Scala analysis: xen06-vyshnegradski-nonoctave-3
Non-octave scale based on the double octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 150.000 cents 150.000000 2: 400.000 cents 400.000000 3: 650.000 cents 650.000000 4: 850.000 cents 850.000000 5: 1000.000 cents 1000.000000 6: 1250.000 cents 1250.000000 7: 1450.000 cents 1450.000000 8: 1700.000 cents 1700.000000 9: 1950.000 cents 1950.000000 10: 2150.000 cents 2150.000000 11: 2400.000 cents 2400.000000
SHOW/INTERVAL
0: 250.0000 cents 250.0000 1: 150.0000 cents 150.0000 2: 250.0000 cents 250.0000 3: 250.0000 cents 250.0000 4: 200.0000 cents 200.0000 5: 150.0000 cents 150.0000 6: 250.0000 cents 250.0000 7: 200.0000 cents 200.0000 8: 250.0000 cents 250.0000 9: 250.0000 cents 250.0000 10: 200.0000 cents 200.0000 11: 250.0000 cents 250.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 150.00000 cents 1: 3 200.00000 cents 1: 6 250.00000 cents 2: 1 350.00000 cents 2: 3 400.00000 cents 2: 5 450.00000 cents 2: 2 500.00000 cents 3: 4 600.00000 cents 3: 2 650.00000 cents 3: 5 700.00000 cents 4: 1 800.00000 cents 4: 6 850.00000 cents 4: 2 900.00000 cents 4: 2 950.00000 cents 5: 1 1000.00000 cents 5: 2 1050.00000 cents 5: 6 1100.00000 cents 5: 2 1150.00000 cents 6: 2 1250.00000 cents 6: 6 1300.00000 cents 6: 2 1350.00000 cents 6: 1 1400.00000 cents 7: 2 1450.00000 cents 7: 2 1500.00000 cents 7: 6 1550.00000 cents 7: 1 1600.00000 cents 8: 5 1700.00000 cents 8: 2 1750.00000 cents 8: 4 1800.00000 cents 9: 2 1900.00000 cents 9: 5 1950.00000 cents 9: 3 2000.00000 cents 9: 1 2050.00000 cents 10: 6 2150.00000 cents 10: 3 2200.00000 cents 10: 2 2250.00000 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.60000 = 18/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 150.0 400.0 650.0 850.0 1000.0 1250.0 1450.0 1700.0 1950.0 2150.0 2400.0 150.0 : 250.0 500.0 700.0 850.0 1100.0 1300.0 1550.0 1800.0 2000.0 2250.0 2400.0 400.0 : 250.0 450.0 600.0 850.0 1050.0 1300.0 1550.0 1750.0 2000.0 2150.0 2400.0 650.0 : 200.0 350.0 600.0 800.0 1050.0 1300.0 1500.0 1750.0 1900.0 2150.0 2400.0 850.0 : 150.0 400.0 600.0 850.0 1100.0 1300.0 1550.0 1700.0 1950.0 2200.0 2400.0 1000.0: 250.0 450.0 700.0 950.0 1150.0 1400.0 1550.0 1800.0 2050.0 2250.0 2400.0 1250.0: 200.0 450.0 700.0 900.0 1150.0 1300.0 1550.0 1800.0 2000.0 2150.0 2400.0 1450.0: 250.0 500.0 700.0 950.0 1100.0 1350.0 1600.0 1800.0 1950.0 2200.0 2400.0 1700.0: 250.0 450.0 700.0 850.0 1100.0 1350.0 1550.0 1700.0 1950.0 2150.0 2400.0 1950.0: 200.0 450.0 600.0 850.0 1100.0 1300.0 1450.0 1700.0 1900.0 2150.0 2400.0 2150.0: 250.0 400.0 650.0 900.0 1100.0 1250.0 1500.0 1700.0 1950.0 2200.0 2400.0 2400.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.0000 .. 250.0000 cents 100.00000 cents 150.00000 cents 2: 350.0000 .. 500.0000 cents 150.00000 cents 100.00000 cents 3: 600.0000 .. 700.0000 cents 100.00000 cents 100.00000 cents 4: 800.0000 .. 