Scala analysis: well270a
270 et ordinaire 6*157+6*158
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 93.333 cents 93.333333 2: 195.556 cents 195.555556 3: 297.778 cents 297.777778 4: 391.111 cents 391.111111 5: 502.222 cents 502.222222 6: 591.111 cents 591.111111 7: 697.778 cents 697.777778 8: 795.556 cents 795.555556 9: 893.333 cents 893.333333 10: 1000.000 cents 1000.000000 11: 1088.889 cents 1088.888889 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 111.1111 cents 111.1111 1: 93.3333 cents 93.3333 2: 102.2222 cents 102.2222 3: 102.2222 cents 102.2222 4: 93.3333 cents 93.3333 5: 111.1111 cents 111.1111 6: 88.8889 cents 88.8889 7: 106.6667 cents 106.6667 8: 97.7778 cents 97.7778 9: 97.7778 cents 97.7778 10: 106.6667 cents 106.6667 11: 88.8889 cents 88.8889 12: 111.1111 cents 111.1111
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 88.88889 cents 1: 2 93.33333 cents 1: 2 97.77778 cents 1: 2 102.22222 cents 1: 2 106.66667 cents 1: 2 111.11111 cents 2: 5 195.55556 cents 2: 2 200.00000 cents 2: 5 204.44444 cents 3: 4 293.33333 cents 3: 2 297.77778 cents 3: 2 302.22222 cents 3: 4 306.66667 cents 4: 3 391.11111 cents 4: 2 395.55556 cents 4: 2 400.00000 cents 4: 2 404.44444 cents 4: 3 408.88889 cents 5: 6 497.77778 cents 5: 6 502.22222 cents 6: 1 586.66667 cents 6: 2 591.11111 cents 6: 2 595.55555 cents 6: 2 600.00000 cents 6: 2 604.44445 cents 6: 2 608.88889 cents 6: 1 613.33333 cents 7: 6 697.77778 cents 7: 6 702.22222 cents 8: 3 791.11111 cents 8: 2 795.55556 cents 8: 2 800.00000 cents 8: 2 804.44444 cents 8: 3 808.88889 cents 9: 4 893.33333 cents 9: 2 897.77778 cents 9: 2 902.22222 cents 9: 4 906.66667 cents 10: 5 995.55556 cents 10: 2 1000.00000 cents 10: 5 1004.44444 cents 11: 2 1088.88889 cents 11: 2 1093.33333 cents 11: 2 1097.77778 cents 11: 2 1102.22222 cents 11: 2 1106.66667 cents 11: 2 1111.11111 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 4.27273 = 47/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 93.3 195.6 297.8 391.1 502.2 591.1 697.8 795.6 893.3 1000.0 1088.9 1200.0 93.3 : 102.2 204.4 297.8 408.9 497.8 604.4 702.2 800.0 906.7 995.6 1106.7 1200.0 195.6 : 102.2 195.6 306.7 395.6 502.2 600.0 697.8 804.4 893.3 1004.4 1097.8 1200.0 297.8 : 93.3 204.4 293.3 400.0 497.8 595.6 702.2 791.1 902.2 995.6 1097.8 1200.0 391.1 : 111.1 200.0 306.7 404.4 502.2 608.9 697.8 808.9 902.2 1004.4 1106.7 1200.0 502.2 : 88.9 195.6 293.3 391.1 497.8 586.7 697.8 791.1 893.3 995.6 1088.9 1200.0 591.1 : 106.7 204.4 302.2 408.9 497.8 608.9 702.2 804.4 906.7 1000.0 1111.1 1200.0 697.8 : 97.8 195.6 302.2 391.1 502.2 595.6 697.8 800.0 893.3 1004.4 1093.3 1200.0 795.6 : 97.8 204.4 293.3 404.4 497.8 600.0 702.2 795.6 906.7 995.6 1102.2 1200.0 893.3 : 106.7 195.6 306.7 400.0 502.2 604.4 697.8 808.9 897.8 1004.4 1102.2 1200.0 1000.0: 88.9 200.0 293.3 395.6 497.8 591.1 702.2 791.1 897.8 995.6 1093.3 1200.0 1088.9: 111.1 204.4 306.7 408.9 502.2 613.3 702.2 808.9 906.7 1004.4 1111.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.8889 .. 111.1111 cents 22.22222 cents 88.88889 cents 2: 195.5556 .. 204.4444 cents 8.88889 cents 84.44444 cents 3: 293.3333 .. 306.6667 cents 13.33333 cents 88.88889 cents 4: 391.1111 .. 408.8889 cents 17.77778 cents 84.44444 cents 5: 497.7778 .. 