Scala analysis: xen18-erlich-superpyth-12
5L 7s MOS for Superpyth, L=166.79, s=51.95
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 51.950 cents 51.950000 2: 218.740 cents 218.740000 3: 270.690 cents 270.690000 4: 437.480 cents 437.480000 5: 489.430 cents 489.430000 6: 541.380 cents 541.380000 7: 708.170 cents 708.170000 8: 760.120 cents 760.120000 9: 926.910 cents 926.910000 10: 978.860 cents 978.860000 11: 1145.650 cents 1145.650000 12: 1197.600 cents 1197.600000
SHOW/INTERVAL
0: 51.9500 cents 51.9500 1: 51.9500 cents 51.9500 2: 166.7900 cents 166.7900 3: 51.9500 cents 51.9500 4: 166.7900 cents 166.7900 5: 51.9500 cents 51.9500 6: 51.9500 cents 51.9500 7: 166.7900 cents 166.7900 8: 51.9500 cents 51.9500 9: 166.7900 cents 166.7900 10: 51.9500 cents 51.9500 11: 166.7900 cents 166.7900 12: 51.9500 cents 51.9500
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 51.95000 cents 1: 5 166.79000 cents 2: 2 103.90000 cents 2: 10 218.74000 cents 3: 9 270.69000 cents 3: 3 385.53000 cents 4: 4 322.64000 cents 4: 8 437.48000 cents 5: 11 489.43000 cents 5: 1 604.27000 cents 6: 6 541.38000 cents 6: 6 656.22000 cents 7: 1 593.33000 cents 7: 11 708.17000 cents 8: 8 760.12000 cents 8: 4 874.96000 cents 9: 3 812.07000 cents 9: 9 926.91000 cents 10: 10 978.86000 cents 10: 2 1093.70000 cents 11: 5 1030.81000 cents 11: 7 1145.65000 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 11 12 0.0 : 51.9 218.7 270.7 437.5 489.4 541.4 708.2 760.1 926.9 978.9 1145.7 1197.6 51.9 : 166.8 218.7 385.5 437.5 489.4 656.2 708.2 875.0 926.9 1093.7 1145.6 1197.6 218.7 : 51.9 218.7 270.7 322.6 489.4 541.4 708.2 760.1 926.9 978.9 1030.8 1197.6 270.7 : 166.8 218.7 270.7 437.5 489.4 656.2 708.2 875.0 926.9 978.9 1145.6 1197.6 437.5 : 51.9 103.9 270.7 322.6 489.4 541.4 708.2 760.1 812.1 978.9 1030.8 1197.6 489.4 : 51.9 218.7 270.7 437.5 489.4 656.2 708.2 760.1 926.9 978.9 1145.6 1197.6 541.4 : 166.8 218.7 385.5 437.5 604.3 656.2 708.2 875.0 926.9 1093.7 1145.6 1197.6 708.2 : 51.9 218.7 270.7 437.5 489.4 541.4 708.2 760.1 926.9 978.9 1030.8 1197.6 760.1 : 166.8 218.7 385.5 437.5 489.4 656.2 708.2 875.0 926.9 978.9 1145.6 1197.6 926.9 : 51.9 218.7 270.7 322.6 489.4 541.4 708.2 760.1 812.1 978.9 1030.8 1197.6 978.9 : 166.8 218.7 270.7 437.5 489.4 656.2 708.2 760.1 926.9 978.9 1145.7 1197.6 1145.7: 51.9 103.9 270.7 322.6 489.4 541.4 593.3 760.1 812.1 978.9 1030.8 1197.6 1197.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.9500 .. 166.7900 cents 114.84000 cents 51.95000 cents 2: 103.9000 .. 218.7400 cents 114.84000 cents -62.89000 cents 3: 270.6900 .. 385.5300 cents 114.84000 cents 51.95000 cents 4: 322.6400 .. 437.4800 cents 114.84000 cents -62.89000 cents 5: 489.4300 .. 604.2700 cents 114.84000 cents 51.95000 cents 6: 541.3800 .. 656.2200 cents 114.84000 cents -62.89000 cents 7: 593.3300 .. 708.1700 cents 114.84000 cents -62.89000 cents 8: 760.1200 .. 874.9600 cents 114.84000 cents 51.95000 cents 9: 812.0700 .. 