Scala analysis: 576_M84
Miscellaneous tetrachord 68/65 * 65/57 * 19/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/65 78.114034 Valentine semitone 2: 68/57 305.487393 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 19/17 192.5576 quasi-meantone 1: 68/65 78.1140 Valentine semitone 2: 65/57 227.3734 3: 19/17 192.5576 quasi-meantone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 68/65 78.114 cents Valentine semitone 1: 1 19/17 192.558 cents quasi-meantone 1: 1 65/57 227.373 cents 2: 1 76/65 270.672 cents 2: 1 68/57 305.487 cents 2: 1 65/51 419.931 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 : 78.1 305.5 498.0 78.1 : 227.4 419.9 498.0 305.5: 192.6 270.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 78.1140 .. 227.3734 cents 4225/3876, 149.2593 cents 68/65, 78.1140 cents 2: 270.6716 .. 419.9310 cents 4225/3876, 149.2593 cents 4332/4225, 43.2983 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 68/65, 78.1140 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 65/57, 227.3734 cents Average / Smallest step : 2.125290 Largest / Average step : 1.369595 Largest / Smallest step : 2.910788 Median interval of one step : 19/17, 192.5576 cents, amount: 1 Least squares average step : 155.94456 cents, oct.: 467.83367 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1645-tone equal temperament with octave 4/3 degrees: 258 1009 1645 Least number of segments generator : 823 of 249.174 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1009 of 305.488 cents and inv. generated superset size: 80 = 77 more = 2666.667% Number of contiguous 1-step segments: 0 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 43.29828 cents Scale diversity : 1.006886 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.400619 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 : 1105/1083, 34.8158 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 : 19 Odd number limit : 65 (O: 65 U: 65) Highest odd numerator or denominator: 65 Scale harmonicity : 0.010262 Average absolute harmonicity : 0.081761 Specific harmonicity : 0.049213 Fundamental : 1/3705, -11.8553 octaves, 0.0706 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 2.519400E+05, 17.94272 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 132.5, average 44.16667 Mersenne's string divisions : 16625 Sum of van Prooijen's expressibility: 4.04591, average 1.34864 Sum of Tenney's harmonic distance : 8.31299, average 2.77100 Vogel's harmonic complexity : 39.00000 Wille's k value : 617 Wilson's harmonic complexity : 57 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 12.94178, average 2.15696 Lattice compactness (without 2's) : 9.87832, average 1.64639 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is JI-epimorphic with val: <7 11 16 26 29 30| Scale is weakly epimorphic with val: <7 11 16 26 30 32| Scale is JI-epimorphic with val: <7 11 16 27 30 31| Scale is weakly epimorphic with val: <7 11 16 28 29 31| Scale is JI-epimorphic with val: <7 11 16 28 31 32| Scale is JI-epimorphic with val: <7 11 17 26 30 31| Scale is weakly epimorphic with val: <7 11 17 27 29 31| Scale is JI-epimorphic with val: <7 11 17 27 31 32| Scale is weakly epimorphic with val: <7 11 17 28 29 30| Scale is weakly epimorphic with val: <7 11 17 28 30 32| Scale is weakly epimorphic with val: <7 11 18 26 29 31| Scale is JI-epimorphic with val: <7 11 18 26 31 32| Scale is weakly epimorphic with val: <7 11 18 27 29 30| Scale is weakly epimorphic with val: <7 11 18 27 30 32| Scale is weakly epimorphic with val: <7 11 18 28 30 31| Scale is weakly epimorphic with val: <7 12 16 26 31 32|
FIT/MODE
3: 0 2 1 N G T3 SD: 47.6316 c. M: 78.1140 c. 4: 0 2 2 P M DE S SD: 55.6480 c. M: 78.1140 c. 5: 1 2 2 SP M ME S SD: 12.9922 c. M:-21.4950 c. 6: 1 3 2 P T3 SD: 15.5826 c. M:-26.5426 c. 7: 1 3 3 SP M DE S SD: 12.7136 c. M: 20.8903 c. 8: 1 4 3 P T3 SD: 9.7472 c. M: 15.8584 c. 11: 2 5 4 SP T3 SD: 9.7614 c. M:-12.4396 c. 12: 2 5 5 SP M DE S SD: 9.0881 c. M: 14.9611 c. 13: 2 6 5 SP T3 SD: 1.0375 c. M: 1.4917 c. 44: 7 20 17 SP T3 SD: 0.6513 c. M:-1.1204 c. 57: 9 26 22 SP T3 SD: 0.3578 c. M:-0.5247 c. 70: 11 32 27 SP T3 SD: 0.2764 c. M:-0.4545 c. 127: 20 58 49 SP T3 SD: 0.2944 c. M:-0.3985 c. 153: 24 70 59 SP T3 SD: 0.2893 c. M:-0.5010 c. 173: 27 79 67 SP T3 SD: 0.2914 c. M: 0.3845 c. 184: 29 84 71 SP T3 SD: 0.3100 c. M:-0.3822 c. 186: 29 85 72 SP T3 SD: 0.2989 c. M: 0.4619 c. 191: 30 87 74 SP T3 SD: 0.2412 c. M: 0.4022 c. 204: 32 93 79 SP T3 SD: 0.1807 c. M: 0.3128 c. 217: 34 99 84 SP T3 SD: 0.1427 c. M: 0.2340 c. 230: 36 105 89 SP T3 SD: 0.1320 c. M: 0.1642 c. 261: 41 119 101 SP T3 SD: 0.1223 c. M: 0.1725 c. 274: 43 125 106 SP T3 SD: 0.0725 c. M: 0.1167 c. 287: 45 131 111 SP T3 SD: 0.0405 c. M: 0.0661 c. 344: 54 157 133 SP T3 SD: 0.0389 c. M:-0.0674 c. 357: 56 163 138 SP T3 SD: 0.0217 c. M:-0.0360 c. 631: 99 288 244 SP T3 SD: 0.0231 c. M: 0.0303 c. 644: 101 294 249 SP T3 SD: 0.0061 c. M: 0.0095 c. 1001: 157 457 387 SP T3 SD: 0.0039 c. M:-0.0067 c. 1645: 258 751 636 SP T3 SD: 0.0007 c. M: 0.0012 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: 80.8263 cents 5 x 6:7 S SD: 42.5377 cents 6 x 7:8 S SD: 19.3082 cents 7 x 8:9 S SD: 48.6994 cents 8 x 10:11 S SD: 48.4017 cents 9:10:11:12 H SD: 37.4665 cents 10:11:12:13 H SD: 32.6159 cents 11:12:13:15 SD: 27.9647 cents 12:13:14:16 S SD: 23.9130 cents 14:15:17:19 SD: 19.9609 cents 15:16:18:20 S SD: 11.7057 cents 20:21:24:27 S SD: 8.2056 cents 21:22:25:28 SD: 1.4578 cents 87:91:104:116 SD: 1.1734 cents 108:113:129:144 SD: 0.7111 cents 129:135:154:172 SD: 0.4412 cents 150:157:179:200 SD: 0.3298 cents 285:298:340:380 SD: 0.2978 cents 306:320:365:408 SD: 0.2370 cents 327:342:390:436 SD: 0.2202 cents 414:433:494:552 SD: 0.1890 cents 435:455:519:580 SD: 0.1138 cents 456:477:544:608 SD: 0.0558 cents