Scala analysis: xen18-erlich-beatles-04
3L 1s MOS for Beatles, L=354.72, s=132.94
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 354.720 cents 354.720000 2: 709.440 cents 709.440000 3: 842.380 cents 842.380000 4: 1197.100 cents 1197.100000
SHOW/INTERVAL
0: 354.7200 cents 354.7200 1: 354.7200 cents 354.7200 2: 354.7200 cents 354.7200 3: 132.9400 cents 132.9400 4: 354.7200 cents 354.7200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 132.94000 cents 1: 3 354.72000 cents 2: 2 487.66000 cents 2: 2 709.44000 cents 3: 3 842.38000 cents 3: 1 1064.16000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 0.0 : 354.7 709.4 842.4 1197.1 354.7 : 354.7 487.7 842.4 1197.1 709.4 : 132.9 487.7 842.4 1197.1 842.4 : 354.7 709.4 1064.2 1197.1 1197.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 132.9400 .. 354.7200 cents 221.78000 cents 132.94000 cents 2: 487.6600 .. 709.4400 cents 221.78000 cents 132.94000 cents 3: 842.3800 .. 1064.1600 cents 221.78000 cents 132.94000 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 132.94000 cents, class 1 Average step (divided formal octave): 299.2750 cents Largest one step interval : 354.72000 cents Average / Smallest step : 2.251204 Largest / Average step : 1.185264 Largest / Smallest step : 2.668271 Median interval of one step : 354.72000 cents, amount: 3 Most common interval of one step : 354.72000 cents, amount: 3 Least squares average step : 302.97133 cents, oct.: 1211.88533 cents Scale is strictly proper Scale has Myhill's property chromas: 221.78000 cents and 88.84000 cents, ratio: 2.496398 generators: 1 of 354.72000 cents and 3 of 842.38000 cents ET pair of linear temperament : 10&27 Scale is distributional even Scale is a mode of a 1684-tone equal temperament with octave 1197.100 cents degrees: 499 998 1185 1684 generators: 499 and 1185 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABA Step pattern size order : LLSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 132.94000 cents Scale diversity : 1.360032 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.444207 Rothenberg efficiency : 0.833333 redundancy: 0.166667 Efficiency x scale size : 3.333333 Number of different interval sizes : 6 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 132.94000 cents Most common intervals : 354.72000 cents & inv., amount: 3 Scale is a chain of 2 triads 0.0 354.720 842.380 cents Most common triad is 0.0 354.720 842.380 cents, amount: 2 Number of recognisable fifths : 2, average 709.4400 cents Number of recognisable fourths : 2, average 487.6600 cents Formal octave complements present : 3 = 75.0000% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 2-3 -- Rational properties --
FIT/MODE
