Scala analysis: 132_C1
Chromatic tetrachord 29/28 * 28/27 * 36/29
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 29/28 60.751288 2: 29/27 123.712192 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 36/29 374.3328 1: 29/28 60.7513 2: 28/27 62.9609 Archytas' 1/3-tone 3: 36/29 374.3328
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 29/28 60.751 cents 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 36/29 374.333 cents 2: 1 29/27 123.712 cents 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 112/87 437.294 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 : 60.8 123.7 498.0 60.8 : 63.0 437.3 498.0 123.7: 374.3 435.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 60.7513 .. 374.3328 cents 1008/841, 313.5815 cents 29/28, 60.7513 cents 2: 123.7122 .. 437.2937 cents 1008/841, 313.5815 cents 841/972,-250.6206 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 29/28, 60.7513 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 36/29, 374.3328 cents Average / Smallest step : 2.732699 Largest / Average step : 2.254813 Largest / Smallest step : 6.161726 Median interval of one step : 28/27, 62.9609 cents, amount: 1 Least squares average step : 128.73648 cents, oct.: 386.20943 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2025-tone equal temperament with octave 4/3 degrees: 247 503 2025 Least number of segments generator : 1013 of 249.145 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1772 of 435.820 cents and inv. generated superset size: 50 = 47 more = 1666.667% 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 60.75129 cents Scale diversity : 0.608900 Lumma stability : 0.243959 Lumma impropriety factor : 0.503209 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 : 784/783, 2.2096 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 311.3719 cents: 2 -- Rational properties -- Prime limit : 29 Odd number limit : 87 (O: 29 U: 87) Highest odd numerator or denominator: 29 Scale harmonicity : 0.013097 Average absolute harmonicity : 0.081822 Specific harmonicity : 0.055983 Fundamental : 1/756, -9.5622 octaves, 0.3461 Hz. Guide tone : 116, 6.8580 octaves, 30348.566 Hz. Exponens Consonantiae : 8.769600E+04, 16.42022 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 60.0, average 20.00000 Mersenne's string divisions : 3192 Sum of van Prooijen's expressibility: 3.40192, average 1.13397 Sum of Tenney's harmonic distance : 6.88250, average 2.29417 Vogel's harmonic complexity : 31.00000 Wille's k value : 391 Wilson's harmonic complexity : 45 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 18.94839, average 3.15807 Lattice compactness (without 2's) : 12.70689, average 2.11781 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.00000 4 3: -3 .. 0 -1.33333 4 1 7: -1 .. 0 -0.33333 1 29: 0 .. 1 0.66667 2 2 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 19 34| Scale is weakly epimorphic with val: <6 10 20 33| Scale is weakly epimorphic with val: <6 10 22 37| Scale is weakly epimorphic with val: <6 11 19 36| Scale is weakly epimorphic with val: <6 11 20 35| Scale is weakly epimorphic with val: <6 11 22 36| Scale is weakly epimorphic with val: <7 10 18 35| Scale is weakly epimorphic with val: <7 10 20 33| Scale is weakly epimorphic with val: <7 10 21 38| Scale is weakly epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 11 18 37| Scale is weakly epimorphic with val: <7 11 20 32| Scale is JI-epimorphic with val: <7 11 20 35| = patent Scale is weakly epimorphic with val: <7 11 20 38| Scale is weakly epimorphic with val: <7 11 21 34| Scale is weakly epimorphic with val: <7 11 21 37| Scale is weakly epimorphic with val: <7 12 20 37| Scale is weakly epimorphic with val: <8 11 18 37| Scale is weakly epimorphic with val: <8 11 19 36| Scale is weakly epimorphic with val: <8 11 22 36| Scale is weakly epimorphic with val: <8 12 19 38|
