Scala analysis: xen12-chalmers-tritriadic-dm-1-7-17
Tritriadic D->M scale built from 1:7:17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/16 104.955410 17th harmonic 2: 17/14 336.129503 supraminor third 3: 289/224 441.084913 4: 49/34 632.696403 5: 28/17 863.870497 submajor sixth 6: 7/4 968.825906 harmonic seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 17/16 104.9554 17th harmonic 2: 8/7 231.1741 septimal whole tone 3: 17/16 104.9554 17th harmonic 4: 5488/4913 191.6115 5: 8/7 231.1741 septimal whole tone 6: 17/16 104.9554 17th harmonic 7: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 17/16 104.955 cents 17th harmonic 1: 1 5488/4913 191.611 cents 1: 3 8/7 231.174 cents septimal whole tone 2: 1 343/289 296.567 cents 2: 5 17/14 336.130 cents supraminor third 2: 1 6272/4913 422.786 cents 3: 2 289/224 441.085 cents 3: 3 392/289 527.741 cents 3: 2 68/49 567.304 cents 4: 2 49/34 632.696 cents 4: 3 289/196 672.259 cents two (supraminor third) 4: 2 448/289 758.915 cents 5: 1 4913/3136 777.214 cents 5: 5 28/17 863.870 cents submajor sixth 5: 1 578/343 903.433 cents 6: 3 7/4 968.826 cents harmonic seventh 6: 1 4913/2744 1008.389 cents 6: 3 32/17 1095.045 cents 17th subharmonic 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 : 105.0 336.1 441.1 632.7 863.9 968.8 1200.0 105.0 : 231.2 336.1 527.7 758.9 863.9 1095.0 1200.0 336.1 : 105.0 296.6 527.7 632.7 863.9 968.8 1200.0 441.1 : 191.6 422.8 527.7 758.9 863.9 1095.0 1200.0 632.7 : 231.2 336.1 567.3 672.3 903.4 1008.4 1200.0 863.9 : 105.0 336.1 441.1 672.3 777.2 968.8 1200.0 968.8 : 231.2 336.1 567.3 672.3 863.9 1095.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 104.9554 .. 231.1741 cents 128/119, 126.2187 cents 17/16, 104.9554 cents 2: 296.5669 .. 422.7856 cents 128/119, 126.2187 cents 2401/2312, 65.3928 cents 3: 441.0849 .. 567.3036 cents 128/119, 126.2187 cents 1419857/1404928, 18.2993 cents 4: 632.6964 .. 758.9151 cents 128/119, 126.2187 cents 2401/2312, 65.3928 cents 5: 777.2144 .. 903.4331 cents 128/119, 126.2187 cents 1419857/1404928, 18.2993 cents 6: 968.8259 .. 1095.0446 cents 128/119, 126.2187 cents 2401/2312, 65.3928 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 17/16, 104.9554 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 1.633347 Largest / Average step : 1.348516 Largest / Smallest step : 2.202593 Median interval of one step : 5488/4913, 191.6115 cents, amount: 1 Least squares average step : 165.45402 cents, oct.: 1158.17813 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACBAB Step pattern size order : SLSMLSL Scale is a Constant Structure, by a margin of 18.29933 cents Scale diversity : 1.424963 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.368907 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 : 1419857/1404928, 18.2993 cents Most common intervals : 17/14, 336.1295 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 231.174 336.130 cents Most common triad is 0.0 336.130 863.870 cents, amount: 3 Number of recognisable fifths : 0 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 : 7 17 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 n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 17 Odd number limit : 4913 (O: 4913 U: 4913) Highest odd numerator or denominator: 289 Scale harmonicity : 0.007800 Average