Scala analysis: xen09-chalmers-tritriadic-27-25-22
Tritriadic scale built from 27:25:22
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/22 221.309485 undecimal acute whole tone 2: 27/22 354.547060 neutral third, Zalzal wosta of al-Farabi 3: 968/729 490.905880 4: 1100/729 712.215365 5: 44/27 845.452940 neutral sixth 6: 50/27 1066.762425 grave major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 1: 25/22 221.3095 undecimal acute whole tone 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 21296/19683 136.3588 4: 25/22 221.3095 undecimal acute whole tone 5: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 6: 25/22 221.3095 undecimal acute whole tone 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 1 21296/19683 136.359 cents 1: 3 25/22 221.309 cents undecimal acute whole tone 2: 1 21296/18225 269.596 cents 2: 5 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 24200/19683 357.668 cents 3: 2 729/550 487.785 cents 3: 3 968/729 490.906 cents 3: 2 675/484 575.857 cents 4: 2 968/675 624.143 cents 4: 3 729/484 709.094 cents two (neutral third, Zalzal wosta of al-Farabi) 4: 2 1100/729 712.215 cents 5: 1 19683/12100 842.332 cents 5: 5 44/27 845.453 cents neutral sixth 5: 1 18225/10648 930.404 cents 6: 3 44/25 978.691 cents undecimal grave minor seventh 6: 1 19683/10648 1063.641 cents 6: 3 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 : 221.3 354.5 490.9 712.2 845.5 1066.8 1200.0 221.3 : 133.2 269.6 490.9 624.1 845.5 978.7 1200.0 354.5 : 136.4 357.7 490.9 712.2 845.5 1066.8 1200.0 490.9 : 221.3 354.5 575.9 709.1 930.4 1063.6 1200.0 712.2 : 133.2 354.5 487.8 709.1 842.3 978.7 1200.0 845.5 : 221.3 354.5 575.9 709.1 845.5 1066.8 1200.0 1066.8: 133.2 354.5 487.8 624.1 845.5 978.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 221.3095 cents 625/594, 88.0719 cents 27/25, 133.2376 cents 2: 269.5964 .. 357.6683 cents 625/594, 88.0719 cents 468512/455625, 48.2869 cents 3: 487.7846 .. 575.8565 cents 625/594, 88.0719 cents 14348907/13310000, 130.1163 cents 4: 624.1435 .. 712.2154 cents 625/594, 88.0719 cents 468512/455625, 48.2869 cents 5: 842.3317 .. 930.4036 cents 625/594, 88.0719 cents 14348907/13310000, 130.1163 cents 6: 978.6905 .. 1066.7624 cents 625/594, 88.0719 cents 468512/455625, 48.2869 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 : 25/22, 221.3095 cents Average / Smallest step : 1.286638 Largest / Average step : 1.290972 Largest / Smallest step : 1.661014 Median interval of one step : 21296/19683, 136.3588 cents, amount: 1 Least squares average step : 173.42730 cents, oct.: 1213.99110 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCABAB Step pattern size order : LSMLSLS Scale is a Constant Structure, by a margin of 48.28691 cents Scale diversity : 1.278198 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.559640 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 : 532400/531441, 3.1212 cents Most common intervals : 27/22, 354.5471 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 221.309 354.547 cents Most common triad is 0.0 354.547 845.453 cents, amount: 3 Number of recognisable fifths : 5, average 710.3426 cents Best fifths form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 11 27 Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 88.0719 cents: 4 -- Rational properties -- Prime limit : 11 Odd number limit : 19683 (O: 19683 U: 19683) Highest odd numerator or denominator: 729 Scale harmonicity : 0.010488 Average absolute harmonicity : 0.169698 Specific harmonicity : 0.056180 Fundamental : 1/16038, -13.9692 octaves, 0.0163 Hz. Guide tone : 653400, 19.3176 octaves, 170946144.368 Hz. Exponens Consonantiae : 1.047923E+10, 33.28681 octaves Euler's gradus suavitatis : 61 Sum of Mann's harmonic distance : 1886.5, average 269.