Scala analysis: xen15-chalmers-triadic-diamond-11-9-tetrachord
Upper tetrachord 88/81 * 243/242 * 11/9 of triadic diamond for M=11/9, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88/81 143.497939 2nd undecimal neutral second 2: 12/11 150.637059 undecimal neutral second, 3/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 11/9 347.4079 undecimal neutral third 1: 88/81 143.4979 2nd undecimal neutral second 2: 243/242 7.1391 neutral third comma, rastma 3: 11/9 347.4079 undecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 243/242 7.139 cents neutral third comma, rastma 1: 1 88/81 143.498 cents 2nd undecimal neutral second 1: 1 11/9 347.408 cents undecimal neutral third 2: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 968/729 490.906 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 0.0 : 143.5 150.6 498.0 143.5: 7.1 354.5 498.0 150.6: 347.4 490.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 7.1391 .. 347.4079 cents 2662/2187, 340.2688 cents 243/242, 7.1391 cents 2: 150.6371 .. 490.9059 cents 2662/2187, 340.2688 cents 108/121,-196.7709 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 243/242, 7.1391 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 11/9, 347.4079 cents Average / Smallest step : 23.254268 Largest / Average step : 2.092630 Largest / Smallest step : 48.662575 Median interval of one step : 88/81, 143.4979 cents, amount: 1 Least squares average step : 138.49336 cents, oct.: 415.48008 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1954-tone equal temperament with octave 4/3 degrees: 563 591 1954 Least number of segments generator : 979 of 249.532 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1847 of 470.772 cents and inv. generated superset size: 32 = 29 more = 1066.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 7.13912 cents Scale diversity : 0.417323 Lumma stability : 0.028669 Lumma impropriety factor : 0.395087 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 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 : 243/242, 7.1391 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 490.9059 cents Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 11 Odd number limit : 729 (O: 243 U: 729) Highest odd numerator or denominator: 81 Scale harmonicity : 0.018976 Average absolute harmonicity : 0.096483 Specific harmonicity : 0.099528 Fundamental : 1/891, -9.7993 octaves, 0.2936 Hz. Guide tone : 264, 8.0444 octaves, 69069.149 Hz. Exponens Consonantiae : 2.352240E+05, 17.84368 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 99.5, average 33.16667 Mersenne's string divisions : 27209 Sum of van Prooijen's expressibility: 3.42700, average 1.14233 Sum of Tenney's harmonic distance : 7.05272, average 2.35091 Vogel's harmonic complexity : 21.33333 Wille's k value : 148 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 20.81450, average 3.46908 Lattice compactness (without 2's) : 17.32083, average 2.88680 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -4 .. 1 -1.33333 6 1 11: -1 .. 1 0.00000 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <8 11 23| Scale is weakly epimorphic with val: <8 11 24|