absolute harmonicity : 0.170147 Specific harmonicity : 0.044025 Fundamental : 1/3808, -11.8948 octaves, 0.0687 Hz. Guide tone : 56644, 15.7896 octaves, 14819518.521 Hz. Exponens Consonantiae : 2.157004E+08, 27.68445 octaves Euler's gradus suavitatis : 74 Sum of Mann's harmonic distance : 359.5, average 51.35714 Mersenne's string divisions : 72597195 Sum of van Prooijen's expressibility: 8.68754, average 1.24108 Sum of Tenney's harmonic distance : 17.26976, average 2.46711 Vogel's harmonic complexity : 34.42857 Wille's k value : 2456 Wilson's harmonic complexity : 72 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 100.33019, average 3.58322 Lattice compactness (without 2's) : 51.25493, average 1.83053 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.42857 16 1 7: -1 .. 2 0.28571 6 1 17: -1 .. 2 0.28571 6 5 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 18 31| Scale is weakly epimorphic with val: <7 19 30| Scale is JI-epimorphic with val: <7 20 29| = patent Scale is weakly epimorphic with val: <7 22 27|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 48.1782 c. M:-73.2008 c. Lebeng 8: 1 1 1 1 2 0 2 P D3 S SD: 38.7763 c. M: 68.8259 c. 10: 1 2 1 1 2 1 2 P M ME S SD: 23.9859 c. M:-38.9151 c. 11: 1 2 1 2 2 1 2 P M ME S SD: 10.9705 c. M:-21.8491 c. 19: 2 3 2 3 4 1 4 P SD: 15.7952 c. M: 21.4575 c. 21: 2 4 2 3 4 2 4 SP T3 SD: 8.0996 c. M:-16.0579 c. 25: 2 5 2 4 5 2 5 P T3 SD: 6.7220 c. M: 9.0849 c. 32: 3 6 3 5 6 3 6 SP T3 SD: 5.3632 c. M:-8.9151 c. 36: 3 7 3 6 7 3 7 P T3 SD: 3.8794 c. M: 7.7516 c. 46: 4 9 4 7 9 4 9 SP T3 SD: 3.3978 c. M: 6.6094 c. 57: 5 11 5 9 11 5 11 SP T3 SD: 0.7135 c. M: 1.1175 c. 125: 11 24 11 20 24 11 24 SP T3 SD: 0.5516 c. M:-0.9036 c. 182: 16 35 16 29 35 16 35 SP T3 SD: 0.3812 c. M:-0.6733 c. 218: 19 42 19 35 42 19 42 SP T3 SD: 0.3790 c. M: 0.7179 c. 239: 21 46 21 38 46 21 46 SP T3 SD: 0.3784 c. M:-0.7561 c. 275: 24 53 24 44 53 24 53 SP T3 SD: 0.1790 c. M: 0.3576 c. 332: 29 64 29 53 64 29 64 SP T3 SD: 0.1096 c. M: 0.1663 c. 457: 40 88 40 73 88 40 88 SP T3 SD: 0.0721 c. M:-0.1264 c. 732: 64 141 64 117 141 64 141 SP T3 SD: 0.0641 c. M: 0.1013 c. 789: 69 152 69 126 152 69 152 SP T3 SD: 0.0101 c. M: 0.0203 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: 34.6293 cents 3 x x 4 x 5 x 6 S SD: 20.1776 cents 4 x 5 x 6 x 7:8 S SD: 21.3822 cents 5 x 6 x 7:8:9:10 S SD: 17.7034 cents 6 x 7:8:9:10:11:12 S SD: 23.4189 cents 7 x x 9:10 x 12:14 SD: 9.8157 cents 8:9:10 x 12:13:14:16 S SD: 22.1435 cents 9:10:11:12:13:15:16:18 SD: 14.6722 cents 11:12:13:14:16:18:19:22 SD: 10.8224 cents 12:13:15 x 17:20:21:24 SD: 11.7263 cents 13:14:16:17:19:21:23:26 SD: 8.7046 cents 14:15:17:18:20:23:25:28 SD: 5.9248 cents 18:19:22:23:26:30:32:36 SD: 5.9146 cents 20:21:24:26:29:33:35:40 SD: 4.8088 cents 27:29:33:35:39:44:47:54 SD: 4.4836 cents 28:30:34:36:40:46:49:56 SD: 3.1840 cents 32:34:39:41:46:53:56:64 SD: 2.4631 cents 45:48:55:58:65:74:79:90 SD: 2.1626 cents 48:51:58:62:69:79:84:96 SD: 1.4111 cents 65:69:79:84:94:107:114:130 SD: 1.1432 cents 79:84:96:102:114:130:138:158 SD: 0.6738 cents 127:135:154:164:183:209:222:254 SD: 0.5508 cents 145:154:176:187:209:239:254:290 SD: 0.3523 cents 224:238:272:289:323:369:392:448 SD: 0.1408 cents 476:506:578:614:686:784:833:952 SD: 0.1322 cents 592:629:719:764:853:975:1036:1184 SD: 0.1003 cents