Scala analysis: 570_M78
Miscellaneous tetrachord 46/45 * 132/115 * 25/22
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46/45 38.050632 23rd-partial chroma 2: 88/75 276.735514 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 25/22 221.3095 undecimal acute whole tone 1: 46/45 38.0506 23rd-partial chroma 2: 132/115 238.6849 3: 25/22 221.3095 undecimal acute whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 46/45 38.051 cents 23rd-partial chroma 1: 1 25/22 221.309 cents undecimal acute whole tone 1: 1 132/115 238.685 cents 2: 1 115/99 259.360 cents 2: 1 88/75 276.736 cents 2: 1 30/23 459.994 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 : 38.1 276.7 498.0 38.1 : 238.7 460.0 498.0 276.7: 221.3 259.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.0506 .. 238.6849 cents 594/529, 200.6343 cents 46/45, 38.0506 cents 2: 259.3601 .. 459.9944 cents 594/529, 200.6343 cents 13225/13068, 20.6752 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 46/45, 38.0506 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 132/115, 238.6849 cents Average / Smallest step : 4.363002 Largest / Average step : 1.437731 Largest / Smallest step : 6.272823 Median interval of one step : 25/22, 221.3095 cents, amount: 1 Least squares average step : 148.97548 cents, oct.: 446.92643 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1204-tone equal temperament with octave 4/3 degrees: 92 669 1204 Least number of segments generator : 603 of 249.436 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 981 of 405.799 cents and inv. generated superset size: 77 = 74 more = 2566.667% 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 20.67523 cents Scale diversity : 0.561865 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.194313 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 : 2904/2875, 17.3754 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% Limited inverse transpositions with margin 200.6343 cents: 1 -- Rational properties -- Prime limit : 23 Odd number limit : 115 (O: 115 U: 115) Highest odd numerator or denominator: 75 Scale harmonicity : 0.012285 Average absolute harmonicity : 0.086604 Specific harmonicity : 0.063591 Fundamental : 1/225, -7.8138 octaves, 1.1628 Hz. Guide tone : 2024, 10.9830 octaves, 529530.144 Hz. Exponens Consonantiae : 4.554000E+05, 18.79677 octaves Euler's gradus suavitatis : 48 Sum of Mann's harmonic distance : 130.5, average 43.50000 Mersenne's string divisions : 14833 Sum of van Prooijen's expressibility: 4.00540, average 1.33513 Sum of Tenney's harmonic distance : 8.21470, average 2.73823 Vogel's harmonic complexity : 20.33333 Wille's k value : 57 Wilson's harmonic complexity : 50 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 16.03272, average 2.67212 Lattice compactness (without 2's) : 11.86710, average 1.97785 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -2 ..-1 -1.33333 4 1 5: -2 .. 0 -1.00000 3 11: 0 .. 1 0.33333 1 1 23: 0 .. 1 0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 15 23 32| Scale is weakly epimorphic with val: <6 10 15 25 30| Scale is weakly epimorphic with val: <6 10 15 25 33| Scale is weakly epimorphic with val: <6 10 15 25 36| Scale is weakly epimorphic with val: <6 10 15 26 32| Scale is weakly epimorphic with val: <6 10 16 25 33| Scale is weakly epimorphic with val: <6 10 16 27 31| Scale is weakly epimorphic with val: <6 10 16 27 34| Scale is weakly epimorphic with val: <6 10 17 24 34| Scale is weakly epimorphic with val: <6 10 17 27 34| Scale is weakly epimorphic with val: <6 10 18 23 35| Scale is weakly epimorphic with val: <6 10 18 26 35| Scale is weakly epimorphic with val: <6 10 19 25 