502.2222 cents 4.44444 cents 88.88889 cents 6: 586.6667 .. 613.3333 cents 26.66667 cents 84.44444 cents 7: 697.7778 .. 702.2222 cents 4.44444 cents 84.44444 cents 8: 791.1111 .. 808.8889 cents 17.77778 cents 88.88889 cents 9: 893.3333 .. 906.6667 cents 13.33333 cents 84.44444 cents 10: 995.5556 .. 1004.4444 cents 8.88889 cents 88.88889 cents 11: 1088.8889 .. 1111.1111 cents 22.22222 cents 84.44444 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 88.88889 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 111.11111 cents Average / Smallest step : 1.125000 Largest / Average step : 1.111111 Largest / Smallest step : 1.250000 Median interval of one step : 100.00000 cents, amount: 0 Least squares average step : 99.48718 cents, oct.: 1193.84615 cents Scale is strictly proper Scale is a mode of a 270-tone equal temperament with octave 1200.000 cents degrees: 21 44 67 88 113 133 157 179 201 225 245 270 Least number of segments generator : 137 of 608.889 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 247 of 1097.778 cents and inv. generated superset size: 185 = 173 more = 1541.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBACDEFFEDC Step pattern size order : BDDBFAECCEAF Scale is a Constant Structure, by a margin of 84.44444 cents Scale diversity : 1.111751 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.866667 Rothenberg efficiency : 0.282558 redundancy: 0.717442 Efficiency x scale size : 3.390693 Number of different interval sizes : 47 = 4.27273 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 4.27273 = 47/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 4.44444 cents Number of recognisable fifths : 12, average 700.0000 cents Scale is a temperament ordinaire Best fifths form a closed circle Formal octave complements present : 3 = 25.0000% Limited transpositions with margin 22.2222 cents: 2 3 5 7 8 9 10 Limited inverse transpositions : 4 Inversional symmetry on degrees : 2 8 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 5.9490 c. M:-11.1111 c. Twelve-tone Chromatic (1/11-comma) 43: 3 4 4 3 4 3 4 4 3 4 3 4 SP M ME SD: 5.8728 c. M:-13.7468 c. 47: 4 4 4 3 5 3 4 4 4 4 4 4 SP D3 SD: 6.8637 c. M:-8.9835 c. 51: 4 4 5 4 4 4 5 4 4 5 3 5 SP D3 SD: 6.7084 c. M:-11.7647 c. 52: 4 4 5 4 5 4 4 4 5 4 4 5 SP D3 SD: 6.5034 c. M: 10.9402 c. 53: 4 4 5 4 5 4 5 4 4 5 4 5 SP M ME SD: 6.0577 c. M: 14.4235 c. 54: 4 5 4 5 5 4 4 5 4 5 4 5 SP D3 SD: 6.2854 c. M: 8.8889 c. 55: 4 5 5 4 5 4 5 4 5 5 4 5 SP M ME SD: 4.3218 c. M: 10.1010 c. Meantone Chromatic (3/17-comma) 65: 5 5 6 5 6 5 6 5 5 6 5 6 SP M ME SD: 4.3838 c. M: 10.9402 c. 67: 5 6 6 5 6 5 6 5 6 6 5 6 SP M ME SD: 3.5836 c. M: 7.4959 c. Meantone Chromatic (4/25-comma) 73: 6 6 6 6 7 5 6 6 6 7 5 7 SP SD: 4.5899 c. M: 7.3668 c. 74: 6 6 6 6 7 5 7 6 6 7 5 7 SP D3 S SD: 3.5014 c. M: 7.3273 c. 77: 6 7 6 6 7 6 7 6 6 7 6 7 SP M ME SD: 3.1262 c. M:-7.0418 c. 78: 6 7 6 6 8 5 7 7 6 7 6 7 SP SD: 4.3537 c. M: 6.4957 c. 79: 6 7 7 6 7 6 7 6 7 7 6 7 SP M ME SD: 3.3247 c. M:-6.0197 c. Meantone Chromatic (3/20-comma) 85: 7 7 7 7 8 6 7 7 7 8 6 8 SP SD: 3.8549 c. M: 6.0131 c. 86: 7 7 7 7 8 6 8 7 7 8 6 8 SP D3 S SD: 2.7291 c. M: 5.0646 c. 90: 7 8 7 7 9 6 8 8 7 8 7 8 SP SD: 3.6289 c. M: 4.4444 c. 91: 7 8 8 7 8 7 8 7 8 8 7 8 SP M ME SD: 3.3062 c. M:-5.6166 c. Meantone Chromatic (1/7-comma), Romieu-12 