Scala analysis: xen18-erlich-augene-15
12L 3s MOS for Augene, L=92.46, s=29.18
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 92.460 cents 92.460000 2: 184.920 cents 184.920000 3: 214.100 cents 214.100000 4: 306.560 cents 306.560000 5: 399.020 cents 399.020000 6: 491.480 cents 491.480000 7: 583.940 cents 583.940000 8: 613.120 cents 613.120000 9: 705.580 cents 705.580000 10: 798.040 cents 798.040000 11: 890.500 cents 890.500000 12: 982.960 cents 982.960000 13: 1012.140 cents 1012.140000 14: 1104.600 cents 1104.600000 15: 1197.060 cents 1197.060000
SHOW/INTERVAL
0: 92.4600 cents 92.4600 1: 92.4600 cents 92.4600 2: 92.4600 cents 92.4600 3: 29.1800 cents 29.1800 4: 92.4600 cents 92.4600 5: 92.4600 cents 92.4600 6: 92.4600 cents 92.4600 7: 92.4600 cents 92.4600 8: 29.1800 cents 29.1800 9: 92.4600 cents 92.4600 10: 92.4600 cents 92.4600 11: 92.4600 cents 92.4600 12: 92.4600 cents 92.4600 13: 29.1800 cents 29.1800 14: 92.4600 cents 92.4600 15: 92.4600 cents 92.4600
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 29.18000 cents 1: 12 92.46000 cents 2: 6 121.64000 cents 2: 9 184.92000 cents 3: 9 214.10000 cents 3: 6 277.38000 cents 4: 12 306.56000 cents 4: 3 369.84000 cents 5: 15 399.02000 cents 6: 3 428.20000 cents 6: 12 491.48000 cents 7: 6 520.66000 cents 7: 9 583.94000 cents 8: 9 613.12000 cents 8: 6 676.40000 cents 9: 12 705.58000 cents 9: 3 768.86000 cents 10: 15 798.04000 cents 11: 3 827.22000 cents 11: 12 890.50000 cents 12: 6 919.68000 cents 12: 9 982.96000 cents 13: 9 1012.14000 cents 13: 6 1075.42000 cents 14: 12 1104.60000 cents 14: 3 1167.88000 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 : 92.5 184.9 214.1 306.6 399.0 491.5 583.9 613.1 705.6 798.0 890.5 983.0 1012.1 1104.6 1197.1 92.5 : 92.5 121.6 214.1 306.6 399.0 491.5 520.7 613.1 705.6 798.0 890.5 919.7 1012.1 1104.6 1197.1 184.9 : 29.2 121.6 214.1 306.6 399.0 428.2 520.7 613.1 705.6 798.0 827.2 919.7 1012.1 1104.6 1197.1 214.1 : 92.5 184.9 277.4 369.8 399.0 491.5 583.9 676.4 768.9 798.0 890.5 983.0 1075.4 1167.9 1197.1 306.6 : 92.5 184.9 277.4 306.6 399.0 491.5 583.9 676.4 705.6 798.0 890.5 983.0 1075.4 1104.6 1197.1 399.0 : 92.5 184.9 214.1 306.6 399.0 491.5 583.9 613.1 705.6 798.0 890.5 983.0 1012.1 1104.6 1197.1 491.5 : 92.5 121.6 214.1 306.6 399.0 491.5 520.7 613.1 705.6 798.0 890.5 919.7 1012.1 1104.6 1197.1 583.9 : 29.2 121.6 214.1 306.6 399.0 428.2 520.7 613.1 705.6 798.0 827.2 919.7 1012.1 1104.6 1197.1 613.1 : 92.5 184.9 277.4 369.8 399.0 491.5 583.9 676.4 768.9 798.0 890.5 983.0 1075.4 1167.9 1197.1 705.6 : 92.5 184.9 277.4 306.6 399.0 491.5 583.9 676.4 705.6 798.0 890.5 983.0 1075.4 1104.6 1197.1 798.0 : 92.5 184.9 214.1 306.6 399.0 491.5 583.9 613.1 705.6 798.0 890.5 983.0 1012.1 1104.6 1197.1 890.5 : 92.5 121.6 214.1 306.6 399.0 491.5 520.7 613.1 705.6 798.0 890.5 919.7 1012.1 1104.6 1197.1 983.0 : 29.2 121.6 214.1 306.6 399.0 428.2 520.7 613.1 705.6 798.0 827.2 919.7 1012.1 1104.6 1197.1 1012.1: 92.5 184.9 277.4 369.8 399.0 491.5 583.9 676.4 768.9 798.0 890.5 983.0 1075.4 1167.9 1197.1 1104.6: 92.5 184.9 277.4 306.6 399.0 491.5 583.9 676.4 705.6 798.0 890.5 983.0 1075.4 1104.6 1197.1 1197.