950.0000 cents 150.00000 cents 100.00000 cents 5: 1000.0000 .. 1150.0000 cents 150.00000 cents 50.00000 cents 6: 1250.0000 .. 1400.0000 cents 150.00000 cents 100.00000 cents 7: 1450.0000 .. 1600.0000 cents 150.00000 cents 50.00000 cents 8: 1700.0000 .. 1800.0000 cents 100.00000 cents 100.00000 cents 9: 1900.0000 .. 2050.0000 cents 150.00000 cents 100.00000 cents 10: 2150.0000 .. 2250.0000 cents 100.00000 cents 100.00000 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 150.00000 cents, class 1 Average step (divided formal octave): 218.1818 cents Largest one step interval : 250.00000 cents Average / Smallest step : 1.454545 Largest / Average step : 1.145833 Largest / Smallest step : 1.666667 Median interval of one step : 250.00000 cents, amount: 6 Most common interval of one step : 250.00000 cents, amount: 6 Least squares average step : 213.43874 cents, oct.: 2347.82609 cents Scale is strictly proper Scale is a mode of a 48-tone equal temperament with octave 2400.000 cents degrees: 3 8 13 17 20 25 29 34 39 43 48 Least number of segments generator : 31 of 1550.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 35 of 1750.000 cents and inv. generated superset size: 21 = 10 more = 190.909% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBCABCBBCB Step pattern size order : SLLMSLMLLML Interval vector is [ 0 0 2 3 6 0 1 3 5 2 0 4 2 5 0 1 6 2 2 1 2 6 2 0 ] Scale is a Constant Structure, by a margin of 50.00000 cents Scale diversity :-0.060859 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.458333 Rothenberg efficiency : 0.357812 redundancy: 0.642188 Efficiency x scale size : 3.935931 Number of different interval sizes : 36 = 3.60000 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.60000 = 18/5 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 50.00000 cents Number of recognisable fifths : 5, average 700.0000 cents Number of recognisable fourths : 2, average 500.0000 cents Scale contains two identical disjunct "tetrachords" of 3 notes Best major thirds form a closed circle Formal octave complements present : 1 = 9.0909% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
11: 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 50.0000 c. M:-90.9091 c. 12: 1 1 1 1 1 1 1 2 1 1 1 P M ME S SD: 50.0000 c. M:-100.0000 c. 17: 1 2 2 1 1 2 1 2 2 1 2 P D3 SD: 26.2318 c. M:-55.8824 c. 20: 1 2 2 2 1 2 2 2 2 2 2 P D3 S SD: 31.1886 c. M: 50.0000 c. 22: 1 3 2 2 1 2 2 3 2 2 2 P T3 SD: 31.1017 c. M: 50.0000 c. 23: 1 3 2 2 2 2 2 2 3 2 2 P D3 SD: 28.4427 c. M: 45.6522 c. 25: 2 2 3 2 1 3 2 3 2 2 3 P T3 SD: 26.1673 c. M:-42.0000 c. 28: 2 3 3 2 2 3 2 3 3 2 3 SP D3 SD: 22.2776 c. M:-35.7143 c. 31: 2 3 3 3 2 3 3 3 3 3 3 SP D3 S SD: 14.3852 c. M: 30.6452 c. 37: 2 4 4 3 2 4 3 4 4 3 4 P SD: 14.8649 c. M: 27.0270 c. 43: 3 4 5 3 3 4 4 4 5 4 4 SP SD: 16.0624 c. M:-26.7442 c. 44: 3 4 5 4 2 5 4 4 5 3 5 P SD: 15.6862 c. M:-22.7273 c. 45: 3 5 4 4 3 4 4 