Scala analysis: 578_M86
Miscellaneous tetrachord 30/29 * 58/51 * 17/15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 30/29 58.691521 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: 30/29 58.6915 2: 58/51 222.6668 3: 17/15 216.6867 septendecimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 30/29 58.692 cents 1: 1 17/15 216.687 cents septendecimal whole tone 1: 1 58/51 222.667 cents 2: 1 34/29 275.378 cents 2: 1 20/17 281.358 cents septendecimal augmented second 2: 1 58/45 439.353 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 : 58.7 281.4 498.0 58.7 : 222.7 439.4 498.0 281.4: 216.7 275.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.6915 .. 222.6668 cents 841/765, 163.9753 cents 30/29, 58.6915 cents 2: 275.3782 .. 439.3535 cents 841/765, 163.9753 cents 867/841, 52.7114 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 30/29, 58.6915 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 58/51, 222.6668 cents Average / Smallest step : 2.828603 Largest / Average step : 1.341245 Largest / Smallest step : 3.793849 Median interval of one step : 17/15, 216.6867 cents, amount: 1 Least squares average step : 151.11022 cents, oct.: 453.33067 cents Scale is strictly 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 52.71143 cents Scale diversity : 0.737316 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.341524 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 : 290/289, 5.9801 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle 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% Limited inverse transpositions with margin 163.9753 cents: 1 -- Rational properties -- Prime limit : 29 Odd number limit : 51 (O: 29 U: 51) Highest odd numerator or denominator: 29 Scale harmonicity : 0.010212 Average absolute harmonicity : 0.085279 Specific harmonicity : 0.053127 Fundamental : 1/1479, -10.5304 octaves, 0.1769 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 8.874000E+04, 16.43730 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 51.5, average 17.16667 Mersenne's string divisions : 15281 Sum of van Prooijen's expressibility: 3.16997, average 1.05666 Sum of Tenney's harmonic distance : 6.55018, average 2.18339 Vogel's harmonic complexity : 38.66667 Wille's k value : 382 Wilson's harmonic complexity : 57 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.06336, average 2.17723 Lattice compactness (without 2's) : 10.05986, average 1.67664 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.66667 2 17: -1 .. 0 -0.33333 1 1 29: -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 33| Scale is weakly epimorphic with val: <6 10 18 27 36| Scale is weakly epimorphic with val: <6 10 19 27 32| Scale is weakly epimorphic with val: <6 10 19 28 34| Scale is weakly epimorphic with val: <6 10 19 28 37| Scale is weakly epimorphic with val: <6 10 19 30 32| Scale is weakly epimorphic with val: <6 11 18 27 33| Scale is weakly epimorphic with val: <6 11 18 27 36| Scale is weakly epimorphic with val: <6 11 18 28 32| Scale is weakly epimorphic with val: <6 11 18 31 32| Scale is weakly epimorphic with val: <6 11 19 28 34| Scale is weakly epimorphic with val: <6 11 19 28 37| Scale is weakly epimorphic with val: <6 11 19 29 33| Scale is weakly epimorphic with val: <6 11 19 32 33| Scale is weakly epimorphic with val: <7 10 16 27 34| Scale is weakly epimorphic with val: <7 10 16 27 37| Scale is weakly epimorphic with val: <7 10 17 28 32| Scale is weakly epimorphic with val: <7 10 17 28 35| Scale is weakly epimorphic with val: <7 10 17 28 38| Scale is weakly epimorphic with val: <7 10 18 27 32| Scale is weakly epimorphic with val: <7 10 18 29 33| Scale is weakly epimorphic with val: <7 10 18 29 36| Scale is weakly epimorphic with val: <7 10 18 30 32| Scale is weakly epimorphic with val: <7 10 19 28 33| Scale is weakly epimorphic with val: <7 10 19 30 34| Scale is weakly epimorphic with val: <7 10 19 30 37| Scale is weakly epimorphic with val: <7 10 19 31 33| Scale is JI-epimorphic