Scala analysis: Neidhard1724rationalETapprox
from his "Canone Harmonico" extracted and compiled by A.Sparschuh
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 99.995 cents 99.994611 2: 199.996 cents 199.996435 3: 299.996 cents 299.996140 4: 399.997 cents 399.997092 5: 499.999 cents 499.998720 6: 599.995 cents 599.995462 7: 699.996 cents 699.996062 8: 799.998 cents 799.998122 9: 899.995 cents 899.994598 10: 999.999 cents 999.998532 11: 1099.994 cents 1099.994110 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 100.0059 cents 100.0059 1: 99.9946 cents 99.9946 2: 100.0018 cents 100.0018 3: 99.9997 cents 99.9997 4: 100.0010 cents 100.0010 5: 100.0016 cents 100.0016 6: 99.9967 cents 99.9967 7: 100.0006 cents 100.0006 8: 100.0021 cents 100.0021 9: 99.9965 cents 99.9965 10: 100.0039 cents 100.0039 11: 99.9956 cents 99.9956 12: 100.0059 cents 100.0059
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 99.99461 cents 1: 1 99.99558 cents 1: 1 99.99648 cents 1: 1 99.99674 cents 1: 1 99.99971 cents 1: 1 100.00060 cents 1: 1 100.00095 cents 1: 1 100.00163 cents 1: 1 100.00182 cents 1: 1 100.00206 cents 1: 1 100.00393 cents 1: 1 100.00589 cents 2: 1 199.99644 cents 2: 1 199.99734 cents 2: 2 199.99837 cents 2: 1 199.99951 cents 2: 2 200.00041 cents 2: 1 200.00066 cents 2: 2 200.00153 cents 2: 2 200.00258 cents 3: 3 299.99614 cents 3: 2 299.99897 cents 3: 2 299.99932 cents 3: 2 300.00228 cents 3: 2 300.00248 cents 3: 1 300.00540 cents 4: 1 399.99588 cents 4: 1 399.99709 cents 4: 2 399.99805 cents 4: 1 399.99903 cents 4: 2 399.99992 cents 4: 1 400.00103 cents 4: 2 400.00188 cents 4: 1 400.00307 cents 4: 1 400.00411 cents 5: 1 499.99649 cents 5: 2 499.99751 cents 5: 2 499.99872 cents 5: 1 499.99963 cents 5: 1 499.99981 cents 5: 1 500.00085 cents 5: 2 500.00198 cents 5: 1 500.00298 cents 5: 1 500.00394 cents 6: 2 599.99546 cents 6: 4 599.99846 cents 6: 3 600.00145 cents 6: 1 600.00169 cents 6: 2 600.00454 cents 7: 1 699.99606 cents 7: 1 699.99702 cents 7: 2 699.99816 cents 7: 1 699.99915 cents 7: 1 700.00019 cents 7: 1 700.00037 cents 7: 2 700.00128 cents 7: 2 700.00239 cents 7: 1 700.00351 cents 8: 1 799.99589 cents 8: 1 799.99693 cents 8: 2 799.99812 cents 8: 1 799.99897 cents 8: 2 799.99999 cents 8: 1 800.00097 cents 8: 2 800.00210 cents 8: 1 800.00291 cents 8: 1 800.00412 cents 9: 1 899.99460 cents 9: 4 899.99768 cents 9: 2 900.00068 cents 9: 2 900.00103 cents 9: 3 900.00392 cents 10: 2 999.99742 cents 10: 2 999.99853 cents 10: 3 999.99950 cents 10: 1 1000.00049 cents 10: 2 1000.00163 cents 10: 1 1000.00266 cents 10: 1 1000.00356 cents 11: 1 1099.99411 cents 11: 1 1099.99607 cents 11: 1 1099.99794 cents 11: 1 1099.99818 cents 11: 1 1099.99837 cents 11: 1 1099.99905 cents 11: 1 1099.99940 cents 11: 1 1100.00030 cents 11: 1 1100.00326 cents 11: 1 1100.00352 cents 11: 1 1100.00442 cents 11: 1 1100.00539 cents Highest number of different intervals for one interval class: 12 Average number of different intervals per interval class: 8.27273 = 91/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 100.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 200.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 300.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 400.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 500.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 600.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 700.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 800.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 900.0 : 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 1000.0: 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 1100.0: 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 1100.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 99.9946 .. 100.0059 cents 0.01128 cents 99.99461 cents 2: 199.9964 .. 200.0026 cents 0.00614 cents 99.99055 cents 3: 299.9961 .. 300.0054 cents 0.00926 cents 99.99356 cents 4: 399.9959 .. 400.0041 cents 0.00823 cents 99.99048 cents 5: 499.9965 .. 500.0039 cents 0.00745 cents 99.99238 cents 6: 599.9955 .. 600.0045 cents 0.00908 cents 99.99152 cents 7: 699.9961 .. 700.0035 cents 0.00745 cents 99.99152 cents 8: 799.9959 .. 800.0041 cents 0.00823 cents 99.99238 cents 9: 899.9946 .. 900.0039 cents 0.00932 cents 99.99048 cents 10: 999.9974 .. 1000.0036 cents 0.00615 cents 99.99350 cents 11: 1099.9941 .. 1100.0054 cents 0.01128 cents 99.99055 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 99.99461 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 100.00589 cents Average / Smallest step : 1.000054 Largest / Average step : 1.000059 Largest / Smallest step : 1.000113 Median interval of one step : 100.00078 cents, amount: 0 Least squares average step : 99.99963 cents, oct.: 1199.99557 cents Scale is strictly proper Scale is a mode of a 12-tone equal temperament with octave 2/1 degrees: 1 2 3 4 5 6 7 8 9 10 11 12 Least number of segments generator : 7 of 700.