Scala analysis: xen18-erlich-beatles-07
3L 4s MOS for Beatles, L=221.78, s=132.94
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 132.940 cents 132.940000 2: 354.720 cents 354.720000 3: 487.660 cents 487.660000 4: 709.440 cents 709.440000 5: 842.380 cents 842.380000 6: 1064.160 cents 1064.160000 7: 1197.100 cents 1197.100000
SHOW/INTERVAL
0: 132.9400 cents 132.9400 1: 132.9400 cents 132.9400 2: 221.7800 cents 221.7800 3: 132.9400 cents 132.9400 4: 221.7800 cents 221.7800 5: 132.9400 cents 132.9400 6: 221.7800 cents 221.7800 7: 132.9400 cents 132.9400
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 132.94000 cents 1: 3 221.78000 cents 2: 1 265.88000 cents 2: 6 354.72000 cents 3: 5 487.66000 cents 3: 2 576.50000 cents 4: 2 620.60000 cents 4: 5 709.44000 cents 5: 6 842.38000 cents 5: 1 931.22000 cents 6: 3 975.32000 cents 6: 4 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 5 6 7 0.0 : 132.9 354.7 487.7 709.4 842.4 1064.2 1197.1 132.9 : 221.8 354.7 576.5 709.4 931.2 1064.2 1197.1 354.7 : 132.9 354.7 487.7 709.4 842.4 975.3 1197.1 487.7 : 221.8 354.7 576.5 709.4 842.4 1064.2 1197.1 709.4 : 132.9 354.7 487.7 620.6 842.4 975.3 1197.1 842.4 : 221.8 354.7 487.7 709.4 842.4 1064.2 1197.1 1064.2: 132.9 265.9 487.7 620.6 842.4 975.3 1197.1 1197.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 132.9400 .. 221.7800 cents 88.84000 cents 132.94000 cents 2: 265.8800 .. 354.7200 cents 88.84000 cents 44.10000 cents 3: 487.6600 .. 576.5000 cents 88.84000 cents 132.94000 cents 4: 620.6000 .. 709.4400 cents 88.84000 cents 44.10000 cents 5: 842.3800 .. 931.2200 cents 88.84000 cents 132.94000 cents 6: 975.3200 .. 1064.1600 cents 88.84000 cents 44.10000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 132.94000 cents, class 1 Average step (divided formal octave): 171.0143 cents Largest one step interval : 221.78000 cents Average / Smallest step : 1.286402 Largest / Average step : 1.296851 Largest / Smallest step : 1.668271 Median interval of one step : 132.94000 cents, amount: 4 Most common interval of one step : 132.94000 cents, amount: 4 Least squares average step : 172.28343 cents, oct.: 1205.98400 cents Scale is strictly proper Scale has Myhill's property chromas: 88.84000 cents and 44.10000 cents, ratio: 2.014512 generators: 2 of 354.72000 cents and 5 of 842.38000 cents ET pair of linear temperament : 10&27 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1738-tone equal temperament with octave 1197.100 cents degrees: 193 515 708 1030 1223 1545 1738 generators: 515 and 1223 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABA Step pattern size order : SLSLSLS Scale is a Constant Structure, by a margin of 44.10000 cents Scale diversity : 1.261308 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.554724 Rothenberg efficiency : 0.761905 redundancy: 0.238095 Efficiency x scale size : 5.333333 Number of different interval sizes : 12 = 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 : 44.10000 cents Most common intervals : 354.72000 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 354.720 709.440 cents Most common triad is 0.0 354.720 842.380 cents, amount: 5 Number of recognisable fifths : 5, average 709.4400 cents Number of recognisable fourths : 5, average 487.6600 cents Scale contains two identical disjunct tetrachords Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 7 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 25.3829 c. M: 38.0743 c. Lebeng 10: 1 2 1 2 1 2 1 P M ME I SD: 8.8200 c. M: 13.2300 c. 17: 2 3 2 3 2 3 2 SP M ME I SD: 5.2635 c. M: 7.8953 c. Neutral Dorian, Maqamic-7 27: 3 5 3 5 3 5 3 SP M DE I SD: 0.0474 c. M:-0.0711 c. 955: 106 177 106 177 106 177 106 SP M DE I SD: 0.0454 c. M: 0.0682 c. 982: 109 182 109 182 109 182 109 SP M DE I SD: 0.0429 c. M: 0.0643 c. 1009: 112 187 112 187 112 187 112 SP M DE I SD: 0.0405 c. M: 0.0607 c. 1036: 115 192 115 192 115 192 115 SP M DE I SD: 0.0382 c. M: 