Scala analysis: xen09-chalmers-tritriadic-7-9-13
Tritriadic scale built from 7:9:13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-tone 2: 117/98 306.785851 3: 9/7 435.084095 septimal major third, BP third 4: 18/13 563.382340 tridecimal augmented fourth 5: 169/98 943.403511 6: 13/7 1071.701755 16/3-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 14/13 128.2982 2/3-tone 1: 14/13 128.2982 2/3-tone 2: 1521/1372 178.4876 3: 14/13 128.2982 2/3-tone 4: 14/13 128.2982 2/3-tone 5: 2197/1764 380.0212 6: 14/13 128.2982 2/3-tone 7: 14/13 128.2982 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 14/13 128.298 cents 2/3-tone 1: 1 1521/1372 178.488 cents 1: 1 2197/1764 380.021 cents 2: 3 196/169 256.596 cents two (2/3-tone) 2: 2 117/98 306.786 cents 2: 2 169/126 508.319 cents 3: 1 2744/2197 384.895 cents 3: 3 9/7 435.084 cents septimal major third, BP third 3: 3 13/9 636.618 cents tridecimal diminished fifth 4: 3 18/13 563.382 cents tridecimal augmented fourth 4: 3 14/9 764.916 cents septimal minor sixth 4: 1 2197/1372 815.105 cents 5: 2 252/169 691.681 cents 5: 2 196/117 893.214 cents 5: 3 169/98 943.404 cents 6: 1 3528/2197 819.979 cents 6: 1 2744/1521 1021.512 cents 6: 5 13/7 1071.702 cents 16/3-tone 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 : 128.3 306.8 435.1 563.4 943.4 1071.7 1200.0 128.3 : 178.5 306.8 435.1 815.1 943.4 1071.7 1200.0 306.8 : 128.3 256.6 636.6 764.9 893.2 1021.5 1200.0 435.1 : 128.3 508.3 636.6 764.9 893.2 1071.7 1200.0 563.4 : 380.0 508.3 636.6 764.9 943.4 1071.7 1200.0 943.4 : 128.3 256.6 384.9 563.4 691.7 820.0 1200.0 1071.7: 128.3 256.6 435.1 563.4 691.7 1071.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 128.2982 .. 380.0212 cents 28561/24696, 251.7229 cents 14/13, 128.2982 cents 2: 256.5965 .. 508.3194 cents 28561/24696, 251.7229 cents 345744/371293,-123.4247 cents 3: 384.8947 .. 636.6177 cents 28561/24696, 251.7229 cents 345744/371293,-123.4247 cents 4: 563.3823 .. 815.1053 cents 28561/24696, 251.7229 cents 162/169,-73.2353 cents 5: 691.6806 .. 943.4035 cents 28561/24696, 251.7229 cents 345744/371293,-123.4247 cents 6: 819.9788 .. 1071.7018 cents 28561/24696, 251.7229 cents 345744/371293,-123.4247 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 14/13, 128.2982 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 2197/1764, 380.0212 cents Average / Smallest step : 1.336172 Largest / Average step : 2.216790 Largest / Smallest step : 2.962014 Median interval of one step : 14/13, 128.2982 cents, amount: 5 Most common interval of one step : 14/13, 128.2982 cents, amount: 5 Least squares average step : 170.34200 cents, oct.: 1192.39398 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABAACAA Step pattern size order : SMSSLSS Scale is a Constant Structure, by a margin of 4.87356 cents Scale diversity : 1.407066 Lumma stability : 0.213830 Lumma impropriety factor : 0.472445 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 : 4840416/4826809, 4.8736 cents Most common intervals : 14/13, 128.2982 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 435.084 1071.702 cents Number of recognisable fifths : 2, average 691.6806 cents Scale contains a complete diamond : 7 13 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 : 13 Odd number limit : 2197 (O: 2197 U: 2197) Highest odd numerator or denominator: 169 Scale harmonicity : 0.009555 Average absolute harmonicity : 0.170774 Specific harmonicity : 0.052449 Fundamental : 1/1274, -10.3151 octaves, 0.2054 Hz. Guide tone : 21294, 14.3782 octaves, 5571054.788 Hz. Exponens Consonantiae : 2.712856E+07, 24.69331 octaves Euler's gradus suavitatis : 61 Sum of Mann's harmonic distance : 289.5, average 41.35714 Mersenne's string divisions : 256255920 Sum of van Prooijen's expressibility: 8.59215, average 1.22745 Sum of Tenney's harmonic distance : 16.96722, average 2.42389 Vogel's harmonic complexity : 29.42857 Wille's k value : 1098 Wilson's harmonic complexity : 66 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 74.05592, average 2.64485 Lattice compactness (without 2's) : 66.59060, average 2.37824 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.14286 5 1 3: 0 .. 