Scala analysis: xen09-chalmers-tritriadic-22-26-33
Tritriadic scale built from 22:26:33
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: 13/11 289.209719 tridecimal minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 52/33 787.254719 tridecimal minor sixth 6: 39/22 991.164720 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 44/39 208.8353 1: 9/8 203.9100 major whole tone 2: 104/99 85.2997 3: 44/39 208.8353 4: 9/8 203.9100 major whole tone 5: 104/99 85.2997 6: 9/8 203.9100 major whole tone 7: 44/39 208.8353
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 104/99 85.300 cents 1: 3 9/8 203.910 cents major whole tone 1: 2 44/39 208.835 cents 2: 3 13/11 289.210 cents tridecimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 33/26 412.745 cents tridecimal major third 3: 1 117/88 493.120 cents tridecimal gentle fourth 3: 5 4/3 498.045 cents perfect fourth 3: 1 297/208 616.655 cents 4: 1 416/297 583.345 cents 4: 5 3/2 701.955 cents perfect fifth 4: 1 176/117 706.880 cents 5: 3 52/33 787.255 cents tridecimal minor sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 3 22/13 910.790 cents tridecimal major sixth 6: 2 39/22 991.165 cents 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 99/52 1114.700 cents 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 : 203.9 289.2 498.0 702.0 787.3 991.2 1200.0 203.9 : 85.3 294.1 498.0 583.3 787.3 996.1 1200.0 289.2 : 208.8 412.7 498.0 702.0 910.8 1114.7 1200.0 498.0 : 203.9 289.2 493.1 702.0 905.9 991.2 1200.0 702.0 : 85.3 289.2 498.0 702.0 787.3 996.1 1200.0 787.3 : 203.9 412.7 616.7 702.0 910.8 1114.7 1200.0 991.2 : 208.8 412.7 498.0 706.9 910.8 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 85.2997 .. 208.8353 cents 363/338, 123.5356 cents 104/99, 85.2997 cents 2: 289.2097 .. 412.7453 cents 363/338, 123.5356 cents 507/484, 80.3744 cents 3: 493.1197 .. 616.6553 cents 363/338, 123.5356 cents 507/484, 80.3744 cents 4: 583.3447 .. 706.8803 cents 363/338, 123.5356 cents 86528/88209,-33.3106 cents 5: 787.2547 .. 910.7903 cents 363/338, 123.5356 cents 507/484, 80.3744 cents 6: 991.1647 .. 1114.7003 cents 363/338, 123.5356 cents 507/484, 80.3744 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 104/99, 85.2997 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 44/39, 208.8353 cents Average / Smallest step : 2.009720 Largest / Average step : 1.218206 Largest / Smallest step : 2.448253 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 : 166.91105 cents, oct.: 1168.37732 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : MSLMSML Scale is a Constant Structure, by a margin of 33.31057 cents Scale diversity : 1.310278 Lumma stability : 0.410081 Lumma impropriety factor : 0.027759 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 : 352/351, 4.9253 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 289.210 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 6, average 702.7759 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 123.5356 cents: 6 -- Rational properties -- Prime limit : 13 Odd number limit : 297 (O: 297 U: 297) Highest odd numerator or denominator: 39 Scale harmonicity : 0.018749 Average absolute harmonicity : 0.239536 Specific harmonicity : 0.085140 Fundamental : 1/264, -8.0444 octaves, 0.9910 Hz. Guide tone : 468, 8.8704 octaves, 122440.765 Hz. Exponens Consonantiae : 1.235520E+05, 16.91476 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 101.0, average 14.42857 Mersenne's string divisions : 871080 Sum of van Prooijen's expressibility: 6.13201, average 0.87600 Sum of Tenney's harmonic distance : 12.33904, average 1.76272 Vogel's harmonic complexity : 18.71429 Wille's k value : 148 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 75.48330, average 2.69583 Lattice compactness (without 2's) : 46.44630, average 1.65880 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 0.00000 10 1 3: -1 .. 