Scala analysis: xen09-chalmers-tritriadic-34-42-51
Tritriadic scale built from 34:42:51
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: 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: 9/8 203.9100 major whole tone 2: 56/51 161.9155 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 : 203.9 365.8 498.0 702.0 863.9 1067.8 1200.0 203.9 : 161.9 294.1 498.0 660.0 863.9 996.1 1200.0 365.8 : 132.2 336.1 498.0 702.0 834.2 1038.1 1200.0 498.0 : 203.9 365.8 569.7 702.0 905.9 1067.8 1200.0 702.0 : 161.9 365.8 498.0 702.0 863.9 996.1 1200.0 863.9 : 203.9 336.1 540.0 702.0 834.2 1038.1 1200.0 1067.8: 132.2 336.1 498.0 630.3 834.2 996.1 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 : 174.02537 cents, oct.: 1218.17757 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : LMSLMLS 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 0.0 365.825 701.955 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 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 : 0.018725 Average absolute harmonicity : 0.239315 Specific harmonicity : 0.084725 Fundamental : 1/408, -8.6724 octaves, 0.6412 Hz. Guide tone : 252, 7.9773 octaves, 65929.642 Hz. Exponens Consonantiae : 1.028160E+05, 16.64971 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 106.0, average 15.14286 Mersenne's string divisions : 19738530 Sum of van Prooijen's expressibility: 6.26049, average 0.89436 Sum of Tenney's harmonic distance : 12.57679, average 1.79668 Vogel's harmonic complexity : 20.85714 Wille's k value : 229 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 76.80430, average 2.74301 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 0.00000 10 1 3: -1 .. 2 0.71429 7 3 7: 0 .. 1 0.42857 3 17: -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 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: 22.9681 c. M: 39.2091 c. Lebeng 10: 2 1 1 2 1 2 1 P M ME S SD: 19.6643 c. M:-36.0900 c. Sethares Neutral, Beatles-7, Dichotic-7 12: 2 2 1 2 2 2 1 P M ME S SD: 22.4699 c. M:-36.1295 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 2 2 3 2 3 2 SP M ME S SD: 9.4219 c. M: 16.8117 c. Beatles-7, Dichotic-7 24: 4 3 3 4 3 4 3 SP M ME S SD: 10.5689 c. M: 17.7805 c. Neutral Lydian, Iced Major 26: 4 4 3 4 4 4 3 SP M ME S SD: 10.5516 c. M: 19.2946 c. Twenty-six tone Major 29: 5 4 3 5 4 5 3 SP T3 SD: 4.5990 c. M:-8.0816 c. Twenty-nine tone "Just" Major 36: 6 5 4 6 5 6 4 SP T3 SD: 2.1613 c. M: 3.9100 c. 53: 9 7 6 9 7 9 6 SP T3 SD: 2.3326 c. M: 3.6296 c. 65: 11 9 7 11 9 11 7 SP T3 SD: 2.2733 c. M:-3.8218 c. 82: 14 11 9 14 11 14 9 SP T3 SD: 0.5178 c. M:-0.9680 c. 118: 20 16 13 20 16 20 13 SP T3 SD: 0.3317 c. M:-0.5363 c. 200: 34 27 22 34 27 34 22 SP T3 SD: 0.1240 c. M:-0.2195 c. 571: 97 77 63 97 77 97 63 SP T3 SD: 0.1036 c. M: 0.1798 c. 653: 111 88 72 111 88 111 72 SP T3 SD: 0.0926 c. M: 0.1645 c. 689: 117 93 76 117 93 117 76 SP T3 SD: 0.0890 c. M: 0.1462 c. 771: 131 104 85 131 104 131 85 SP T3 SD: 0.0449 c. M: 0.0762 c. 971: 165 131 107 165 131 165 107 SP T3 SD: 0.0113 c. M: 0.0188 c. 2142: 364 289 236 364 289 364 236 SP 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: 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 6:7 x 8:9:10:11:12 S SD: 11.4541 cents 7:8 x 9:11:12:13:14 SD: 21.0856 cents 8:9:10:11:12:13:15:16 SD: 9.2829 cents 14:16:17:19:21:23:26:28 SD: 7.2830 cents 16:18:20:21:24:26:30:32 SD: 6.5897 cents 18:20:22:24:27:30:33:36 S SD: 5.6437 cents 22:25:27:29:33:36:41:44 SD: 4.6245 cents 26:29:32:35:39:43:48:52 SD: 3.5763 cents 30:34:37:40:45:49:56:60 SD: 3.3318 cents 34:38:42:45:51:56:63:68 SD: 2.4416 cents 42:47:52:56:63:69:78:84 SD: 1.6577 cents 48:54:59:64:72:79:89:96 SD: 1.2542 cents 72:81:89:96:108:119:133:144 SD: 1.1602 cents 80:90:99:107:120:132:148:160 SD: 1.0673 cents 88:99:109:117:132:145:163:176 SD: 0.9796 cents 90:101:111:120:135:148:167:180 SD: 0.8967 cents 96:108:119:128:144:158:178:192 SD: 0.8919 cents 102:115:126:136:153:168:189:204 SD: 0.5382 cents 136:153:168:181:204:224:252:272 SD: 0.4550 cents 144:162:178:192:216:237:267:288 SD: 0.2956 cents 216:243:267:288:324:356:400:432 SD: 0.2732 cents 264:297:326:352:396:435:489:528 SD: 0.1612 cents 408:459:504:544:612:672:756:816 SD: 0.0000 cents