Scala analysis: xen09-chalmers-tritriadic-9-7-10
Tritriadic scale built from 9:7:10
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 100/81 364.807424 grave major third 3: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 4: 14/9 764.915905 septimal minor sixth 5: 140/81 947.319617 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 10/9 182.4037 minor whole tone 2: 10/9 182.4037 minor whole tone 3: 567/500 217.7048 4: 10/9 182.4037 minor whole tone 5: 10/9 182.4037 minor whole tone 6: 729/700 70.2767 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 729/700 70.277 cents 1: 5 10/9 182.404 cents minor whole tone 1: 1 567/500 217.705 cents 2: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 3 100/81 364.807 cents grave major third 2: 2 63/50 400.108 cents quasi-equal major third 3: 3 9/7 435.084 cents septimal major third, BP third 3: 1 1000/729 547.211 cents 3: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 3 10/7 617.488 cents Euler's tritone 4: 1 729/500 652.789 cents 4: 3 14/9 764.916 cents septimal minor sixth 5: 2 100/63 799.892 cents quasi-equal minor sixth 5: 3 81/50 835.193 cents acute minor sixth 5: 2 140/81 947.320 cents 6: 1 1000/567 982.295 cents 6: 5 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 1400/729 1129.723 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 : 182.4 364.8 582.5 764.9 947.3 1017.6 1200.0 182.4 : 182.4 400.1 582.5 764.9 835.2 1017.6 1200.0 364.8 : 217.7 400.1 582.5 652.8 835.2 1017.6 1200.0 582.5 : 182.4 364.8 435.1 617.5 799.9 982.3 1200.0 764.9 : 182.4 252.7 435.1 617.5 799.9 1017.6 1200.0 947.3 : 70.3 252.7 435.1 617.5 835.2 1017.6 1200.0 1017.6: 182.4 364.8 547.2 764.9 947.3 1129.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.2767 .. 217.7048 cents 49/45, 147.4281 cents 729/700, 70.2767 cents 2: 252.6804 .. 400.1085 cents 49/45, 147.4281 cents 50/49, 34.9756 cents 3: 435.0841 .. 582.5122 cents 49/45, 147.4281 cents 50/49, 34.9756 cents 4: 617.4878 .. 764.9159 cents 49/45, 147.4281 cents 50/49, 34.9756 cents 5: 799.8915 .. 947.3196 cents 49/45, 147.4281 cents 50/49, 34.9756 cents 6: 982.2952 .. 1129.7233 cents 49/45, 147.4281 cents 50/49, 34.9756 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 729/700, 70.2767 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 567/500, 217.7048 cents Average / Smallest step : 2.439338 Largest / Average step : 1.269944 Largest / Smallest step : 3.097824 Median interval of one step : 10/9, 182.4037 cents, amount: 5 Most common interval of one step : 10/9, 182.4037 cents, amount: 5 Least squares average step : 178.29568 cents, oct.: 1248.06973 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: AABAACA Step pattern size order : MMLMMSM Scale is a Constant Structure, by a margin of 34.97561 cents Scale diversity : 1.376338 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.262860 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 : 50/49, 34.9756 cents Most common intervals : 10/9, 182.4037 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 582.512 1017.596 cents Most common triad is 0.0 182.404 1017.596 cents, amount: 3 Number of recognisable fifths : 0 Best fifths form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 5 9 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% -- Rational properties -- Prime limit : 7 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 81 Scale harmonicity : 0.021059 Average absolute harmonicity : 0.193885 Specific harmonicity : 0.109298 Fundamental : 1/405, -8.6618 octaves, 0.6460 Hz. Guide tone : 6300, 12.6211 octaves, 1648241.061 Hz. Exponens Consonantiae : 2.551500E+06, 21.28291 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 236.5, average 33.78571 Mersenne's string divisions : 1468356708 Sum of van Prooijen's expressibility: 7.52480, average 1.07497 Sum of Tenney's harmonic distance : 15.51602, average 2.21657 Vogel's harmonic complexity : 18.14286 Wille's k value : 364 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 90.94670, average 3.24810 Lattice compactness (without 2's) : 85.08042, average 3.03859 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.00000 7 1 3: -4 .. 