Scala analysis: 310_C24
Chromatic tetrachord 20/19 * 38/35 * 7/6, Ptolemy
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 20/19 88.800698 small undevicesimal semitone 2: 8/7 231.174094 septimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 20/19 88.8007 small undevicesimal semitone 2: 38/35 142.3734 3: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 20/19 88.801 cents small undevicesimal semitone 1: 1 38/35 142.373 cents 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 70/57 355.672 cents 2: 1 19/15 409.244 cents undevicesimal ditone 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 : 88.8 231.2 498.0 88.8 : 142.4 409.2 498.0 231.2: 266.9 355.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.8007 .. 266.8709 cents 133/120, 178.0702 cents 20/19, 88.8007 cents 2: 231.1741 .. 409.2443 cents 133/120, 178.0702 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 20/19, 88.8007 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 1.869524 Largest / Average step : 1.607511 Largest / Smallest step : 3.005279 Median interval of one step : 38/35, 142.3734 cents, amount: 1 Least squares average step : 146.09171 cents, oct.: 438.27512 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1088-tone equal temperament with octave 4/3 degrees: 194 505 1088 Least number of segments generator : 545 of 249.480 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 641 of 293.425 cents and inv. generated superset size: 138 = 135 more = 4600.000% 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 35.69681 cents Scale diversity : 1.129828 Lumma stability : 0.356597 Lumma impropriety factor : 0.071674 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 : 49/48, 35.6968 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle 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 n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 19 Odd number limit : 57 (O: 35 U: 57) Highest odd numerator or denominator: 19 Scale harmonicity : 0.017712 Average absolute harmonicity : 0.104360 Specific harmonicity : 0.094466 Fundamental : 1/399, -8.6402 octaves, 0.6557 Hz. Guide tone : 40, 5.3219 octaves, 10465.023 Hz. Exponens Consonantiae : 1.596000E+04, 13.96217 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 30.5, average 10.16667 Mersenne's string divisions : 1365 Sum of van Prooijen's expressibility: 2.60097, average 0.86699 Sum of Tenney's harmonic distance : 5.40715, average 1.80238 Vogel's harmonic complexity : 23.33333 Wille's k value : 66 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.31194, average 2.21866 Lattice compactness (without 2's) : 8.29253, average 1.38209 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 0 -0.33333 1 1 5: 0 .. 1 0.33333 1 7: -1 .. 0 -0.33333 1 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <6 10 19 20 28| Scale is weakly epimorphic with val: <6 11 19 19 28| Scale is weakly epimorphic with val: <6 11 19 22 28| Scale is weakly epimorphic with val: <7 10 15 18 30| Scale is weakly epimorphic with val: <7 10 15 18 33| Scale is weakly epimorphic with val: <7 10 16 18 28| Scale is weakly epimorphic with val: <7 10 16 18 31| Scale is weakly epimorphic with val: <7 10 16 18 34| Scale is weakly epimorphic with val: <7 10 17 18 29| Scale is weakly epimorphic with val: <7 10 17 18 32| Scale is weakly epimorphic with val: <7 10 17 19 28| Scale is weakly epimorphic with val: <7 10 17 22 28| Scale is weakly epimorphic with val: <7 10 18 18 30| Scale is weakly epimorphic with val: <7 10 18 18 33| Scale is weakly epimorphic with