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.1800 .. 92.4600 cents 63.28000 cents 29.18000 cents 2: 121.6400 .. 184.9200 cents 63.28000 cents 29.18000 cents 3: 214.1000 .. 277.3800 cents 63.28000 cents 29.18000 cents 4: 306.5600 .. 369.8400 cents 63.28000 cents 29.18000 cents 5: 399.0200 .. 399.0200 cents 1/1, 0.0000 cents 29.18000 cents 6: 428.2000 .. 491.4800 cents 63.28000 cents 29.18000 cents 7: 520.6600 .. 583.9400 cents 63.28000 cents 29.18000 cents 8: 613.1200 .. 676.4000 cents 63.28000 cents 29.18000 cents 9: 705.5800 .. 768.8600 cents 63.28000 cents 29.18000 cents 10: 798.0400 .. 798.0400 cents 1/1, 0.0000 cents 29.18000 cents 11: 827.2200 .. 890.5000 cents 63.28000 cents 29.18000 cents 12: 919.6800 .. 982.9600 cents 63.28000 cents 29.18000 cents 13: 1012.1400 .. 1075.4200 cents 63.28000 cents 29.18000 cents 14: 1104.6000 .. 1167.8800 cents 63.28000 cents 29.18000 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 29.18000 cents, class 1 Average step (divided formal octave): 79.8040 cents Largest one step interval : 92.46000 cents Average / Smallest step : 2.734887 Largest / Average step : 1.158589 Largest / Smallest step : 3.168609 Median interval of one step : 92.46000 cents, amount: 12 Most common interval of one step : 92.46000 cents, amount: 12 Least squares average step : 79.65090 cents, oct.: 1194.76355 cents Scale is strictly proper Scale has 3 repeating blocks of 5 notes Blocks have Myhill's property chromas: 63.28000 cents and 34.10000 cents, ratio: 1.855718 generators: 1 of 92.46000 cents and 4 of 306.56000 cents ET pair of linear temperament : 39&207 Scale is distributional even Scale is a mode of a 2175-tone equal temperament with octave 1197.060 cents degrees: 168 336 389 557 725 893 1061 1114 1282 1450 1618 1786 1839 2007 2175 Least number of segments generator : 1088 of 598.805 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1282 of 705.577 cents and inv. generated superset size: 1455 = 1440 more = 9700.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAAABAAAABAA Step pattern size order : LLSLLLLSLLLLSLL Scale is a Constant Structure, by a margin of 29.18000 cents Scale diversity : 1.167695 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.365646 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 : 29.18000 cents Most common intervals : 399.02000 cents & inv., amount: 15 Most common triad is 0.0 399.020 798.040 cents, amount: 15 Number of recognisable fifths : 12, average 705.5800 cents Number of recognisable fourths : 12, average 491.4800 cents Formal octave complements present : 15 = 100.0000% 2/1 octave complements present : 0 = 0.0000% 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 --
FIT/MODE
