Scala analysis: xen09-chalmers-tritriadic-26-33-39
Tritriadic scale built from 26:33:39
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: 33/26 412.745281 tridecimal major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 22/13 910.790281 tridecimal major sixth 6: 99/52 1114.700282 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 104/99 85.2997 1: 9/8 203.9100 major whole tone 2: 44/39 208.8353 3: 104/99 85.2997 4: 9/8 203.9100 major whole tone 5: 44/39 208.8353 6: 9/8 203.9100 major whole tone 7: 104/99 85.2997
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 : 203.9 412.7 498.0 702.0 910.8 1114.7 1200.0 203.9 : 208.8 294.1 498.0 706.9 910.8 996.1 1200.0 412.7 : 85.3 289.2 498.0 702.0 787.3 991.2 1200.0 498.0 : 203.9 412.7 616.7 702.0 905.9 1114.7 1200.0 702.0 : 208.8 412.7 498.0 702.0 910.8 996.1 1200.0 910.8 : 203.9 289.2 493.1 702.0 787.3 991.2 1200.0 1114.7: 85.3 289.2 498.0 583.3 787.3 996.1 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 : 178.38220 cents, oct.: 1248.67543 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : MLSMLMS 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 0.0 412.745 701.955 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: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 297 (O: 297 U: 297) Highest odd numerator or denominator: 99 Scale harmonicity : 0.018749 Average absolute harmonicity : 0.239272 Specific harmonicity : 0.084726 Fundamental : 1/312, -8.2854 octaves, 0.8385 Hz. Guide tone : 396, 8.6294 octaves, 103603.724 Hz. Exponens Consonantiae : 1.235520E+05, 16.91476 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 138.5, average 19.78571 Mersenne's string divisions : 15902565 Sum of van Prooijen's expressibility: 6.53658, average 0.93380 Sum of Tenney's harmonic distance : 13.11719, average 1.87388 Vogel's harmonic complexity : 19.85714 Wille's k value : 175 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 76.33125, average 2.72612 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 -0.42857 11 1 3: -1 .. 2 0.71429 7 3 11: 0 .. 1 0.42857 3 13: -1 .. 0 -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 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: 48.9360 c. M: 86.1289 c. Lebeng 9: 2 1 1 1 2 1 1 P M ME S SD: 36.6583 c. M:-62.7567 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 34.5615 c. M: 52.7453 c. Pseudo Rast 11: 2 2 1 1 2 2 1 P D3 S SD: 32.2305 c. M:-47.4095 c. 12: 2 2 1 2 2 2 1 P M ME S SD: 8.6015 c. M: 14.7003 c. G.Lydian, M.Ionian, M.Hypolydian, Major, Bilaval That, Mela Shankarabharanam, Raga Atana, Ghana Heptatonic, Peruvian Major, Matzore, Rast ascending: Greece, 4th plagal Byzantine, Ararai: Ethiopia, Makam Cargah, Ajam Ashiran, Dastgah-e Mahur, Dastgah-e Rast Panjgah, Xin: China, DS2, Heptatonia prima 17: 3 3 1 3 3 3 1 N M DE S SD: 8.2140 c. M:-14.7115 c. Seventeen-tone Major 29: 5 5 2 5 5 5 2 N M DE S SD: 1.7375 c. M:-2.9865 c. Twenty-nine tone Major 70: 12 12 5 12 12 12 5 N M DE S SD: 1.2935 c. M: 2.2189 c. 99: 17 17 7 17 17 17 7 N M DE S SD: 1.2200 c. M:-2.1506 c. 125: 21 22 9 21 22 21 9 N T3 SD: 1.2353 c. M: 2.3100 c. 142: 24 25 10 24 25 24 10 N T3 SD: 1.0536 c. M:-1.8858 c. 154: 26 27 11 26 27 26 11 N T3 SD: 0.7192 c. M: 1.3126 c. 183: 31 32 13 31 32 31 13 N T3 SD: 0.4152 c. M:-0.6851 c. 212: 36 37 15 36 37 36 15 N T3 SD: 0.3113 c. M:-0.5305 c. 224: 38 39 16 38 39 38 16 N T3 SD: 0.2419 c. M: 0.4146 c. 253: 43 44 18 43 44 43 18 N T3 SD: 0.0675 c. M: 0.1183 c. 718: 122 125 51 122 125 122 51 N T3 SD: 0.0449 c. M:-0.0732 c. 971: 165 169 69 165 169 165 69 N T3 SD: 0.0165 c. M:-0.0268 c. 1224: 208 213 87 208 213 208 87 N T3 SD: 0.0062 c. M:-0.0116 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: 8.8105 cents 4 x 5 x 6:7 x 8 S SD: 15.9428 cents 5 x 6:7 x 8 x 10 S SD: 40.3059 cents 6:7 x 8:9:10:11:12 S SD: 15.7513 cents 7:8:9 x 11:12:13:14 SD: 16.7303 cents 8:9:10:11:12:14:15:16 S SD: 12.4568 cents 10:11:13 x 15:17:19:20 SD: 9.5847 cents 13:15 x 17:20:22:25:26 SD: 12.1051 cents 14:16:18:19:21:24:27:28 SD: 8.0551 cents 15:17:19:20:23:25:29:30 SD: 7.8636 cents 16:18:20:21:24:27:30:32 S SD: 6.6468 cents 18:20:23:24:27:30:34:36 SD: 5.5007 cents 22:25:28:29:33:37:42:44 SD: 4.1783 cents 26:29:33:35:39:44:50:52 SD: 4.0357 cents 30:34:38:40:45:51:57:60 SD: 2.2561 cents 42:47:53:56:63:71:80:84 SD: 1.9639 cents 48:54:61:64:72:81:91:96 SD: 1.2963 cents 72:81:91:96:108:122:137:144 SD: 1.0976 cents 78:88:99:104:117:132:149:156 SD: 1.0891 cents 90:101:114:120:135:152:171:180 SD: 1.0603 cents 96:108:122:128:144:162:183:192 SD: 0.8306 cents 104:117:132:139:156:176:198:208 SD: 0.5938 cents 126:142:160:168:189:213:240:252 SD: 0.5385 cents 144:162:183:192:216:244:274:288 SD: 0.4627 cents 168:189:213:224:252:284:320:336 SD: 0.3970 cents 186:209:236:248:279:315:354:372 SD: 0.3650 cents 208:234:264:277:312:352:396:416 SD: 0.2974 cents 264:297:335:352:396:447:503:528 SD: 0.2352 cents 312:351:396:416:468:528:594:624 SD: 0.0000 cents