0.0573 c. 1063: 118 197 118 197 118 197 118 SP M DE I SD: 0.0360 c. M: 0.0540 c. 1090: 121 202 121 202 121 202 121 SP M DE I SD: 0.0339 c. M: 0.0509 c. 1117: 124 207 124 207 124 207 124 SP M DE I SD: 0.0320 c. M: 0.0480 c. 1144: 127 212 127 212 127 212 127 SP M DE I SD: 0.0301 c. M: 0.0452 c. 1171: 130 217 130 217 130 217 130 SP M DE I SD: 0.0283 c. M: 0.0425 c. 1198: 133 222 133 222 133 222 133 SP M DE I SD: 0.0266 c. M: 0.0399 c. 1225: 136 227 136 227 136 227 136 SP M DE I SD: 0.0250 c. M: 0.0375 c. 1252: 139 232 139 232 139 232 139 SP M DE I SD: 0.0234 c. M: 0.0351 c. 1279: 142 237 142 237 142 237 142 SP M DE I SD: 0.0219 c. M: 0.0329 c. 1306: 145 242 145 242 145 242 145 SP M DE I SD: 0.0205 c. M: 0.0307 c. 1333: 148 247 148 247 148 247 148 SP M DE I SD: 0.0191 c. M: 0.0287 c. 1360: 151 252 151 252 151 252 151 SP M DE I SD: 0.0178 c. M: 0.0267 c. 1387: 154 257 154 257 154 257 154 SP M DE I SD: 0.0165 c. M:-0.0248 c. 1414: 157 262 157 262 157 262 157 SP M DE I SD: 0.0153 c. M: 0.0230 c. 1441: 160 267 160 267 160 267 160 SP M DE I SD: 0.0141 c. M: 0.0212 c. 1468: 163 272 163 272 163 272 163 SP M DE I SD: 0.0130 c. M: 0.0195 c. 1495: 166 277 166 277 166 277 166 SP M DE I SD: 0.0119 c. M:-0.0179 c. 1522: 169 282 169 282 169 282 169 SP M DE I SD: 0.0109 c. M: 0.0163 c. 1549: 172 287 172 287 172 287 172 SP M DE I SD: 0.0098 c. M: 0.0148 c. 1576: 175 292 175 292 175 292 175 SP M DE I SD: 0.0089 c. M: 0.0133 c. 1603: 178 297 178 297 178 297 178 SP M DE I SD: 0.0079 c. M: 0.0119 c. 1630: 181 302 181 302 181 302 181 SP M DE I SD: 0.0070 c. M: 0.0105 c. 1657: 184 307 184 307 184 307 184 SP M DE I SD: 0.0061 c. M: 0.0092 c. 1684: 187 312 187 312 187 312 187 SP M DE I SD: 0.0052 c. M: 0.0079 c. 1711: 190 317 190 317 190 317 190 SP M DE I SD: 0.0044 c. M: 0.0066 c. 1738: 193 322 193 322 193 322 193 SP M DE I SD: 0.0036 c. M: 0.0054 c. 1765: 196 327 196 327 196 327 196 SP M DE I SD: 0.0028 c. M:-0.0042 c. 1792: 199 332 199 332 199 332 199 SP M DE I SD: 0.0021 c. M: 0.0031 c. 1819: 202 337 202 337 202 337 202 SP M DE I SD: 0.0013 c. M: 0.0020 c. 1846: 205 342 205 342 205 342 205 SP M DE I SD: 0.0006 c. M: 0.0009 c. 1873: 208 347 208 347 208 347 208 SP M DE I SD: 0.0001 c. M:-0.0001 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 2.9000 cents 2 x x x 3 x x 4 S SD: 4.0136 cents 3 x x 4 x 5 x 6 S SD: 14.4471 cents 4 x 5 x 6 x 7:8 S SD: 25.1883 cents 5 x 6:7 x 8:9:10 S SD: 23.2585 cents 6 x 7:8:9:10:11:12 S SD: 16.5587 cents 7:8 x 9 x 11:13:14 SD: 25.3504 cents 8:9:10:11:12:13:15:16 SD: 14.8023 cents 9:10:11:12:14:15:17:18 SD: 13.4139 cents 10:11:12:13:15:16:18:20 SD: 11.7194 cents 12:13:15:16:18:20:22:24 SD: 8.0602 cents 13:14:16:17:20:21:24:26 SD: 6.4962 cents 21:23:26:28:32:34:39:42 SD: 5.4592 cents 22:24:27:29:33:36:41:44 SD: 3.9249 cents 27:29:33:36:41:44:50:54 SD: 3.0651 cents 35:38:43:46:53:57:65:70 SD: 3.0354 cents 39:42:48:52:59:63:72:78 SD: 2.7385 cents 40:43:49:53:60:65:74:80 SD: 1.6911 cents 53:57:65:70:80:86:98:106 SD: 1.6018 cents 61:66:75:81:92:99:113:122 SD: 1.1956 cents 89:96:109:118:134:145:165:178 SD: 1.0612 cents 101:109:124:134:152:164:187:202 SD: 0.7969 cents 126:136:155:167:190:205:233:252 SD: 0.7409 cents 150:162:184:199:226:244:277:299 SD: 0.5971 cents 166:179:204:220:250:270:307:331 SD: 0.5758 cents 172:186:211:228:259:280:318:343 SD: 0.5371 cents 185:200:227:245:279:301:342:369 SD: 0.5165 cents 199:215:244:264:300:324:368:397 SD: 0.5077 cents 203:219:249:269:306:330:375:405 SD: 0.4746 cents 211:228:259:280:318:343:390:421 SD: 0.4529 cents 212:229:260:281:319:345:392:423 SD: 0.4126 cents 225:243:276:298:339:366:416:449 SD: 0.2692 cents 286:309:351:379:431:465:529:571 SD: 0.2264 cents 326:352:400:432:491:530:603:651 SD: 0.2045 cents 338:365:415:448:509:550:625:675 SD: 0.1558 cents 501:541:615:664:755:815:926:1000 SD: 0.1557 cents 541:584:664:717:815:880:1000:1080 SD: 0.1245 cents 563:608:691:746:848:916:1041:1124 SD: 0.0927 cents