15: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 17.8983 c. M: 25.3120 c. 20: 2 1 1 1 2 1 2 0 2 1 2 1 1 1 2 N D3 I SD: 17.2669 c. M:-27.2460 c. 21: 2 1 1 1 2 2 1 1 1 2 2 1 1 1 2 N B D3 I SD: 16.2203 c. M: 21.5457 c. 22: 2 1 1 2 1 2 2 0 2 2 1 2 1 1 2 P D3 I SD: 15.0199 c. M: 21.6845 c. 24: 2 2 0 2 2 2 2 0 2 2 2 2 0 2 2 P B DE I SD: 10.3167 c. M: 14.5900 c. 27: 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 SP B ME I SD: 5.3583 c. M: 7.5778 c. 39: 3 3 1 3 3 3 3 1 3 3 3 3 1 3 3 SP B DE I SD: 0.5352 c. M: 0.7569 c. Augmented-15 129: 10 10 3 10 10 10 10 3 10 10 10 10 3 10 10 SP B DE I SD: 0.4743 c. M: 0.6707 c. 168: 13 13 4 13 13 13 13 4 13 13 13 13 4 13 13 SP B DE I SD: 0.2399 c. M: 0.3393 c. 207: 16 16 5 16 16 16 16 5 16 16 16 16 5 16 16 SP B DE I SD: 0.0939 c. M: 0.1328 c. 246: 19 19 6 19 19 19 19 6 19 19 19 19 6 19 19 SP B DE I SD: 0.0059 c. M: 0.0083 c. 1929: 149 149 47 149 149 149 149 47 149 149 149 149 47 149 149 SP B DE I SD: 0.0048 c. M: 0.0068 c. 2175: 168 168 53 168 168 168 168 53 168 168 168 168 53 168 168 SP B DE I SD: 0.0036 c. M: 0.0051 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x x 2 S SD: 2.9400 cents 2 x x x x x x x x 3 x x x x x 4 S SD: 2.3337 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 3.1527 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 4.8926 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 3.8353 cents 6 x x x 7 x 8 x x 9 x 10 x 11 x 12 S SD: 9.2246 cents 7 x x 8 x 9 x x 10 x 11:12 x x 13:14 S SD: 9.8573 cents 8 x x 9 x 10 x 11 x 12:13 x 14 x 15:16 S SD: 7.5239 cents 9 x 10 x 11 x 12 x 13 x 14:15:16 x 17:18 S SD: 6.6655 cents 10 x 11 x 12 x 13:14 x 15:16:17 x 18:19:20 S SD: 5.4788 cents 11 x 12 x 13:14:15 x 16 x 17:18:19:20:21:22 S SD: 9.3873 cents 12:13 x x 14:15:16 x 17:18:19:20:21:22:23:24 S SD: 6.5252 cents 13:14 x 15 x 16:17:18:19:20:21:22:23 x 25:26 SD: 8.7052 cents 14:15 x 16:17:18:19 x 20:21:22:23 x 25:27:28 SD: 6.9460 cents 15:16 x 17:18:19:20:21 x 23:24:25:26:27:28:30 SD: 4.6390 cents 16:17 x 18:19:20:21:22:23:24:25:27:28:29:30:32 SD: 4.4606 cents 17:18:19 x 20:21:23:24 x 26:27:28:30:31:32:34 SD: 5.7148 cents 18:19:20 x 21:23:24:25:26:27:29:30:32 x 34:36 SD: 4.9014 cents 19:20:21:22:23:24:25 x 27:29:30:32 x 34:36:38 SD: 4.5919 cents 20:21:22:23:24:25:27:28:29:30:32:33:35:36:38:40 SD: 4.3580 cents 21:22:23:24:25:26:28:29:30:32:33:35:37:38:40:42 SD: 4.1870 cents 22:23:24:25:26:28:29:31 x 33:35:37:39 x 42:44 SD: 4.0813 cents 23:24 x 26:27:29:31:32:33:35:36:38 x 41:44:46 SD: 4.8740 cents 24:25 x 27:29:30:32 x 34:36:38:40:42:43:45:48 SD: 3.3245 cents 25:26:28 x 30:31:33:35:36:38:40:42:44:45:47:50 SD: 3.8069 cents 26:27:29 x 31:33:35:36:37:39:41:43:46:47:49:52 SD: 3.6733 cents 27:28:30:31:32:34:36:38 x 41:43:45:48 x 51:54 SD: 3.7382 cents 28:30:31:32:33:35:37:39:40:42:44:47:49:50:53:56 SD: 3.3480 cents 29:31:32:33:35:37:39 x 41:44:46:49:51:52:55:58 SD: 3.8984 cents 30:32:33:34:36:38:40:42:43:45:48:50:53:54:57:60 SD: 2.5753 cents 32:34 x 36:38:40:43:45:46:48:51:54:56:57:61:64 SD: 3.2117 cents 33:35:37 x 39:42:44:46:47:50:52:55:58:59:62:66 SD: 2.8825 cents 34:36:38 