val: <7 10 18 19 29| Scale is weakly epimorphic with val: <7 10 18 22 29| Scale is weakly epimorphic with val: <7 10 19 19 30| Scale is weakly epimorphic with val: <7 10 19 22 30| Scale is JI-epimorphic with val: <7 11 15 19 28| Scale is weakly epimorphic with val: <7 11 15 19 31| Scale is weakly epimorphic with val: <7 11 15 19 34| Scale is weakly epimorphic with val: <7 11 15 20 30| Scale is weakly epimorphic with val: <7 11 15 20 33| Scale is weakly epimorphic with val: <7 11 15 22 28| Scale is weakly epimorphic with val: <7 11 15 22 31| Scale is weakly epimorphic with val: <7 11 15 22 34| Scale is JI-epimorphic with val: <7 11 16 19 29| Scale is weakly epimorphic with val: <7 11 16 19 32| Scale is weakly epimorphic with val: <7 11 16 20 28| Scale is weakly epimorphic with val: <7 11 16 20 31| Scale is weakly epimorphic with val: <7 11 16 20 34| Scale is weakly epimorphic with val: <7 11 16 22 29| Scale is weakly epimorphic with val: <7 11 16 22 32| Scale is JI-epimorphic with val: <7 11 17 19 30| Scale is weakly epimorphic with val: <7 11 17 19 33| Scale is weakly epimorphic with val: <7 11 17 20 29| Scale is weakly epimorphic with val: <7 11 17 20 32| Scale is weakly epimorphic with val: <7 11 17 22 30| Scale is weakly epimorphic with val: <7 11 17 22 33| Scale is weakly epimorphic with val: <7 11 18 19 28| Scale is JI-epimorphic with val: <7 11 18 19 31| Scale is weakly epimorphic with val: <7 11 18 19 34| Scale is weakly epimorphic with val: <7 11 18 20 30| Scale is weakly epimorphic with val: <7 11 18 20 33| Scale is weakly epimorphic with val: <7 11 18 22 28| Scale is weakly epimorphic with val: <7 11 18 22 31| Scale is weakly epimorphic with val: <7 11 18 22 34| Scale is weakly epimorphic with val: <7 11 19 19 29| Scale is JI-epimorphic with val: <7 11 19 19 32| Scale is weakly epimorphic with val: <7 11 19 20 28| Scale is weakly epimorphic with val: <7 11 19 20 31| Scale is weakly epimorphic with val: <7 11 19 20 34| Scale is weakly epimorphic with val: <7 11 19 22 29| Scale is weakly epimorphic with val: <7 11 19 22 32| Scale is weakly epimorphic with val: <7 12 15 18 28| Scale is weakly epimorphic with val: <7 12 15 18 31| Scale is weakly epimorphic with val: <7 12 15 18 34| Scale is weakly epimorphic with val: <7 12 16 18 29| Scale is weakly epimorphic with val: <7 12 16 18 32| Scale is weakly epimorphic with val: <7 12 17 18 30| Scale is weakly epimorphic with val: <7 12 17 18 33| Scale is weakly epimorphic with val: <7 12 17 20 28| Scale is weakly epimorphic with val: <7 12 18 18 28| Scale is weakly epimorphic with val: <7 12 18 18 31| Scale is weakly epimorphic with val: <7 12 18 18 34| Scale is weakly epimorphic with val: <7 12 18 20 29| Scale is weakly epimorphic with val: <7 12 19 20 30| Scale is weakly epimorphic with val: <8 11 15 20 28| Scale is weakly epimorphic with val: <8 11 15 21 30| Scale is weakly epimorphic with val: <8 11 15 21 33| Scale is weakly epimorphic with val: <8 11 16 20 29| Scale is weakly epimorphic with val: <8 11 16 21 28| Scale is weakly epimorphic with val: <8 11 16 21 31| Scale is weakly epimorphic with val: <8 11 16 21 34| Scale is weakly epimorphic with val: <8 11 17 20 30| Scale is weakly epimorphic with val: <8 11 17 21 29| Scale is weakly epimorphic with val: <8 11 17 21 32| Scale is weakly epimorphic with val: <8 11 18 20 31| Scale is weakly epimorphic with val: <8 11 18 21 30| Scale is weakly epimorphic with val: <8 11 18 21 33| Scale is weakly epimorphic with val: <8 11 19 20 32| Scale is weakly epimorphic with