98: 8 8 8 8 9 7 9 8 8 9 7 9 SP D3 S SD: 2.3542 c. M:-4.6259 c. 108: 8 10 9 8 10 8 10 9 8 10 8 10 SP T3 SD: 2.9397 c. M: 4.4444 c. 110: 9 9 9 9 10 8 10 9 9 10 8 10 SP D3 S SD: 2.2556 c. M:-4.8485 c. 120: 9 11 10 9 11 9 11 10 9 11 9 11 SP T3 SD: 2.5860 c. M:-4.4444 c. 121: 9 11 10 9 12 9 10 10 10 11 9 11 SP SD: 2.8315 c. M: 4.3343 c. 122: 10 10 10 10 11 9 11 10 10 11 9 11 SP D3 S SD: 2.3197 c. M:-5.0273 c. 125: 10 10 11 10 11 10 11 10 10 11 9 12 SP SD: 2.6153 c. M:-4.0889 c. 126: 10 11 10 10 12 9 11 11 10 11 9 12 SP SD: 2.5331 c. M:-4.4444 c. 128: 10 11 11 10 12 9 11 11 10 12 9 12 SP SD: 2.3677 c. M: 4.0278 c. 129: 10 11 11 10 12 10 11 11 10 12 9 12 SP SD: 2.2370 c. M:-4.6512 c. 130: 10 11 11 10 12 10 11 11 11 11 10 12 SP D3 S SD: 2.6186 c. M: 5.4701 c. 132: 10 12 11 10 12 10 12 11 10 12 10 12 SP T3 SD: 2.4193 c. M:-4.4444 c. 134: 11 11 11 11 12 10 12 11 11 12 10 12 SP D3 S SD: 2.4617 c. M:-5.1741 c. 136: 10 12 12 10 13 10 12 11 11 12 10 13 SP S SD: 2.4255 c. M: 5.0980 c. 138: 11 11 12 11 13 10 12 11 12 12 10 13 SP SD: 2.3141 c. M: 4.2512 c. 140: 11 12 12 11 13 10 13 11 11 13 10 13 SP S SD: 2.4316 c. M:-5.0794 c. 141: 11 12 12 11 13 10 13 11 12 12 11 13 SP SD: 2.0466 c. M: 4.2553 c. 144: 11 12 13 11 13 11 13 11 12 13 11 13 SP T3 SD: 2.2164 c. M: 3.8889 c. 145: 11 13 12 11 14 10 13 12 12 13 11 13 SP SD: 2.2546 c. M: 3.5249 c. 148: 11 13 13 11 14 11 13 12 12 13 11 14 SP S SD: 1.9122 c. M: 4.1441 c. 149: 12 12 13 12 13 11 14 12 12 13 11 14 SP SD: 2.2994 c. M:-3.5198 c. 150: 12 12 13 12 14 11 13 12 13 13 11 14 SP SD: 2.0688 c. M: 3.5556 c. 152: 12 13 13 12 14 11 14 12 12 14 11 14 SP S SD: 2.4013 c. M:-4.8538 c. 153: 12 13 13 12 14 11 14 12 13 13 12 14 SP SD: 1.8191 c. M: 3.9216 c. 156: 12 13 14 12 14 12 14 12 13 14 12 14 SP T3 SD: 2.0930 c. M:-3.4188 c. 157: 12 14 13 12 15 11 14 13 13 14 11 15 SP SD: 1.9691 c. M: 3.5386 c. 160: 12 14 14 12 15 12 14 13 13 14 12 15 SP S SD: 1.5508 c. M: 3.3333 c. 162: 13 13 14 13 15 12 14 13 14 14 12 15 SP SD: 1.9598 c. M: 2.9630 c. 165: 13 14 14 13 15 12 15 13 14 15 12 15 SP SD: 1.7339 c. M:-3.6364 c. 169: 13 15 14 13 16 12 15 14 14 15 12 16 SP SD: 1.6386 c. M:-3.2610 c. 172: 13 15 15 13 16 13 15 14 14 15 13 16 SP S SD: 1.3413 c. M: 2.6357 c. 180: 14 15 16 14 16 14 16 14 15 16 13 17 SP SD: 1.8144 c. M: 2.2222 c. 181: 14 15 16 14 17 13 16 15 15 16 13 17 SP SD: 1.4312 c. M: 3.2904 c. 184: 14 16 16 14 17 14 16 15 15 16 14 17 SP S SD: 1.2756 c. M:-2.3671 c. 193: 15 16 17 15 18 14 17 16 16 17 14 18 SP SD: 1.2472 c. M: 2.8094 c. 203: 16 17 17 16 19 15 18 16 17 18 15 19 SP SD: 1.3687 c. M: 3.4373 c. 205: 16 17 18 16 19 15 18 17 17 18 15 19 SP SD: 1.1846 c. M: 2.3848 c. 215: 17 18 18 17 20 16 19 18 17 19 16 20 SP SD: 1.1056 c. M:-2.5840 c. 217: 17 18 19 17 20 16 19 18 18 19 16 20 SP SD: 1.2209 c. M:-2.5192 c. 220: 17 19 19 17 20 16 20 18 18 19 17 20 SP SD: 1.3689 c. M:-2.2222 c. 222: 17 19 19 17 21 16 20 18 18 20 16 21 SP S SD: 1.2863 c. M: 2.4024 c. 223: 17 19 19 18 20 17 20 18 18 20 16 21 SP SD: 1.4466 c. M: 1.8934 c. 227: 18 19 19 18 21 17 20 18 19 20 17 21 SP SD: 1.1125 c. M: 2.6040 c. 234: 18 20 20 18 22 17 21 19 19 21 17 22 SP S SD: 0.9152 c. M: 1.7094 c. 246: 19 21 21 19 23 18 22 20 20 22 18 23 SP S SD: 0.5804 c. M: 1.0840 c. 258: 20 22 22 20 24 19 23 21 21 23 19 24 SP S SD: 0.2767 