926.9100 cents 114.84000 cents -62.89000 cents 10: 978.8600 .. 1093.7000 cents 114.84000 cents 51.95000 cents 11: 1030.8100 .. 1145.6500 cents 114.84000 cents -62.89000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 51.95000 cents, class 1 Average step (divided formal octave): 99.8000 cents Largest one step interval : 166.79000 cents Average / Smallest step : 1.921078 Largest / Average step : 1.671242 Largest / Smallest step : 3.210587 Median interval of one step : 51.95000 cents, amount: 7 Most common interval of one step : 51.95000 cents, amount: 7 Least squares average step : 99.82945 cents, oct.: 1197.95335 cents Scale is not proper Scale has Myhill's property chromas: 114.84000 cents and 62.89000 cents, ratio: 1.826045 generators: 5 of 489.43000 cents and 7 of 708.17000 cents ET pair of linear temperament : 22&93 Scale is distributional even Scale is a mode of a 438-tone equal temperament with octave 1197.600 cents degrees: 19 80 99 160 179 198 259 278 339 358 419 438 generators: 179 and 259 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABAABABABA Step pattern size order : SLSLSSLSLSLS Scale is a Constant Structure, by a margin of 10.94000 cents Scale diversity : 1.249630 Lumma stability : 0.260271 Lumma impropriety factor : 0.305945 Rothenberg efficiency : 0.722222 redundancy: 0.277778 Efficiency x scale size : 8.666667 Number of different interval sizes : 22 = 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 : 10.94000 cents Most common intervals : 489.43000 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 51.950 708.170 cents Most common triad is 0.0 489.430 708.170 cents, amount: 10 Number of recognisable fifths : 11, average 708.1700 cents Number of recognisable fourths : 11, average 489.4300 cents Scale contains two identical disjunct hexachords Formal octave complements present : 11 = 91.6667% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 8-9 -- Rational properties --
FIT/MODE
12: 0 2 1 1 1 0 2 0 2 1 1 1 N T3 SD: 34.8795 c. M: 61.5200 c. 13: 1 1 1 2 0 1 2 0 2 1 1 1 N D3 SD: 26.6646 c. M: 40.1731 c. 16: 0 3 0 3 0 1 2 1 2 1 2 1 N SD: 28.3371 c. M: 51.9500 c. 17: 1 2 1 2 1 1 2 1 2 1 2 1 P M ME SD: 12.9038 c. M:-22.1965 c. Supra-12 22: 1 3 1 3 1 1 3 1 3 1 3 1 N M DE SD: 1.7345 c. M:-2.9836 c. Supra-12 71: 3 10 3 10 3 3 10 3 10 3 10 3 N M DE SD: 0.9398 c. M: 1.6166 c. 93: 4 13 4 13 4 4 13 4 13 4 13 4 N M DE SD: 0.3072 c. M: 0.5284 c. 115: 5 16 5 16 5 5 16 5 16 5 16 5 N M DE SD: 0.0834 c. M:-0.1435 c. 323: 14 45 14 45 14 14 45 14 45 14 45 14 N M DE SD: 0.0290 c. M: 0.0500 c. 438: 19 61 19 61 19 19 61 19 61 19 61 19 N M DE SD: 0.0005 c. M:-0.0008 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 2.4000 cents 2 x x x x x x 3 x x x x 4 S SD: 3.3311 cents 3 x x x x 4 x x x 5 x x 6 S SD: 14.4936 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 13.1412 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 17.9868 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 13.8589 cents 7 x 8 x 