val: <8 11 19 21 28| Scale is weakly epimorphic with val: <8 11 19 21 31| Scale is weakly epimorphic with val: <8 11 19 21 34| Scale is weakly epimorphic with val: <8 12 15 19 28| Scale is weakly epimorphic with val: <8 12 15 21 29| Scale is weakly epimorphic with val: <8 12 15 21 32| Scale is weakly epimorphic with val: <8 12 15 22 28| Scale is weakly epimorphic with val: <8 12 16 19 29| Scale is weakly epimorphic with val: <8 12 16 21 30| Scale is weakly epimorphic with val: <8 12 16 21 33| Scale is weakly epimorphic with val: <8 12 16 22 29| Scale is weakly epimorphic with val: <8 12 17 19 30| Scale is weakly epimorphic with val: <8 12 17 21 28| Scale is weakly epimorphic with val: <8 12 17 21 31| Scale is weakly epimorphic with val: <8 12 17 21 34| Scale is weakly epimorphic with val: <8 12 17 22 30| Scale is weakly epimorphic with val: <8 12 18 19 31| Scale is weakly epimorphic with val: <8 12 18 21 29| Scale is weakly epimorphic with val: <8 12 18 21 32| Scale is weakly epimorphic with val: <8 12 18 22 31| Scale is weakly epimorphic with val: <8 12 19 19 32| Scale is weakly epimorphic with val: <8 12 19 21 30| Scale is weakly epimorphic with val: <8 12 19 21 33| Scale is weakly epimorphic with val: <8 12 19 22 32|
FIT/MODE
3: 0 1 2 N G T3 SD: 63.5905 c. M: 88.8007 c. 4: 1 1 2 P M ME S SD: 23.0493 c. M:-35.7106 c. 5: 1 1 3 N M DE S SD: 19.4766 c. M: 31.9561 c. 6: 1 2 3 P T3 SD: 10.8340 c. M:-17.8484 c. 7: 1 2 4 N T3 SD: 14.4429 c. M: 17.7262 c. 9: 2 2 5 N M DE S SD: 13.8444 c. M:-21.8760 c. 10: 2 3 5 P T3 SD: 12.0469 c. M:-17.8484 c. 11: 2 3 6 N T3 SD: 2.9449 c. M: 4.7900 c. 17: 3 5 9 N T3 SD: 1.9208 c. M:-3.2000 c. 28: 5 8 15 N T3 SD: 0.0860 c. M:-0.1359 c. 528: 94 151 283 N T3 SD: 0.0881 c. M: 0.1336 c. 556: 99 159 298 N T3 SD: 0.0793 c. M: 0.1200 c. 584: 104 167 313 N T3 SD: 0.0714 c. M: 0.1078 c. 612: 109 175 328 N T3 SD: 0.0642 c. M: 0.0966 c. 640: 114 183 343 N T3 SD: 0.0577 c. M: 0.0864 c. 668: 119 191 358 N T3 SD: 0.0517 c. M: 0.0771 c. 696: 124 199 373 N T3 SD: 0.0462 c. M: 0.0685 c. 724: 129 207 388 N T3 SD: 0.0411 c. M: 0.0606 c. 752: 134 215 403 N T3 SD: 0.0364 c. M: 0.0533 c. 780: 139 223 418 N T3 SD: 0.0320 c. M: 0.0465 c. 808: 144 231 433 N T3 SD: 0.0280 c. M: 0.0402 c. 836: 149 239 448 N T3 SD: 0.0242 c. M: 0.0343 c. 864: 154 247 463 N T3 SD: 0.0207 c. M: 0.0288 c. 892: 159 255 478 N T3 SD: 0.0174 c. M: 0.0236 c. 920: 164 263 493 N T3 SD: 0.0143 c. M: 0.0188 c. 948: 169 271 508 N T3 SD: 0.0115 c. M: 0.0142 c. 976: 174 279 523 N T3 SD: 0.0089 c. M: 0.0118 c. 1004: 179 287 538 N T3 SD: 0.0066 c. M: 0.0098 c. 1032: 184 295 553 N T3 SD: 0.0047 c. M: 0.0079 c. 1060: 189 303 568 N T3 SD: 0.0036 c. M: 0.0060 c. 1088: 194 311 583 N T3 SD: 0.0039 c. M:-0.0051 c. 2092: 373 598 1121 N T3 SD: 0.0040 c. M: 0.0069 c. 2148: 383 614 1151 N T3 SD: 0.0036 c. M: 0.0052 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: 59.7273 cents 6 x 7:8 S SD: 17.8484 cents 7 x 8:9 S SD: 31.4805 cents 8 x 9:11 SD: 29.9221 cents 9 x 10:12 S SD: 24.3852 cents 10 x 11:13 SD: 39.6850 cents 11:12:13:15 SD: 31.1011 cents 12:13:14:16 S SD: 20.4165 cents 13:14:15:17 SD: 18.1495 cents 14:15:16:19 SD: 14.4448 cents 15:16:17:20 SD: 9.0412 cents 20:21:23:27 SD: 8.1490 cents 21:22:24:28 S SD: 2.7546 cents 36:38:41:48 SD: 2.5674 cents 57:60:65:76 SD: 1.2669 cents 78:82:89:104 SD: 1.1852 cents 111:117:127:148 SD: 1.0145 cents 132:139:151:176 SD: 0.5883 cents 153:161:175:204 SD: 0.5076 cents 189:199:216:252 SD: 0.1526 cents 210:221:240:280 SD: 0.1374 cents 399:420:456:532 SD: 0.0000 cents