Scala analysis: xen18-erlich-pajara-12
10L 2s MOS for Pajara, L=106.57, s=65.60
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 106.570 cents 106.570000 2: 213.140 cents 213.140000 3: 319.710 cents 319.710000 4: 385.310 cents 385.310000 5: 491.880 cents 491.880000 6: 598.450 cents 598.450000 7: 705.020 cents 705.020000 8: 811.590 cents 811.590000 9: 918.160 cents 918.160000 10: 983.760 cents 983.760000 11: 1090.330 cents 1090.330000 12: 1196.900 cents 1196.900000
SHOW/INTERVAL
0: 106.5700 cents 106.5700 1: 106.5700 cents 106.5700 2: 106.5700 cents 106.5700 3: 106.5700 cents 106.5700 4: 65.6000 cents 65.6000 5: 106.5700 cents 106.5700 6: 106.5700 cents 106.5700 7: 106.5700 cents 106.5700 8: 106.5700 cents 106.5700 9: 106.5700 cents 106.5700 10: 65.6000 cents 65.6000 11: 106.5700 cents 106.5700 12: 106.5700 cents 106.5700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 65.60000 cents 1: 10 106.57000 cents 2: 4 172.17000 cents 2: 8 213.14000 cents 3: 6 278.74000 cents 3: 6 319.71000 cents 4: 8 385.31000 cents 4: 4 426.28000 cents 5: 10 491.88000 cents 5: 2 532.85000 cents 6: 12 598.45000 cents 7: 2 664.05000 cents 7: 10 705.02000 cents 8: 4 770.62000 cents 8: 8 811.59000 cents 9: 6 877.19000 cents 9: 6 918.16000 cents 10: 8 983.76000 cents 10: 4 1024.73000 cents 11: 10 1090.33000 cents 11: 2 1131.30000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.90909 = 21/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 106.6 213.1 319.7 385.3 491.9 598.4 705.0 811.6 918.2 983.8 1090.3 1196.9 106.6 : 106.6 213.1 278.7 385.3 491.9 598.4 705.0 811.6 877.2 983.8 1090.3 1196.9 213.1 : 106.6 172.2 278.7 385.3 491.9 598.4 705.0 770.6 877.2 983.8 1090.3 1196.9 319.7 : 65.6 172.2 278.7 385.3 491.9 598.4 664.1 770.6 877.2 983.8 1090.3 1196.9 385.3 : 106.6 213.1 319.7 426.3 532.9 598.4 705.0 811.6 918.2 1024.7 1131.3 1196.9 491.9 : 106.6 213.1 319.7 426.3 491.9 598.4 705.0 811.6 918.2 1024.7 1090.3 1196.9 598.4 : 106.6 213.1 319.7 385.3 491.9 598.4 705.0 811.6 918.2 983.8 1090.3 1196.9 705.0 : 106.6 213.1 278.7 385.3 491.9 598.4 705.0 811.6 877.2 983.8 1090.3 1196.9 811.6 : 106.6 172.2 278.7 385.3 491.9 598.5 705.0 770.6 877.2 983.8 1090.3 1196.9 918.2 : 65.6 172.2 278.7 385.3 491.9 598.4 664.1 770.6 877.2 983.8 1090.3 1196.9 983.8 : 106.6 213.1 319.7 426.3 532.8 598.4 705.0 811.6 918.2 1024.7 1131.3 1196.9 1090.3: 106.6 213.1 319.7 426.3 491.9 598.5 705.0 811.6 918.2 1024.7 1090.3 1196.9 1196.9
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 65.6000 .. 106.5700 cents 40.97000 cents 65.60000 cents 2: 172.1700 .. 213.1400 cents 40.97000 cents 65.60000 cents 3: 278.7400 .. 319.7100 cents 40.97000 cents 65.60000 cents 4: 385.3100 .. 426.2800 cents 40.97000 cents 65.60000 cents 5: 491.8800 .. 532.8500 cents 40.97000 cents 65.60000 cents 6: 598.4500 .. 598.4500 cents 1/1, 0.0000 cents 65.60000 cents 7: 664.0500 .. 705.0200 cents 40.97000 cents 65.60000 cents 8: 770.6200 .. 811.5900 cents 40.97000 cents 65.60000 cents 9: 877.1900 .. 918.1600 cents 40.97000 cents 65.60000 cents 10: 983.7600 .. 1024.7300 cents 40.97000 cents 65.60000 cents 11: 1090.3300 .. 1131.3000 cents 40.97000 cents 65.60000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 65.60000 cents, class 1 Average step (divided formal octave): 99.7417 cents Largest one step interval : 106.57000 cents Average / Smallest step : 1.520452 Largest / Average step : 1.068460 Largest / Smallest step : 1.624543 Median interval of one step : 106.57000 cents, amount: 10 Most common interval of one step : 106.57000 cents, amount: 10 Least squares average step : 99.95177 cents, oct.: 1199.42123 cents Scale is strictly proper Scale has 2 repeating blocks of 6 notes Blocks have Myhill's property chromas: 40.97000 cents and 24.63000 cents, ratio: 1.663419 generators: 1 of 106.57000 cents and 5 of 491.88000 cents ET pair of linear temperament : 22&34 Scale is maximally even for L / S <= 2 Scale is distributional even Step pattern alph. order: AAABAAAAABAA Step pattern size order : LLLSLLLLLSLL Scale is a Constant Structure, by a margin of 65.60000 cents Scale diversity : 1.226316 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.657699 Rothenberg efficiency (ambiguous key): 0.505556 