9 x 10 x 11:12 x x 14 S SD: 13.4347 cents 8 x 9 x 10 x 11:12 x x 14 x 16 S SD: 9.2523 cents 9 x 10:11 x 12 x x 14:15:16:17:18 S SD: 13.3499 cents 10 x 11:12:13 x 14:15:16:17:18:19:20 S SD: 11.2024 cents 11 x 12:13:14 x 15 x 17:19 x 21:22 SD: 10.0817 cents 12 x x 14:15:16 x 18:19 x 21:23:24 SD: 8.3679 cents 13:14 x 15 x 17:18 x 20:22:23:25:26 SD: 10.0607 cents 14:15:16 x 18 x 19:21:22:24:25:27:28 SD: 7.8464 cents 15:16:17:18:19:20:21 x 23:26 x 29:30 SD: 9.6092 cents 16:17:18:19 x 21:22:24:25:27:28:31:32 SD: 6.3898 cents 17:18:19:20:22 x 23 x 26:29:30:33:34 SD: 6.3674 cents 18:19:20:21:23:24:25:27:28:31:32:35:36 SD: 5.6893 cents 19:20 x 22:24:25:26:29 x 32:33:37:38 SD: 6.8673 cents 20:21:23 x 26 x 27:30:31:34:35:39:40 SD: 5.1760 cents 21:22:24:25:27:28:29:32:33:36:37:41:42 SD: 4.9133 cents 22:23:25:26:28:29:30:33:34:38:39:43:44 SD: 4.0308 cents 23:24:26:27:30 x 31:35:36:39:40:45:46 SD: 5.0872 cents 24:25:27:28:31:32:33:36:37:41:42:47:48 SD: 3.0846 cents 26:27 x 30:33:34:36:39:40:44:46:50:52 SD: 5.1419 cents 27:28:31:32:35:36:37:41:42:46:48:52:54 SD: 3.7369 cents 28:29:32:33:36:37:38:42:43:48:49:54:56 SD: 2.8838 cents 30:31:34:35:39:40:41:45:47:51:53:58:60 SD: 2.4465 cents 35:36:40:41:45:46:48:53:54:60:62:68:70 SD: 2.4321 cents 36:37:41:42:46:48:49:54:56:61:63:70:72 SD: 2.3185 cents 38:39:43:44:49:50:52:57:59:65:67:74:76 SD: 2.2033 cents 46:47:52:54:59:61:63:69:71:79:81:89:92 SD: 2.0018 cents 52:54:59:61:67:69:71:78:81:89:92:101:104 SD: 1.7041 cents 58:60:66:68:75:77:79:87:90:99:102:112:116 SD: 1.3961 cents 59:61:67:69:76:78:81:89:92:101:104:114:118 SD: 1.3804 cents 65:67:74:76:84:86:89:98:101:111:114:126:130 SD: 1.0707 cents 89:92:101:104:115:118:122:134:138:152:157:172:178 SD: 0.9802 cents 95:98:108:111:122:126:130:143:147:162:167:184:190 SD: 0.7358 cents 125:129:142:146:161:166:171:188:194:214:220:242:250 SD: 0.5699 cents 163:168:185:191:210:216:223:245:253:278:287:316:326 SD: 0.5452 cents 164:169:186:192:211:218:224:247:254:280:289:318:328 SD: 0.5267 cents 171:176:194:200:220:227:234:257:265:292:301:331:342 SD: 0.4716 cents 194:200:220:227:250:257:265:292:301:331:341:376:387 SD: 0.4457 cents 196:202:222:229:252:260:268:295:304:335:345:380:391 SD: 0.3984 cents 223:230:253:261:287:296:305:336:346:381:393:432:445 SD: 0.3456 cents 229:236:260:268:295:304:313:345:355:391:403:444:457 SD: 0.2863 cents 254:262:288:297:327:337:347:382:394:434:447:492:507 SD: 0.2827 cents 261:269:296:305:336:346:357:393:405:446:459:506:521 SD: 0.2469 cents 325:335:369:380:418:431:444:489:504:555:572:630:649 SD: 0.2387 cents 354:365:402:414:456:470:484:533:549:605:623:686:707 SD: 0.2171 cents 386:398:438:451:497:512:528:581:599:659:679:748:771 SD: 0.2092 cents 392:404:445:458:505:520:536:590:608:670:690:760:783 SD: 0.1902 cents 401:413:455:469:516:532:548:604:622:685:706:777:801 SD: 0.1641 cents 425:438:482:497:547:564:581:640:659:726:748:824:849 SD: 0.1382 cents 566:583:642:662:729:751:774:852:878:967:996:1097:1130 SD: 0.1354 cents