Scala analysis: xen09-chalmers-tritriadic-28-33-42
Tritriadic scale built from 28:33:42
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: 33/28 284.447037 undecimal minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 11/7 782.492036 undecimal augmented fifth 6: 99/56 986.402038 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 112/99 213.5980 1: 9/8 203.9100 major whole tone 2: 22/21 80.5370 undecimal minor semitone 3: 112/99 213.5980 4: 9/8 203.9100 major whole tone 5: 22/21 80.5370 undecimal minor semitone 6: 9/8 203.9100 major whole tone 7: 112/99 213.5980
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 22/21 80.537 cents undecimal minor semitone 1: 3 9/8 203.910 cents major whole tone 1: 2 112/99 213.598 cents 2: 3 33/28 284.447 cents undecimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 297/224 488.357 cents 3: 5 4/3 498.045 cents perfect fourth 3: 1 63/44 621.418 cents 4: 1 88/63 578.582 cents 4: 5 3/2 701.955 cents perfect fifth 4: 1 448/297 711.643 cents 5: 3 11/7 782.492 cents undecimal augmented fifth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 3 56/33 915.553 cents 6: 2 99/56 986.402 cents 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 21/11 1119.463 cents undecimal 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 : 203.9 284.4 498.0 702.0 782.5 986.4 1200.0 203.9 : 80.5 294.1 498.0 578.6 782.5 996.1 1200.0 284.4 : 213.6 417.5 498.0 702.0 915.6 1119.5 1200.0 498.0 : 203.9 284.4 488.4 702.0 905.9 986.4 1200.0 702.0 : 80.5 284.4 498.0 702.0 782.5 996.1 1200.0 782.5 : 203.9 417.5 621.4 702.0 915.6 1119.5 1200.0 986.4 : 213.6 417.5 498.0 711.6 915.6 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 213.5980 cents 392/363, 133.0609 cents 22/21, 80.5370 cents 2: 284.4470 .. 417.5080 cents 392/363, 133.0609 cents 3267/3136, 70.8491 cents 3: 488.3570 .. 621.4180 cents 392/363, 133.0609 cents 3267/3136, 70.8491 cents 4: 578.5820 .. 711.6430 cents 392/363, 133.0609 cents 3872/3969,-42.8359 cents 5: 782.4920 .. 915.5530 cents 392/363, 133.0609 cents 3267/3136, 70.8491 cents 6: 986.4020 .. 1119.4630 cents 392/363, 133.0609 cents 3267/3136, 70.8491 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 112/99, 213.5980 cents Average / Smallest step : 2.128568 Largest / Average step : 1.245988 Largest / Smallest step : 2.652171 Median interval of one step : 9/8, 203.9100 cents, amount: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 166.46880 cents, oct.: 1165.28157 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2354-tone equal temperament with octave 2/1 degrees: 400 558 977 1377 1535 1935 2354 Least number of segments generator : 1179 of 601.020 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2263 of 1153.611 cents and inv. generated superset size: 124 = 117 more = 1771.429% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCABAC Step pattern size order : MSLMSML Scale is a Constant Structure, by a margin of 42.83593 cents Scale diversity : 1.324962 Lumma stability : 0.370392 Lumma impropriety factor : 0.035697 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 : 896/891, 9.6880 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 284.447 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 6, average 703.5697 cents Scale is Lydian octave species of abstract tetrachord 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 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 133.0609 cents: 6 -- Rational properties -- Prime limit : 11 Odd number limit : 297 (O: 297 U: 297) Highest odd numerator or denominator: 99 Scale harmonicity : 0.024115 Average absolute harmonicity : 0.242784 Specific harmonicity : 0.109900 Fundamental : 1/168, -7.3923 octaves, 1.5573 Hz. Guide tone : 396, 8.6294 octaves, 103603.724 Hz. Exponens Consonantiae : 6.652800E+04, 16.02167 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 133.0, average 19.00000 Mersenne's string divisions : 20252610 Sum of van Prooijen's expressibility: 6.46403, average 0.92343 Sum of Tenney's harmonic distance : 12.61168, average 1.80167 Vogel's harmonic complexity : 16.00000 Wille's k value : 148 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 80.12734, average 2.86169 Lattice compactness (without 2's) : 47.16374, average 1.68442 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.85714 12 1 3: -1 .. 