Scala analysis: 208_C12
Chromatic tetrachord 18/17 * 187/180 * 40/33
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 18/17 98.954592 Arabic lute index finger 2: 11/10 165.004228 Ptolemy's second, 4/5-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 40/33 333.0408 1: 18/17 98.9546 Arabic lute index finger 2: 187/180 66.0496 3: 40/33 333.0408
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 187/180 66.050 cents 1: 1 18/17 98.955 cents Arabic lute index finger 1: 1 40/33 333.041 cents 2: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 1 34/27 399.090 cents septendecimal major third 2: 1 240/187 431.995 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 : 99.0 165.0 498.0 99.0 : 66.0 399.1 498.0 165.0: 333.0 432.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.0496 .. 333.0408 cents 2400/2057, 266.9911 cents 187/180, 66.0496 cents 2: 165.0042 .. 431.9954 cents 2400/2057, 266.9911 cents 363/400,-168.0365 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 187/180, 66.0496 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 40/33, 333.0408 cents Average / Smallest step : 2.513488 Largest / Average step : 2.006088 Largest / Smallest step : 5.042280 Median interval of one step : 18/17, 98.9546 cents, amount: 1 Least squares average step : 137.36415 cents, oct.: 412.09244 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1817-tone equal temperament with octave 4/3 degrees: 361 602 1817 Least number of segments generator : 909 of 249.160 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1412 of 387.033 cents and inv. generated superset size: 36 = 33 more = 1200.000% 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 66.04964 cents Scale diversity : 0.880872 Lumma stability : 0.265236 Lumma impropriety factor : 0.337392 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 : 3240/3179, 32.9050 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% -- Rational properties -- Prime limit : 17 Odd number limit : 187 (O: 187 U: 187) Highest odd numerator or denominator: 17 Scale harmonicity : 0.015221 Average absolute harmonicity : 0.093603 Specific harmonicity : 0.080767 Fundamental : 1/510, -8.9944 octaves, 0.5130 Hz. Guide tone : 396, 8.6294 octaves, 103603.724 Hz. Exponens Consonantiae : 2.019600E+05, 17.62371 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 31.5, average 10.50000 Mersenne's string divisions : 105 Sum of van Prooijen's expressibility: 2.74896, average 0.91632 Sum of Tenney's harmonic distance : 5.60630, average 1.86877 Vogel's harmonic complexity : 24.00000 Wille's k value : 280 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 16.51496, average 2.75249 Lattice compactness (without 2's) : 12.19036, average 2.03173 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 2 0.33333 3 1 5: -1 .. 0 -0.33333 1 11: 0 .. 1 0.33333 1 1 17: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 15 24 28| Scale is weakly epimorphic with val: <6 10 15 24 31| Scale is weakly epimorphic with val: <6 10 16 25 28| Scale is weakly epimorphic with val: <6 10 16 25 31| Scale is weakly epimorphic with val: <6 10 17 26 28| Scale is weakly epimorphic with val: <6 10 17 26 31| Scale is weakly epimorphic with val: <6 10 18 27 28| Scale is weakly epimorphic with val: <6 10 18 27 31| Scale is weakly epimorphic with val: <6 11 15 24 29| Scale is weakly epimorphic with val: <6 11 15 24 32| Scale is weakly epimorphic with val: <6 11 16 25 29| Scale is weakly epimorphic with val: <6 11 16 25 32| Scale is weakly epimorphic with val: <6 11 17 26 29| Scale is weakly epimorphic with val: <6 11 17 26 32| Scale is weakly epimorphic with val: <6 11 18 27 29| Scale is weakly epimorphic with val: <6 11 18 27 32| Scale is weakly epimorphic with val: <7 10 15 25 28| Scale is weakly