Scala analysis: 155_C4
Chromatic tetrachord 24/23 * 207/200 * 100/81
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 24/23 73.680654 vicesimotertial minor semitone 2: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 100/81 364.8074 grave major third 1: 24/23 73.6807 vicesimotertial minor semitone 2: 207/200 59.5569 3: 100/81 364.8074 grave major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 207/200 59.557 cents 1: 1 24/23 73.681 cents vicesimotertial minor semitone 1: 1 100/81 364.807 cents grave major third 2: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 1 23/18 424.364 cents vicesimotertial major third 2: 1 800/621 438.488 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 : 73.7 133.2 498.0 73.7 : 59.6 424.4 498.0 133.2: 364.8 438.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 59.5569 .. 364.8074 cents 20000/16767, 305.2505 cents 207/200, 59.5569 cents 2: 133.2376 .. 438.4881 cents 20000/16767, 305.2505 cents 2187/2500,-231.5698 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 207/200, 59.5569 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 100/81, 364.8074 cents Average / Smallest step : 2.787501 Largest / Average step : 2.197437 Largest / Smallest step : 6.125357 Median interval of one step : 24/23, 73.6807 cents, amount: 1 Least squares average step : 131.02077 cents, oct.: 393.06231 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1656-tone equal temperament with octave 4/3 degrees: 245 443 1656 Least number of segments generator : 829 of 249.323 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 839 of 252.331 cents and inv. generated superset size: 54 = 51 more = 1800.000% 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 59.55692 cents Scale diversity : 0.673274 Lumma stability : 0.239163 Lumma impropriety factor : 0.464958 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 : 1600/1587, 14.1237 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 305.2505 cents: 2 -- Rational properties -- Prime limit : 23 Odd number limit : 621 (O: 207 U: 621) Highest odd numerator or denominator: 27 Scale harmonicity : 0.014587 Average absolute harmonicity : 0.094434 Specific harmonicity : 0.076071 Fundamental : 1/1725, -10.7524 octaves, 0.1517 Hz. Guide tone : 216, 7.7549 octaves, 56511.122 Hz. Exponens Consonantiae : 3.726000E+05, 18.50727 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 53.0, average 17.66667 Mersenne's string divisions : 17108 Sum of van Prooijen's expressibility: 3.27021, average 1.09007 Sum of Tenney's harmonic distance : 6.65042, average 2.21681 Vogel's harmonic complexity : 29.66667 Wille's k value : 931 Wilson's harmonic complexity : 45 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 20.74935, average 3.45823 Lattice compactness (without 2's) : 15.72797, average 2.62133 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 3 1.66667 5 3: -1 .. 3 1.00000 5 1 5: -2 .. 0 -0.66667 2 1 23: -1 .. 0 -0.33333 1 1 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 15 30| Scale is weakly epimorphic with val: <6 11 15 33| Scale is weakly epimorphic with val: <6 11 15 36| Scale is weakly epimorphic with val: <7 11 16 30| Scale is weakly epimorphic with val: <7 11 16 33| Scale is weakly epimorphic with val: <7 11 16 36| Scale is weakly epimorphic with val: <7 11 17 31| Scale is weakly epimorphic with val: <7 11 17 34| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <7 11 19 33| Scale is weakly epimorphic with val: <7 11 19 36| Scale is weakly epimorphic with val: <7 12 16 30| Scale is weakly epimorphic with val: <7 12 19 30| Scale is weakly epimorphic with val: <8 11 15 31| Scale is weakly epimorphic with val: <8 11 15 34| Scale is weakly epimorphic with val: <8 11 16 32| Scale is weakly epimorphic with val: <8 11 19 32| Scale is weakly epimorphic with val: <8 12 17 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 46.5589 c. M: 73.6807 c. 4: 1 0 3 N G T3 SD: 29.7764 c. M:-50.8306 c. 5: 1 0 4 N G T3 SD: 24.5164 c. M: 33.6286 c. 6: 1 1 4 N M DE S SD: 19.6753 c. M:-32.7774 c. 7: 1 1 5 N M DE S SD: 5.4317 c. M:-9.0610 c. 15: 2 2 11 N M DE S SD: 4.2072 c. M: 7.2747 c. 19: 3 2 14 N T3 SD: 3.1254 c. M:-4.9580 c. 26: 4 3 19 N T3 SD: 1.7681 c. M:-2.9417 c. 33: 5 4 24 N T3 SD: 1.8160 c. M:-2.5929 c. 34: 5 4 25 N T3 SD: 0.8482 c. M: 1.4021 c. 41: 6 5 30 N T3 SD: 0.5103 c. M: 0.7960 c. 67: 10 8 49 N T3 SD: 0.4994 c. M:-0.6544 c. 75: 11 9 55 N T3 SD: 0.4409 c. M: 0.6341 c. 101: 15 12 74 N T3 SD: 0.1746 c. M:-0.2864 c. 142: 21 17 104 N T3 SD: 0.0286 c. M:-0.0421 c. 385: 57 46 282 N T3 SD: 0.0324 c. M:-0.0559 c. 527: 78 63 386 N T3 SD: 0.0214 c. M:-0.0338 c. 669: 99 80 490 N T3 SD: 0.0172 c. M:-0.0211 c. 811: 120 97 594 N T3 SD: 0.0161 c. M:-0.0248 c. 987: 146 118 723 N T3 SD: 0.0135 c. M: 0.0219 c. 1129: 167 135 827 N T3 SD: 0.0101 c. M: 0.0138 c. 1271: 188 152 931 N T3 SD: 0.0084 c. M: 0.0123 c. 1413: 209 169 1035 N T3 SD: 0.0081 c. M: 0.0137 c. 1514: 224 181 1109 N T3 SD: 0.0063 c. M: 0.0089 c. 1656: 245 198 1213 N T3 SD: 0.0033 c. M: 0.0045 c. 1798: 266 215 1317 N T3 SD: 0.0008 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 x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 100.5060 cents 6 x 7:8 S SD: 66.8167 cents 7 x 8:9 S SD: 58.2143 cents 8 x 9:11 SD: 44.2510 cents 9 x 10:12 S SD: 24.5831 cents 10 x 11:13 SD: 27.0660 cents 11 x 12:15 S SD: 21.3096 cents 12 x 13:16 SD: 2.6675 cents 13 x 14:17 SD: 16.9891 cents 14 x 15:19 SD: 16.8020 cents 15 x 16:20 S SD: 10.7531 cents 16 x 17:21 SD: 19.6419 cents 17:18 x 23 SD: 17.8714 cents 18:19 x 24 SD: 9.9612 cents 21:22:23:28 SD: 8.4021 cents 23:24:25:31 SD: 7.2560 cents 24:25:26:32 SD: 2.0416 cents 75:78:81:100 SD: 1.9268 cents 87:91:94:116 SD: 1.4019 cents 90:94:97:120 SD: 1.3031 cents 111:116:120:148 SD: 1.0407 cents 114:119:123:152 SD: 0.6009 cents 138:144:149:184 SD: 0.1549 cents 300:313:324:400 SD: 0.0802 cents 438:457:473:584 SD: 0.0735 cents