Scala analysis: 228_C14
Chromatic tetrachord 100/99 * 11/10 * 6/5, Hofmann
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 100/99 17.399484 Ptolemy's comma 2: 10/9 182.403712 minor whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 100/99 17.3995 Ptolemy's comma 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 100/99 17.399 cents Ptolemy's comma 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 40/33 333.041 cents 2: 1 33/25 480.646 cents 2 pentatones 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 : 17.4 182.4 498.0 17.4 : 165.0 480.6 498.0 182.4: 315.6 333.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 17.3995 .. 315.6413 cents 297/250, 298.2418 cents 100/99, 17.3995 cents 2: 182.4037 .. 480.6455 cents 297/250, 298.2418 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 100/99, 17.3995 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 9.541375 Largest / Average step : 1.901282 Largest / Smallest step : 18.140842 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 134.02442 cents, oct.: 402.07327 cents Scale is not proper Scale has trivalence property 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 17.39948 cents Scale diversity : 0.538521 Lumma stability : 0.069871 Lumma impropriety factor : 0.267521 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 : 100/99, 17.3995 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 480.6455 cents Number of appreciable fourths : 0 All steps are superparticular (epimoric) 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% Scale is differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 33 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.026099 Average absolute harmonicity : 0.106306 Specific harmonicity : 0.127987 Fundamental : 1/99, -6.6294 octaves, 2.6427 Hz. Guide tone : 100, 6.6439 octaves, 26162.557 Hz. Exponens Consonantiae : 9.900000E+03, 13.27321 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 112.5, average 37.50000 Mersenne's string divisions : 26467 Sum of van Prooijen's expressibility: 3.42700, average 1.14233 Sum of Tenney's harmonic distance : 7.02906, average 2.34302 Vogel's harmonic complexity : 15.00000 Wille's k value : 27 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 14.20470, average 2.36745 Lattice compactness (without 2's) : 11.51398, average 1.91900 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -2 ..-1 -1.66667 5 1 5: 0 .. 2 1.00000 3 1 11: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 17 25| Scale is weakly epimorphic with val: <6 10 18 25| Scale is weakly epimorphic with val: <6 11 18 23| Scale is weakly epimorphic with val: <6 11 19 23| Scale is weakly epimorphic with val: <6 11 19 26| Scale is weakly epimorphic with val: <7 10 16 24| Scale is weakly epimorphic with val: <7 10 16 27| Scale is weakly epimorphic with val: <7 10 18 27| Scale is weakly epimorphic with val: <7 11 16 25| Scale is JI-epimorphic with val: <7 11 17 25| = patent Scale is weakly epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 12 18 23| Scale is weakly epimorphic with val: <8 11 17 24| Scale is weakly epimorphic with val: <8 11 17 27| Scale is weakly epimorphic with val: <8 11 18 27| Scale is weakly epimorphic with val: <8 12 18 25| Scale is weakly epimorphic with val: <8 12 19 25|
FIT/MODE
3: 0 1 2 N G T3 SD: 13.8001 c. M: 17.3995 c. 8: 0 3 5 N G T3 SD: 10.3566 c. M: 17.3995 c. 11: 0 4 7 N G T3 SD: 10.0734 c. M: 17.3995 c. 14: 0 5 9 N G T3 SD: 10.3805 c. M: 17.3995 c. 16: 1 5 10 N T3 SD: 8.3167 c. M:-13.7283 c. 19: 1 6 12 N T3 SD: 5.1269 c. M:-8.8134 c. 20: 1 6 13 N T3 SD: 6.3694 c. M: 8.0880 c. 21: 1 7 13 N T3 SD: 5.5857 c. M:-7.3277 c. 22: 1 7 14 N T3 SD: 3.1159 c. M:-5.2389 c. 24: 1 8 15 N T3 SD: 3.1768 c. M:-4.3632 c. 25: 1 8 16 N T3 SD: 2.3108 c. M: 3.1075 c. 27: 1 9 17 N T3 SD: 1.3327 c. M:-2.0574 c. 30: 1 10 19 N T3 SD: 0.4768 c. M: 0.7980 c. 85: 3 28 54 N T3 SD: 0.4529 c. M: 0.7638 c. 112: 4 37 71 N T3 SD: 0.2291 c. M:-0.3878 c. 142: 5 47 90 N T3 SD: 0.0802 c. M:-0.1373 c. 172: 6 57 109 N T3 SD: 0.0188 c. M: 0.0258 c. 486: 17 161 308 N T3 SD: 0.0134 c. M:-0.0218 c. 658: 23 218 417 N T3 SD: 0.0083 c. M:-0.0109 c. 830: 29 275 526 N T3 SD: 0.0075 c. M:-0.0128 c. 2146: 75 711 1360 N T3 SD: 0.0077 c. M:-0.0117 c. 2318: 81 768 1469 N T3 SD: 0.0075 c. M:-0.0123 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: 78.8780 cents 6 x 7:8 S SD: 42.2336 cents 7 x 8:9 S SD: 39.8203 cents 8 x 9:11 SD: 28.7251 cents 9 x 10:12 S SD: 0.0000 cents 10 x 11:13 SD: 23.5791 cents 11 x 12:15 S SD: 25.1136 cents 12 x 13:16 SD: 21.9155 cents 13 x 14:17 SD: 31.8493 cents 14 x 16:19 SD: 28.7988 cents 15 x 17:20 SD: 17.1415 cents 16 x 18:21 S SD: 17.3627 cents 26:27:29:35 SD: 17.0511 cents 27:28:30:36 S SD: 15.1871 cents 29:30:32:39 SD: 15.1636 cents 30:31:33:40 SD: 14.3470 cents 33:34:37:44 SD: 12.5645 cents 34:35:38:45 SD: 12.2074 cents 35:36:39:47 SD: 11.3547 cents 36:37:40:48 SD: 10.0115 cents 39:40:43:52 SD: 9.8734 cents 42:43:47:56 SD: 8.7969 cents 43:44:48:57 SD: 8.6167 cents 44:45:49:59 SD: 7.9873 cents 45:46:50:60 SD: 6.8837 cents 51:52:57:68 SD: 6.3781 cents 52:53:58:69 SD: 6.2931 cents 53:54:59:71 SD: 5.7817 cents 54:55:60:72 S SD: 4.7891 cents 60:61:67:80 SD: 4.7184 cents 61:62:68:81 SD: 4.6934 cents 62:63:69:83 SD: 4.2482 cents 63:64:70:84 SD: 3.2882 cents 71:72:79:95 SD: 3.1517 cents 72:73:80:96 SD: 2.1600 cents 81:82:90:108 SD: 1.2810 cents 90:91:100:120 SD: 0.5768 cents 99:100:110:132 S SD: 0.0000 cents