Scala analysis: 565_M73
Miscellaneous tetrachord 60/59 * 59/51 * 17/15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 60/59 29.097055 2: 20/17 281.358304 septendecimal augmented second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 17/15 216.6867 septendecimal whole tone 1: 60/59 29.0971 2: 59/51 252.2612 3: 17/15 216.6867 septendecimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 60/59 29.097 cents 1: 1 17/15 216.687 cents septendecimal whole tone 1: 1 59/51 252.261 cents 2: 1 68/59 245.784 cents 2: 1 20/17 281.358 cents septendecimal augmented second 2: 1 59/45 468.948 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 : 29.1 281.4 498.0 29.1 : 252.3 468.9 498.0 281.4: 216.7 245.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.0971 .. 252.2612 cents 3481/3060, 223.1642 cents 60/59, 29.0971 cents 2: 245.7838 .. 468.9479 cents 3481/3060, 223.1642 cents 3468/3481,-6.4775 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 60/59, 29.0971 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 59/51, 252.2612 cents Average / Smallest step : 5.705560 Largest / Average step : 1.519509 Largest / Smallest step : 8.669649 Median interval of one step : 17/15, 216.6867 cents, amount: 1 Least squares average step : 148.99633 cents, oct.: 446.98900 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 6.47750 cents Scale diversity : 0.509451 Lumma stability : 0.116845 Lumma impropriety factor : 0.013006 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 : 3481/3468, 6.4775 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% -- Rational properties -- Prime limit : 59 Odd number limit : 59 (O: 59 U: 59) Highest odd numerator or denominator: 59 Scale harmonicity : 0.022805 Fundamental : 1/3009, -11.5551 octaves, 0.0869 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 1.805400E+05, 17.46196 octaves Euler's gradus suavitatis : 85 Sum of Mann's harmonic distance : 81.5, average 27.16667 Mersenne's string divisions : 4403 Sum of van Prooijen's expressibility: 3.47842, average 1.15947 Sum of Tenney's harmonic distance : 7.15966, average 2.38655 Vogel's harmonic complexity : 59.00000 Wille's k value : 501 Wilson's harmonic complexity : 87 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 12.51738, average 2.08623 Lattice compactness (without 2's) : 9.21076, average 1.53513 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.66667 2 17: -1 .. 0 -0.33333 1 1 59: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 18 27 42| Scale is weakly epimorphic with val: <6 10 19 28 43| Scale is weakly epimorphic with val: <6 11 18 27 42| Scale is weakly epimorphic with val: <6 11 19 28 43| Scale is weakly epimorphic with val: <7 10 16 27 44| Scale is weakly epimorphic with val: <7 10 17 28 42| Scale is weakly epimorphic with val: <7 10 18 29 43| Scale is weakly epimorphic with val: <7 10 19 30 44| Scale is weakly epimorphic with val: <7 11 15 27 42| Scale is weakly epimorphic with val: <7 11 15 28 44| Scale is weakly epimorphic with val: <7 11 15 30 42| Scale is weakly epimorphic with val: <7 11 15 31 44| Scale is weakly epimorphic with val: <7 11 15 33 42| Scale is weakly epimorphic with val: <7 11 16 28 43| Scale is weakly epimorphic with val: <7 11 16 29 42| Scale is weakly epimorphic with val: <7 11 16 31 43| Scale is weakly epimorphic with val: <7 11 16 32 42| Scale is weakly epimorphic with val: <7 11 17 27 43| Scale is weakly epimorphic with val: <7 11 17 29 44| Scale is weakly epimorphic with val: <7 11 17 30 43| = patent Scale is weakly epimorphic with val: <7 11 17 32 44| Scale is weakly epimorphic with val: <7 11 17 33 43| Scale is weakly epimorphic with val: <7 11 18 27 42| Scale is weakly epimorphic with val: <7 11 18 28 44| Scale is JI-epimorphic with