Scala analysis: 15-27
15 out of 27-ET
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88.889 cents 88.888889 2: 177.778 cents 177.777778 3: 222.222 cents 222.222222 4: 311.111 cents 311.111111 5: 400.000 cents 400.000000 6: 488.889 cents 488.888889 7: 577.778 cents 577.777778 8: 622.222 cents 622.222222 9: 711.111 cents 711.111111 10: 800.000 cents 800.000000 11: 888.889 cents 888.888889 12: 977.778 cents 977.777778 13: 1022.222 cents 1022.222220 14: 1111.111 cents 1111.111110 15: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 88.8889 cents 88.8889 1: 88.8889 cents 88.8889 2: 88.8889 cents 88.8889 3: 44.4444 cents 44.4444 4: 88.8889 cents 88.8889 5: 88.8889 cents 88.8889 6: 88.8889 cents 88.8889 7: 88.8889 cents 88.8889 8: 44.4444 cents 44.4444 9: 88.8889 cents 88.8889 10: 88.8889 cents 88.8889 11: 88.8889 cents 88.8889 12: 88.8889 cents 88.8889 13: 44.4444 cents 44.4444 14: 88.8889 cents 88.8889 15: 88.8889 cents 88.8889
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 44.44444 cents 1: 12 88.88889 cents 2: 6 133.33333 cents 2: 9 177.77778 cents 3: 9 222.22222 cents 3: 6 266.66667 cents 4: 12 311.11111 cents 4: 3 355.55556 cents 5: 15 400.00000 cents 6: 3 444.44444 cents 6: 12 488.88889 cents 7: 6 533.33333 cents 7: 9 577.77778 cents 8: 9 622.22222 cents 8: 6 666.66667 cents 9: 12 711.11111 cents 9: 3 755.55556 cents 10: 15 800.00000 cents 11: 3 844.44444 cents 11: 12 888.88889 cents 12: 6 933.33333 cents 12: 9 977.77778 cents 13: 9 1022.22222 cents 13: 6 1066.66667 cents 14: 12 1111.11111 cents 14: 3 1155.55556 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.85714 = 13/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 88.9 177.8 222.2 311.1 400.0 488.9 577.8 622.2 711.1 800.0 888.9 977.8 1022.2 1111.1 1200.0 88.9 : 88.9 133.3 222.2 311.1 400.0 488.9 533.3 622.2 711.1 800.0 888.9 933.3 1022.2 1111.1 1200.0 177.8 : 44.4 133.3 222.2 311.1 400.0 444.4 533.3 622.2 711.1 800.0 844.4 933.3 1022.2 1111.1 1200.0 222.2 : 88.9 177.8 266.7 355.6 400.0 488.9 577.8 666.7 755.6 800.0 888.9 977.8 1066.7 1155.6 1200.0 311.1 : 88.9 177.8 266.7 311.1 400.0 488.9 577.8 666.7 711.1 800.0 888.9 977.8 1066.7 1111.1 1200.0 400.0 : 88.9 177.8 222.2 311.1 400.0 488.9 577.8 622.2 711.1 800.0 888.9 977.8 1022.2 1111.1 1200.0 488.9 : 88.9 133.3 222.2 311.1 400.0 488.9 533.3 622.2 711.1 800.0 888.9 933.3 1022.2 1111.1 1200.0 577.8 : 44.4 133.3 222.2 311.1 400.0 444.4 533.3 622.2 711.1 800.0 844.4 933.3 1022.2 1111.1 1200.0 622.2 : 88.9 177.8 266.7 355.6 400.0 488.9 577.8 666.7 755.6 800.0 888.9 977.8 1066.7 1155.6 1200.0 711.1 : 88.9 177.8 266.7 311.1 400.0 488.9 577.8 666.7 711.1 800.0 888.9 977.8 1066.7 1111.1 1200.0 800.0 : 88.9 177.8 222.2 311.1 400.0 488.9 577.8 622.2 711.1 800.0 888.9 977.8 1022.2 1111.1 1200.0 888.9 : 88.9 133.3 222.2 311.1 400.0 488.9 533.3 622.2 711.1 800.0 888.9 933.3 1022.2 1111.1 1200.0 977.8 : 44.4 133.3 222.2 311.1 400.0 444.4 533.3 622.2 711.1 800.0 844.4 933.3 1022.2 1111.1 1200.0 1022.2: 88.9 177.8 266.7 355.6 400.0 488.9 577.8 666.7 755.6 800.0 888.9 977.8 1066.7 1155.6 1200.0 1111.1: 88.9 177.8 266.7 311.1 400.0 488.9 577.8 666.7 711.1 800.0 888.9 977.8 1066.7 1111.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.4444 .. 88.8889 cents 44.44444 cents 44.44444 cents 2: 133.3333 .. 177.7778 cents 44.44444 cents 44.44444 cents 3: 222.2222 .. 266.6667 cents 44.44444 cents 44.44444 cents 4: 311.1111 .. 