2 0.85714 6 7: -2 .. 1 -0.71429 7 1 13: -1 .. 2 0.28571 6 5 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 19 / 7 = 2.71429 Scale is weakly epimorphic with val: <7 10 18 29| Scale is weakly epimorphic with val: <7 10 19 28| Scale is weakly epimorphic with val: <7 10 21 26| Scale is weakly epimorphic with val: <7 10 22 25| Scale is weakly epimorphic with val: <7 11 18 26| Scale is JI-epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 11 20 24| Scale is weakly epimorphic with val: <7 12 19 29| Scale is weakly epimorphic with val: <7 12 20 28| Scale is JI-epimorphic with val: <7 12 21 27| Scale is weakly epimorphic with val: <7 12 22 26|
FIT/MODE
7: 0 1 1 1 2 1 1 N T3 SD: 88.6401 c. M: 135.3573 c. 8: 1 1 1 1 2 1 1 P M ME S SD: 25.1714 c. M: 43.4035 c. 9: 1 1 1 1 3 1 1 N M DE S SD: 23.5902 c. M: 40.1192 c. 11: 1 2 1 1 4 1 1 N T3 SD: 20.5506 c. M:-38.4147 c. 15: 2 2 1 2 5 1 2 N SD: 22.9981 c. M: 35.0841 c. 17: 2 2 2 2 5 2 2 N M DE S SD: 15.7086 c. M: 25.7565 c. 19: 2 3 2 2 6 2 2 N T3 SD: 5.0615 c. M:-9.0036 c. 28: 3 4 3 3 9 3 3 N T3 SD: 4.2735 c. M: 6.7859 c. 47: 5 7 5 5 15 5 5 N T3 SD: 0.9649 c. M: 1.6802 c. 113: 12 17 12 12 36 12 12 N T3 SD: 0.9469 c. M:-1.7292 c. 149: 16 22 16 16 47 16 16 N T3 SD: 0.6116 c. M: 1.1216 c. 168: 18 25 18 18 53 18 18 N T3 SD: 0.5055 c. M:-0.9034 c. 196: 21 29 21 21 62 21 21 N T3 SD: 0.3880 c. M: 0.6634 c. 215: 23 32 23 23 68 23 23 N T3 SD: 0.1904 c. M:-0.3386 c. 262: 28 39 28 28 83 28 28 N T3 SD: 0.0610 c. M:-0.1079 c. 720: 77 107 77 77 228 77 77 N T3 SD: 0.0666 c. M: 0.1192 c. 739: 79 110 79 79 234 79 79 N T3 SD: 0.0670 c. M:-0.1154 c. 935: 100 139 100 100 296 100 100 N T3 SD: 0.0471 c. M: 0.0880 c. 982: 105 146 105 105 311 105 105 N T3 SD: 0.0371 c. M: 0.0649 c. 1197: 128 178 128 128 379 128 128 N T3 SD: 0.0242 c. M: 0.0451 c. 1244: 133 185 133 133 394 133 133 N T3 SD: 0.0236 c. M: 0.0383 c. 1459: 156 217 156 156 462 156 156 N T3 SD: 0.0109 c. M: 0.0176 c. 1721: 184 256 184 184 545 184 184 N T3 SD: 0.0078 c. M:-0.0125 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: 69.2863 cents 3 x x 4 x 5 x 6 S SD: 28.7718 cents 4 x x 5:6:7 x 8 S SD: 37.2720 cents 5 x 6 x 7 x 9:10 SD: 14.5167 cents 6 x 7:8 x 10:11:12 S SD: 19.5372 cents 7 x 8:9:10:12:13:14 S SD: 15.5903 cents 8:9 x 10:11:14:15:16 SD: 15.9531 cents 9:10:11:12 x 16:17:18 S SD: 18.3927 cents 10:11:12:13:14:17:19:20 SD: 9.4013 cents 11:12:13:14:15:19:20:22 SD: 8.0440 cents 14:15:17:18:19:24:26:28 SD: 6.7745 cents 15:16:18:19:21:26:28:30 SD: 5.6122 cents 21:23:25:27:29:36:39:42 SD: 4.5251 cents 25:27:30:32:35:43:46:50 SD: 4.0566 cents 26:28:31:33:36:45:48:52 SD: 3.6404 cents 36:39:43:46:50:62:67:72 SD: 2.3407 cents 41:44:49:53:57:71:76:82 SD: 2.2109 cents 42:45:50:54:58:72:78:84 SD: 2.1638 cents 50:54:60:64:69:86:93:100 SD: 2.1340 cents 52:56:62:67:72:90:97:104 SD: 1.5466 cents 62:67:74:80:86:107:115:124 SD: 1.3571 cents 76:82:91:98:105:131:141:152 SD: 1.2765 cents 77:83:92:99:107:133:143:154 SD: 1.0206 cents 91:98:109:117:126:157:169:182 SD: 0.8194 cents 104:112:124:134:144:179:193:208 SD: 0.8046 cents 119:128:142:153:165:205:221:238 SD: 0.5388 cents 171:184:204:220:237:295:318:342 SD: 0.5302 cents 181:195:216:233:251:312:336:362 SD: 0.5278 cents 182:196:217:234:252:314:338:364 SD: 0.3443 cents 221:238:264:284:306:381:410:442 SD: 0.3288 cents 258:278:308:332:357:445:479:516 SD: 0.3121 cents 273:294:326:351:378:471:507:546 SD: 0.1249 cents 588:633:702:756:814:1014:1092:1176 SD: 0.1015 cents