Scala analysis: xen12-chalmers-tritriadic-dm-17-21-7
Tritriadic D->M scale built from 17:21:7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 56/51 161.915496 2: 21/17 365.825498 submajor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 28/17 863.870497 submajor sixth 6: 63/34 1067.780499 submajor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 68/63 132.2195 supraminor second 1: 56/51 161.9155 2: 9/8 203.9100 major whole tone 3: 68/63 132.2195 supraminor second 4: 9/8 203.9100 major whole tone 5: 56/51 161.9155 6: 9/8 203.9100 major whole tone 7: 68/63 132.2195 supraminor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 68/63 132.220 cents supraminor second 1: 2 56/51 161.915 cents 1: 3 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 17/14 336.130 cents supraminor third 2: 3 21/17 365.825 cents submajor third 3: 5 4/3 498.045 cents perfect fourth 3: 1 153/112 540.040 cents 3: 1 189/136 569.735 cents 4: 1 272/189 630.265 cents 4: 1 224/153 659.960 cents 4: 5 3/2 701.955 cents perfect fifth 5: 3 34/21 834.175 cents supraminor sixth 5: 3 28/17 863.870 cents submajor sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 51/28 1038.085 cents 6: 2 63/34 1067.780 cents submajor 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 : 161.9 365.8 498.0 702.0 863.9 1067.8 1200.0 161.9 : 203.9 336.1 540.0 702.0 905.9 1038.1 1200.0 365.8 : 132.2 336.1 498.0 702.0 834.2 996.1 1200.0 498.0 : 203.9 365.8 569.7 702.0 863.9 1067.8 1200.0 702.0 : 161.9 365.8 498.0 660.0 863.9 996.1 1200.0 863.9 : 203.9 336.1 498.0 702.0 834.2 1038.1 1200.0 1067.8: 132.2 294.1 498.0 630.3 834.2 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 132.2195 .. 203.9100 cents 567/544, 71.6905 cents 68/63, 132.2195 cents 2: 294.1350 .. 365.8255 cents 567/544, 71.6905 cents 256/243, 90.2250 cents 3: 498.0450 .. 569.7355 cents 567/544, 71.6905 cents 68/63, 132.2195 cents 4: 630.2645 .. 701.9550 cents 567/544, 71.6905 cents 36992/35721, 60.5290 cents 5: 834.1745 .. 905.8650 cents 567/544, 71.6905 cents 68/63, 132.2195 cents 6: 996.0900 .. 1067.7805 cents 567/544, 71.6905 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 68/63, 132.2195 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.296545 Largest / Average step : 1.189475 Largest / Smallest step : 1.542208 Median interval of one step : 56/51, 161.9155 cents, amount: 2 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 173.72541 cents, oct.: 1216.07785 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCBABC Step pattern size order : MLSLMLS Scale is a Constant Structure, by a margin of 60.52900 cents Scale diversity : 1.341977 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.641547 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 : 294/289, 29.6960 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 336.130 701.955 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 Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords 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 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 17 Odd number limit : 189 (O: 189 U: 189) Highest odd numerator or denominator: 63 Scale harmonicity : 0.019083 Average absolute harmonicity : 0.225273 Specific harmonicity : 0.081309 Fundamental : 1/102, -6.6724 octaves, 2.5650 Hz. Guide tone : 504, 8.9773 octaves, 131859.285 Hz. Exponens Consonantiae : 5.140800E+04, 15.64971 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 151.0, average 21.57143 Mersenne's string divisions : 124236630 Sum of van Prooijen's expressibility: 7.01382, average 1.00197 Sum of Tenney's harmonic distance : 14.17522, average 2.02503 Vogel's harmonic complexity : 17.00000 Wille's k value : 94 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 71.73032, average 2.56180 Lattice compactness (without 2's) : 46.89579, average 1.67485 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 0.85714 10 1 3: -1 .. 