Scala analysis: xen09-chalmers-tritriadic-9-13-10
Tritriadic scale built from 9:13:10
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: 13/10 454.213948 tridecimal semi-diminished fourth 4: 13/9 636.617660 tridecimal diminished fifth 5: 130/81 819.021372 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: 1053/1000 89.4065 4: 10/9 182.4037 minor whole tone 5: 10/9 182.4037 minor whole tone 6: 729/650 198.5749 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1053/1000 89.407 cents 1: 5 10/9 182.404 cents minor whole tone 1: 1 729/650 198.575 cents 2: 2 117/100 271.810 cents 2: 3 100/81 364.807 cents grave major third 2: 2 81/65 380.979 cents 3: 3 13/10 454.214 cents tridecimal semi-diminished fourth 3: 1 1000/729 547.211 cents 3: 3 18/13 563.382 cents tridecimal augmented fourth 4: 3 13/9 636.618 cents tridecimal diminished fifth 4: 1 729/500 652.789 cents 4: 3 20/13 745.786 cents tridecimal semi-augmented fifth 5: 2 130/81 819.021 cents 5: 3 81/50 835.193 cents acute minor sixth 5: 2 200/117 928.190 cents 6: 1 1300/729 1001.425 cents 6: 5 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 2000/1053 1110.593 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 : 182.4 364.8 454.2 636.6 819.0 1017.6 1200.0 182.4 : 182.4 271.8 454.2 636.6 835.2 1017.6 1200.0 364.8 : 89.4 271.8 454.2 652.8 835.2 1017.6 1200.0 454.2 : 182.4 364.8 563.4 745.8 928.2 1110.6 1200.0 636.6 : 182.4 381.0 563.4 745.8 928.2 1017.6 1200.0 819.0 : 198.6 381.0 563.4 745.8 835.2 1017.6 1200.0 1017.6: 182.4 364.8 547.2 636.6 819.0 1001.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 89.4065 .. 198.5749 cents 180/169, 109.1684 cents 1053/1000, 89.4065 cents 2: 271.8102 .. 380.9786 cents 180/169, 109.1684 cents 169/162, 73.2353 cents 3: 454.2139 .. 563.3823 cents 180/169, 109.1684 cents 169/162, 73.2353 cents 4: 636.6177 .. 745.7861 cents 180/169, 109.1684 cents 169/162, 73.2353 cents 5: 819.0214 .. 928.1898 cents 180/169, 109.1684 cents 169/162, 73.2353 cents 6: 1001.4251 .. 1110.5935 cents 180/169, 109.1684 cents 169/162, 73.2353 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 1053/1000, 89.4065 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 729/650, 198.5749 cents Average / Smallest step : 1.917406 Largest / Average step : 1.158354 Largest / Smallest step : 2.221034 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 : 167.29868 cents, oct.: 1171.09078 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: AABAACA Step pattern size order : MMSMMLM Scale is a Constant Structure, by a margin of 73.23532 cents Scale diversity : 1.390251 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.454158 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 : 6561/6500, 16.1712 cents Most common intervals : 10/9, 182.4037 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 454.214 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% Limited inverse transpositions with margin 109.1684 cents: 5 -- Rational properties -- Prime limit : 13 Odd number limit : 1053 (O: 1053 U: 1053) Highest odd numerator or denominator: 81 Scale harmonicity : 0.016569 Average absolute harmonicity : 0.185444 Specific harmonicity : 0.083488 Fundamental : 1/810, -9.6618 octaves, 0.3230 Hz. Guide tone : 11700, 13.5142 octaves, 3061019.114 Hz. Exponens Consonantiae : 9.477000E+06, 23.17600 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 236.5, average 33.78571 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.95334, average 1.13619 Sum of Tenney's harmonic distance : 16.02153, average 2.28879 Vogel's harmonic complexity : 21.28571 Wille's k value : 526 Wilson's harmonic complexity : 46 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 93.15156, average 3.32684 Lattice compactness (without 2's) : 85.08042, average 3.03859 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 6 1 3: -4 .. 