355.5556 cents 44.44444 cents 44.44444 cents 5: 400.0000 .. 400.0000 cents 1/1, 0.0000 cents 44.44444 cents 6: 444.4444 .. 488.8889 cents 44.44444 cents 44.44444 cents 7: 533.3333 .. 577.7778 cents 44.44444 cents 44.44444 cents 8: 622.2222 .. 666.6667 cents 44.44444 cents 44.44444 cents 9: 711.1111 .. 755.5556 cents 44.44444 cents 44.44444 cents 10: 800.0000 .. 800.0000 cents 1/1, 0.0000 cents 44.44444 cents 11: 844.4444 .. 888.8889 cents 44.44445 cents 44.44444 cents 12: 933.3333 .. 977.7778 cents 44.44445 cents 44.44444 cents 13: 1022.2222 .. 1066.6667 cents 44.44445 cents 44.44444 cents 14: 1111.1111 .. 1155.5556 cents 44.44445 cents 44.44444 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 44.44444 cents, class 1 Average step (divided formal octave): 80.0000 cents Largest one step interval : 88.88889 cents Average / Smallest step : 1.800000 Largest / Average step : 1.111111 Largest / Smallest step : 2.000000 Median interval of one step : 88.88889 cents, amount: 12 Most common interval of one step : 88.88889 cents, amount: 12 Least squares average step : 79.89247 cents, oct.: 1198.38710 cents Scale is strictly proper Scale is maximally even in 27-tone equal temperament Scale has 3 repeating blocks of 5 notes Blocks have Myhill's property chromas: 44.44444 cents and 0.00000 cents, ratio: 49382738.463745 generators: 1 of 88.88889 cents and 4 of 311.11111 cents ET pair of linear temperament : 27&27 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 27-tone equal temperament with octave 2/1 degrees: 2 4 5 7 9 11 13 14 16 18 20 22 23 25 27 Least number of segments generator : 16 of 711.111 cents and inv. number of contiguous generator circle segments: 2 Shortest superset generator : 16 of 711.111 cents and inv. generated superset size: 23 = 8 more = 153.333% Number of contiguous 1-step segments: 3 Scale is fully connected major-minor triadic in 27-tone equal temperament Step pattern alph. order: AABAAAABAAAABAA Step pattern size order : LLSLLLLSLLLLSLL Interval vector is [ 3 12 6 9 9 6 12 3 15 3 12 6 9 ] Scale is a Constant Structure, by a margin of 44.44444 cents Scale diversity : 1.217052 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.555556 Number of different interval sizes : 26 = 1.85714 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.85714 = 13/7 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 44.44444 cents Most common intervals : 400.00000 cents & inv., amount: 15 Most common triad is 0.0 400.000 800.000 cents, amount: 15 Number of recognisable fifths : 12, average 711.1111 cents Best minor thirds form a closed circle Formal octave complements present : 15 = 100.0000% Limited transpositions : 5 10 Limited inverse transpositions : 5 10 Inversional symmetry on degrees : 0 5 10 Inversional symmetry on intervals : 2-3 7-8 12-13 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
15: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 12.5708 c. M:-17.7778 c. 27: 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 SP B ME I SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x x 3 x x x x x 4 S SD: 4.5781 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 3.4052 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 4.6856 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 3.1727 cents 6 x x x 7 x 8 x x 9 x 10 x 11 x 12 S SD: 8.9474 cents 7 x x 8 x 9 x x 10 x 11:12 x x 13:14 S SD: 10.2522 cents 8 x x 9 x 10 x 11 x 12:13 x 14 x 15:16 S SD: 7.4488 cents 