36| Scale is weakly epimorphic with val: <6 11 15 25 34| Scale is weakly epimorphic with val: <6 11 15 26 30| Scale is weakly epimorphic with val: <6 11 15 26 33| Scale is weakly epimorphic with val: <6 11 15 26 36| Scale is weakly epimorphic with val: <6 11 16 24 35| Scale is weakly epimorphic with val: <6 11 16 27 35| Scale is weakly epimorphic with val: <6 11 17 23 36| Scale is weakly epimorphic with val: <6 11 17 26 36| Scale is weakly epimorphic with val: <7 10 15 24 31| Scale is weakly epimorphic with val: <7 10 15 27 31| Scale is weakly epimorphic with val: <7 10 16 23 32| Scale is weakly epimorphic with val: <7 10 16 24 31| Scale is weakly epimorphic with val: <7 10 16 24 34| Scale is weakly epimorphic with val: <7 10 16 26 32| Scale is weakly epimorphic with val: <7 10 17 25 33| Scale is weakly epimorphic with val: <7 10 17 26 32| Scale is weakly epimorphic with val: <7 10 17 26 35| Scale is weakly epimorphic with val: <7 10 18 24 34| Scale is weakly epimorphic with val: <7 10 18 27 34| Scale is weakly epimorphic with val: <7 10 19 23 35| Scale is weakly epimorphic with val: <7 10 19 26 35| Scale is weakly epimorphic with val: <7 11 15 24 32| Scale is weakly epimorphic with val: <7 11 15 24 35| Scale is weakly epimorphic with val: <7 11 15 25 31| Scale is weakly epimorphic with val: <7 11 15 25 34| Scale is weakly 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 16 23 30| Scale is weakly epimorphic with val: <7 11 16 23 33| Scale is weakly epimorphic with val: <7 11 16 23 36| Scale is JI-epimorphic with val: <7 11 16 24 32| Scale is weakly epimorphic with val: <7 11 16 24 35| Scale is weakly epimorphic with val: <7 11 16 26 30| Scale is weakly epimorphic with val: <7 11 16 26 33| Scale is weakly epimorphic with val: <7 11 16 26 36| Scale is weakly epimorphic with val: <7 11 16 27 32| Scale is weakly epimorphic with val: <7 11 16 27 35| Scale is weakly epimorphic with val: <7 11 17 23 30| Scale is weakly epimorphic with val: <7 11 17 23 33| Scale is weakly epimorphic with val: <7 11 17 23 36| Scale is weakly epimorphic with val: <7 11 17 25 31| Scale is weakly epimorphic with val: <7 11 17 25 34| Scale is weakly epimorphic with val: <7 11 17 26 30| Scale is JI-epimorphic with val: <7 11 17 26 33| Scale is weakly epimorphic with val: <7 11 17 26 36| Scale is weakly epimorphic with val: <7 11 18 24 32| Scale is weakly epimorphic with val: <7 11 18 24 35| Scale is weakly epimorphic with val: <7 11 18 25 31| Scale is weakly epimorphic with val: <7 11 18 25 34| 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 19 23 30| Scale is weakly epimorphic with val: <7 11 19 23 33| Scale is weakly epimorphic with val: <7 11 19 23 36| Scale is weakly epimorphic with val: <7 11 19 24 32| Scale is weakly epimorphic with val: <7 11 19 24 35| Scale is weakly epimorphic with val: <7 11 19 26 30| Scale is weakly epimorphic with val: <7 11 19 26 33| Scale is weakly epimorphic with val: <7 11 19 26 36| Scale is weakly epimorphic with val: <7 11 19 27 32| Scale is weakly epimorphic with val: <7 11 19 27 35| Scale is weakly epimorphic with val: <7 12 15 24 30| Scale is weakly epimorphic with val: <7 12 15 24 33| Scale is weakly epimorphic with val: <7 12 15 24 36| Scale is weakly epimorphic with val: <7 12 15 25 35| Scale is weakly epimorphic with val: <7 12 16 24 36| Scale is weakly epimorphic with val: <7 12 16 26 31| Scale is weakly epimorphic with val: <7 12 16 26 34| Scale is weakly epimorphic with val: <7 12 16 27 36| Scale is weakly epimorphic with val: <8 11 15 24 32| Scale is weakly epimorphic with val: <8 11 15 27 32| Scale is weakly epimorphic with val: <8 11 16 23 33| Scale