Scala analysis: 284_C21
Chromatic tetrachord 17/16 * 16/15 * 20/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/16 104.955410 17th harmonic 2: 17/15 216.686695 septendecimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 20/17 281.3583 septendecimal augmented second 1: 17/16 104.9554 17th harmonic 2: 16/15 111.7313 minor diatonic semitone 3: 20/17 281.3583 septendecimal augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 17/16 104.955 cents 17th harmonic 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 20/17 281.358 cents septendecimal augmented second 2: 1 17/15 216.687 cents septendecimal whole tone 2: 1 5/4 386.314 cents major third 2: 1 64/51 393.090 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 : 105.0 216.7 498.0 105.0: 111.7 393.1 498.0 216.7: 281.4 386.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 104.9554 .. 281.3583 cents 320/289, 176.4029 cents 17/16, 104.9554 cents 2: 216.6867 .. 393.0896 cents 320/289, 176.4029 cents 289/300,-64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 17/16, 104.9554 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 20/17, 281.3583 cents Average / Smallest step : 1.581767 Largest / Average step : 1.694776 Largest / Smallest step : 2.680741 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 145.17599 cents, oct.: 435.52796 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1471-tone equal temperament with octave 4/3 degrees: 310 640 1471 Least number of segments generator : 736 of 249.192 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1308 of 442.857 cents and inv. generated superset size: 39 = 36 more = 1300.000% 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 64.67161 cents Scale diversity : 1.125177 Lumma stability : 0.421470 Lumma impropriety factor : 0.129851 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 : 256/255, 6.7759 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 : 2 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 169.6270 cents: 2 -- Rational properties -- Prime limit : 17 Odd number limit : 51 (O: 17 U: 51) Highest odd numerator or denominator: 17 Scale harmonicity : 0.022132 Average absolute harmonicity : 0.089705 Specific harmonicity : 0.095047 Fundamental : 1/240, -7.9069 octaves, 1.0901 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 1.632000E+04, 13.99435 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 36.0, average 12.00000 Mersenne's string divisions : 7392 Sum of van Prooijen's expressibility: 2.93802, average 0.97934 Sum of Tenney's harmonic distance : 5.92029, average 1.97343 Vogel's harmonic complexity : 19.00000 Wille's k value : 127 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 20.94777, average 3.49129 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.66667 6 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 2 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 15 28| Scale is weakly epimorphic with val: <6 10 16 27| Scale is weakly epimorphic with val: <6 10 18 31| Scale is weakly epimorphic with val: <6 10 19 27| Scale is weakly epimorphic with val: <6 11 15 29| Scale is weakly epimorphic with val: <6 11 17 27| Scale is weakly epimorphic with val: <6 11 18 32| Scale is weakly epimorphic with val: <7 10 16 31| Scale is weakly epimorphic with val: <7 10 17 30| Scale is weakly epimorphic with val: <7 10 19 31| Scale is weakly epimorphic with val: <7 11 15 27| Scale is weakly epimorphic with val: <7 11 15 30| Scale is weakly epimorphic with val: <7 11 15 33| Scale is JI-epimorphic with val: <7 11 16 29| Scale is weakly epimorphic with val: <7 11 16 32| Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 18 33| Scale is weakly epimorphic with val: <7 11 19 29| Scale is weakly epimorphic with val: <7 11 19 32| Scale is weakly epimorphic with val: <7 12 15 31| Scale is weakly epimorphic with val: <7 12 17 32| Scale is weakly epimorphic with val: <7 12 18 31| Scale is weakly epimorphic with val: <8 11 16 30| Scale is weakly epimorphic with val: <8 11 19 33| Scale is weakly epimorphic with val: <8 12 16 31|
FIT/MODE
3: 0 1 2 N G T3 SD: 67.2886 c. M: 104.9554 c. 4: 1 1 2 P M ME S SD: 21.8177 c. M:-32.3358 c. 5: 1 1 3 N M DE S SD: 10.5473 c. M: 17.4687 c. 9: 2 2 5 N M DE S SD: 4.2626 c. M:-5.7213 c. 14: 3 3 8 N M DE S SD: 2.1306 c. M: 3.2388 c. 23: 5 5 13 N M DE S SD: 1.9159 c. M:-3.3152 c. 34: 7 8 19 N T3 SD: 2.2418 c. M:-3.0390 c. 37: 8 8 21 N M DE S SD: 1.7497 c. M:-2.7300 c. 39: 8 9 22 N T3 SD: 1.6294 c. M: 2.7923 c. 48: 10 11 27 N T3 SD: 0.9815 c. M:-1.2080 c. 53: 11 12 30 N T3 SD: 0.9708 c. M: 1.5876 c. 62: 13 14 35 N T3 SD: 0.3260 c. M: 0.5266 c. 76: 16 17 43 N T3 SD: 0.2556 c. M: 0.4303 c. 138: 29 31 78 N T3 SD: 0.1892 c. M: 0.2938 c. 147: 31 33 83 N T3 SD: 0.0963 c. M:-0.1492 c. 223: 47 50 126 N T3 SD: 0.0290 c. M: 0.0483 c. 370: 78 83 209 N T3 SD: 0.0280 c. M:-0.0379 c. 593: 125 133 335 N T3 SD: 0.0166 c. M:-0.0288 c. 655: 138 147 370 N T3 SD: 0.0179 c. M: 0.0238 c. 816: 172 183 461 N T3 SD: 0.0160 c. M:-0.0247 c. 878: 185 197 496 N T3 SD: 0.0084 c. M: 0.0143 c. 1101: 232 247 622 N T3 SD: 0.0067 c. M: 0.0086 c. 1248: 263 280 705 N T3 SD: 0.0063 c. M:-0.0108 c. 1471: 310 330 831 N T3 SD: 0.0021 c. M:-0.0031 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: 65.0514 cents 6 x 7:8 S SD: 25.0921 cents 7 x 8:9 S SD: 32.3031 cents 8 x 9:11 SD: 27.3918 cents 9 x 10:12 S SD: 17.1415 cents 10 x 11:13 SD: 33.8830 cents 11:12 x 15 S SD: 30.0020 cents 12:13:14:16 S SD: 20.1345 cents 13:14:15:17 SD: 17.1250 cents 14:15:16:19 SD: 12.2869 cents 15:16:17:20 SD: 2.2586 cents 66:70:75:88 SD: 1.8532 cents 81:86:92:108 SD: 1.3240 cents 96:102:109:128 SD: 1.0598 cents 111:118:126:148 SD: 0.9664 cents 129:137:146:172 SD: 0.8327 cents 144:153:163:192 SD: 0.7076 cents 159:169:180:212 SD: 0.6755 cents 195:207:221:260 SD: 0.5225 cents 210:223:238:280 SD: 0.3234 cents 225:239:255:300 SD: 0.1509 cents 240:255:272:320 SD: 0.0000 cents