epimorphic with val: <7 11 17 22| Scale is weakly epimorphic with val: <7 11 18 20| Scale is weakly epimorphic with val: <7 12 16 18| Scale is weakly epimorphic with val: <7 12 16 21| Scale is weakly epimorphic with val: <8 11 15 19| Scale is weakly epimorphic with val: <8 12 19 20|
FIT/MODE
3: 0 1 2 N G T3 SD: 70.2217 c. M: 92.1787 c. 4: 1 1 2 P M ME S SD: 18.7863 c. M:-32.3325 c. 6: 1 2 3 P T3 SD: 5.7006 c. M: 9.1712 c. 10: 2 3 5 P T3 SD: 4.7815 c. M:-7.4303 c. 16: 3 5 8 P T3 SD: 2.2235 c. M:-3.6579 c. 26: 5 8 13 P T3 SD: 2.9628 c. M:-3.6579 c. 28: 5 9 14 P T3 SD: 2.8220 c. M:-3.6579 c. 33: 6 10 17 N T3 SD: 2.4331 c. M: 3.8883 c. 37: 7 11 19 N T3 SD: 2.1312 c. M: 3.0725 c. 38: 7 12 19 P T3 SD: 2.1267 c. M:-3.6579 c. 39: 7 12 20 N T3 SD: 2.2509 c. M: 2.7860 c. 43: 8 13 22 N T3 SD: 1.2626 c. M: 2.1333 c. 49: 9 15 25 N T3 SD: 0.9165 c. M: 1.4242 c. 59: 11 18 30 N T3 SD: 0.5084 c. M:-0.6771 c. 65: 12 20 33 N T3 SD: 0.1671 c. M: 0.2319 c. 146: 27 45 74 N T3 SD: 0.1487 c. M:-0.2466 c. 205: 38 63 104 N T3 SD: 0.0823 c. M:-0.1418 c. 211: 39 65 107 N T3 SD: 0.0981 c. M: 0.1230 c. 270: 50 83 137 N T3 SD: 0.0350 c. M:-0.0518 c. 335: 62 103 170 N T3 SD: 0.0340 c. M: 0.0589 c. 481: 89 148 244 N T3 SD: 0.0243 c. M:-0.0339 c. 686: 127 211 348 N T3 SD: 0.0216 c. M:-0.0278 c. 751: 139 231 381 N T3 SD: 0.0062 c. M:-0.0104 c. 1567: 290 482 795 N T3 SD: 0.0044 c. M: 0.0070 c. 1837: 340 565 932 N T3 SD: 0.0016 c. M: 0.0022 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: 54.9398 cents 6 x 7:8 S SD: 10.7531 cents 7 x 8:9 S SD: 32.2701 cents 8 x 9:11 SD: 33.7509 cents 9 x 10:12 S SD: 31.4805 cents 11:12:13:15 SD: 27.5951 cents 12:13:14:16 S SD: 17.0454 cents 13:14:15:17 SD: 16.4668 cents 14:15:16:19 SD: 14.4670 cents 15:16:17:20 SD: 11.5697 cents 18:19:21:24 SD: 7.1845 cents 21:22:24:28 S SD: 6.1183 cents 33:35:38:44 SD: 3.2510 cents 39:41:45:52 SD: 2.0275 cents 72:76:83:96 SD: 0.5401 cents 165:174:190:220 SD: 0.3828 cents 183:193:211:244 SD: 0.3723 cents 237:250:273:316 SD: 0.2037 cents 276:291:318:368 SD: 0.1912 cents 348:367:401:464 SD: 0.0522 cents