2 -1.42857 14 5: -1 .. 2 0.28571 6 3 13: 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 28| Scale is weakly epimorphic with val: <7 10 16 25| Scale is weakly epimorphic with val: <7 10 17 29| Scale is weakly epimorphic with val: <7 10 18 26| Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 12 16 27| Scale is JI-epimorphic with val: <7 12 18 28|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 34.2158 c. M:-60.0718 c. Lebeng 9: 1 2 0 2 1 2 1 N D3 SD: 38.2813 c. M: 54.2139 c. 10: 2 1 1 1 2 1 2 N D3 SD: 36.0627 c. M: 57.5963 c. 13: 2 2 1 2 2 2 2 SP M ME S SD: 6.6756 c. M:-11.7479 c. Oukranian 32: 5 5 2 5 5 5 5 SP M DE S SD: 5.4787 c. M:-10.1926 c. 40: 6 6 3 6 6 7 6 SP T3 SD: 5.0370 c. M: 9.0214 c. 45: 7 7 3 7 7 7 7 SP M DE S SD: 5.0667 c. M:-8.5259 c. 47: 7 7 4 7 7 8 7 SP T3 SD: 4.0853 c. M: 7.3606 c. 53: 8 8 4 8 8 9 8 SP T3 SD: 2.2068 c. M: 3.9270 c. 66: 10 10 5 10 10 11 10 SP T3 SD: 0.6477 c. M: 1.1711 c. 145: 22 22 11 22 22 24 22 SP T3 SD: 0.5429 c. M:-0.9585 c. 211: 32 32 16 32 32 35 32 SP T3 SD: 0.4974 c. M: 0.8264 c. 217: 33 33 16 33 33 36 33 SP T3 SD: 0.4498 c. M: 0.7577 c. 230: 35 35 17 35 35 38 35 SP T3 SD: 0.2280 c. M:-0.4100 c. 296: 45 45 22 45 45 49 45 SP T3 SD: 0.0912 c. M: 0.1599 c. 605: 92 92 45 92 92 100 92 SP T3 SD: 0.0951 c. M:-0.1522 c. 658: 100 100 49 100 100 109 100 SP T3 SD: 0.1003 c. M: 0.1764 c. 671: 102 102 50 102 102 111 102 SP T3 SD: 0.0310 c. M:-0.0546 c. 967: 147 147 72 147 147 160 147 SP T3 SD: 0.0184 c. M:-0.0323 c. 1638: 249 249 122 249 249 271 249 SP T3 SD: 0.0169 c. M:-0.0277 c. 1704: 259 259 127 259 259 282 259 SP T3 SD: 0.0101 c. M: 0.0187 c. 2375: 361 361 177 361 361 393 361 SP T3 SD: 0.0099 c. M:-0.0176 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: 32.6687 cents 3 x x 4 x 5 x 6 S SD: 26.2258 cents 4 x 5 x 6 x 7:8 S SD: 21.0803 cents 5 x 6 x 7:8:9:10 S SD: 14.6604 cents 6:7 x 8:9:10:11:12 S SD: 22.7321 cents 7:8 x 9:10:11:13:14 SD: 14.3103 cents 8:9:10 x 12:13:14:16 S SD: 14.9398 cents 9:10:11:12:13:14:16:18 S SD: 10.7036 cents 11:12 x 14:16:18:20:22 S SD: 10.4506 cents 13:14:16:17:19:21:23:26 SD: 9.5748 cents 16:18:20:21:23:26:29:32 SD: 6.1862 cents 18:20:22:23:26:29:32:36 SD: 5.8909 cents 20:22:25:26:29:32:36:40 SD: 4.1352 cents 26:29:32:34:38:42:47:52 SD: 3.9704 cents 27:30:33:35:39:43:49:54 SD: 3.7991 cents 30:33:37:39:43:48:54:60 SD: 3.2354 cents 34:38:42:44:49:55:61:68 SD: 2.8562 cents 43:48:53:56:62:69:77:86 SD: 1.8748 cents 54:60:67:70:78:87:97:108 SD: 1.7833 cents 56:62:69:73:81:90:101:112 SD: 1.3967 cents 63:70:78:82:91:101:113:126 SD: 1.1944 cents 81:90:100:105:117:130:146:162 SD: 0.7828 cents 106:118:131:138:153:170:191:212 SD: 0.7372 cents 119:132:147:155:172:191:214:238 SD: 0.7092 cents 124:138:153:161:179:199:223:248 SD: 0.5879 cents 144:160:178:187:208:231:259:288 SD: 0.4647 cents 180:200:222:234:260:289:324:360 SD: 0.2651 cents 243:270:300:316:351:390:437:486 SD: 0.2394 cents 306:340:378:398:442:491:551:612 SD: 0.2186 cents 324:360:400:421:468:520:583:648 SD: 0.1449 cents 486:540:600:632:702:780:875:972 SD: 0.0966 cents