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 7 of 700.000 cents and inv. generated superset size: 12 = 0 more = 100.000% Number of contiguous 1-step segments: 1 Step pattern alph. order: ABCDEFGHIJKL Step pattern size order : AGDFGCEHCIBJ Interval vector is [ 1 2 1 1 1 2 ] Scale is a Constant Structure, by a margin of 99.99048 cents Scale diversity : 1.000063 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.999922 Rothenberg efficiency : 0.200505 redundancy: 0.799495 Efficiency x scale size : 2.406061 Number of different interval sizes : 91 = 8.27273 / class Number of one step interval sizes : 12 Highest interval variety : 12 Mean interval variety : 8.45455 = 93/11 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 0.00018 cents Most common intervals : 599.99846 cents & inv., amount: 4 Number of recognisable fifths : 12, average 700.0000 cents Scale is a well-temperament. It has 9 different sizes of fifth Scale has monotonic third-sizes over circle of fifths Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited transpositions : 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions : 1 2 3 4 5 6 7 8 9 10 11 Inversional symmetry on degrees : 0 1 2 3 4 5 6 7 8 9 10 11 Inversional symmetry on intervals : 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 0.0038 c. M:-0.0059 c. Twelve-tone Chromatic (1/11-comma)
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: 0.9795 cents 3 x x x x 4 x x x 5 x x 6 S SD: 5.2525 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.5250 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.4730 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.2554 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.8083 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.1239 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.1604 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.9608 cents 11 x 12:13:14:15:16 x 17:19:20:21:22 SD: 11.1726 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.2446 cents 13:14:15 x 16:17:18:19:21:22:23:25:26 SD: 9.7028 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.0903 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.9585 cents 19:20:21:23:24:25:27:28:30:32:34:36:38 SD: 4.9341 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 4.0787 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 4.0271 cents 26:28:29:31:33:35:37:39:41:44:46:49:52 SD: 3.5790 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.3908 cents 31:33:35:37:39:41:44:46:49:52:55:59:62 SD: 2.7907 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.1816 cents 46:49:52:55:58:61:65:69:73:77:82:87:92 SD: 1.9377 cents 48:51:54:57:60:64:68:72:76:81:86:91:96 SD: 1.7687 cents 50:53:56:59:63:67:71:75:79:84:89:94:100 SD: 1.7020 cents 51:54:57:61:64:68:72:76:81:86:91:96:102 SD: 1.5752 cents 54:57:61:64:68:72:76:81:86:91:96:102:108 SD: 1.5263 cents 63:67:71:75:79:84:89:94:100:106:112:119:126 SD: 1.2877 cents 65:69:73:77:82:87:92:97:103:109:116:123:130 SD: 1.1601 cents 80:85:90:95:101:107:113:120:127:135:143:151:160 SD: 0.9996 cents 84:89:94:100:106:112:119:126:133:141:150:159:168 SD: 0.9221 cents 89:94:100:106:112:119:126:133:141:150:159:168:178 SD: 0.9200 cents 96:102:108:114:121:128:136:144:152:161:171:181:192 SD: 0.8792 cents 99:105:111:118:125:132:140:148:157:166:176:187:198 SD: 0.8395 cents 101:107:113:120:127:135:143:151:160:170:180:191:202 SD: 0.8065 cents 104:110:117:124:131:139:147:156:165:175:185:196:208 SD: 0.7068 cents 116:123:130:138:146:155:164:174:184:195:207:219:232 SD: 0.4529 cents 169:179:190:201:213:226:239:253:268:284:301:319:338 SD: 0.4237 cents 170:180:191:202:214:227:240:255:270:286:303:321:340 SD: 0.3987 cents 189:200:212:225:238:252:267:283:300:318:337:357:378 SD: 0.3871 cents 215:228:241:256:271:287:304:322:341:362:383:406:430 SD: 0.3801 cents 220:233:247:262:277:294:311:330:349:370:392:415:440 SD: 0.3641 cents 238:252:267:283:300:318:337:357:378:400:424:449:476 SD: 0.3470 cents 239:253:268:284:301:319:338:358:379:402:426:451:478 SD: 0.2836 cents 269:285:302:320:339:359:380:403:427:452:479:508:538 SD: 0.2425 cents 301:319:338:358:379:402:426:451:478:506:536:568:602 SD: 0.2226 cents 353:374:396:420:445:471:499:529:560:594:629:666:706 SD: 0.2194 cents 385:408:432:458:485:514:544:577:611:647:686:727:770 SD: 0.1983 cents 400:424:449:476:504:534:566:599:635:673:713:755:800 SD: 0.1872 cents 403:427:452:479:508:538:570:604:640:678:718:761:806 SD: 0.1866 cents 418:443:469:497:527:558:591:626:664:703:745:789:836 SD: 0.1831 cents 427:452:479:508:538:570:604:640:678:718:761:806:854 SD: 0.1831 cents 434:460:487:516:547:579:614:650:689:730:773:819:868 SD: 0.1682 cents 439:465:493:522:553:586:621:658:697:738:782:829:878 SD: 0.1394 cents 490:519:550:583:617:654:693:734:778:824:873:925:980 SD: 0.1283 cents 538:570:604:640:678:718:761:806:854:905:959:1016:1076 SD: 0.1175 cents 570:604:640:678:718:761:806:854:905:959:1016:1076:1140 SD: 0.1129 cents