redundancy: 0.494444 Efficiency x scale size : 6.066667 Number of different interval sizes : 21 = 1.90909 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.90909 = 21/11 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 40.97000 cents Most common intervals : 598.45000 cents & inv., amount: 12 Number of recognisable fifths : 10, average 705.0200 cents Number of recognisable fourths : 10, average 491.8800 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 10 = 83.3333% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 6 Limited inverse transpositions : 1 7 Inversional symmetry on intervals : 0-1 3-4 6-7 9-10 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 12.1511 c. M: 20.4850 c. Twelve-tone Chromatic (1/11-comma) 22: 2 2 2 1 2 2 2 2 2 1 2 2 SP B ME SD: 3.9845 c. M:-6.7173 c. Pajara-12 34: 3 3 3 2 3 3 3 3 3 2 3 3 SP B ME SD: 1.7104 c. M: 2.8835 c. Diaschismic-12, Pajara-12 56: 5 5 5 3 5 5 5 5 5 3 5 5 SP B DE SD: 0.5269 c. M:-0.8882 c. Pajara-12 90: 8 8 8 5 8 8 8 8 8 5 8 8 SP B DE SD: 0.3183 c. M: 0.5367 c. Pajara-12 146: 13 13 13 8 13 13 13 13 13 8 13 13 SP B DE SD: 0.0059 c. M:-0.0099 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 3.1000 cents 2 x x x x x x 3 x x x x 4 S SD: 2.1797 cents 3 x x x x 4 x x x 5 x x 6 S SD: 11.4995 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 3.8974 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.5617 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 12.5497 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.6812 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.2794 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.1652 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.4903 cents 11:12 x 13:14:15:16:17:18:19 x 21:22 SD: 11.8965 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 7.5035 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 7.7383 cents 14:15:16:17 x 19:20:21:22:24:25:26:28 SD: 5.9725 cents 15:16:17:18:19:20:21:23:24:25:26:28:30 SD: 5.5208 cents 16:17:18:19:20:21:23:24:26:27:28:30:32 SD: 4.6778 cents 18:19:20:22 x 24:25:27:29:31:32:34:36 SD: 5.6140 cents 20:21:23:24:25:27:28:30:32:34:35:38:40 SD: 4.5936 cents 24:26:27:29:30:32:34:36:38:41:42:45:48 SD: 3.5503 cents 29:31:33:35:36:39:41:44:46:49:51:54:58 SD: 3.3166 cents 30:32:34:36:37:40:42:45:48:51:53:56:60 SD: 2.5867 cents 39:41:44:47:49:52:55:59:62:66:69:73:78 SD: 2.4974 cents 40:43:45:48:50:53:57:60:64:68:71:75:80 SD: 2.3698 cents 43:46:49:52:54:57:61:65:69:73:76:81:86 SD: 2.2280 cents 44:47:50:53:55:58:62:66:70:75:78:83:88 SD: 1.9907 cents 46:49:52:55:57:61:65:69:74:78:81:86:92 SD: 1.9724 cents 48:51:54:58:60:64:68:72:77:82:85:90:96 SD: 1.6411 cents 60:64:68:72:75:80:85:90:96:102:106:113:120 SD: 1.0956 cents 77:82:87:93:96:102:109:116:123:131:136:145:154 SD: 1.0917 cents 80:85:90:96:100:106:113:120:128:136:141:150:160 SD: 1.0618 cents 84:89:95:101:105:112:119:126:134:143:148:158:168 SD: 1.0567 cents 89:95:101:107:111:118:126:134:142:151:157:167:178 SD: 1.0126 cents 92:98:104:111:115:122:130:138:147:156:162:173:184 SD: 0.8731 cents 97:103:110:117:121:129:137:146:155:165:171:182:194 SD: 0.7797 cents 107:114:121:129:134:142:151:161:171:182:189:201:214 SD: 0.7070 cents 124:132:140:149:155:165:175:186:198:211:219:233:248 SD: 0.6260 cents 137:146:155:165:171:182:194:206:219:233:242:257:274 SD: 0.5934 cents 153:163:173:184:191:203:216:230:245:260:270:287:305 SD: 0.5274 cents 173:184:196:208:216:230:244:260:276:294:305:325:345 SD: 0.5250 cents 177:188:200:213:221:235:250:266:283:301:312:332:353 SD: 0.4064 cents 189:201:214:227:236:251:267:284:302:321:334:355:377 SD: 0.3725 cents 221:235:250:266:276:294:312:332:353:376:390:415:441 SD: 0.3172 cents 237:252:268:285:296:315:335:356:379:403:418:445:473 SD: 0.2143 cents 344:366:389:414:430:457:486:517:550:585:607:646:687 SD: 0.1985 cents 366:389:414:440:457:486:517:550:585:622:646:687:731 SD: 0.1788 cents 457:486:517:550:571:607:646:687:730:777:807:858:912 SD: 0.1781 cents 472:502:534:568:590:627:667:709:754:802:833:886:942 SD: 0.1556 cents 473:503:535:569:591:628:668:711:756:804:835:888:944 SD: 0.1459 cents 489:520:553:588:611:650:691:735:781:831:863:918:976 SD: 0.1380 cents 533:567:603:641:666:708:753:801:852:906:941:1001:1064 SD: 0.1141 cents