Scala analysis: 569_M77
Miscellaneous tetrachord 8/7 * 81/80 * 280/243
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 81/70 252.680383 Al-Hwarizmi's lute middle finger 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 280/243 245.3646 1: 8/7 231.1741 septimal whole tone 2: 81/80 21.5063 syntonic comma, Didymus comma 3: 280/243 245.3646
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 81/80 21.506 cents syntonic comma, Didymus comma 1: 1 8/7 231.174 cents septimal whole tone 1: 1 280/243 245.365 cents 2: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 7/6 266.871 cents septimal minor third 2: 1 320/243 476.539 cents grave 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 : 231.2 252.7 498.0 231.2: 21.5 266.9 498.0 252.7: 245.4 476.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 245.3646 cents 22400/19683, 223.8583 cents 81/80, 21.5063 cents 2: 252.6804 .. 476.5387 cents 22400/19683, 223.8583 cents 19683/19600, 7.3158 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 81/80, 21.5063 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 280/243, 245.3646 cents Average / Smallest step : 7.719370 Largest / Average step : 1.477967 Largest / Smallest step : 11.408970 Median interval of one step : 8/7, 231.1741 cents, amount: 1 Least squares average step : 159.33356 cents, oct.: 478.00068 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1088-tone equal temperament with octave 4/3 degrees: 505 552 1088 Least number of segments generator : 545 of 249.480 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 883 of 404.204 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 : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 0.389763 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.101052 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 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 7 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.029395 Average absolute harmonicity : 0.108275 Specific harmonicity : 0.139930 Fundamental : 1/210, -7.7142 octaves, 1.2458 Hz. Guide tone : 648, 9.3399 octaves, 169533.366 Hz. Exponens Consonantiae : 1.360800E+05, 17.05410 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 86.5, average 28.83333 Mersenne's string divisions : 15855 Sum of van Prooijen's expressibility: 3.23070, average 1.07690 Sum of Tenney's harmonic distance : 6.58095, average 2.19365 Vogel's harmonic complexity : 14.00000 Wille's k value : 121 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 23.23386, average 3.87231 Lattice compactness (without 2's) : 16.97611, average 2.82935 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.33333 6 3: -1 .. 4 1.00000 5 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.66667 2 2 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 11 16 19| Scale is weakly epimorphic with val: <7 10 16 18| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly 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 18 20| Scale is weakly epimorphic with val: <8 11 17 21| Scale is weakly epimorphic with val: <8 12 15 22| Scale is weakly epimorphic with val: <8 12 17 21| Scale is weakly epimorphic with val: <8 12 18 19|
FIT/MODE
