Scala analysis: xen10-chalmers-tritriadic-5-1-27
Tritriadic scale built from 5:1:27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 2: 32/27 294.134997 Pythagorean minor third 3: 27/20 519.551289 acute fourth 4: 40/27 680.448711 grave fifth 5: 8/5 813.686286 minor sixth 6: 729/400 1039.102577 acute minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 800/729 160.8974 grave whole tone 1: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 2: 800/729 160.8974 grave whole tone 3: 729/640 225.4163 acute major second 4: 800/729 160.8974 grave whole tone 5: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 6: 729/640 225.4163 acute major second 7: 800/729 160.8974 grave whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 3 800/729 160.897 cents grave whole tone 1: 2 729/640 225.416 cents acute major second 2: 3 32/27 294.135 cents Pythagorean minor third 2: 1 19683/16000 358.654 cents 2: 3 5/4 386.314 cents major third 3: 1 25600/19683 455.032 cents 3: 5 27/20 519.551 cents acute fourth 3: 1 1000/729 547.211 cents 4: 1 729/500 652.789 cents 4: 5 40/27 680.449 cents grave fifth 4: 1 19683/12800 744.968 cents 5: 3 8/5 813.686 cents minor sixth 5: 1 32000/19683 841.346 cents 5: 3 27/16 905.865 cents Pythagorean major sixth 6: 2 1280/729 974.584 cents grave minor seventh 6: 3 729/400 1039.103 cents acute minor seventh 6: 2 50/27 1066.762 cents grave major seventh 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 4 5 6 7 0.0 : 133.2 294.1 519.6 680.4 813.7 1039.1 1200.0 133.2 : 160.9 386.3 547.2 680.4 905.9 1066.8 1200.0 294.1 : 225.4 386.3 519.6 745.0 905.9 1039.1 1200.0 519.6 : 160.9 294.1 519.6 680.4 813.7 974.6 1200.0 680.4 : 133.2 358.7 519.6 652.8 813.7 1039.1 1200.0 813.7 : 225.4 386.3 519.6 680.4 905.9 1066.8 1200.0 1039.1: 160.9 294.1 455.0 680.4 841.3 974.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 225.4163 cents 135/128, 92.1787 cents 27/25, 133.2376 cents 2: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 20480/19683, 68.7187 cents 3: 455.0324 .. 547.2111 cents 135/128, 92.1787 cents 20480/19683, 68.7187 cents 4: 652.7889 .. 744.9676 cents 135/128, 92.1787 cents 531441/500000, 105.5777 cents 5: 813.6863 .. 905.8650 cents 135/128, 92.1787 cents 20480/19683, 68.7187 cents 6: 974.5837 .. 1066.7624 cents 135/128, 92.1787 cents 20480/19683, 68.7187 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 27/25, 133.2376 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 729/640, 225.4163 cents Average / Smallest step : 1.286638 Largest / Average step : 1.314928 Largest / Smallest step : 1.691837 Median interval of one step : 800/729, 160.8974 cents, amount: 3 Most common interval of one step : 800/729, 160.8974 cents, amount: 3 Least squares average step : 169.32145 cents, oct.: 1185.25016 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1432-tone equal temperament with octave 2/1 degrees: 159 351 620 812 971 1240 1432 Least number of segments generator : 717 of 600.838 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1229 of 1029.888 cents and inv. generated superset size: 46 = 39 more = 657.143% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCBACB Step pattern size order : SMLMSLM Scale is a Constant Structure, by a margin of 68.71871 cents Scale diversity : 1.396467 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.539106 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 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 : 20000/19683, 27.6598 cents Most common intervals : 27/20, 519.5513 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 294.135 680.449 cents Most common triad is 0.0 519.551 680.449 cents, amount: 3 Number of recognisable fifths : 0 Best fifths form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 5 27 