with val: <7 11 15 27 32| Scale is weakly epimorphic with val: <7 11 15 27 35| Scale is weakly epimorphic with val: <7 11 15 27 38| Scale is weakly epimorphic with val: <7 11 15 28 34| Scale is weakly epimorphic with val: <7 11 15 28 37| Scale is weakly epimorphic with val: <7 11 15 30 32| Scale is weakly epimorphic with val: <7 11 15 30 35| Scale is weakly epimorphic with val: <7 11 15 30 38| Scale is weakly epimorphic with val: <7 11 15 31 34| Scale is weakly epimorphic with val: <7 11 15 31 37| Scale is weakly epimorphic with val: <7 11 15 33 35| Scale is weakly epimorphic with val: <7 11 15 33 38| Scale is JI-epimorphic with val: <7 11 16 28 33| Scale is weakly epimorphic with val: <7 11 16 28 36| Scale is weakly epimorphic with val: <7 11 16 29 32| Scale is weakly epimorphic with val: <7 11 16 29 35| Scale is weakly epimorphic with val: <7 11 16 29 38| Scale is weakly epimorphic with val: <7 11 16 31 33| Scale is weakly epimorphic with val: <7 11 16 31 36| Scale is weakly epimorphic with val: <7 11 16 32 32| Scale is weakly epimorphic with val: <7 11 16 32 35| Scale is weakly epimorphic with val: <7 11 16 32 38| Scale is weakly epimorphic with val: <7 11 17 27 33| Scale is weakly epimorphic with val: <7 11 17 27 36| Scale is JI-epimorphic with val: <7 11 17 29 34| Scale is weakly epimorphic with val: <7 11 17 29 37| Scale is weakly epimorphic with val: <7 11 17 30 33| Scale is weakly epimorphic with val: <7 11 17 30 36| Scale is weakly epimorphic with val: <7 11 17 32 34| Scale is weakly epimorphic with val: <7 11 17 32 37| Scale is weakly epimorphic with val: <7 11 17 33 33| Scale is weakly epimorphic with val: <7 11 17 33 36| Scale is weakly epimorphic with val: <7 11 18 27 32| Scale is weakly epimorphic with val: <7 11 18 27 35| Scale is weakly epimorphic with val: <7 11 18 27 38| Scale is weakly epimorphic with val: <7 11 18 28 34| Scale is weakly epimorphic with val: <7 11 18 28 37| Scale is weakly epimorphic with val: <7 11 18 30 32| Scale is JI-epimorphic with val: <7 11 18 30 35| Scale is weakly epimorphic with val: <7 11 18 30 38| Scale is weakly epimorphic with val: <7 11 18 31 34| Scale is weakly epimorphic with val: <7 11 18 31 37| Scale is weakly epimorphic with val: <7 11 18 33 35| Scale is weakly epimorphic with val: <7 11 18 33 38| Scale is weakly epimorphic with val: <7 11 19 28 33| Scale is weakly epimorphic with val: <7 11 19 28 36| Scale is weakly epimorphic with val: <7 11 19 29 32| Scale is weakly epimorphic with val: <7 11 19 29 35| Scale is weakly epimorphic with val: <7 11 19 29 38| Scale is weakly epimorphic with val: <7 11 19 31 33| Scale is JI-epimorphic with val: <7 11 19 31 36| Scale is weakly epimorphic with val: <7 11 19 32 32| Scale is weakly epimorphic with val: <7 11 19 32 35| Scale is weakly epimorphic with val: <7 11 19 32 38| Scale is weakly epimorphic with val: <7 12 16 27 34| Scale is weakly epimorphic with val: <7 12 16 27 37| Scale is weakly epimorphic with val: <7 12 16 29 32| Scale is weakly epimorphic with val: <7 12 16 32 32| Scale is weakly epimorphic with val: <7 12 17 27 33| Scale is weakly epimorphic with val: <7 12 17 28 32| Scale is weakly epimorphic with val: <7 12 17 28 35| Scale is weakly epimorphic with val: <7 12 17 28 38| Scale is weakly epimorphic with val: <7 12 17 30 33| Scale is weakly epimorphic with val: <7 12 17 33 33| Scale is weakly epimorphic with val: <7 12 18 28 34| Scale is weakly epimorphic with val: <7 12 18 29 33| Scale is weakly epimorphic with val: <7 12 18 29 36| Scale is weakly epimorphic with val: <7 12 18 31 34| Scale is weakly epimorphic with val: <7 12 19 29 35| Scale is weakly epimorphic with val: <7 12 19 30 34| Scale is weakly epimorphic with val: <7 12 19 30 37| Scale is weakly epimorphic with val: <7 12 19 32 35| Scale is weakly epimorphic with val: <8 11 15 28 33| Scale is weakly epimorphic with val: <8 11 15 28 36| Scale is weakly epimorphic with val: <8 11 16 28 32| Scale is weakly epimorphic with val: <8 11 16 29 34| Scale is weakly epimorphic with val: <8 11 16 29 37| Scale is weakly epimorphic with val: <8 11 16 31 32| Scale is weakly epimorphic with val: <8 11 17 29 33| Scale is weakly epimorphic with val: <8 11 17 30 32| Scale is weakly epimorphic with val: <8 11 17 30 35| Scale is weakly epimorphic with val: <8 11 17 30 38| Scale is weakly epimorphic with val: <8 11 17 32 33| Scale is weakly epimorphic with val: <8 11 18 27 34| Scale is weakly epimorphic with val: <8 11 18 30 34| Scale is weakly epimorphic with val: <8 11 18 31 33| Scale is weakly epimorphic with val: <8 11 18 31 36| Scale is weakly epimorphic with val: <8 11 18 33 34| Scale is weakly epimorphic with val: <8 11 19 28 35| Scale is weakly epimorphic with val: <8 11 19 31 35| Scale is weakly epimorphic with val: <8 11 19 32 34| Scale is weakly epimorphic with val: <8 11 19 32 37| Scale is weakly epimorphic with val: <8 12 15 28 33| Scale is weakly epimorphic with val: <8 12 15 28 36| Scale is weakly epimorphic with val: <8 12 15 29 32| Scale is weakly epimorphic with val: <8 12 15 32 32| Scale is weakly epimorphic with val: <8 12 16 27 33| Scale is weakly epimorphic with val: <8 12 16 29 34| Scale is weakly epimorphic with val: <8 12 16 29 37| Scale is weakly epimorphic with val: <8 12 16 30 33| Scale is weakly epimorphic with val: <8 12 16 33 33| Scale is weakly epimorphic with val: <8 12 17 28 34| Scale is weakly epimorphic with val: <8 12 17 30 32| Scale is weakly epimorphic with val: <8 12 17 30 35| Scale is weakly epimorphic with val: <8 12 17 30 38| Scale is weakly epimorphic with val: <8 12 17 31 34| Scale is weakly epimorphic with val: <8 12 18 29 35| Scale is weakly epimorphic with val: <8 12 18 31 33| Scale is weakly epimorphic with val: <8 12 18 31 36| Scale is weakly epimorphic with val: <8 12 18 32 35| Scale is weakly epimorphic with val: <8 12 19 27 36| Scale is weakly epimorphic with val: <8 12 19 30 36| Scale is weakly epimorphic with val: <8 12 19 32 34| Scale is weakly epimorphic with val: <8 12 19 32 37| Scale is weakly epimorphic with val: <8 12 19 33 36|
FIT/MODE
3: 0 2 1 N G T3 SD: 44.7672 c. M: 58.6915 c. 4: 0 2 2 P M DE S SD: 38.6881 c. M: 58.6915 c. 5: 1 2 2 SP M ME S SD: 25.6865 c. M:-40.9175 c. 6: 1 2 3 P T3 SD: 23.3586 c. M: 32.3358 c. 7: 1 3 3 SP M DE S SD: 7.4316 c. M:-12.4578 c. 9: 1 4 4 SP M DE S SD: 3.3177 c. M: 4.6666 c. 16: 2 7 7 SP M DE S SD: 2.1727 c. M:-3.5641 c. 25: 3 11 11 SP M DE S SD: 1.5461 c. M: 2.4531 c. 34: 4 15 15 SP M DE S SD: 1.7555 c. M: 3.0390 c. 41: 5 18 18 SP M DE S SD: 1.6386 c. M:-2.0457 c. 42: 5 19 18 SP T3 SD: 1.9017 c. M:-3.2388 c. 44: 5 20 19 SP T3 SD: 1.5299 c. M: 2.0955 c. 51: 6 23 22 SP T3 SD: 1.0660 c. M:-1.8438 c. 60: 7 27 26 SP T3 SD: 0.6044 c. M:-0.8672 c. 69: 8 31 30 SP T3 SD: 0.5533 c. M: 0.9472 c. 76: 9 34 33 SP T3 SD: 0.2988 c. M:-0.4303 c. 85: 10 38 37 SP T3 SD: 0.0848 c. M: 0.1094 c. 246: 29 110 107 SP T3 SD: 0.0353 c. M:-0.0574 c. 331: 39 148 144 SP T3 SD: 0.0100 c. M:-0.0146 c. 747: 88 334 325 SP T3 SD: 0.0113 c. M: 0.0196 c. 1078: 127 482 469 SP T3 SD: 0.0099 c. M: 0.0165 c. 1409: 166 630 613 SP T3 SD: 0.0095 c. M: 0.0148 c. 1740: 205 778 757 SP T3 SD: 0.0094 c. M: 0.0138 c. 1841: 217 823 801 SP T3 SD: 0.0089 c. M:-0.0134 c. 1926: 227 861 838 SP T3 SD: 0.0085 c. M: 0.0120 c. 2087: 246 933 908 SP T3 SD: 0.0083 c. M:-0.0143 c. 2172: 256 971 945 SP T3 SD: 0.0062 c. M:-0.0099 c. 2257: 266 1009 982 SP T3 SD: 0.0058 c. M: 0.0081 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 12:13:14:16 S SD: 27.0614 cents 15:16:18:20 S SD: 21.0516 cents 16:17:19:21 SD: 18.6924 cents 17:18:20:23 SD: 15.8461 cents 18:19:21:24 SD: 12.5994 cents 21:22:25:28 SD: 9.9833 cents 22:23:26:29 SD: 9.3495 cents 23:24:27:31 SD: 8.0909 cents 24:25:28:32 SD: 6.2665 cents 27:28:32:36 S SD: 4.4904 cents 33:34:39:44 SD: 3.5083 cents 51:53:60:68 SD: 2.6342 cents 57:59:67:76 SD: 0.6085 cents 147:152:173:196 SD: 0.3272 cents 204:211:240:272 SD: 0.0943 cents 465:481:547:620 SD: 0.0746 cents