val: <7 11 18 30 42| Scale is weakly epimorphic with val: <7 11 18 31 44| Scale is weakly epimorphic with val: <7 11 18 33 42| Scale is weakly epimorphic with val: <7 11 19 28 43| Scale is weakly epimorphic with val: <7 11 19 29 42| Scale is JI-epimorphic with val: <7 11 19 31 43| Scale is weakly epimorphic with val: <7 11 19 32 42| Scale is weakly epimorphic with val: <7 12 16 27 44| Scale is weakly epimorphic with val: <7 12 17 28 42| Scale is weakly epimorphic with val: <7 12 18 29 43| Scale is weakly epimorphic with val: <7 12 19 29 42| Scale is weakly epimorphic with val: <7 12 19 30 44| Scale is weakly epimorphic with val: <7 12 19 32 42| Scale is weakly epimorphic with val: <8 11 15 28 44| Scale is weakly epimorphic with val: <8 11 16 29 42| Scale is weakly epimorphic with val: <8 11 17 30 43| Scale is weakly epimorphic with val: <8 11 18 27 42| Scale is weakly epimorphic with val: <8 11 18 30 42| Scale is weakly epimorphic with val: <8 11 18 31 44| Scale is weakly epimorphic with val: <8 11 18 33 42| Scale is weakly epimorphic with val: <8 11 19 28 43| Scale is weakly epimorphic with val: <8 11 19 31 43| Scale is weakly epimorphic with val: <8 11 19 32 42| Scale is weakly epimorphic with val: <8 12 15 28 44| Scale is weakly epimorphic with val: <8 12 16 29 42| Scale is weakly epimorphic with val: <8 12 17 28 42| Scale is weakly epimorphic with val: <8 12 17 30 43| Scale is weakly epimorphic with val: <8 12 17 31 42| Scale is weakly epimorphic with val: <8 12 18 29 43| Scale is weakly epimorphic with val: <8 12 18 31 44| Scale is weakly epimorphic with val: <8 12 18 32 43| Scale is weakly epimorphic with val: <8 12 19 27 44| Scale is weakly epimorphic with val: <8 12 19 30 44| Scale is weakly epimorphic with val: <8 12 19 32 42| Scale is weakly epimorphic with val: <8 12 19 33 44|
FIT/MODE
3: 0 2 1 N G T3 SD: 33.7355 c. M:-50.6717 c. 4: 0 2 2 P M DE S SD: 25.1147 c. M: 32.3358 c. 5: 0 3 2 N G T3 SD: 19.5942 c. M: 29.0971 c. 7: 0 4 3 N G T3 SD: 16.9029 c. M: 29.0971 c. 9: 0 5 4 N G T3 SD: 17.0139 c. M: 29.0971 c. 11: 1 5 5 SP M DE S SD: 10.8907 c. M:-16.1798 c. 12: 1 6 5 P T3 SD: 8.9065 c. M:-12.4067 c. 14: 1 7 6 P T3 SD: 4.1813 c. M:-6.4776 c. 16: 1 8 7 P T3 SD: 1.3642 c. M:-2.0308 c. 51: 3 26 22 N T3 SD: 1.0707 c. M:-1.8438 c. 53: 3 27 23 N T3 SD: 0.6130 c. M: 0.9058 c. 69: 4 35 30 N T3 SD: 0.1546 c. M: 0.2249 c. 85: 5 43 37 N T3 SD: 0.1315 c. M:-0.1997 c. 154: 9 78 67 N T3 SD: 0.0061 c. M:-0.0095 c. 1763: 103 893 767 N T3 SD: 0.0059 c. M:-0.0103 c. 1917: 112 971 834 N T3 SD: 0.0057 c. M:-0.0098 c. 2071: 121 1049 901 N T3 SD: 0.0055 c. M:-0.0095 c. 2225: 130 1127 968 N T3 SD: 0.0054 c. M:-0.0091 c. 2379: 139 1205 1035 N T3 SD: 0.0053 c. M:-0.0089 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: 104.9554 cents 5 x 6:7 S SD: 45.5797 cents 6 x 7:8 S SD: 7.2437 cents 7 x 8:9 S SD: 40.2571 cents 8 x 9:11 SD: 47.0007 cents 9 x 11:12 SD: 33.0248 cents 10 x 12:13 S SD: 27.8230 cents 16:17:19:21 SD: 27.4040 cents 17:18:20:23 SD: 24.7630 cents 18:19:21:24 SD: 22.0376 cents 21:22:25:28 SD: 18.4567 cents 22:23:26:29 SD: 17.4599 cents 23:24:27:31 SD: 16.1665 cents 24:25:28:32 SD: 14.6757 cents 27:28:32:36 S SD: 12.0647 cents 28:29:33:37 SD: 11.7974 cents 29:30:34:39 SD: 11.2172 cents 30:31:35:40 SD: 10.4110 cents 33:34:39:44 SD: 7.9704 cents 36:37:42:48 SD: 7.7898 cents 38:39:45:51 SD: 7.5255 cents 39:40:46:52 SD: 5.1288 cents 45:46:53:60 SD: 3.0526 cents 51:52:60:68 SD: 1.5067 cents 57:58:67:76 SD: 0.6085 cents 231:235:272:308 SD: 0.5411 cents 237:241:279:316 SD: 0.3674 cents 243:247:286:324 SD: 0.3649 cents 294:299:346:392 SD: 0.1990 cents 300:305:353:400 SD: 0.1870 cents 351:357:413:468 SD: 0.1162 cents 357:363:420:476 SD: 0.0808 cents 414:421:487:552 SD: 0.0735 cents