3: 1 0 2 N G T3 SD: 62.6008 c. M: 86.6654 c. 4: 2 0 2 P M DE I SD: 10.5190 c. M:-17.8484 c. 10: 5 0 5 P M DE I SD: 10.5190 c. M:-17.8484 c. 13: 6 1 6 SP M DE I SD: 8.9794 c. M:-15.4977 c. 15: 7 1 7 SP M DE I SD: 7.5076 c. M:-12.9436 c. 16: 7 1 8 P T3 SD: 7.9524 c. M: 13.2794 c. 17: 8 1 8 SP M DE I SD: 6.6089 c. M:-10.9905 c. 18: 8 1 9 P T3 SD: 6.0505 c. M: 9.8208 c. 19: 9 1 9 SP M DE I SD: 6.1036 c. M:-9.4486 c. 20: 9 1 10 P T3 SD: 4.5875 c. M: 7.0538 c. 22: 10 1 11 P T3 SD: 3.4797 c. M: 4.7900 c. 24: 11 1 12 P T3 SD: 2.6963 c. M: 3.6579 c. 26: 12 1 13 P T3 SD: 2.2427 c. M: 3.6579 c. 28: 13 1 14 P T3 SD: 2.1122 c. M: 3.6579 c. 35: 16 2 17 SP T3 SD: 2.8388 c. M: 3.4964 c. 37: 17 2 18 SP T3 SD: 2.2307 c. M:-3.0725 c. 39: 18 2 19 SP T3 SD: 1.7461 c. M:-2.7273 c. 41: 19 2 20 SP T3 SD: 1.4113 c. M:-2.4158 c. 43: 20 2 21 SP T3 SD: 1.2618 c. M:-2.1333 c. 45: 21 2 22 SP T3 SD: 1.3005 c. M:-1.8759 c. 63: 29 3 31 SP T3 SD: 1.1188 c. M: 1.9153 c. 65: 30 3 32 SP T3 SD: 0.7613 c. M: 1.3072 c. 67: 31 3 33 SP T3 SD: 0.4259 c. M: 0.7354 c. 69: 32 3 34 SP T3 SD: 0.1170 c. M: 0.1967 c. 140: 65 6 69 SP T3 SD: 0.0679 c. M: 0.1004 c. 209: 97 9 103 SP T3 SD: 0.0501 c. M: 0.0834 c. 278: 129 12 137 SP T3 SD: 0.0579 c. M: 0.0748 c. 349: 162 15 172 SP T3 SD: 0.0524 c. M: 0.0902 c. 487: 226 21 240 SP T3 SD: 0.0533 c. M: 0.0785 c. 558: 259 24 275 SP T3 SD: 0.0506 c. M: 0.0877 c. 601: 279 26 296 SP T3 SD: 0.0450 c. M:-0.0712 c. 668: 310 29 329 SP T3 SD: 0.0482 c. M:-0.0700 c. 670: 311 29 330 SP T3 SD: 0.0343 c. M:-0.0589 c. 739: 343 32 364 SP T3 SD: 0.0289 c. M:-0.0488 c. 741: 344 32 365 SP T3 SD: 0.0310 c. M:-0.0388 c. 808: 375 35 398 SP T3 SD: 0.0281 c. M:-0.0405 c. 810: 376 35 399 SP T3 SD: 0.0206 c. M:-0.0313 c. 879: 408 38 433 SP T3 SD: 0.0145 c. M:-0.0250 c. 948: 440 41 467 SP T3 SD: 0.0139 c. M:-0.0197 c. 950: 441 41 468 SP T3 SD: 0.0153 c. M:-0.0236 c. 1019: 473 44 502 SP T3 SD: 0.0068 c. M:-0.0087 c. 1088: 505 47 536 SP T3 SD: 0.0035 c. M: 0.0043 c. 2107: 978 91 1038 SP T3 SD: 0.0036 c. M:-0.0060 c. 2247: 1043 97 1107 SP T3 SD: 0.0033 c. M:-0.0057 c. 2316: 1075 100 1141 SP T3 SD: 0.0012 c. M: 0.0021 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: 52.6754 cents 6 x 7:8 S SD: 7.0953 cents 7:8 x 9 S SD: 31.4805 cents 8:9 x 11 SD: 29.9221 cents 9:10 x 12 S SD: 24.3852 cents 11 x 13:15 SD: 26.6836 cents 12 x 14:16 S SD: 7.0953 cents 13 x 15:17 SD: 16.9891 cents 14:16 x 19 SD: 15.3211 cents 15:17 x 20 SD: 7.2437 cents 18 x 21:24 S SD: 7.0953 cents 19 x 22:25 SD: 11.4791 cents 20 x 23:27 SD: 12.0149 cents 21:24 x 28 S SD: 0.0000 cents 22:25 x 29 SD: 11.0543 cents 24:27:28:32 S SD: 10.2453 cents 25 x 29:33 SD: 8.9578 cents 26 x 30:35 SD: 8.6438 cents 27:31 x 36 SD: 3.9982 cents 28:32 x 37 SD: 7.7634 cents 30:34:35:40 SD: 6.7598 cents 32 x 37:43 SD: 6.7694 cents 33 x 38:44 SD: 4.2202 cents 34:39 x 45 SD: 7.1345 cents 36:41:42:48 SD: 5.1384 cents 39 x 45:52 SD: 2.4697 cents 40 x 46:53 SD: 7.6277 cents 41:47 x 55 SD: 5.8850 cents 42:48:49:56 S SD: 4.7302 cents 43:49:50:57 SD: 4.6947 cents 46 x 53:61 SD: 6.0107 cents 47:54 x 63 SD: 6.4943 cents 48:55:56:64 SD: 4.9626 cents 49:56:57:65 SD: 4.2411 cents 50:57:58:67 SD: 3.5208 cents 51:58:59:68 SD: 2.8392 cents 53 x 61:71 SD: 6.1819 cents 54:62 x 72 SD: 3.9982 cents 56:64:65:75 SD: 3.1257 cents 57:65:66:76 SD: 1.3212 cents 60 x 69:80 SD: 5.3599 cents 61:70:71:81 SD: 4.7531 cents 62:71:72:83 SD: 3.3176 cents 63:72:73:84 SD: 0.7911 cents 141:161:163:188 SD: 0.7558 cents 147:168:170:196 SD: 0.3394 cents 210:240:243:280 SD: 0.0000 cents