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.41749, average 1.63107 Sum of Tenney's harmonic distance : 23.77305, average 3.39615 Vogel's harmonic complexity : 32.00000 Wille's k value : 9841 Wilson's harmonic complexity : 70 Rectangular lattice diameter : 14 Triangular lattice diameter : 9 Lattice compactness : 135.86763, average 4.85242 Lattice compactness (without 2's) : 124.17704, average 4.43489 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.00000 11 1 3: -6 .. 3 -2.14286 21 5: 0 .. 2 0.85714 6 1 11: -1 .. 2 0.28571 6 5 Average exponent except 2's :-7 / 7 =-1.00000 Average absolute exponent except 2's: 33 / 7 = 4.71429 Scale is weakly epimorphic with val: <7 10 17 24| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 11 18 25| Scale is weakly epimorphic with val: <7 12 15 24| Scale is weakly epimorphic with val: <7 12 17 25|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 27.9512 c. M: 49.8809 c. Lebeng 9: 2 1 1 1 1 2 1 N D3 S SD: 37.9172 c. M: 45.5487 c. 10: 2 1 1 2 1 2 1 P M ME S SD: 10.4443 c. M:-18.6905 c. Sethares Neutral, Beatles-7, Dichotic-7 17: 3 2 2 3 2 3 2 SP M ME S SD: 5.4734 c. M: 9.5448 c. Beatles-7, Dichotic-7 27: 5 3 3 5 3 5 3 SP M DE S SD: 1.0799 c. M: 2.0170 c. Beatles-7, Dichotic-7 98: 18 11 11 18 11 18 11 SP M DE S SD: 1.1229 c. M: 2.0113 c. 125: 23 14 14 23 14 23 14 SP M DE S SD: 1.0326 c. M: 1.8154 c. 152: 28 17 17 28 17 28 17 SP M DE S SD: 0.9959 c. M: 1.6890 c. 179: 33 20 20 33 20 33 20 SP M DE S SD: 0.9815 c. M: 1.6008 c. 200: 37 22 23 37 22 37 22 SP T3 SD: 0.9992 c. M:-1.7846 c. 206: 38 23 23 38 23 38 23 SP M DE S SD: 0.9771 c. M: 1.5855 c. 217: 40 24 25 40 24 40 24 SP T3 SD: 0.7543 c. M:-1.2600 c. 227: 42 25 26 42 25 42 25 SP T3 SD: 0.8054 c. M:-1.4410 c. 234: 43 26 27 43 26 43 26 SP T3 SD: 0.7519 c. M:-1.4018 c. 244: 45 27 28 45 27 45 27 SP T3 SD: 0.5632 c. M:-0.8994 c. 271: 50 30 31 50 30 50 30 SP T3 SD: 0.4154 c. M:-0.6998 c. 288: 53 32 33 53 32 53 32 SP T3 SD: 0.4115 c. M:-0.7608 c. 298: 55 33 34 55 33 55 33 SP T3 SD: 0.3033 c. M:-0.5363 c. 315: 58 35 36 58 35 58 35 SP T3 SD: 0.2863 c. M:-0.5227 c. 325: 60 36 37 60 36 60 36 SP T3 SD: 0.2253 c. M:-0.4000 c. 342: 63 38 39 63 38 63 38 SP T3 SD: 0.1833 c. M:-0.3222 c. 352: 65 39 40 65 39 65 39 SP T3 SD: 0.1853 c. M:-0.2846 c. 369: 68 41 42 68 41 68 41 SP T3 SD: 0.1022 c. M: 0.1713 c. 396: 73 44 45 73 44 73 44 SP T3 SD: 0.0627 c. M: 0.0974 c. 748: 138 83 85 138 83 138 83 SP T3 SD: 0.0540 c. M:-0.0841 c. 1117: 206 124 127 206 124 206 124 SP T3 SD: 0.0318 c. M:-0.0520 c. 1144: 211 127 130 211 127 211 127 SP T3 SD: 0.0137 c. M:-0.0224 c. 1540: 284 171 175 284 171 284 171 SP T3 SD: 0.0062 c. M: 0.0108 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: 5.1302 cents 3 x x 4 x 5 x 6 S SD: 13.1851 cents 4 x 5 x 6 x 7:8 S SD: 25.8674 cents 5 x 6:7 x 8:9:10 S SD: 23.0927 cents 6:7 x 8:9:10:11:12 S SD: 10.6046 cents 7:8 x 9 x 11:13:14 SD: 16.9727 cents 8:9:10:11:12:13:15:16 SD: 10.6460 cents 11 x 14:15:17:18:20:22 SD: 15.6880 cents 12:14:15:16:18:20:22:24 S SD: 10.1596 cents 13:15:16:17:20:21:24:26 SD: 7.5734 cents 14:16:17:19:21:23:26:28 SD: 6.6846 cents 21:24:26:28:32:34:39:42 SD: 4.0909 cents 22:25:27:29:33:36:41:44 SD: 2.9856 cents 36:41:44:48:54:59:67:72 SD: 2.8311 cents 43:49:53:57:65:70:80:86 SD: 1.8346 cents 49:56:60:65:74:80:91:98 SD: 1.7646 cents 57:65:70:76:86:93:106:114 SD: 1.7275 cents 61:69:75:81:92:99:113:122 SD: 1.5967 cents 65:74:80:86:98:106:120:130 SD: 1.4650 cents 67:76:82:89:101:109:124:134 SD: 0.9639 cents 88:100:108:117:133:143:163:176 SD: 0.8711 cents 110:125:135:146:166:179:204:220 SD: 0.5192 cents 167:190:205:222:252:272:309:334 SD: 0.4789 cents 189:215:232:251:285:308:350:378 SD: 0.3129 cents 256:291:314:340:386:417:474:512 SD: 0.2747 cents 299:340:367:397:451:487:554:598 SD: 0.2677 cents 308:350:378:409:465:502:570:616 SD: 0.2135 cents 330:375:405:438:498:538:611:660 SD: 0.1572 cents 418:475:513:555:631:681:774:836 SD: 0.1298 cents 440:500:540:584:664:717:815:880 SD: 0.1247 cents 580:659:712:770:875:945:1074:1160 SD: 0.1118 cents 586:666:719:778:884:955:1085:1172 SD: 0.1109 cents