Scala analysis: xen09-chalmers-tritriadic-22-25-27
Tritriadic scale built from 22:25:27
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: 675/484 575.856546 4: 729/484 709.094120 two (neutral third, Zalzal wosta of al-Farabi) 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: 25/22 221.3095 undecimal acute whole tone 4: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 5: 21296/19683 136.3588 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 : 221.3 354.5 575.9 709.1 845.5 1066.8 1200.0 221.3 : 133.2 354.5 487.8 624.1 845.5 978.7 1200.0 354.5 : 221.3 354.5 490.9 712.2 845.5 1066.8 1200.0 575.9 : 133.2 269.6 490.9 624.1 845.5 978.7 1200.0 709.1 : 136.4 357.7 490.9 712.2 845.5 1066.8 1200.0 845.5 : 221.3 354.5 575.9 709.1 930.4 1063.6 1200.0 1066.8: 133.2 354.5 487.8 709.1 842.3 978.7 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 : 175.15849 cents, oct.: 1226.10945 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABABCAB Step pattern size order : LSLSMLS 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 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: 1 -- 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 : 0.169244 Specific harmonicity : 0.055634 Fundamental : 1/13068, -13.6738 octaves, 0.0200 Hz. Guide tone : 801900, 19.6131 octaves, 209797540.815 Hz. Exponens Consonantiae : 1.047923E+10, 33.28681 octaves Euler's gradus suavitatis : 61 Sum of Mann's harmonic distance : 1309.5, average 187.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.38406, average 1.62629 Sum of Tenney's harmonic distance : 23.08205, average 3.29744 Vogel's harmonic complexity : 31.71429 Wille's k value : 9841 Wilson's harmonic complexity : 70 Rectangular lattice diameter : 14 Triangular lattice diameter : 9 Lattice compactness : 134.25844, average 4.79494 Lattice compactness (without 2's) : 121.89702, average 4.35347 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.28571 10 1 3: -3 .. 6 0.85714 18 5: 0 .. 2 0.85714 6 1 11: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 7 / 7 = 1.00000 Average absolute exponent except 2's: 31 / 7 = 4.42857 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: 34.9644 c. M: 61.5708 c. Lebeng 10: 2 1 2 1 1 2 1 P M ME S SD: 13.5535 c. M:-24.1435 c. 17: 3 2 3 2 2 3 2 SP M ME S SD: 6.4801 c. M: 11.1507 c. 27: 5 3 5 3 3 5 3 SP M DE S SD: 1.2326 c. M:-2.0170 c. 71: 13 8 13 8 8 13 8 SP M DE S SD: 1.1191 c. M: 1.9737 c. 98: 18 11 18 11 11 18 11 SP M DE S SD: 0.8368 c. M: 1.4563 c. 125: 23 14 23 14 14 23 14 SP M DE S SD: 0.7736 c. M:-1.3059 c. 200: 37 22 37 22 23 37 22 SP T3 SD: 0.7392 c. M:-1.2376 c. 217: 40 24 40 24 25 40 24 SP T3 SD: 0.6774 c. M: 1.2600 c. 227: 42 25 42 25 26 42 25 SP T3 SD: 0.6083 c. M:-1.0790 c. 244: 45 27 45 27 28 45 27 SP T3 SD: 0.4797 c. M: 0.8974 c. 271: 50 30 50 30 31 50 30 SP T3 SD: 0.3301 c. M: 0.6070 c. 298: 55 33 55 33 34 55 33 SP T3 SD: 0.2257 c. M: 0.3693 c. 325: 60 36 60 36 37 60 36 SP T3 SD: 0.1756 c. M:-0.3145 c. 352: 65 39 65 39 40 65 39 SP T3 SD: 0.1842 c. M:-0.2830 c. 369: 68 41 68 41 42 68 41 SP T3 SD: 0.1382 c. M: 0.2468 c. 396: 73 44 73 44 45 73 44 SP T3 SD: 0.0638 c. M: 0.0990 c. 721: 133 80 133 80 82 133 80 SP T3 SD: 0.0533 c. M:-0.0892 c. 748: 138 83 138 83 85 138 83 SP T3 SD: 0.0530 c. M:-0.0825 c. 1117: 206 124 206 124 127 206 124 SP T3 SD: 0.0279 c. M: 0.0520 c. 1144: 211 127 211 127 130 211 127 SP T3 SD: 0.0127 c. M:-0.0208 c. 1540: 284 171 284 171 175 284 171 SP T3 SD: 0.0073 c. M: 0.0124 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: 3.5696 cents 3 x x 4 x 5 x 6 S SD: 28.9987 cents 4 x 5 x 6 x 7:8 S SD: 25.8017 cents 5 x 6:7 x 8:9:10 S SD: 14.1200 cents 6:7 x 8:9:10:11:12 S SD: 16.6649 cents 7:8:9:10 x 11:13:14 SD: 18.4881 cents 8:9:10:11:12:13:15:16 SD: 7.0736 cents 11 x 14:15:17:18:20:22 SD: 15.3857 cents 12:14:15:17:18:20:22:24 SD: 10.7752 cents 13:15:16:18:20:21:24:26 SD: 7.1204 cents 14:16:17:20:21:23:26:28 SD: 7.0579 cents 18:20:22:25:27:29:33:36 SD: 6.9411 cents 20:23:25:28:30:33:37:40 SD: 6.3830 cents 21:24:26:29:32:34:39:42 SD: 4.8990 cents 22:25:27:31:33:36:41:44 SD: 3.3245 cents 30:34:37:42:45:49:56:60 SD: 2.8396 cents 35:40:43:49:53:57:65:70 SD: 2.2883 cents 43:49:53:60:65:70:80:86 SD: 1.9490 cents 53:60:65:74:80:86:98:106 SD: 1.5923 cents 65:74:80:91:98:106:120:130 SD: 1.5093 cents 67:76:82:93:101:109:124:134 SD: 1.5065 cents 73:83:90:102:110:119:135:146 SD: 1.2797 cents 75:85:92:105:113:122:139:150 SD: 1.2660 cents 79:90:97:110:119:129:146:158 SD: 1.0294 cents 87:99:107:121:131:142:161:174 SD: 1.0190 cents 89:101:109:124:134:145:165:178 SD: 0.7252 cents 119:135:146:166:179:194:220:238 SD: 0.6870 cents 124:141:152:173:187:202:230:248 SD: 0.6186 cents 132:150:162:184:199:215:244:264 SD: 0.5338 cents 154:175:189:215:232:251:285:308 SD: 0.3129 cents 162:184:199:226:244:264:300:324 SD: 0.2683 cents 243:276:298:339:366:396:450:486 SD: 0.2375 cents 251:285:308:350:378:409:465:502 SD: 0.2304 cents 316:359:388:441:476:515:585:632 SD: 0.2283 cents 322:366:395:449:485:525:596:644 SD: 0.2197 cents 330:375:405:460:497:538:611:660 SD: 0.1670 cents 405:460:497:565:610:660:750:810 SD: 0.1462 cents 484:550:594:675:729:789:896:968 SD: 0.1153 cents