9 x 10 x 11 x 12 x 13 x 14:15:16 x 17:18 S SD: 6.4002 cents 10 x 11 x 12 x 13:14 x 15:16:17 x 18:19:20 S SD: 5.0855 cents 11 x 12 x 13:14 x 15:16:17 x 18:19:20:21:22 S SD: 8.2553 cents 12 x 13 x 14:15:16 x 17:18:19:20:21:22:23:24 S SD: 6.0708 cents 13:14 x 15 x 16:17:18:19:20:21:22:23 x 25:26 SD: 7.9048 cents 14:15 x 16:17:18:19 x 20:21:22:23 x 25:27:28 SD: 6.8442 cents 15:16 x 17:18:19:20:21 x 23:24:25:26:27:29:30 SD: 4.4800 cents 16:17 x 18:19:20:21:22:23:24:25:27:28:29:30:32 SD: 4.4076 cents 17:18:19 x 20:21:23:24 x 26:27:28:30:31:32:34 SD: 5.8383 cents 18:19:20 x 22:23:24:25:26:27:29:30:32 x 34:36 SD: 4.5688 cents 19:20:21:22:23:24:25 x 27:29:30:32:33:34:36:38 SD: 4.0662 cents 20:21:22:23:24:25:27:28:29:30:32:33:35:36:38:40 SD: 3.6752 cents 21:22:23:24:25:26:28:29:30:32:33:35:37:38:40:42 SD: 3.4843 cents 24:25 x 27:29:30:32 x 34:36:38:40:42:43:46:48 SD: 3.5884 cents 25:26:28 x 30:32:33:35:36:38:40:42:44:45:48:50 SD: 3.5992 cents 27:28:30:31:32:34:36:38:39:41:43:45:47:49:51:54 SD: 3.3157 cents 30:32:33:34:36:38:40:42:43:45:48:50:53:54:57:60 SD: 2.4014 cents 36:38:40:41:43:45:48:50:52:54:57:60:63:65:68:72 SD: 2.0341 cents 37:39:41:42:44:47:49:52:53:56:59:62:65:67:70:74 SD: 1.7522 cents 46:48:51:52:55:58:61:64:66:69:73:77:81:83:87:92 SD: 1.5471 cents 55:58:61:63:66:69:73:77:79:83:87:92:97:99:104:110 SD: 1.4138 cents 58:61:64:66:69:73:77:81:83:87:92:97:102:105:110:116 SD: 1.1597 cents 71:75:79:81:85:89:94:99:102:107:113:119:125:128:135:142 SD: 1.1436 cents 73:77:81:83:87:92:97:102:105:110:116:122:128:132:139:146 SD: 0.9311 cents 92:97:102:105:110:116:122:128:132:139:146:154:162:166:175:184 SD: 0.7567 cents 101:106:112:115:121:127:134:141:145:152:160:169:178:182:192:202 SD: 0.7099 cents 111:117:123:126:133:140:147:155:159:167:176:185:195:200:211:222 SD: 0.6009 cents 116:122:129:132:139:146:154:162:166:175:184:194:204:209:220:232 SD: 0.5897 cents 131:138:145:149:157:165:174:183:188:198:208:219:230:236:249:262 SD: 0.5471 cents 132:139:146:150:158:166:175:184:189:199:210:221:232:238:251:264 SD: 0.5340 cents 138:145:153:157:165:174:183:193:198:208:219:231:243:249:262:276 SD: 0.4628 cents 169:178:187:192:202:213:224:236:242:255:268:282:297:305:321:338 SD: 0.3647 cents 204:215:226:232:244:257:271:285:292:308:324:341:359:368:388:408 SD: 0.3464 cents 212:223:235:241:254:267:281:296:304:320:337:354:373:383:403:424 SD: 0.3298 cents 240:253:266:273:287:302:318:335:344:362:381:401:422:433:456:480 SD: 0.2903 cents 250:263:277:284:299:315:332:349:358:377:397:418:440:451:475:500 SD: 0.2426 cents 270:284:299:307:323:340:358:377:387:407:429:451:475:487:513:540 SD: 0.2183 cents 349:367:387:397:418:440:463:487:500:526:554:583:614:630:663:698 SD: 0.2177 cents 358:377:397:407:428:451:475:500:513:540:568:598:630:646:680:716 SD: 0.2008 cents 361:380:400:410:432:455:479:504:517:544:573:603:635:652:686:722 SD: 0.1920 cents 380:400:421:432:455:479:504:531:544:573:603:635:668:686:722:760 SD: 0.1727 cents 416:438:461:473:498:524:552:581:596:627:660:695:732:751:790:832 SD: 0.1388 cents 472:497:523:537:565:595:626:659:676:712:749:789:830:852:897:944 SD: 0.1376 cents 518:545:574:589:620:653:687:723:742:781:822:866:911:935:984:1036 SD: 0.1228 cents 548:577:607:623:656:690:727:765:785:826:870:916:964:989:1041:1096 SD: 0.1199 cents 585:616:648:665:700:737:776:817:838:882:929:978:1029:1056:1111:1170 SD: 0.1178 cents 589:620:653:670:705:742:781:822:844:888:935:984:1036:1063:1119:1178 SD: 0.1113 cents