2 0.28571 6 2 7: 0 .. 1 0.57143 4 17: -1 .. 0 -0.57143 4 4 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is weakly epimorphic with val: <7 10 18 30| Scale is weakly epimorphic with val: <7 10 19 31| Scale is weakly epimorphic with val: <7 10 20 32| Scale is weakly epimorphic with val: <7 10 21 26| Scale is weakly epimorphic with val: <7 10 22 27| Scale is JI-epimorphic with val: <7 11 18 27| Scale is JI-epimorphic with val: <7 11 19 28| Scale is JI-epimorphic with val: <7 11 20 29| = patent Scale is JI-epimorphic with val: <7 11 21 30| Scale is JI-epimorphic with val: <7 11 22 31| Scale is weakly epimorphic with val: <7 12 18 31| Scale is weakly epimorphic with val: <7 12 19 32| Scale is weakly epimorphic with val: <7 12 20 26| Scale is weakly epimorphic with val: <7 12 21 27| Scale is weakly epimorphic with val: <7 12 22 28|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 19.7418 c. M: 39.2091 c. Lebeng 12: 2 2 1 2 2 2 1 P M ME S SD: 26.6442 c. M:-38.0845 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 15: 2 3 1 3 2 2 2 SP D3 S SD: 20.1945 c. M:-34.1745 c. 17: 2 3 2 3 2 3 2 SP M ME I SD: 11.8913 c. M: 20.7390 c. Neutral Dorian, Maqamic-7 22: 3 4 2 4 3 4 2 P T3 SD: 11.7955 c. M:-23.1286 c. Raga Jogiya 24: 3 4 3 4 3 4 3 SP M ME I SD: 11.3930 c. M: 17.7805 c. Neutral Dorian, Misaelides 2nd Byzantine mode, Iced Fridgian, Maqam Sikah Baladi, Maqamic-7 27: 4 4 3 5 3 5 3 SP D3 S SD: 11.3601 c. M: 19.4261 c. 29: 4 5 3 5 4 5 3 SP T3 SD: 4.6615 c. M:-8.0816 c. 36: 5 6 4 6 5 6 4 SP T3 SD: 2.3900 c. M:-4.7512 c. 53: 7 9 6 9 7 9 6 SP T3 SD: 2.6672 c. M: 3.6296 c. 75: 10 13 8 13 10 13 8 SP T3 SD: 2.2227 c. M:-4.2195 c. 82: 11 14 9 14 11 14 9 SP T3 SD: 0.5103 c. M: 0.9399 c. 118: 16 20 13 20 16 20 13 SP T3 SD: 0.4024 c. M:-0.7964 c. 200: 27 34 22 34 27 34 22 SP T3 SD: 0.1234 c. M:-0.2195 c. 571: 77 97 63 97 77 97 63 SP T3 SD: 0.1074 c. M: 0.1798 c. 689: 93 117 76 117 93 117 76 SP T3 SD: 0.0759 c. M: 0.1462 c. 771: 104 131 85 131 104 131 85 SP T3 SD: 0.0478 c. M: 0.0762 c. 889: 120 151 98 151 120 151 98 SP T3 SD: 0.0427 c. M:-0.0643 c. 971: 131 165 107 165 131 165 107 SP T3 SD: 0.0137 c. M: 0.0205 c. 1171: 158 199 129 199 158 199 129 SP T3 SD: 0.0124 c. M:-0.0248 c. 2142: 289 364 236 364 289 364 236 SP T3 SD: 0.0060 c. M: 0.0107 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: 6.8294 cents 4 x 5 x 6 x 7:8 S SD: 25.2633 cents 5 x 6:7 x 8:9:10 S SD: 24.2405 cents 6 x 7:8:9:10:11:12 S SD: 17.1197 cents 7:8 x 9:11:12:13:14 SD: 23.6051 cents 8:9:10:11:12:13:15:16 SD: 11.0527 cents 12:13:15:16:18:20:22:24 SD: 5.9309 cents 18:20:22:24:27:30:33:36 S SD: 5.5658 cents 20:22:25:27:30:33:37:40 SD: 4.3069 cents 22:24:27:29:33:36:41:44 SD: 4.2194 cents 30:33:37:40:45:49:56:60 SD: 2.8220 cents 39:43:48:52:59:64:72:78 SD: 2.8171 cents 40:44:49:53:60:66:74:80 SD: 2.6891 cents 42:46:52:56:63:69:78:84 SD: 1.1940 cents 60:66:74:80:90:99:111:120 SD: 0.8355 cents 90:99:111:120:135:148:167:180 SD: 0.7906 cents 102:112:126:136:153:168:189:204 SD: 0.0000 cents