epimorphic with val: <7 10 15 25 31| Scale is weakly epimorphic with val: <7 10 16 26 28| Scale is weakly epimorphic with val: <7 10 16 26 31| Scale is weakly epimorphic with val: <7 10 17 27 28| Scale is weakly epimorphic with val: <7 10 17 27 31| Scale is weakly epimorphic with val: <7 11 15 23 27| Scale is weakly epimorphic with val: <7 11 15 23 30| Scale is weakly epimorphic with val: <7 11 15 23 33| Scale is JI-epimorphic with val: <7 11 15 24 28| Scale is weakly epimorphic with val: <7 11 15 24 31| Scale is weakly epimorphic with val: <7 11 15 26 27| Scale is weakly epimorphic with val: <7 11 15 26 30| Scale is weakly epimorphic with val: <7 11 15 26 33| Scale is weakly epimorphic with val: <7 11 15 27 28| Scale is weakly epimorphic with val: <7 11 15 27 31| Scale is weakly epimorphic with val: <7 11 16 24 27| Scale is weakly epimorphic with val: <7 11 16 24 30| Scale is weakly epimorphic with val: <7 11 16 24 33| Scale is JI-epimorphic with val: <7 11 16 25 28| Scale is weakly epimorphic with val: <7 11 16 25 31| Scale is weakly epimorphic with val: <7 11 16 27 27| Scale is weakly epimorphic with val: <7 11 16 27 30| Scale is weakly epimorphic with val: <7 11 16 27 33| Scale is weakly epimorphic with val: <7 11 17 23 28| Scale is weakly epimorphic with val: <7 11 17 23 31| Scale is weakly epimorphic with val: <7 11 17 25 27| Scale is weakly epimorphic with val: <7 11 17 25 30| = patent Scale is weakly epimorphic with val: <7 11 17 25 33| Scale is JI-epimorphic with val: <7 11 17 26 28| Scale is weakly epimorphic with val: <7 11 17 26 31| Scale is weakly epimorphic with val: <7 11 18 23 27| Scale is weakly epimorphic with val: <7 11 18 23 30| Scale is weakly epimorphic with val: <7 11 18 23 33| Scale is weakly epimorphic with val: <7 11 18 24 28| Scale is weakly epimorphic with val: <7 11 18 24 31| Scale is weakly epimorphic with val: <7 11 18 26 27| Scale is weakly epimorphic with val: <7 11 18 26 30| Scale is weakly epimorphic with val: <7 11 18 26 33| Scale is JI-epimorphic with val: <7 11 18 27 28| Scale is weakly epimorphic with val: <7 11 18 27 31| Scale is weakly epimorphic with val: <7 11 19 24 27| Scale is weakly epimorphic with val: <7 11 19 24 30| Scale is weakly epimorphic with val: <7 11 19 24 33| Scale is weakly epimorphic with val: <7 11 19 25 28| Scale is weakly epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 27 27| Scale is weakly epimorphic with val: <7 11 19 27 30| Scale is weakly epimorphic with val: <7 11 19 27 33| Scale is weakly epimorphic with val: <7 12 15 23 28| Scale is weakly epimorphic with val: <7 12 15 25 27| Scale is weakly epimorphic with val: <7 12 15 25 30| Scale is weakly epimorphic with val: <7 12 15 25 33| Scale is weakly epimorphic with val: <7 12 15 26 28| Scale is weakly epimorphic with val: <7 12 16 24 28| Scale is weakly epimorphic with val: <7 12 16 26 27| Scale is weakly epimorphic with val: <7 12 16 26 30| Scale is weakly epimorphic with val: <7 12 16 26 33| Scale is weakly epimorphic with val: <7 12 16 27 28| Scale is weakly epimorphic with val: <7 12 17 25 28| Scale is weakly epimorphic with val: <7 12 17 27 27| Scale is weakly epimorphic with val: <7 12 17 27 30| Scale is weakly epimorphic with val: <7 12 17 27 33| Scale is weakly epimorphic with val: <7 12 18 23 28| Scale is weakly epimorphic with val: <7 12 18 26 28| Scale is weakly epimorphic with val: <7 12 19 24 28| Scale is weakly epimorphic with val: <7 12 19 27 28| Scale is weakly epimorphic with val: <8 11 15 24 27| Scale is weakly epimorphic with val: <8 11 15 26 29| Scale is weakly epimorphic with val: <8 11 15 26 32| Scale is weakly epimorphic with val: <8 11 15 27 27| Scale is weakly epimorphic with val: <8 11 16 25 27| Scale is weakly epimorphic with val: <8 11 