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Limited inverse transpositions with margin 92.1787 cents: 1 -- Rational properties -- Prime limit : 5 Odd number limit : 19683 (O: 19683 U: 19683) Highest odd numerator or denominator: 729 Scale harmonicity : 0.019157 Average absolute harmonicity : 0.197188 Specific harmonicity : 0.107744 Fundamental : 1/10800, -13.3987 octaves, 0.0242 Hz. Guide tone : 116640, 16.8317 octaves, 30516005.937 Hz. Exponens Consonantiae : 1.259712E+09, 30.23045 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 685.0, average 97.85714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.28715, average 1.32674 Sum of Tenney's harmonic distance : 18.89951, average 2.69993 Vogel's harmonic complexity : 22.85714 Wille's k value : 9841 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 12 Triangular lattice diameter : 9 Lattice compactness : 153.76819, average 5.49172 Lattice compactness (without 2's) : 111.83093, average 3.99396 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.85714 18 1 3: -3 .. 6 0.85714 18 1 5: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 25 / 7 = 3.57143 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 29.0006 c. M:-48.7221 c. Lebeng 9: 1 1 2 1 1 2 1 P M ME S SD: 17.2441 c. M:-27.5641 c. 16: 2 2 3 2 2 3 2 SP M ME S SD: 9.4227 c. M:-16.7624 c. Antimixolydian 25: 3 3 5 3 3 5 3 SP M DE S SD: 9.1582 c. M:-16.8974 c. Antimixolydian 28: 3 4 5 4 3 5 4 SP T3 SD: 5.6428 c. M: 10.5311 c. 37: 4 5 7 5 4 7 5 SP T3 SD: 2.0002 c. M: 3.5078 c. 53: 6 7 10 7 6 10 7 SP T3 SD: 1.5827 c. M:-2.6115 c. 81: 9 11 15 11 9 15 11 SP T3 SD: 1.3285 c. M:-2.1613 c. 90: 10 12 17 12 10 17 12 SP T3 SD: 0.5324 c. M:-0.8974 c. 171: 19 23 32 23 19 32 23 SP T3 SD: 0.3540 c. M:-0.6018 c. 208: 23 28 39 28 23 39 28 SP T3 SD: 0.3729 c. M: 0.6410 c. 224: 25 30 42 30 25 42 30 SP T3 SD: 0.4044 c. M:-0.6910 c. 261: 29 35 49 35 29 49 35 SP T3 SD: 0.0709 c. M:-0.1179 c. 612: 68 82 115 82 68 115 82 SP T3 SD: 0.0657 c. M:-0.1131 c. 820: 91 110 154 110 91 154 110 SP T3 SD: 0.0456 c. M: 0.0782 c. 910: 101 122 171 122 101 171 122 SP T3 SD: 0.0404 c. M: 0.0691 c. 1081: 120 145 203 145 120 203 145 SP T3 SD: 0.0347 c. M: 0.0646 c. 1171: 130 157 220 157 130 220 157 SP T3 SD: 0.0157 c. M: 0.0274 c. 1432: 159 192 269 192 159 269 192 SP T3 SD: 0.0020 c. M:-0.0036 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 10.7531 cents 3 x x 4 x 5 x 6 S SD: 24.6241 cents 4 x 5 x 6 x 7:8 S SD: 29.4727 cents 5 x 6:7 x 8:9:10 S SD: 13.9844 cents 6 x 7:8:9:10:11:12 S SD: 13.7116 cents 7 x 8:9:10:11:13:14 SD: 21.7936 cents 8:9 x 11:12:13:15:16 SD: 16.3333 cents 9:10:11:12:13:14:16:18 S SD: 15.5627 cents 10:11:12:14:15:16:18:20 S SD: 11.3935 cents 11:12:13:15:16:18:20:22 SD: 8.0425 cents 12:13:14:16:18:19:22:24 SD: 6.5943 cents 17:18:20:23:25:27:31:34 SD: 5.8558 cents 22:24:26:30:33:35:40:44 SD: 4.9620 cents 23:25:27:31:34:37:42:46 SD: 3.2541 cents 37:40:44:50:55:59:67:74 SD: 2.1787 cents 48:52:57:65:71:77:87:96 SD: 1.9518 cents 60:65:71:81:89:96:109:120 SD: 1.2060 cents 75:81:89:101:111:120:137:150 SD: 0.9217 cents 97:105:115:131:144:155:177:194 SD: 0.8884 cents 102:110:121:138:151:163:186:204 SD: 0.7843 cents 112:121:133:151:166:179:204:224 SD: 0.6755 cents 123:133:146:166:182:197:224:246 SD: 0.6515 cents 125:135:148:169:185:200:228:250 SD: 0.5458 cents 135:146:160:182:200:216:246:270 SD: 0.4813 cents 162:175:192:219:240:259:295:324 SD: 0.4435 cents 200:216:237:270:296:320:365:400 SD: 0.4215 cents 226:244:268:305:335:362:412:452 SD: 0.3607 cents 237:256:281:320:351:379:432:474 SD: 0.1929 cents 388:419:460:524:575:621:707:776 SD: 0.1749 cents 400:432:474:540:593:640:729:800 SD: 0.1743 cents 463:500:549:625:686:741:844:926 SD: 0.1499 cents 523:565:620:706:775:837:953:1046 SD: 0.1326 cents 540:583:640:729:800:864:984:1080 SD: 0.0928 cents