5 5 3 5 SP SD: 15.4069 c. M:-26.6667 c. 47: 3 5 5 4 3 4 4 5 5 4 5 SP SD: 14.7792 c. M: 24.4681 c. 48: 3 5 5 4 3 5 4 5 5 4 5 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x 2 x x 3 x 4 S SD: 23.1140 cents 2 x x 3 x x 4 x 5:6:7:8 S SD: 24.0293 cents 3 x 4 x 5 x 6:7:8:9:10:12 S SD: 17.7654 cents 4 x 5:6 x 7:8:9:11:12:14:16 SD: 13.0427 cents 5 x 6:7:8:9:10:12:13:15:17:20 SD: 15.9675 cents 7:8:9:10:11:12:14:16:19:22:24:28 SD: 13.7642 cents 8:9:10:12:13:14:16:18:21:25:28:32 SD: 10.4442 cents 9:10:11:13:15:16:19:21:24:28:31:36 SD: 7.9678 cents 11:12:14:16:18:20:23:25:29:34:38:44 SD: 5.4472 cents 13:14:16:19:21:23:27:30:35:40:45:52 SD: 5.1217 cents 18:20:23:26:29:32:37:42:48:56:62:72 SD: 5.0011 cents 19:21:24:28:31:34:39:44:51:59:66:76 SD: 3.3699 cents 22:24:28:32:36:39:45:51:59:68:76:88 SD: 2.2948 cents 31:34:39:45:51:55:64:72:83:96:107:124 SD: 2.0892 cents 33:36:42:48:54:59:68:76:88:102:114:132 SD: 1.8580 cents 35:38:44:51:57:62:72:81:93:108:121:140 SD: 1.5536 cents 46:50:58:67:75:82:95:106:123:142:159:184 SD: 0.9957 cents 55:60:69:80:90:98:113:127:147:170:190:220 SD: 0.9465 cents 68:74:86:99:111:121:140:157:182:210:235:272 SD: 0.9094 cents 77:84:97:112:126:137:159:178:206:238:267:308 SD: 0.8021 cents 88:96:111:128:144:157:181:203:235:271:305:352 SD: 0.5735 cents 112:122:141:163:183:200:231:259:299:345:388:448 SD: 0.5683 cents 119:130:150:173:194:212:245:275:318:367:412:476 SD: 0.5228 cents 120:131:151:175:196:214:247:277:320:370:415:480 SD: 0.5138 cents 123:134:155:179:201:219:253:284:328:379:426:492 SD: 0.3634 cents 142:155:179:207:232:253:292:328:379:438:492:568 SD: 0.3602 cents 169:184:213:246:276:301:348:391:451:521:585:676 SD: 0.3587 cents 178:194:224:259:291:317:366:411:475:549:616:712 SD: 0.3439 cents 188:205:237:274:307:335:387:434:502:580:651:752 SD: 0.2818 cents 189:206:238:275:309:337:389:437:505:583:654:756 SD: 0.2755 cents 200:218:252:291:327:356:412:462:534:617:692:800 SD: 0.2665 cents 219:239:276:319:358:390:451:506:585:675:758:876 SD: 0.2583 cents 235:256:296:342:384:419:484:543:627:725:814:940 SD: 0.2511 cents 254:277:320:370:415:453:523:587:678:783:879:1016 SD: 0.2221 cents 257:280:324:374:420:458:529:594:686:793:890:1028 SD: 0.2055 cents 308:336:388:448:503:549:634:712:822:950:1066:1232 SD: 0.1932 cents 312:340:393:454:510:556:642:721:833:962:1080:1248 SD: 0.1758 cents 320:349:403:466:523:570:659:739:854:987:1108:1280 SD: 0.1684 cents 331:361:417:482:541:590:681:765:884:1021:1146:1324 SD: 0.1525 cents 342:373:431:498:559:609:704:790:913:1055:1184:1368 SD: 0.1432 cents 377:411:475:549:616:672:776:871:1006:1163:1305:1508 SD: 0.1325 cents 408:445:514:594:667:727:840:943:1089:1258:1413:1632 SD: 0.1314 cents 454:495:572:661:742:809:935:1049:1212:1400:1572:1816 SD: 0.1001 cents 531:579:669:773:868:946:1093:1227:1418:1638:1838:2124 SD: 0.0981 cents 573:625:722:834:936:1021:1180:1324:1530:1767:1984:2292 SD: 0.0925 cents