c. M: 0.5168 c. 270: 21 23 23 21 25 20 24 22 22 24 20 25 SP S SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 2.0886 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.2997 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.9541 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.4231 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.5521 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.0174 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.5590 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.1298 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.3657 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.9457 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.8360 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.5353 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.6363 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.9432 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.2618 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.5801 cents 27:28:30:32:34:36:38:40:43:45:48:51:54 SD: 3.5707 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 3.1251 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.0737 cents 48:51:54:57:60:64:68:72:76:80:86:90:96 SD: 2.0010 cents 50:53:56:59:63:67:70:75:79:84:89:94:100 SD: 1.7305 cents 56:59:63:67:70:75:79:84:89:94:100:105:112 SD: 1.6298 cents 58:61:65:69:73:78:82:87:92:97:103:109:116 SD: 1.5882 cents 59:62:66:70:74:79:83:88:93:99:105:111:118 SD: 1.1873 cents 74:78:83:88:93:99:104:111:117:124:132:139:148 SD: 0.7462 cents 110:116:123:131:138:147:155:165:174:184:196:206:220 SD: 0.7100 cents 111:117:124:132:139:148:156:166:176:186:198:208:222 SD: 0.6559 cents 123:130:138:146:154:164:173:184:195:206:219:231:246 SD: 0.6138 cents 127:134:142:151:159:170:179:190:201:213:226:238:254 SD: 0.5328 cents 143:151:160:170:179:191:201:214:226:240:255:268:286 SD: 0.5152 cents 160:169:179:190:201:214:225:239:253:268:285:300:320 SD: 0.5001 cents 161:170:180:191:202:215:227:241:255:270:287:302:322 SD: 0.4790 cents 175:185:196:208:219:234:246:262:277:293:312:328:350 SD: 0.4262 cents 182:192:204:216:228:243:256:272:288:305:324:341:364 SD: 0.3954 cents 201:212:225:239:252:269:283:301:318:337:358:377:402 SD: 0.3518 cents 202:213:226:240:253:270:284:302:320:338:360:379:404 SD: 0.3318 cents 234:247:262:278:293:313:329:350:370:392:417:439:468 SD: 0.3041 cents 250:264:280:297:313:334:352:374:396:419:445:469:500 SD: 0.2913 cents 252:266:282:299:316:337:355:377:399:422:449:473:504 SD: 0.2885 cents 256:270:287:304:321:342:360:383:405:429:456:480:512 SD: 0.2845 cents 268:283:300:318:336:358:377:401:424:449:478:503:536 SD: 0.2743 cents 276:291:309:328:346:369:388:413:437:462:492:518:552 SD: 0.2677 cents 292:308:327:347:366:390:411:437:462:489:520:548:584 SD: 0.2353 cents 324:342:363:385:406:433:456:485:513:543:577:608:648 SD: 0.1884 cents 395:417:442:469:495:528:556:591:625:662:704:741:790 SD: 0.1712 cents 437:461:489:519:548:584:615:654:692:732:779:820:874 SD: 0.1559 cents 469:495:525:557:588:627:660:702:743:786:836:880:938 SD: 0.1424 cents 526:555:589:625:659:703:740:787:833:881:937:987:1052 SD: 0.1353 cents 560:591:627:665:702:748:788:838:887:938:998:1050:1120 SD: 0.1284 cents 576:608:645:684:722:770:810:862:912:965:1026:1080:1152 SD: 0.1129 cents