2 0.28571 6 3 11: -1 .. 0 -0.42857 3 13: 0 .. 1 0.42857 3 3 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 22 27| Scale is weakly epimorphic with val: <7 10 23 28| Scale is weakly epimorphic with val: <7 10 24 29| Scale is JI-epimorphic with val: <7 11 22 24| Scale is JI-epimorphic with val: <7 11 23 25| Scale is JI-epimorphic with val: <7 11 24 26| = patent Scale is JI-epimorphic with val: <7 11 25 27| Scale is JI-epimorphic with val: <7 11 26 28| Scale is weakly epimorphic with val: <7 12 22 28| Scale is weakly epimorphic with val: <7 12 23 29|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 39.1777 c. M:-69.8881 c. Lebeng 9: 2 0 2 1 1 1 2 N T3 SD: 38.6265 c. M:-62.7567 c. 11: 2 1 2 1 1 2 2 N D3 SD: 31.1517 c. M:-47.4095 c. 12: 2 1 2 2 1 2 2 P M ME S SD: 7.3666 c. M:-12.7453 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: 6.1463 c. M: 10.7841 c. Seventeen-tone Natural Minor 29: 5 2 5 5 2 5 5 N M DE S SD: 1.6228 c. M:-2.9865 c. Twenty-nine tone Minor 70: 12 5 12 12 5 12 12 N M DE S SD: 1.7436 c. M:-3.1210 c. 99: 17 7 17 17 7 17 17 N M DE S SD: 1.5997 c. M:-2.7747 c. 125: 21 9 22 21 9 21 22 N T3 SD: 1.4669 c. M: 2.3647 c. 137: 23 10 24 23 10 23 24 N T3 SD: 1.3138 c. M: 2.4501 c. 142: 24 10 25 24 10 24 25 N T3 SD: 1.3658 c. M: 2.4323 c. 154: 26 11 27 26 11 26 27 N T3 SD: 0.9154 c. M: 1.5543 c. 166: 28 12 29 28 12 28 29 N T3 SD: 0.8027 c. M: 1.5004 c. 183: 31 13 32 31 13 31 32 N T3 SD: 0.5613 c. M: 1.0008 c. 195: 33 14 34 33 14 33 34 N T3 SD: 0.4455 c. M: 0.8331 c. 212: 36 15 37 36 15 36 37 N T3 SD: 0.3548 c. M: 0.5987 c. 224: 38 16 39 38 16 38 39 N T3 SD: 0.1877 c. M: 0.3386 c. 253: 43 18 44 43 18 43 44 N T3 SD: 0.0807 c. M:-0.1396 c. 718: 122 51 125 122 51 122 125 N T3 SD: 0.0483 c. M: 0.0784 c. 971: 165 69 169 165 69 165 169 N T3 SD: 0.0154 c. M: 0.0251 c. 1224: 208 87 213 208 87 208 213 N T3 SD: 0.0073 c. M:-0.0118 c. 2195: 373 156 382 373 156 373 382 N T3 SD: 0.0063 c. M: 0.0110 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: 32.3680 cents 4 x 5 x 6 x 7:8 S SD: 24.9101 cents 5 x 6:7 x 8:9:10 S SD: 19.2152 cents 6 x 7:8:9 x 11:12 SD: 12.4676 cents 7:8 x 9 x 11:12:14 SD: 17.9980 cents 8:9 x 11:12:13:14:16 SD: 13.0969 cents 9:10:11:12 x 14:16:18 S SD: 11.0212 cents 10:11:12:13:15:16:18:20 SD: 10.6241 cents 11:12:13:15 x 17:20:22 SD: 14.3401 cents 12 x 14:16:18:19:21:24 SD: 5.4441 cents 13 x 15:17 x 20:23:26 SD: 13.5368 cents 14:16:17:19:21:22:25:28 SD: 9.1094 cents 15:17:18:20:23:24:27:30 SD: 8.6979 cents 16:18:19:21:24:25:28:32 SD: 5.5792 cents 18:20:21:24:27:28:32:36 S SD: 5.5048 cents 22:25:26:29:33:35:39:44 SD: 4.4462 cents 24:27:28:32:36:38:43:48 SD: 4.3011 cents 26:29:31:35:39:41:46:52 SD: 3.8931 cents 32:36:38:43:48:50:57:64 SD: 3.2992 cents 38:43:45:51:57:60:67:76 SD: 2.6462 cents 40:45:47:53:60:63:71:80 SD: 2.1370 cents 48:54:57:64:72:76:85:96 SD: 1.6982 cents 54:61:64:72:81:85:96:108 SD: 1.4463 cents 66:74:78:88:99:104:117:132 SD: 0.8341 cents 104:117:123:139:156:164:184:208 SD: 0.8111 cents 120:135:142:160:180:189:213:240 SD: 0.4636 cents 144:162:170:192:216:227:255:288 SD: 0.3868 cents 198:223:234:264:297:312:351:396 SD: 0.2774 cents 264:297:312:352:396:416:468:528 SD: 0.0000 cents