Scala analysis: xen09-chalmers-tritriadic-18-22-27
Tritriadic scale built from 18:22:27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 44/27 845.452940 neutral sixth 6: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 9/8 203.9100 major whole tone 2: 88/81 143.4979 2nd undecimal neutral second 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 9/8 203.9100 major whole tone 5: 88/81 143.4979 2nd undecimal neutral second 6: 9/8 203.9100 major whole tone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 88/81 143.498 cents 2nd undecimal neutral second 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 3 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 11/9 347.408 cents undecimal neutral third 2: 3 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 5 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 243/176 558.457 cents 4: 1 352/243 641.543 cents 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 5 3/2 701.955 cents perfect fifth 5: 3 44/27 845.453 cents neutral sixth 5: 3 18/11 852.592 cents undecimal neutral sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 2 81/44 1056.502 cents 2nd undecimal neutral 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 : 203.9 347.4 498.0 702.0 845.5 1049.4 1200.0 203.9 : 143.5 294.1 498.0 641.5 845.5 996.1 1200.0 347.4 : 150.6 354.5 498.0 702.0 852.6 1056.5 1200.0 498.0 : 203.9 347.4 551.3 702.0 905.9 1049.4 1200.0 702.0 : 143.5 347.4 498.0 702.0 845.5 996.1 1200.0 845.5 : 203.9 354.5 558.5 702.0 852.6 1056.5 1200.0 1049.4: 150.6 354.5 498.0 648.7 852.6 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 143.4979 .. 203.9100 cents 729/704, 60.4121 cents 88/81, 143.4979 cents 2: 294.1350 .. 354.5471 cents 729/704, 60.4121 cents 256/243, 90.2250 cents 3: 498.0450 .. 558.4571 cents 729/704, 60.4121 cents 88/81, 143.4979 cents 4: 641.5429 .. 701.9550 cents 729/704, 60.4121 cents 61952/59049, 83.0859 cents 5: 845.4529 .. 905.8650 cents 729/704, 60.4121 cents 88/81, 143.4979 cents 6: 996.0900 .. 1056.5021 cents 729/704, 60.4121 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 88/81, 143.4979 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.194641 Largest / Average step : 1.189475 Largest / Smallest step : 1.420996 Median interval of one step : 12/11, 150.6371 cents, amount: 2 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 172.31517 cents, oct.: 1206.20616 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : LSMLSLM Scale is a Constant Structure, by a margin of 83.08588 cents Scale diversity : 1.264781 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.697940 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 : 243/242, 7.1391 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 347.408 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Lydian octave species of abstract tetrachord Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 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 classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 Limited inverse transpositions with margin 60.4121 cents: 4 -- Rational properties -- Prime limit : 11 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.027386 Average absolute harmonicity : 0.247256 Specific harmonicity : 0.135384 Fundamental : 1/216, -7.7549 octaves, 1.2112 Hz. Guide tone : 396, 8.6294 octaves, 103603.724 Hz. Exponens Consonantiae : 8.553600E+04, 16.38424 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 70.0, average 10.00000 Mersenne's string divisions : 506940 Sum of van Prooijen's expressibility: 5.42263, average 0.77466 Sum of Tenney's harmonic distance : 10.90569, average 1.55796 Vogel's harmonic complexity : 15.00000 Wille's k value : 121 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 85.71369, average 3.06120 Lattice compactness (without 2's) : 58.18125, average 2.07790 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 0.00000 10 1 3: -3 .. 2 -0.57143 10 3 11: 0 .. 1 0.42857 3 3 Average exponent except 2's :-1 / 7 =-0.14286 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 25| Scale is JI-epimorphic with val: <7 11 24| = patent Scale is weakly epimorphic with val: <7 12 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 17.6158 c. M: 32.4814 c. Lebeng 16: 3 2 2 2 2 3 2 P D3 S SD: 20.9693 c. M:-27.5921 c. 17: 3 2 2 3 2 3 2 SP M ME S SD: 5.5452 c. M:-9.4606 c. Beatles-7, Dichotic-7 24: 4 3 3 4 3 4 3 SP M ME S SD: 2.6921 c. M:-4.5471 c. Neutral Lydian, Iced Major 41: 7 5 5 7 5 7 5 SP M DE S SD: 2.5483 c. M:-4.2956 c. Beatles-7, Dichotic-7 65: 11 8 8 11 8 11 8 SP M DE S SD: 2.2451 c. M:-3.7778 c. 94: 16 11 12 16 11 16 12 SP T3 SD: 1.7948 c. M: 2.8997 c. 111: 19 13 14 19 13 19 14 SP T3 SD: 1.2470 c. M: 2.2097 c. 118: 20 14 15 20 14 20 15 SP T3 SD: 1.1124 c. M: 1.9053 c. 135: 23 16 17 23 16 23 17 SP T3 SD: 0.5631 c. M: 1.0085 c. 159: 27 19 20 27 19 27 20 SP T3 SD: 0.1721 c. M: 0.3063 c. 335: 57 40 42 57 40 57 42 SP T3 SD: 0.1482 c. M:-0.2691 c. 359: 61 43 45 61 43 61 45 SP T3 SD: 0.1470 c. M:-0.2295 c. 494: 84 59 62 84 59 84 62 SP T3 SD: 0.0785 c. M:-0.1386 c. 518: 88 62 65 88 62 88 65 SP T3 SD: 0.0600 c. M:-0.1069 c. 677: 115 81 85 115 81 115 85 SP T3 SD: 0.0375 c. M: 0.0695 c. 1012: 172 121 127 172 121 172 127 SP T3 SD: 0.0272 c. M:-0.0442 c. 1171: 199 140 147 199 140 199 147 SP T3 SD: 0.0128 c. M: 0.0217 c. 1689: 287 202 212 287 202 287 212 SP T3 SD: 0.0109 c. M:-0.0178 c. 1848: 314 221 232 314 221 314 232 SP T3 SD: 0.0082 c. M: 0.0139 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 12.9686 cents 4 x 5 x 6 x 7:8 S SD: 22.3605 cents 5 x 6:7 x 8:9:10 S SD: 20.1614 cents 6:7 x 8:9:10:11:12 S SD: 12.3353 cents 7:8 x 9 x 11:13:14 SD: 19.1525 cents 8:9:10:11:12:13:15:16 SD: 10.9634 cents 13:15:16:17:20:21:24:26 SD: 10.5893 cents 14:16:17:19:21:23:26:28 SD: 7.1491 cents 18:20:22:24:27:29:33:36 SD: 4.1747 cents 24:27:29:32:36:39:44:48 SD: 2.9128 cents 32:36:39:43:48:52:59:64 SD: 2.5803 cents 40:45:49:53:60:65:73:80 SD: 2.1176 cents 48:54:59:64:72:78:88:96 SD: 1.5680 cents 54:61:66:72:81:88:99:108 SD: 1.0157 cents 72:81:88:96:108:117:132:144 SD: 0.7036 cents 126:142:154:168:189:205:231:252 SD: 0.5928 cents 144:162:176:192:216:235:264:288 SD: 0.3511 cents 162:182:198:216:243:264:297:324 SD: 0.3395 cents 216:243:264:288:324:352:396:432 SD: 0.0000 cents