Scala analysis: xen09-chalmers-tritriadic-14-17-21
Tritriadic scale built from 14:17:21
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: 17/14 336.129503 supraminor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 34/21 834.174502 supraminor sixth 6: 51/28 1038.084504 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 56/51 161.9155 1: 9/8 203.9100 major whole tone 2: 68/63 132.2195 supraminor second 3: 56/51 161.9155 4: 9/8 203.9100 major whole tone 5: 68/63 132.2195 supraminor second 6: 9/8 203.9100 major whole tone 7: 56/51 161.9155
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 : 203.9 336.1 498.0 702.0 834.2 1038.1 1200.0 203.9 : 132.2 294.1 498.0 630.3 834.2 996.1 1200.0 336.1 : 161.9 365.8 498.0 702.0 863.9 1067.8 1200.0 498.0 : 203.9 336.1 540.0 702.0 905.9 1038.1 1200.0 702.0 : 132.2 336.1 498.0 702.0 834.2 996.1 1200.0 834.2 : 203.9 365.8 569.7 702.0 863.9 1067.8 1200.0 1038.1: 161.9 365.8 498.0 660.0 863.9 996.1 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 : 171.26788 cents, oct.: 1198.87518 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : LSMLSLM 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 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: 51 Scale harmonicity : 0.018725 Average absolute harmonicity : 0.239434 Specific harmonicity : 0.084912 Fundamental : 1/168, -7.3923 octaves, 1.5573 Hz. Guide tone : 612, 9.2574 octaves, 160114.846 Hz. Exponens Consonantiae : 1.028160E+05, 16.64971 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 98.5, average 14.07143 Mersenne's string divisions : 48086115 Sum of van Prooijen's expressibility: 6.16872, average 0.88125 Sum of Tenney's harmonic distance : 12.40070, average 1.77153 Vogel's harmonic complexity : 17.71429 Wille's k value : 94 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 76.20148, average 2.72148 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 -0.42857 11 1 3: -1 .. 2 0.28571 6 3 7: -1 .. 0 -0.42857 3 17: 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 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: 17.9120 c. M: 32.4814 c. Lebeng 17: 3 2 2 3 2 3 2 SP M ME S SD: 11.7795 c. M:-20.7390 c. Beatles-7, Dichotic-7 22: 4 2 3 4 2 4 3 P T3 SD: 9.5820 c. M: 15.9927 c. Twenty-two tone Natural Minor 24: 4 3 3 4 3 4 3 SP M ME S SD: 9.3178 c. M:-15.8255 c. Neutral Lydian, Iced Major 29: 5 3 4 5 3 5 4 SP T3 SD: 3.6978 c. M: 6.5883 c. Twenty-nine tone Natural Minor 36: 6 4 5 6 4 6 5 SP T3 SD: 2.7783 c. M: 4.7512 c. 53: 9 6 7 9 6 9 7 SP T3 SD: 2.2880 c. M:-3.5613 c. 75: 13 8 10 13 8 13 10 SP T3 SD: 2.1878 c. M:-4.0900 c. 82: 14 9 11 14 9 14 11 SP T3 SD: 0.5973 c. M:-0.9680 c. 118: 20 13 16 20 13 20 16 SP T3 SD: 0.4478 c. M: 0.7964 c. 200: 34 22 27 34 22 34 27 SP T3 SD: 0.0975 c. M: 0.1745 c. 571: 97 63 77 97 63 97 77 SP T3 SD: 0.0859 c. M:-0.1512 c. 689: 117 76 93 117 76 117 93 SP T3 SD: 0.0732 c. M: 0.1364 c. 771: 131 85 104 131 85 131 104 SP T3 SD: 0.0388 c. M:-0.0667 c. 971: 165 107 131 165 107 165 131 SP T3 SD: 0.0124 c. M:-0.0205 c. 1171: 199 129 158 199 129 199 158 SP T3 SD: 0.0107 c. M:-0.0183 c. 2142: 364 236 289 364 236 364 289 SP T3 SD: 0.0070 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: 16.7281 cents 4 x 5 x 6 x 7:8 S SD: 21.3822 cents 5 x 6:7 x 8:9:10 S SD: 18.3238 cents 6:7 x 8:9:10:11:12 S SD: 13.5500 cents 7:8 x 9 x 11:13:14 SD: 18.4484 cents 8:9:10:11:12:13:15:16 SD: 12.7097 cents 10:11:12:13:15:16:18:20 SD: 9.7877 cents 14:16:17:19:21:23:26:28 SD: 8.3924 cents 15:17:18:20:23:24:27:30 SD: 7.6537 cents 16:18:19:21:24:26:29:32 SD: 6.9213 cents 18:20:22:24:27:29:33:36 SD: 4.0135 cents 24:27:29:32:36:39:44:48 SD: 2.2129 cents 42:47:51:56:63:68:77:84 SD: 2.0778 cents 48:54:58:64:72:78:87:96 SD: 1.9437 cents 56:63:68:75:84:91:102:112 SD: 1.4274 cents 66:74:80:88:99:107:120:132 SD: 1.0929 cents 90:101:109:120:135:146:164:180 SD: 1.0195 cents 102:115:124:136:153:165:186:204 SD: 0.7057 cents 126:142:153:168:189:204:230:252 SD: 0.6925 cents 136:153:165:181:204:220:248:272 SD: 0.6164 cents 144:162:175:192:216:233:262:288 SD: 0.3694 cents 168:189:204:224:252:272:306:336 SD: 0.0000 cents