FIT/MODE
3: 1 0 2 N G T3 SD: 15.7427 c. M:-22.5171 c. 7: 2 0 5 N G T3 SD: 4.8638 c. M: 8.3385 c. 10: 3 0 7 N G T3 SD: 3.4876 c. M:-5.9156 c. 17: 5 0 12 N G T3 SD: 2.9532 c. M: 4.1532 c. 27: 8 0 19 N G T3 SD: 2.9431 c. M:-4.0709 c. 36: 10 1 25 N T3 SD: 3.1052 c. M: 5.1521 c. 37: 11 0 26 N G T3 SD: 3.0267 c. M:-4.5695 c. 39: 11 1 27 N T3 SD: 2.3052 c. M: 3.0237 c. 42: 12 1 29 N T3 SD: 2.1469 c. M:-3.5197 c. 45: 13 1 31 N T3 SD: 2.4983 c. M:-4.3103 c. 46: 13 1 32 N T3 SD: 1.6761 c. M: 2.7461 c. 49: 14 1 34 N T3 SD: 1.2612 c. M:-1.8257 c. 52: 15 1 36 N T3 SD: 1.5086 c. M:-2.6076 c. 53: 15 1 37 N T3 SD: 1.4766 c. M: 2.5418 c. 56: 16 1 39 N T3 SD: 0.7630 c. M: 1.1994 c. 59: 17 1 41 N T3 SD: 0.7557 c. M:-1.3089 c. 63: 18 1 44 N T3 SD: 0.7362 c. M: 1.1994 c. 66: 19 1 46 N T3 SD: 0.1792 c. M:-0.2857 c. 139: 40 2 97 N T3 SD: 0.1328 c. M: 0.1756 c. 205: 59 3 143 N T3 SD: 0.0915 c. M: 0.1582 c. 215: 62 3 150 N T3 SD: 0.0811 c. M:-0.1243 c. 281: 81 4 196 N T3 SD: 0.0397 c. M:-0.0666 c. 347: 100 5 242 N T3 SD: 0.0432 c. M:-0.0682 c. 420: 121 6 293 N T3 SD: 0.0231 c. M: 0.0377 c. 486: 140 7 339 N T3 SD: 0.0167 c. M: 0.0282 c. 701: 202 10 489 N T3 SD: 0.0141 c. M:-0.0186 c. 767: 221 11 535 N T3 SD: 0.0070 c. M:-0.0102 c. 1187: 342 17 828 N T3 SD: 0.0039 c. M: 0.0068 c. 1954: 563 28 1363 N T3 SD: 0.0013 c. M:-0.0022 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 92.6837 cents 6 x 7:8 S SD: 58.1169 cents 7 x 8:9 S SD: 51.1133 cents 8 x 9:11 SD: 37.6697 cents 9 x 10:12 S SD: 15.8833 cents 10 x 11:13 SD: 23.0628 cents 11 x 12:15 S SD: 19.4529 cents 12:13 x 16 SD: 2.4626 cents 13:14 x 17 SD: 18.4469 cents 14:15 x 19 SD: 19.4781 cents 15:16 x 20 S SD: 15.8833 cents 16:17 x 21 SD: 23.6054 cents 17:18:19:23 SD: 22.0611 cents 18 x 20:24 S SD: 15.8833 cents 19 x 21:25 SD: 16.1087 cents 20 x 22:27 SD: 12.9319 cents 21 x 23:28 SD: 3.4282 cents 22 x 24:29 SD: 9.8929 cents 23:25 x 31 SD: 9.3679 cents 24:26 x 32 SD: 2.4626 cents 25:27 x 33 SD: 10.0997 cents 26:28 x 35 S SD: 11.2416 cents 27:29 x 36 SD: 9.8929 cents 29 x 32:39 SD: 12.3724 cents 30 x 33:40 SD: 7.1836 cents 31 x 34:41 SD: 8.4065 cents 32 x 35:43 SD: 7.1026 cents 33 x 36:44 SD: 0.0000 cents 34:37 x 45 SD: 6.5498 cents 35:38 x 47 SD: 6.1866 cents 36:39 x 48 SD: 2.4626 cents 37:40 x 49 SD: 7.2542 cents 38:41 x 51 SD: 8.2408 cents 39:42:43:52 SD: 7.9548 cents 41 x 45:55 SD: 7.4418 cents 42 x 46:56 SD: 3.4282 cents 43 x 47:57 SD: 5.3183 cents 44 x 48:59 SD: 4.9044 cents 45 x 49:60 SD: 1.6045 cents 46:50 x 61 SD: 4.7366 cents 47:51 x 63 SD: 4.7100 cents 48:52 x 64 SD: 2.4626 cents 49:53 x 65 SD: 5.8495 cents 51:55:56:68 SD: 5.6808 cents 53 x 58:71 SD: 4.8969 cents 54 x 59:72 SD: 1.3348 cents 55 x 60:73 SD: 3.9436 cents 56 x 61:75 SD: 