is weakly epimorphic with val: <8 11 16 26 33| Scale is weakly epimorphic with val: <8 11 17 24 32| Scale is weakly epimorphic with val: <8 11 17 24 35| Scale is weakly epimorphic with val: <8 11 17 25 34| Scale is weakly epimorphic with val: <8 11 18 24 35| Scale is weakly epimorphic with val: <8 11 18 26 30| Scale is weakly epimorphic with val: <8 11 18 26 33| Scale is weakly epimorphic with val: <8 11 18 26 36| Scale is weakly epimorphic with val: <8 11 18 27 35| Scale is weakly epimorphic with val: <8 11 19 23 36| Scale is weakly epimorphic with val: <8 11 19 26 36| Scale is weakly epimorphic with val: <8 12 15 23 34| Scale is weakly epimorphic with val: <8 12 15 26 34| Scale is weakly epimorphic with val: <8 12 16 23 31| Scale is weakly epimorphic with val: <8 12 16 23 34| Scale is weakly epimorphic with val: <8 12 16 25 35| Scale is weakly epimorphic with val: <8 12 17 24 36| Scale is weakly epimorphic with val: <8 12 17 25 32| Scale is weakly epimorphic with val: <8 12 17 25 35| Scale is weakly epimorphic with val: <8 12 17 27 36| Scale is weakly epimorphic with val: <8 12 18 27 30| Scale is weakly epimorphic with val: <8 12 18 27 33| Scale is weakly epimorphic with val: <8 12 18 27 36|
FIT/MODE
3: 0 2 1 N G T3 SD: 38.7528 c. M:-55.2945 c. 4: 0 2 2 P M DE S SD: 27.1776 c. M: 38.0506 c. 5: 0 3 2 N G T3 SD: 25.4027 c. M: 38.0506 c. 6: 0 3 3 P M DE S SD: 27.1776 c. M: 38.0506 c. 7: 1 3 3 SP M DE S SD: 19.6412 c. M:-33.0987 c. 8: 1 3 4 P T3 SD: 21.2438 c. M: 27.7130 c. 9: 1 4 4 SP M DE S SD: 9.9811 c. M:-17.2877 c. 11: 1 5 5 SP M DE S SD: 5.0980 c. M:-7.2262 c. 13: 1 6 6 SP M DE S SD: 4.9429 c. M: 8.5574 c. 14: 1 7 6 P T3 SD: 4.7587 c. M:-7.8616 c. 16: 1 8 7 P T3 SD: 4.4567 c. M: 6.9228 c. 23: 2 11 10 SP T3 SD: 4.0979 c. M:-5.2576 c. 25: 2 12 11 SP T3 SD: 1.6250 c. M:-2.1697 c. 27: 2 13 12 SP T3 SD: 0.6693 c. M: 1.1584 c. 52: 4 25 23 SP T3 SD: 0.6080 c. M:-1.0204 c. 65: 5 31 29 SP T3 SD: 0.5383 c. M: 0.8952 c. 79: 6 38 35 SP T3 SD: 0.4006 c. M:-0.6566 c. 90: 7 43 40 SP T3 SD: 0.3970 c. M:-0.6862 c. 92: 7 44 41 SP T3 SD: 0.3833 c. M: 0.6454 c. 106: 8 51 47 SP T3 SD: 0.3840 c. M:-0.4782 c. 117: 9 56 52 SP T3 SD: 0.1525 c. M:-0.2605 c. 144: 11 69 64 SP T3 SD: 0.0255 c. M: 0.0438 c. 628: 48 301 279 SP T3 SD: 0.0273 c. M:-0.0443 c. 655: 50 314 291 SP T3 SD: 0.0298 c. M:-0.0406 c. 772: 59 370 343 SP T3 SD: 0.0176 c. M:-0.0278 c. 799: 61 383 355 SP T3 SD: 0.0215 c. M: 0.0272 c. 916: 70 439 407 SP T3 SD: 0.0110 c. M:-0.0166 c. 1060: 81 508 471 SP T3 SD: 0.0065 c. M:-0.0084 c. 1204: 92 577 535 SP T3 SD: 0.0037 c. M:-0.0060 c. 1348: 103 646 599 SP T3 SD: 0.0032 c. M:-0.0047 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: 109.5782 cents 5 x 6:7 S SD: 46.4983 cents 6 x 7:8 S SD: 4.9323 cents 7 x 8:9 S SD: 38.8585 cents 8 x 9:11 SD: 45.1153 cents 9 x 11:12 SD: 35.3362 cents 10 x 12:13 S SD: 29.3037 cents 15:16:18:20 S SD: 27.7739 cents 16:17:19:21 SD: 25.0583 cents 17:18:20:23 SD: 22.0339 cents 18:19:21:24 SD: 18.8071 cents 21:22:25:28 SD: 16.4508 cents 22:23:26:29 SD: 15.1318 cents 23:24:27:31 SD: 13.4186 cents 24:25:28:32 SD: 11.3602 cents 27:28:32:36 S SD: 10.1284 cents 28:29:33:37 SD: 9.5212 cents 29:30:34:39 SD: 8.4900 cents 30:31:35:40 SD: 7.0522 cents 33:34:39:44 SD: 6.1593 cents 34:35:40:45 S SD: 6.0721 cents 35:36:41:47 SD: 5.5243 cents 36:37:42:48 SD: 4.5382 cents 39:40:46:52 SD: 3.5812 cents 42:43:49:56 SD: 3.4079 cents 45:46:53:60 SD: 2.1818 cents 51:52:60:68 SD: 2.1350 cents 81:83:95:108 SD: 1.4133 cents 87:89:102:116 SD: 0.6259 cents 132:135:155:176 SD: 0.5301 cents 138:141:162:184 SD: 0.3945 cents 219:224:257:292 SD: 0.3551 cents 225:230:264:300 SD: 0.0000 cents