Scala analysis: xen18-erlich-beatles-10
7L 3s MOS for Beatles, L=132.94, s=88.84
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: 221.780 cents 221.780000 3: 354.720 cents 354.720000 4: 487.660 cents 487.660000 5: 576.500 cents 576.500000 6: 709.440 cents 709.440000 7: 842.380 cents 842.380000 8: 975.320 cents 975.320000 9: 1064.160 cents 1064.160000 10: 1197.100 cents 1197.100000
SHOW/INTERVAL
0: 132.9400 cents 132.9400 1: 132.9400 cents 132.9400 2: 88.8400 cents 88.8400 3: 132.9400 cents 132.9400 4: 132.9400 cents 132.9400 5: 88.8400 cents 88.8400 6: 132.9400 cents 132.9400 7: 132.9400 cents 132.9400 8: 132.9400 cents 132.9400 9: 88.8400 cents 88.8400 10: 132.9400 cents 132.9400
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 88.84000 cents 1: 7 132.94000 cents 2: 6 221.78000 cents 2: 4 265.88000 cents 3: 9 354.72000 cents 3: 1 398.82000 cents 4: 2 443.56000 cents 4: 8 487.66000 cents 5: 5 576.50000 cents 5: 5 620.60000 cents 6: 8 709.44000 cents 6: 2 753.54000 cents 7: 1 798.28000 cents 7: 9 842.38000 cents 8: 4 931.22000 cents 8: 6 975.32000 cents 9: 7 1064.16000 cents 9: 3 1108.26000 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 8 9 10 0.0 : 132.9 221.8 354.7 487.7 576.5 709.4 842.4 975.3 1064.2 1197.1 132.9 : 88.8 221.8 354.7 443.6 576.5 709.4 842.4 931.2 1064.2 1197.1 221.8 : 132.9 265.9 354.7 487.7 620.6 753.5 842.4 975.3 1108.3 1197.1 354.7 : 132.9 221.8 354.7 487.7 620.6 709.4 842.4 975.3 1064.2 1197.1 487.7 : 88.8 221.8 354.7 487.7 576.5 709.4 842.4 931.2 1064.2 1197.1 576.5 : 132.9 265.9 398.8 487.7 620.6 753.5 842.4 975.3 1108.3 1197.1 709.4 : 132.9 265.9 354.7 487.7 620.6 709.4 842.4 975.3 1064.2 1197.1 842.4 : 132.9 221.8 354.7 487.7 576.5 709.4 842.4 931.2 1064.2 1197.1 975.3 : 88.8 221.8 354.7 443.6 576.5 709.4 798.3 931.2 1064.2 1197.1 1064.2: 132.9 265.9 354.7 487.7 620.6 709.4 842.4 975.3 1108.3 1197.1 1197.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.8400 .. 132.9400 cents 44.10000 cents 88.84000 cents 2: 221.7800 .. 265.8800 cents 44.10000 cents 88.84000 cents 3: 354.7200 .. 398.8200 cents 44.10000 cents 88.84000 cents 4: 443.5600 .. 487.6600 cents 44.10000 cents 44.74000 cents 5: 576.5000 .. 620.6000 cents 44.10000 cents 88.84000 cents 6: 709.4400 .. 753.5400 cents 44.10000 cents 88.84000 cents 7: 798.2800 .. 842.3800 cents 44.10000 cents 44.74000 cents 8: 931.2200 .. 975.3200 cents 44.10000 cents 88.84000 cents 9: 1064.1600 .. 1108.2600 cents 44.10000 cents 88.84000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 88.84000 cents, class 1 Average step (divided formal octave): 119.7100 cents Largest one step interval : 132.94000 cents Average / Smallest step : 1.347479 Largest / Average step : 1.110517 Largest / Smallest step : 1.496398 Median interval of one step : 132.94000 cents, amount: 7 Most common interval of one step : 132.94000 cents, amount: 7 Least squares average step : 119.42364 cents, oct.: 1194.23636 cents Scale is strictly proper Scale has Myhill's property chromas: 44.10000 cents and 44.74000 cents, ratio: 1.014512 generators: 3 of 354.72000 cents and 7 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 1792-tone equal temperament with octave 1197.100 cents degrees: 199 332 531 730 863 1062 1261 1460 1593 1792 generators: 531 and 1261 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAAABA Step pattern size order : LSLLSLLLSL Scale is a Constant Structure, by a margin of 44.74000 cents Scale diversity : 1.231251 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.668449 Rothenberg efficiency : 0.733333 redundancy: 0.266667 Efficiency x scale size : 7.333333 Number of different interval sizes : 18 = 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: 9 Scale is a chain of 5 triads 0.0 221.780 842.380 cents Most common triad is 0.0 354.720 842.380 cents, amount: 8 Number of recognisable fifths : 8, average 709.4400 cents Number of recognisable fourths : 8, average 487.6600 cents Best major thirds form a closed circle Formal octave complements present : 9 = 90.0000% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 6-7 -- Rational properties --
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 12.8572 c. M:-22.0500 c. 17: 2 1 2 2 1 2 2 2 1 2 P M ME SD: 7.6728 c. M: 13.1588 c. Neutral Dorian Decatonic, Maqamic-10 27: 3 2 3 3 2 3 3 3 2 3 SP M ME SD: 0.0691 c. M: 0.1185 c. 955: 106 71 106 106 71 106 106 106 71 106 SP M DE SD: 0.0662 c. M:-0.1136 c. 982: 109 73 109 109 73 109 109 109 73 109 SP M DE SD: 0.0625 c. M:-0.1072 c. 1009: 112 75 112 112 75 112 112 112 75 112 SP M DE SD: 0.0590 c. M:-0.1012 c. 1036: 115 77 115 115 77 115 115 115 77 115 SP M DE SD: 0.0557 c. M:-0.0955 c. 1063: 118 79 118 118 79 118 118 118 79 118 SP M DE SD: 0.0525 c. M:-0.0900 c. 1090: 121 81 121 121 81 121 121 121 81 121 SP M DE SD: 0.0495 c. M:-0.0849 c. 1117: 124 83 124 124 83 124 124 124 83 124 SP M DE SD: 0.0466 c. M:-0.0799 c. 1144: 127 85 127 127 85 127 127 127 85 127 SP M DE SD: 0.0439 c. M:-0.0753 c. 1171: 130 87 130 130 87 130 130 130 87 130 SP M DE SD: 0.0413 c. M:-0.0708 c. 1198: 133 89 133 133 89 133 133 133 89 133 SP M DE SD: 0.0388 c. M:-0.0665 c. 1225: 136 91 136 136 91 136 136 136 91 136 SP M DE SD: 0.0364 c. M:-0.0624 c. 1252: 139 93 139 139 93 139 139 139 93 139 SP M DE SD: 0.0341 c. M:-0.0585 c. 1279: 142 95 142 142 95 142 142 142 95 142 SP M DE SD: 0.0320 c. M:-0.0548 c. 1306: 145 97 145 145 97 145 145 145 97 145 SP M DE SD: 0.0299 c. M:-0.0512 c. 1333: 148 99 148 148 99 148 148 148 99 148 SP M DE SD: 0.0279 c. M:-0.0478 c. 1360: 151 101 151 151 101 151 151 151 101 151 SP M DE SD: 0.0259 c. M:-0.0445 c. 1387: 154 103 154 154 103 154 154 154 103 154 SP M DE SD: 0.0241 c. M:-0.0413 c. 1414: 157 105 157 157 105 157 157 157 105 157 SP M DE SD: 0.0223 c. M:-0.0383 c. 1441: 160 107 160 160 107 160 160 160 107 160 SP M DE SD: 0.0206 c. M:-0.0353 c. 1468: 163 109 163 163 109 163 163 163 109 163 SP M DE SD: 0.0189 c. M:-0.0325 c. 1495: 166 111 166 166 111 166 166 166 111 166 SP M DE SD: 0.0174 c. M:-0.0298 c. 1522: 169 113 169 169 113 169 169 169 113 169 SP M DE SD: 0.0158 c. M:-0.0271 c. 1549: 172 115 172 172 115 172 172 172 115 172 SP M DE SD: 0.0143 c. M:-0.0246 c. 1576: 175 117 175 175 117 175 175 175 117 175 SP M DE SD: 0.0129 c. M:-0.0221 c. 1603: 178 119 178 178 119 178 178 178 119 178 SP M DE SD: 0.0115 c. M:-0.0198 c. 1630: 181 121 181 181 121 181 181 181 121 181 SP M DE SD: 0.0102 c. M:-0.0175 c. 1657: 184 123 184 184 123 184 184 184 123 184 SP M DE SD: 0.0089 c. M:-0.0153 c. 1684: 187 125 187 187 125 187 187 187 125 187 SP M DE SD: 0.0077 c. M:-0.0131 c. 1711: 190 127 190 190 127 190 190 190 127 190 SP M DE SD: 0.0064 c. M:-0.0110 c. 1738: 193 129 193 193 129 193 193 193 129 193 SP M DE SD: 0.0053 c. M:-0.0090 