4.0655 cents 57:62 x 76 SD: 1.0348 cents 58:63 x 77 SD: 3.7430 cents 59:64 x 79 SD: 3.8959 cents 60:65 x 80 SD: 2.4626 cents 64 x 70:85 SD: 4.0677 cents 65 x 71:87 SD: 3.5031 cents 66 x 72:88 SD: 0.0000 cents 67 x 73:89 SD: 3.4106 cents 68:74 x 91 SD: 3.4899 cents 69:75 x 92 SD: 0.4276 cents 70:76 x 93 SD: 3.1477 cents 71:77 x 95 SD: 3.4035 cents 76 x 83:101 SD: 3.0057 cents 77 x 84:103 SD: 2.8059 cents 78 x 85:104 SD: 0.9253 cents 79:86 x 105 SD: 3.2496 cents 80:87 x 107 SD: 2.8345 cents 81:88 x 108 SD: 0.0000 cents 82:89 x 109 SD: 2.7734 cents 87 x 95:116 SD: 0.8287 cents 88 x 96:117 SD: 2.4626 cents 89 x 97:119 SD: 2.5599 cents 90 x 98:120 SD: 1.6045 cents 91:99 x 121 SD: 2.6613 cents 92:100 x 123 SD: 2.3876 cents 93:101 x 124 SD: 0.3174 cents 99 x 108:132 SD: 0.0000 cents 100 x 109:133 SD: 2.2838 cents 101 x 110:135 SD: 2.5736 cents 102:111 x 136 SD: 1.4453 cents 103:112 x 137 SD: 2.2379 cents 104:113 x 139 SD: 2.0805 cents 108:117:118:144 SD: 1.8674 cents 110 x 120:147 SD: 1.9651 cents 111 x 121:148 SD: 0.6501 cents 112 x 122:149 SD: 2.3245 cents 113:123 x 151 SD: 2.5278 cents 114:124 x 152 SD: 1.0348 cents 115:125 x 153 SD: 1.9317 cents 117:127:128:156 SD: 1.7176 cents 120:130:131:160 SD: 1.6899 cents 122 x 133:163 SD: 1.8681 cents 123 x 134:164 SD: 1.1737 cents 124 x 135:165 SD: 2.4706 cents 125:136 x 167 SD: 2.1387 cents 126:137 x 168 SD: 0.7023 cents 134 x 146:179 SD: 1.9401 cents 135 x 147:180 SD: 1.6045 cents 136:148 x 181 SD: 2.1507 cents 137:149 x 183 SD: 1.8333 cents 138:150:151:184 SD: 1.7630 cents 139:151:152:185 SD: 1.7297 cents 140:152:153:187 SD: 1.5035 cents 141:153:154:188 SD: 0.9757 cents 145 x 158:193 SD: 1.7951 cents 146 x 159:195 SD: 2.0962 cents 147:160 x 196 SD: 1.6045 cents 148:161 x 197 SD: 1.8484 cents 150:163:164:200 SD: 1.2877 cents 152:165:166:203 SD: 1.2348 cents 153:166:167:204 SD: 0.8335 cents 157 x 171:209 SD: 1.9509 cents 158:172 x 211 SD: 2.2149 cents 159:173 x 212 SD: 1.2982 cents 162:176:177:216 SD: 0.8899 cents 165:179:180:220 SD: 0.8352 cents 168 x 183:224 SD: 1.2891 cents 169 x 184:225 SD: 2.1361 cents 170:185 x 227 SD: 1.9254 cents 171:186:187:228 SD: 1.5647 cents 172:187:188:229 SD: 1.4590 cents 173:188:189:231 SD: 1.1882 cents 174:189:190:232 SD: 0.5639 cents 180 x 196:240 SD: 1.6045 cents 181:197 x 241 SD: 1.9776 cents 182:198:199:243 SD: 1.7310 cents 183:199:200:244 SD: 1.1796 cents 184:200:201:245 SD: 1.1449 cents 185:201:202:247 SD: 0.9373 cents 186:202:203:248 SD: 0.3340 cents 191 x 208:255 SD: 1.8890 cents 192:209 x 256 SD: 1.6890 cents 194:211:212:259 SD: 1.3949 cents 195:212:213:260 SD: 0.8423 cents 197:214:215:263 SD: 0.7744 cents 198:215:216:264 SD: 0.2982 cents 203 x 221:271 SD: 2.0732 cents 204:222:223:272 SD: 1.5215 cents 205:223:224:273 SD: 1.3840 cents 206:224:225:275 SD: 1.1131 cents 207:225:226:276 SD: 0.5449 cents 210:228:229:280 SD: 0.4393 cents 219:238:239:292 SD: 0.2837 cents 231:251:252:308 SD: 0.0852 cents