16 27 29| Scale is weakly epimorphic with val: <8 11 16 27 32| Scale is weakly epimorphic with val: <8 11 17 23 27| Scale is weakly epimorphic with val: <8 11 17 26 27| Scale is weakly epimorphic with val: <8 11 18 24 27| Scale is weakly epimorphic with val: <8 11 18 27 27| Scale is weakly epimorphic with val: <8 11 19 25 27| Scale is weakly epimorphic with val: <8 12 15 25 29| Scale is weakly epimorphic with val: <8 12 15 26 27| Scale is weakly epimorphic with val: <8 12 15 26 30| Scale is weakly epimorphic with val: <8 12 15 26 33| Scale is weakly epimorphic with val: <8 12 16 23 29| Scale is weakly epimorphic with val: <8 12 16 26 29| Scale is weakly epimorphic with val: <8 12 16 27 27| Scale is weakly epimorphic with val: <8 12 16 27 30| Scale is weakly epimorphic with val: <8 12 16 27 33| Scale is weakly epimorphic with val: <8 12 17 24 29| Scale is weakly epimorphic with val: <8 12 17 27 29| Scale is weakly epimorphic with val: <8 12 18 25 29| Scale is weakly epimorphic with val: <8 12 19 23 29| Scale is weakly epimorphic with val: <8 12 19 26 29|
FIT/MODE
3: 1 0 2 N G T3 SD: 38.7217 c. M:-67.0604 c. 4: 1 0 3 N G T3 SD: 27.6455 c. M: 40.4930 c. 5: 1 1 3 N M DE S SD: 19.7569 c. M:-34.2138 c. 6: 1 1 4 N M DE S SD: 9.2255 c. M: 15.9471 c. 9: 2 1 6 N T3 SD: 6.7929 c. M:-11.7221 c. 15: 3 2 10 N T3 SD: 0.6952 c. M:-1.0108 c. 66: 13 9 44 N T3 SD: 0.7643 c. M:-1.0108 c. 81: 16 11 54 N T3 SD: 0.6715 c. M:-1.0108 c. 85: 17 11 57 N T3 SD: 0.6624 c. M: 0.9423 c. 91: 18 12 61 N T3 SD: 0.5341 c. M: 0.8136 c. 100: 20 13 67 N T3 SD: 0.5323 c. M:-0.6544 c. 106: 21 14 71 N T3 SD: 0.3605 c. M: 0.5554 c. 121: 24 16 81 N T3 SD: 0.2302 c. M: 0.3613 c. 136: 27 18 91 N T3 SD: 0.1293 c. M: 0.2099 c. 151: 30 20 101 N T3 SD: 0.0513 c. M: 0.0887 c. 166: 33 22 111 N T3 SD: 0.0320 c. M:-0.0544 c. 317: 63 42 212 N T3 SD: 0.0259 c. M: 0.0366 c. 483: 96 64 323 N T3 SD: 0.0237 c. M:-0.0357 c. 649: 129 86 434 N T3 SD: 0.0245 c. M:-0.0405 c. 800: 159 106 535 N T3 SD: 0.0240 c. M:-0.0319 c. 815: 162 108 545 N T3 SD: 0.0254 c. M:-0.0433 c. 1017: 202 135 680 N T3 SD: 0.0255 c. M:-0.0313 c. 1117: 222 148 747 N T3 SD: 0.0244 c. M:-0.0302 c. 1132: 225 150 757 N T3 SD: 0.0240 c. M:-0.0385 c. 1138: 226 151 761 N T3 SD: 0.0271 c. M: 0.0458 c. 1147: 228 152 767 N T3 SD: 0.0269 c. M:-0.0465 c. 1153: 229 153 771 N T3 SD: 0.0213 c. M: 0.0367 c. 1168: 232 155 781 N T3 SD: 0.0185 c. M: 0.0278 c. 1304: 259 173 872 N T3 SD: 0.0196 c. M: 0.0331 c. 1319: 262 175 882 N T3 SD: 0.0148 c. M: 0.0253 c. 1334: 265 177 892 N T3 SD: 0.0134 c. M: 0.0176 c. 1470: 292 195 983 N T3 SD: 0.0138 c. M: 0.0232 c. 1485: 295 197 993 N T3 SD: 0.0098 c. M: 0.0164 c. 1500: 298 199 1003 N T3 SD: 0.0101 c. M:-0.0147 c. 1636: 325 217 1094 N T3 SD: 0.0091 c. M: 0.0153 c. 1651: 328 219 1104 N T3 SD: 0.0061 c. M: 0.0093 c. 1802: 358 239 1205 N T3 SD: 0.0054 c. M: 0.0089 c. 1817: 361 241 1215 N T3 SD: 0.0039 c. M:-0.0057 c. 1968: 391 261 1316 N T3 SD: 0.0022 c. M: 0.0036 c. 2134: 424 283 1427 N T3 SD: 0.0006 c. M:-0.0009 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: 86.3514 cents 6 x 7:8 S SD: 50.9333 cents 7 x 8:9 S SD: 45.6687 cents 8 x 9:11 SD: 32.9836 cents 9 x 10:12 S SD: 8.6997 cents 10 x 11:13 SD: 21.9155 cents 11 x 12:15 S SD: 20.7369 cents 12 x 13:16 SD: 13.2158 cents 13:14 x 17 SD: 22.3113 cents 14:15 x 19 SD: 18.4303 cents 15:16:17:20 SD: 17.7461 cents 16:17:18:21 S SD: 15.9618 cents 17:18:19:23 SD: 12.4631 cents 18:19:20:24 S SD: 6.0680 cents 30:32:33:40 SD: 4.2589 cents 48:51:53:64 SD: 2.9599 cents 50:53:55:67 SD: 2.9487 cents 51:54:56:68 SD: 1.0296 cents 69:73:76:92 SD: 0.8907 cents 120:127:132:160 SD: 0.2672 cents 270:286:297:360 SD: 0.2374 cents 339:359:373:452 SD: 0.1813 cents 390:413:429:520 SD: 0.0822 cents 510:540:561:680 SD: 0.0000 cents