FIT/MODE
3: 0 1 2 N G T3 SD: 42.7405 c. M: 60.7513 c. 4: 0 1 3 N G T3 SD: 35.0778 c. M: 60.7513 c. 5: 0 1 4 N G T3 SD: 37.7345 c. M: 60.7513 c. 6: 1 1 4 N M DE S SD: 27.5975 c. M:-42.3028 c. 7: 1 1 5 N M DE S SD: 12.2960 c. M:-18.5864 c. 8: 1 1 6 N M DE S SD: 0.9835 c. M:-1.5043 c. 57: 7 7 43 N M DE S SD: 0.8345 c. M: 1.3853 c. 65: 8 8 49 N M DE S SD: 0.7177 c. M: 1.1165 c. 73: 9 9 55 N M DE S SD: 0.6446 c. M: 0.9066 c. 81: 10 10 61 N M DE S SD: 0.6017 c. M: 0.7381 c. 89: 11 11 67 N M DE S SD: 0.5796 c. M:-0.8048 c. 97: 12 12 73 N M DE S SD: 0.5712 c. M:-0.8625 c. 105: 13 13 79 N M DE S SD: 0.5716 c. M:-0.9114 c. 113: 14 14 85 N M DE S SD: 0.5775 c. M:-0.9534 c. 117: 14 15 88 N T3 SD: 0.6848 c. M: 1.1562 c. 121: 15 15 91 N M DE S SD: 0.5867 c. M:-0.9898 c. 124: 15 16 93 N T3 SD: 0.5454 c. M:-0.7991 c. 125: 15 16 94 N T3 SD: 0.5805 c. M: 0.9859 c. 132: 16 17 99 N T3 SD: 0.5114 c. M:-0.7991 c. 133: 16 17 100 N T3 SD: 0.4892 c. M: 0.8361 c. 140: 17 18 105 N T3 SD: 0.4878 c. M:-0.7991 c. 141: 17 18 106 N T3 SD: 0.4089 c. M: 0.7033 c. 149: 18 19 112 N T3 SD: 0.3383 c. M: 0.5848 c. 157: 19 20 118 N T3 SD: 0.2762 c. M: 0.4783 c. 165: 20 21 124 N T3 SD: 0.2221 c. M: 0.3822 c. 173: 21 22 130 N T3 SD: 0.1763 c. M: 0.2950 c. 181: 22 23 136 N T3 SD: 0.1400 c. M: 0.2154 c. 189: 23 24 142 N T3 SD: 0.1155 c. M: 0.1426 c. 197: 24 25 148 N T3 SD: 0.1059 c. M:-0.1670 c. 205: 25 26 154 N T3 SD: 0.1110 c. M:-0.1917 c. 213: 26 27 160 N T3 SD: 0.1263 c. M:-0.2145 c. 246: 30 31 185 N T3 SD: 0.1234 c. M: 0.2132 c. 254: 31 32 191 N T3 SD: 0.1065 c. M: 0.1813 c. 262: 32 33 197 N T3 SD: 0.0985 c. M: 0.1514 c. 270: 33 34 203 N T3 SD: 0.0997 c. M: 0.1232 c. 411: 50 52 309 N T3 SD: 0.1129 c. M: 0.1619 c. 419: 51 53 315 N T3 SD: 0.0921 c. M: 0.1301 c. 427: 52 54 321 N T3 SD: 0.0722 c. M: 0.0994 c. 435: 53 55 327 N T3 SD: 0.0531 c. M: 0.0699 c. 443: 54 56 333 N T3 SD: 0.0350 c. M: 0.0441 c. 451: 55 57 339 N T3 SD: 0.0187 c. M: 0.0292 c. 459: 56 58 345 N T3 SD: 0.0111 c. M: 0.0147 c. 910: 111 115 684 N T3 SD: 0.0126 c. M: 0.0219 c. 1107: 135 140 832 N T3 SD: 0.0106 c. M: 0.0141 c. 1115: 136 141 838 N T3 SD: 0.0102 c. M:-0.0174 c. 1558: 190 197 1171 N T3 SD: 0.0081 c. M: 0.0141 c. 1566: 191 198 1177 N T3 SD: 0.0043 c. M: 0.0063 c. 1574: 192 199 1183 N T3 SD: 0.0047 c. M:-0.0080 c. 2017: 246 255 1516 N T3 SD: 0.0051 c. M: 0.0081 c. 2025: 247 256 1522 N T3 SD: 0.0012 c. M: 0.0021 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 71.5794 cents 7 x 8:9 S SD: 62.2739 cents 8 x 9:11 SD: 48.1396 cents 9 x 10:12 S SD: 29.3458 cents 10 x 11:13 SD: 30.1089 cents 11 x 12:15 S SD: 23.6570 cents 12 x 13:16 SD: 7.4302 cents 13 x 14:17 SD: 16.9643 cents 14 x 15:19 SD: 15.4691 cents 15 x 16:20 S SD: 5.9905 cents 16 x 17:21 SD: 16.5465 cents 17 x 18:23 SD: 17.6898 cents 18 x 19:24 SD: 15.0546 cents 19:20 x 25 S SD: 18.1148 cents 20:21 x 27 SD: 16.0075 cents 21:22:23:28 SD: 13.0497 cents 22:23:24:29 SD: 12.3784 cents 23:24:25:31 SD: 10.2389 cents 24:25:26:32 SD: 5.9560 cents 26:27:28:35 S SD: 5.9304 cents 27:28:29:36 SD: 0.7365 cents 201:208:216:268 SD: 0.5774 cents 228:236:245:304 SD: 0.4364 cents 255:264:274:340 SD: 0.3311 cents 282:292:303:376 SD: 0.2544 cents 309:320:332:412 SD: 0.2036 cents 336:348:361:448 SD: 0.1776 cents 363:376:390:484 SD: 0.1733 cents 393:407:422:524 SD: 0.1601 cents 420:435:451:560 SD: 0.1422 cents 447:463:480:596 SD: 0.1408 cents