Scala analysis: 153_C4
Chromatic tetrachord 40/39 * 1053/1000 * 100/81
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/39 43.831051 tridecimal minor diesis 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: 40/39 43.8311 tridecimal minor diesis 2: 1053/1000 89.4065 3: 100/81 364.8074 grave major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 1053/1000 89.407 cents 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 4000/3159 408.638 cents 2: 1 13/10 454.214 cents tridecimal semi-diminished fourth 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 : 43.8 133.2 498.0 43.8 : 89.4 454.2 498.0 133.2: 364.8 408.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 364.8074 cents 65/54, 320.9764 cents 40/39, 43.8311 cents 2: 133.2376 .. 454.2139 cents 65/54, 320.9764 cents 2187/2500,-231.5698 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 100/81, 364.8074 cents Average / Smallest step : 3.787612 Largest / Average step : 2.197437 Largest / Smallest step : 8.323036 Median interval of one step : 1053/1000, 89.4065 cents, amount: 1 Least squares average step : 128.88866 cents, oct.: 386.66597 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1727-tone equal temperament with octave 4/3 degrees: 152 462 1727 Least number of segments generator : 864 of 249.167 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1141 of 329.050 cents and inv. generated superset size: 42 = 39 more = 1400.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 43.83105 cents Scale diversity : 0.625242 Lumma stability : 0.176012 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 : 40/39, 43.8311 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing 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 : 13 Odd number limit : 3159 (O: 1053 U: 3159) Highest odd numerator or denominator: 39 Scale harmonicity : 0.018175 Average absolute harmonicity : 0.097195 Specific harmonicity : 0.094268 Fundamental : 1/975, -9.9293 octaves, 0.2683 Hz. Guide tone : 1080, 10.0768 octaves, 282555.611 Hz. Exponens Consonantiae : 1.053000E+06, 20.00607 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 69.0, average 23.00000 Mersenne's string divisions : 28756 Sum of van Prooijen's expressibility: 3.49955, average 1.16652 Sum of Tenney's harmonic distance : 7.10161, average 2.36720 Vogel's harmonic complexity : 22.66667 Wille's k value : 526 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 8 Triangular lattice diameter : 5 Lattice compactness : 21.85283, average 3.64214 Lattice compactness (without 2's) : 17.32297, average 2.88716 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 3 1.66667 5 3: -1 .. 3 0.33333 5 1 5: -2 .. 1 -0.33333 3 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 11 15 26| Scale is weakly epimorphic with val: <6 11 15 29| Scale is weakly epimorphic with val: <7 10 17 25| Scale is weakly epimorphic with val: <7 11 16 27| Scale is weakly epimorphic with val: <7 11 16 30| Scale is weakly epimorphic with val: <7 11 17 26| Scale is weakly epimorphic with val: <7 11 17 29| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <7 12 19 25| Scale is weakly epimorphic with val: <8 11 15 27| Scale is weakly epimorphic with val: <8 11 15 30| Scale is weakly epimorphic with val: <8 11 16 26| Scale is weakly epimorphic with val: <8 11 19 29| Scale is weakly epimorphic with val: <8 12 17 26|
FIT/MODE
3: 0 1 2 N G T3 SD: 31.5992 c. M: 43.8311 c. 4: 0 1 3 N G T3 SD: 25.8025 c. M: 43.8311 c. 7: 1 1 5 N M DE S SD: 16.6171 c. M:-27.3182 c. 8: 1 1 6 N M DE S SD: 11.7702 c. M:-18.4246 c. 10: 1 2 7 N T3 SD: 9.9556 c. M:-16.1759 c. 11: 1 2 8 N T3 SD: 1.7140 c. M:-2.5929 c. 34: 3 6 25 N T3 SD: 0.8122 c. M: 1.4021 c. 45: 4 8 33 N T3 SD: 0.3533 c. M:-0.4396 c. 56: 5 10 41 N T3 SD: 0.3804 c. M:-0.6373 c. 101: 9 18 74 N T3 SD: 0.3220 c. M:-0.5492 c. 146: 13 26 107 N T3 SD: 0.3188 c. M:-0.5154 c. 161: 14 29 118 N T3 SD: 0.3273 c. M: 0.5228 c. 172: 15 31 126 N T3 SD: 0.2303 c. M: 0.3969 c. 183: 16 33 134 N T3 SD: 0.1789 c. M: 0.2861 c. 194: 17 35 142 N T3 SD: 0.1848 c. M:-0.2590 c. 217: 19 39 159 N T3 SD: 0.1463 c. M: 0.2234 c. 228: 20 41 167 N T3 SD: 0.0828 c. M: 0.1429 c. 239: 21 43 175 N T3 SD: 0.0852 c. M:-0.1301 c. 273: 24 49 200 N T3 SD: 0.0443 c. M: 0.0607 c. 284: 25 51 208 N T3 SD: 0.0251 c. M:-0.0421 c. 557: 49 100 408 N T3 SD: 0.0111 c. M: 0.0174 c. 841: 74 151 616 N T3 SD: 0.0068 c. M:-0.0087 c. 1170: 103 210 857 N T3 SD: 0.0080 c. M:-0.0139 c. 1398: 123 251 1024 N T3 SD: 0.0068 c. M: 0.0116 c. 1443: 127 259 1057 N T3 SD: 0.0067 c. M: 0.0114 c. 1727: 152 310 1265 N T3 SD: 0.0027 c. M:-0.0038 c. 2284: 201 410 1673 N T3 SD: 0.0024 c. M: 0.0040 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 x 18:23 SD: 21.2961 cents 18 x 19:24 SD: 19.8173 cents 19 x 21:25 SD: 23.0664 cents 20:21:22:27 SD: 18.6277 cents 21:22:23:28 SD: 14.6654 cents 22:23:24:29 SD: 14.1087 cents 23:24:25:31 SD: 12.3146 cents 24:25:26:32 SD: 9.1222 cents 27:28:29:36 SD: 7.1234 cents 33:34:36:44 SD: 6.3630 cents 35:36:38:47 SD: 5.3717 cents 36:37:39:48 SD: 2.1459 cents 39:40:42:52 SD: 1.6464 cents 75:77:81:100 SD: 0.5768 cents 162:166:175:216 SD: 0.5506 cents 198:203:214:264 SD: 0.4838 cents 201:206:217:268 SD: 0.4805 cents 237:243:256:316 SD: 0.2037 cents 312:320:337:416 SD: 0.0685 cents