2 -1.42857 14 5: -1 .. 2 0.28571 6 3 7: 0 .. 1 0.42857 3 3 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 23 / 7 = 3.28571 Scale is weakly epimorphic with val: <7 10 15 21| Scale is weakly epimorphic with val: <7 10 16 18| Scale is weakly epimorphic with val: <7 10 17 22| Scale is weakly epimorphic with val: <7 10 18 19| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 18 20| Scale is weakly epimorphic with val: <7 12 16 20| Scale is JI-epimorphic with val: <7 12 18 21|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 53.1606 c. M: 90.1768 c. Lebeng 8: 1 1 2 1 1 1 1 P M ME S SD: 35.9910 c. M: 64.8074 c. 10: 1 2 2 1 2 0 2 N T3 S SD: 37.2611 c. M: 62.4037 c. 12: 2 2 2 2 2 0 2 P M DE S SD: 29.6882 c. M:-52.6804 c. 13: 2 2 2 2 2 1 2 SP M ME S SD: 17.4791 c. M: 28.6660 c. Karakalian 14: 2 2 3 2 2 1 2 P T3 SD: 12.4836 c. M: 21.9503 c. 19: 3 3 3 3 3 1 3 SP M DE S SD: 8.8460 c. M:-14.1399 c. 20: 3 3 4 3 3 1 3 P T3 SD: 10.2037 c. M:-17.4878 c. 27: 4 4 5 4 4 2 4 SP T3 SD: 7.8744 c. M: 13.9863 c. 33: 5 5 6 5 5 2 5 SP T3 SD: 1.0457 c. M: 1.8651 c. 105: 16 16 19 16 16 6 16 SP T3 SD: 0.7128 c. M:-1.2518 c. 138: 21 21 25 21 21 8 21 SP T3 SD: 0.2949 c. M:-0.5065 c. 171: 26 26 31 26 26 10 26 SP T3 SD: 0.0561 c. M:-0.1049 c. 546: 83 83 99 83 83 32 83 SP T3 SD: 0.0549 c. M: 0.0946 c. 717: 109 109 130 109 109 42 109 SP T3 SD: 0.0477 c. M: 0.0854 c. 888: 135 135 161 135 135 52 135 SP T3 SD: 0.0454 c. M: 0.0798 c. 1059: 161 161 192 161 161 62 161 SP T3 SD: 0.0449 c. M: 0.0759 c. 1230: 187 187 223 187 187 72 187 SP T3 SD: 0.0452 c. M: 0.0732 c. 1605: 244 244 291 244 244 94 244 SP T3 SD: 0.0462 c. M: 0.0823 c. 1862: 283 283 338 283 283 109 283 SP T3 SD: 0.0490 c. M:-0.0872 c. 1895: 288 288 344 288 288 111 288 SP T3 SD: 0.0426 c. M:-0.0736 c. 2033: 309 309 369 309 309 119 309 SP T3 SD: 0.0429 c. M:-0.0751 c. 2066: 314 314 375 314 314 121 314 SP T3 SD: 0.0357 c. M:-0.0628 c. 2099: 319 319 381 319 319 123 319 SP T3 SD: 0.0357 c. M: 0.0623 c. 2204: 335 335 400 335 335 129 335 SP T3 SD: 0.0382 c. M:-0.0649 c. 2237: 340 340 406 340 340 131 340 SP T3 SD: 0.0301 c. M:-0.0537 c. 2270: 345 345 412 345 345 133 345 SP T3 SD: 0.0291 c. M: 0.0497 c. 2375: 361 361 431 361 361 139 361 SP T3 SD: 0.0346 c. M:-0.0562 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: 31.4805 cents 3 x x 4 x 5 x 6 S SD: 35.1169 cents 4 x 5 x 6:7 x 8 S SD: 17.4806 cents 5 x 6:7:8 x 9:10 S SD: 13.8504 cents 6:7 x 8:9:10:11:12 S SD: 25.3896 cents 7:8:9:10:11:12:13:14 H SD: 15.6351 cents 8:9:10:11:12:14 x 16 S SD: 13.2547 cents 9:10:11:13:14 x 16:18 SD: 10.1279 cents 15:17:19:21:23:26:27:30 SD: 8.8004 cents 16:18:20:22:25:28:29:32 SD: 7.2332 cents 17:19:21:24:26:29:31:34 SD: 6.6942 cents 18:20:22:25:28:31:32:36 SD: 4.5038 cents 25:28:31:35:39:43:45:50 SD: 2.6477 cents 38:42:47:53:59:66:68:76 SD: 2.5598 cents 43:48:53:60:67:74:77:86 SD: 2.2613 cents 45:50:56:63:70:78:81:90 SD: 2.0932 cents 47:52:58:66:73:81:85:94 SD: 1.9237 cents 52:58:64:73:81:90:94:104 SD: 1.8126 cents 55:61:68:77:86:95:99:110 SD: 1.4141 cents 63:70:78:88:98:109:113:126 SD: 1.2808 cents 80:89:99:112:124:138:144:160 SD: 1.2079 cents 81:90:100:113:126:140:146:162 SD: 0.9374 cents 90:100:111:126:140:156:162:180 SD: 0.7477 cents 110:122:136:154:171:190:198:220 SD: 0.6192 cents 115:128:142:161:179:199:207:230 SD: 0.5433 cents 162:180:200:227:252:280:292:324 SD: 0.4031 cents 180:200:222:252:280:311:324:360 SD: 0.2627 cents 225:250:278:315:350:389:405:450 SD: 0.2100 cents 380:422:469:532:591:657:684:760 SD: 0.1746 cents 405:450:500:567:630:700:729:810 SD: 0.0000 cents