2 0.71429 7 3 7: -1 .. 0 -0.42857 3 11: 0 .. 1 0.42857 3 3 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 20 22| Scale is weakly epimorphic with val: <7 10 21 23| Scale is weakly epimorphic with val: <7 10 22 24| Scale is JI-epimorphic with val: <7 11 18 23| Scale is JI-epimorphic with val: <7 11 19 24| Scale is JI-epimorphic with val: <7 11 20 25| Scale is JI-epimorphic with val: <7 11 21 26| Scale is weakly epimorphic with val: <7 12 18 26| Scale is weakly epimorphic with val: <7 12 21 22| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 41.9954 c. M:-74.6508 c. Lebeng 8: 1 1 1 2 0 2 1 P D3 S SD: 42.8707 c. M:-63.5980 c. 9: 2 0 2 1 1 1 2 N T3 SD: 37.5460 c. M:-62.7567 c. 10: 2 0 2 2 1 1 2 P D3 S SD: 33.6654 c. M:-57.5080 c. 11: 2 1 2 1 1 2 2 N D3 SD: 31.4179 c. M:-47.4095 c. 12: 2 1 2 2 1 2 2 P M ME S SD: 10.3941 c. M:-17.5080 c. G.M.Hypodorian, G.M.Aeolian, G.Hyperphrygian, Natural Minor, Melodic Minor descending, Asavari That, Mela Natabhairavi, Raga Jaunpuri, Adana, Darbari, Dhanyasi, Jingla, Gregorian nr.2, Makam Buselik, Nihavend, Peruvian Minor, Se, Chiao: China, Geez, Ezel: Ethiopia, Kiourdi descending: Greece, Cushak: Armenia 17: 3 1 3 3 1 3 3 N M DE S SD: 4.4167 c. M:-7.8547 c. Seventeen-tone Natural Minor 29: 5 2 5 5 2 5 5 N M DE S SD: 3.7647 c. M:-6.7014 c. Twenty-nine tone Minor 46: 8 3 8 8 3 8 8 N M DE S SD: 3.0401 c. M:-4.9023 c. 72: 12 5 13 12 5 12 13 N T3 SD: 2.2135 c. M: 3.9100 c. 89: 15 6 16 15 6 15 16 N T3 SD: 1.2310 c. M: 2.1324 c. 101: 17 7 18 17 7 17 18 N T3 SD: 1.1291 c. M: 1.9298 c. 106: 18 7 19 18 7 18 19 N T3 SD: 0.9378 c. M: 1.4964 c. 118: 20 8 21 20 8 20 21 N T3 SD: 0.3399 c. M:-0.5588 c. 135: 23 9 24 23 9 23 24 N T3 SD: 0.2857 c. M:-0.5344 c. 253: 43 17 45 43 17 43 45 N T3 SD: 0.0931 c. M:-0.1592 c. 612: 104 41 109 104 41 104 109 N T3 SD: 0.0875 c. M: 0.1391 c. 730: 124 49 130 124 49 124 130 N T3 SD: 0.0575 c. M: 0.1007 c. 865: 147 58 154 147 58 147 154 N T3 SD: 0.0370 c. M: 0.0643 c. 983: 167 66 175 167 66 167 175 N T3 SD: 0.0249 c. M: 0.0443 c. 1118: 190 75 199 190 75 190 199 N T3 SD: 0.0153 c. M:-0.0256 c. 2101: 357 141 374 357 141 357 374 N T3 SD: 0.0082 c. M: 0.0146 c. 2354: 400 158 419 400 158 400 419 N T3 SD: 0.0034 c. M:-0.0058 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: 33.9556 cents 4 x 5 x 6 x 7:8 S SD: 25.8430 cents 5 x 6:7 x 8:9:10 S SD: 20.0539 cents 6 x 7:8:9 x 11:12 SD: 13.0736 cents 7:8 x 9 x 11:12:14 SD: 17.3729 cents 8:9 x 11:12:13:14:16 SD: 13.4527 cents 9:10:11:12 x 14:16:18 S SD: 11.5823 cents 10:11:12:13:15:16:18:20 SD: 11.3875 cents 11:12:13:15 x 17:19:22 SD: 13.7674 cents 12 x 14:16:18:19:21:24 SD: 4.6802 cents 13 x 15:17 x 20:23:26 SD: 12.3719 cents 14:16:17:19:21:22:25:28 SD: 9.7479 cents 15:17:18:20:23:24:27:30 SD: 9.6154 cents 16:18:19:21:24:25:28:32 SD: 5.1908 cents 18:20:21:24:27:28:32:36 S SD: 4.8953 cents 24:27:28:32:36:38:42:48 SD: 4.0116 cents 30:34:35:40:45:47:53:60 SD: 3.1980 cents 33:37:39:44:50:52:58:66 SD: 3.1434 cents 38:43:45:51:57:60:67:76 SD: 2.8161 cents 39:44:46:52:59:61:69:78 SD: 2.5169 cents 40:45:47:53:60:63:71:80 SD: 2.0682 cents 56:63:66:75:84:88:99:112 SD: 1.1016 cents 72:81:85:96:108:113:127:144 SD: 0.7613 cents 96:108:113:128:144:151:170:192 SD: 0.5705 cents 112:126:132:149:168:176:198:224 SD: 0.5527 cents 152:171:179:203:228:239:269:304 SD: 0.5432 cents 168:189:198:224:252:264:297:336 SD: 0.0000 cents