c. 1765: 196 131 196 196 131 196 196 196 131 196 SP M DE SD: 0.0041 c. M:-0.0071 c. 1792: 199 133 199 199 133 199 199 199 133 199 SP M DE SD: 0.0030 c. M:-0.0052 c. 1819: 202 135 202 202 135 202 202 202 135 202 SP M DE SD: 0.0020 c. M:-0.0034 c. 1846: 205 137 205 205 137 205 205 205 137 205 SP M DE SD: 0.0009 c. M:-0.0016 c. 1873: 208 139 208 208 139 208 208 208 139 208 SP M DE SD: 0.0001 c. M: 0.0002 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 2.9000 cents 2 x x x x x 3 x x x 4 S SD: 4.0136 cents 3 x x x 4 x x 5 x x 6 S SD: 14.4471 cents 4 x x 5 x x 6 x 7 x 8 S SD: 8.3095 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 12.9342 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 10.7840 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 14.2603 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 6.4261 cents 9 x 10:11:12:13:14:15:16:17:18 S SD: 12.1544 cents 10:11 x 12:13:14:15:16:18 x 20 S SD: 9.9883 cents 11:12 x 14 x 15:17:18:19:20:22 SD: 12.2376 cents 12:13:14:15:16:17:18:20:21:22:24 S SD: 7.7207 cents 13:14:15:16:17:18:20:21:23:24:26 SD: 5.5392 cents 21:23:24:26:28:29:32:34:37:39:42 SD: 4.3469 cents 22:24:25:27:29:31:33:36:39:41:44 SD: 3.6091 cents 27:29:31:33:36:38:41:44:47:50:54 SD: 3.5186 cents 28:30:32:34:37:39:42:46:49:52:56 SD: 3.3247 cents 34:37:39:42:45:47:51:55:60:63:68 SD: 3.2371 cents 35:38:40:43:46:49:53:57:61:65:70 SD: 2.7570 cents 36:39:41:44:48:50:54:59:63:67:72 SD: 2.5764 cents 37:40:42:45:49:52:56:60:65:68:74 SD: 2.5246 cents 38:41:43:47:50:53:57:62:67:70:76 SD: 2.3910 cents 40:43:45:49:53:56:60:65:70:74:80 SD: 2.3190 cents 45:49:51:55:60:63:68:73:79:83:90 SD: 2.2643 cents 48:52:55:59:64:67:72:78:84:89:96 SD: 2.1735 cents 49:53:56:60:65:68:74:80:86:91:98 SD: 1.8040 cents 53:57:60:65:70:74:80:86:93:98:106 SD: 1.3420 cents 61:66:69:75:81:85:92:99:107:113:122 SD: 1.2314 cents 65:70:74:80:86:91:98:106:114:120:130 SD: 1.1830 cents 73:79:83:90:97:102:110:119:128:135:146 SD: 1.1498 cents 86:93:98:106:114:120:130:140:151:159:172 SD: 1.1114 cents 87:94:99:107:115:121:131:142:153:161:174 SD: 1.0771 cents 88:95:100:108:117:123:133:143:155:163:176 SD: 1.0707 cents 89:96:101:109:118:124:134:145:156:165:178 SD: 0.9076 cents 101:109:115:124:134:141:152:164:177:187:202 SD: 0.7580 cents 123:133:140:151:163:172:185:200:216:227:246 SD: 0.7443 cents 124:134:141:152:164:173:187:202:218:229:248 SD: 0.6692 cents 139:150:158:171:184:194:209:226:244:257:278 SD: 0.6605 cents 154:166:175:189:204:215:232:251:271:285:307 SD: 0.6488 cents 160:173:182:196:212:223:241:260:281:296:319 SD: 0.5680 cents 175:189:199:215:232:244:264:285:307:324:349 SD: 0.5325 cents 184:199:209:226:244:257:277:299:323:340:367 SD: 0.5109 cents 185:200:210:227:245:258:279:301:325:342:369 SD: 0.4366 cents 190:205:216:233:252:265:286:309:334:351:379 SD: 0.3918 cents 212:229:241:260:281:296:319:345:372:392:423 SD: 0.3678 cents 225:243:256:276:298:314:339:366:395:416:449 SD: 0.2766 cents 276:298:314:339:366:385:416:449:485:510:551 SD: 0.2729 cents 286:309:325:351:379:399:431:465:502:529:571 SD: 0.2112 cents 316:341:359:388:419:441:476:514:555:584:631 SD: 0.2083 cents 365:394:415:448:484:509:550:594:641:675:729 SD: 0.1754 cents 440:475:500:540:583:614:663:716:773:814:879 SD: 0.1715 cents 476:514:541:584:631:664:717:774:836:880:950 SD: 0.1424 cents 541:584:615:664:717:755:815:880:950:1000:1080 SD: 0.1171 cents