4: 1 1 1 1 SP B ME I SD: 67.9060 c. M: 110.8900 c. 6: 2 2 0 2 P M DE SD: 54.2725 c. M:-88.6267 c. 7: 2 2 1 2 SP M ME SD: 15.5438 c. M: 25.3829 c. 10: 3 3 1 3 SP M DE SD: 5.4011 c. M:-8.8200 c. 17: 5 5 2 5 SP M DE SD: 3.2232 c. M: 5.2635 c. 27: 8 8 3 8 SP M DE SD: 0.0290 c. M: 0.0474 c. 955: 283 283 106 283 SP M DE SD: 0.0278 c. M:-0.0454 c. 982: 291 291 109 291 SP M DE SD: 0.0263 c. M:-0.0429 c. 1009: 299 299 112 299 SP M DE SD: 0.0248 c. M:-0.0405 c. 1036: 307 307 115 307 SP M DE SD: 0.0234 c. M:-0.0382 c. 1063: 315 315 118 315 SP M DE SD: 0.0221 c. M:-0.0360 c. 1090: 323 323 121 323 SP M DE SD: 0.0208 c. M:-0.0339 c. 1117: 331 331 124 331 SP M DE SD: 0.0196 c. M:-0.0320 c. 1144: 339 339 127 339 SP M DE SD: 0.0184 c. M:-0.0301 c. 1171: 347 347 130 347 SP M DE SD: 0.0173 c. M:-0.0283 c. 1198: 355 355 133 355 SP M DE SD: 0.0163 c. M:-0.0266 c. 1225: 363 363 136 363 SP M DE SD: 0.0153 c. M:-0.0250 c. 1252: 371 371 139 371 SP M DE SD: 0.0143 c. M:-0.0234 c. 1279: 379 379 142 379 SP M DE SD: 0.0134 c. M:-0.0219 c. 1306: 387 387 145 387 SP M DE SD: 0.0125 c. M:-0.0205 c. 1333: 395 395 148 395 SP M DE SD: 0.0117 c. M:-0.0191 c. 1360: 403 403 151 403 SP M DE SD: 0.0109 c. M:-0.0178 c. 1387: 411 411 154 411 SP M DE SD: 0.0101 c. M:-0.0165 c. 1414: 419 419 157 419 SP M DE SD: 0.0094 c. M:-0.0153 c. 1441: 427 427 160 427 SP M DE SD: 0.0087 c. M:-0.0141 c. 1468: 435 435 163 435 SP M DE SD: 0.0080 c. M:-0.0130 c. 1495: 443 443 166 443 SP M DE SD: 0.0073 c. M:-0.0119 c. 1522: 451 451 169 451 SP M DE SD: 0.0066 c. M:-0.0109 c. 1549: 459 459 172 459 SP M DE SD: 0.0060 c. M:-0.0098 c. 1576: 467 467 175 467 SP M DE SD: 0.0054 c. M:-0.0089 c. 1603: 475 475 178 475 SP M DE SD: 0.0048 c. M:-0.0079 c. 1630: 483 483 181 483 SP M DE SD: 0.0043 c. M:-0.0070 c. 1657: 491 491 184 491 SP M DE SD: 0.0037 c. M:-0.0061 c. 1684: 499 499 187 499 SP M DE SD: 0.0032 c. M:-0.0052 c. 1711: 507 507 190 507 SP M DE SD: 0.0027 c. M:-0.0044 c. 1738: 515 515 193 515 SP M DE SD: 0.0022 c. M:-0.0036 c. 1765: 523 523 196 523 SP M DE SD: 0.0017 c. M:-0.0028 c. 1792: 531 531 199 531 SP M DE SD: 0.0013 c. M:-0.0021 c. 1819: 539 539 202 539 SP M DE SD: 0.0008 c. M:-0.0013 c. 1846: 547 547 205 547 SP M DE SD: 0.0004 c. M:-0.0006 c. 1873: 555 555 208 555 SP M DE SD: 0.0000 c. M: 0.0001 c.
FIT/HARMONIC
1 x x x 2 S SD: 2.9000 cents 2 x 3 x 4 S SD: 4.0136 cents 3:4 x 5:6 S SD: 49.7914 cents 4:5:6:7:8 H SD: 32.6450 cents 5:6 x 8:10 S SD: 16.1895 cents 7:9 x 11:14 SD: 33.4222 cents 8:10:12:13:16 SD: 8.1625 cents 14:17:21:23:28 SD: 6.6209 cents 18:22:27:29:36 SD: 4.9826 cents 22:27:33:36:44 SD: 3.2476 cents 35:43:53:57:70 SD: 2.4317 cents 40:49:60:65:80 SD: 2.2263 cents 48:59:72:78:96 SD: 2.1520 cents 53:65:80:86:106 SD: 1.5958 cents 61:75:92:99:122 SD: 1.5283 cents 67:82:101:109:134 SD: 1.4642 cents 75:92:113:122:150 SD: 0.7710 cents 150:184:226:244:299 SD: 0.7664 cents 158:194:238:257:315 SD: 0.6693 cents 180:221:271:293:359 SD: 0.6304 cents 193:237:291:314:385 SD: 0.5806 cents 198:243:298:322:395 SD: 0.5725 cents 207:254:312:337:413 SD: 0.5291 cents 211:259:318:343:421 SD: 0.4648 cents 225:276:339:366:449 SD: 0.3540 cents 233:286:351:379:465 SD: 0.2100 cents 308:378:464:501:615 SD: 0.0575 cents