x 41:43:45:48 x 51:54:57:60:61:64:68 SD: 2.1920 cents 36:38:40:41:43:45:48:50:51:54:57:60:64:65:68:72 SD: 2.1465 cents 37:39:41:42:44:47:49:52:53:56:59:62:65:66:70:74 SD: 2.0085 cents 40:42 x 45:48:50:53:56:57:60:63:67:71:72:76:80 SD: 1.9911 cents 41:43:46 x 49:52:54:57:58:62:65:69:72:74:78:82 SD: 2.7644 cents 42:44:47:48:50:53:56:59:60:63:67:70:74:75:79:84 SD: 2.1188 cents 43:45:48:49:51:54:57:60:61:65:68:72:76:77:81:86 SD: 1.9482 cents 46:49:51:52:55:58:61:64:66:69:73:77:81:83:87:92 SD: 1.8532 cents 49:52 x 55:58:62:65:69:70:74:78:82:86:88:93:98 SD: 2.1663 cents 50:53:56:57:60:63:66:70:71:75:79:84:88:90:95:100 SD: 1.8969 cents 51:54:57:58:61:64:68:71:73:77:81:85:90:92:97:102 SD: 1.7853 cents 52:55:58:59:62:65:69:73:74:78:82:87:92:93:98:104 SD: 1.4420 cents 54:57:60:61:64:68:72:76:77:81:86:90:95:97:102:108 SD: 1.3889 cents 55:58:61:62:66:69:73:77:78:83:87:92:97:99:104:110 SD: 1.2975 cents 68:72:76:77:81:86:90:95:97:102:108:114:120:122:129:136 SD: 1.1575 cents 70:74:78:79:84:88:93:98:100:105:111:117:124:126:132:140 SD: 1.1484 cents 73:77:81:83:87:92:97:102:104:110:116:122:129:131:138:146 SD: 0.8926 cents 77:81:86:87:92:97:102:108:110:116:122:129:136:138:146:154 SD: 0.8679 cents 89:94:99:101:106:112:118:125:127:134:141:149:157:160:168:178 SD: 0.7687 cents 92:97:102:104:110:116:122:129:131:138:146:154:162:165:174:184 SD: 0.6931 cents 107:113:119:121:128:135:142:150:152:161:170:179:189:192:203:214 SD: 0.6910 cents 113:119:126:128:135:142:150:158:161:170:179:189:199:203:214:226 SD: 0.6043 cents 143:151:159:162:171:180:190:200:204:215:227:239:252:257:271:286 SD: 0.5283 cents 150:158:167:170:179:189:199:210:214:225:238:251:265:269:284:299 SD: 0.4972 cents 159:168:177:180:190:200:211:223:227:239:252:266:281:285:301:317 SD: 0.4755 cents 165:174:184:187:197:208:219:231:235:248:262:276:291:296:312:329 SD: 0.4452 cents 167:176:186:189:199:210:222:234:238:251:265:279:295:300:316:333 SD: 0.4296 cents 177:187:197:200:211:223:235:248:252:266:281:296:312:318:335:353 SD: 0.4193 cents 195:206:217:221:233:246:259:273:278:293:309:326:344:350:369:389 SD: 0.3886 cents 204:215:227:231:244:257:271:286:291:307:323:341:360:366:386:407 SD: 0.3875 cents 205:216:228:232:245:258:272:287:292:308:325:343:362:368:388:409 SD: 0.3071 cents 258:272:287:292:308:325:343:361:368:388:409:432:455:463:488:515 SD: 0.2922 cents 259:273:288:293:309:326:344:363:369:389:411:433:457:465:490:517 SD: 0.2270 cents 336:354:374:380:401:423:446:471:479:505:533:562:593:603:636:671 SD: 0.2099 cents 362:382:403:410:432:456:481:507:516:544:574:605:639:650:685:723 SD: 0.2084 cents 366:386:407:414:437:461:486:513:522:550:580:612:646:657:693:731 SD: 0.1929 cents 381:402:424:431:455:480:506:534:543:573:604:637:672:684:721:761 SD: 0.1556 cents 471:497:524:533:562:593:626:660:671:708:747:788:831:845:891:940 SD: 0.1376 cents 531:560:591:601:634:669:705:744:757:798:842:888:937:953:1005:1060 SD: 0.1190 cents 548:578:610:620:654:690:728:768:781:824:869:917:967:983:1037:1094 SD: 0.1074 cents