Scala analysis: marpurg2
Marpurg 2. Neue Methode (1790)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 109.775 cents 109.775000 2: 9/8 203.910002 major whole tone 3: 313.685 cents 313.685000 4: 81/64 407.820003 Pythagorean major third 5: 4/3 498.044999 perfect fourth 6: 607.820 cents 607.820000 7: 3/2 701.955001 perfect fifth 8: 811.730 cents 811.730000 9: 27/16 905.865003 Pythagorean major sixth 10: 1015.640 cents 1015.640000 11: 1105.865 cents 1105.865000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 94.1350 cents 94.1350 1: 109.7750 cents 109.7750 2: 94.1350 cents 94.1350 3: 109.7750 cents 109.7750 4: 94.1350 cents 94.1350 5: 256/243 90.2250 limma, Pythagorean minor second 6: 109.7750 cents 109.7750 7: 94.1350 cents 94.1350 8: 109.7750 cents 109.7750 9: 94.1350 cents 94.1350 10: 109.7750 cents 109.7750 11: 90.2250 cents 90.2250 12: 94.1350 cents 94.1350
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 256/243 90.225 cents limma, Pythagorean minor second 1: 5 94.13500 cents 1: 5 109.77500 cents 2: 2 184.36000 cents 2: 2 200.00000 cents 2: 8 9/8 203.910 cents major whole tone 3: 6 32/27 294.135 cents Pythagorean minor third 3: 3 298.04500 cents 3: 3 313.68500 cents 4: 4 388.27000 cents 4: 4 403.91000 cents 4: 4 81/64 407.820 cents Pythagorean major third 5: 10 4/3 498.045 cents perfect fourth 5: 1 501.95500 cents 5: 1 517.59500 cents 6: 6 592.18000 cents 6: 6 607.82000 cents 7: 1 682.40500 cents 7: 1 698.04500 cents 7: 10 3/2 701.955 cents perfect fifth 8: 4 792.18000 cents 8: 4 796.09000 cents 8: 4 811.73000 cents 9: 3 886.31500 cents 9: 3 901.95500 cents 9: 6 27/16 905.865 cents Pythagorean major sixth 10: 8 996.09000 cents 10: 2 1000.00000 cents 10: 2 1015.64000 cents 11: 5 1090.22500 cents 11: 5 1105.86500 cents 11: 2 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.90909 = 32/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 109.8 203.9 313.7 407.8 498.0 607.8 702.0 811.7 905.9 1015.6 1105.9 1200.0 109.8 : 94.1 203.9 298.0 388.3 498.0 592.2 702.0 796.1 905.9 996.1 1090.2 1200.0 203.9 : 109.8 203.9 294.1 403.9 498.0 607.8 702.0 811.7 902.0 996.1 1105.9 1200.0 313.7 : 94.1 184.4 294.1 388.3 498.0 592.2 702.0 792.2 886.3 996.1 1090.2 1200.0 407.8 : 90.2 200.0 294.1 403.9 498.0 607.8 698.0 792.2 902.0 996.1 1105.9 1200.0 498.0 : 109.8 203.9 313.7 407.8 517.6 607.8 702.0 811.7 905.9 1015.6 1109.8 1200.0 607.8 : 94.1 203.9 298.0 407.8 498.0 592.2 702.0 796.1 905.9 1000.0 1090.2 1200.0 702.0 : 109.8 203.9 313.7 403.9 498.0 607.8 702.0 811.7 905.9 996.1 1105.9 1200.0 811.7 : 94.1 203.9 294.1 388.3 498.0 592.2 702.0 796.1 886.3 996.1 1090.2 1200.0 905.9 : 109.8 200.0 294.1 403.9 498.0 607.8 702.0 792.2 902.0 996.1 1105.9 1200.0 1015.6: 90.2 184.4 294.1 388.3 498.0 592.2 682.4 792.2 886.3 996.1 1090.2 1200.0 1105.9: 94.1 203.9 298.0 407.8 502.0 592.2 702.0 796.1 905.9 1000.0 1109.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 109.7750 cents 19.55000 cents 256/243, 90.2250 cents 2: 184.3600 .. 203.9100 cents 19.55000 cents 74.58500 cents 3: 294.1350 .. 313.6850 cents 19.55000 cents 256/243, 90.2250 cents 4: 388.2700 .. 407.8200 cents 19.55000 cents 74.58500 cents 5: 498.0450 .. 517.5950 cents 19.55000 cents 256/243, 90.2250 cents 6: 592.1800 .. 607.8200 cents 15.64000 cents 74.58500 cents 7: 682.4050 .. 701.9550 cents 19.55000 cents 74.58500 cents 8: 792.1800 .. 811.7300 cents 19.55000 cents 90.22500 cents 9: 886.3150 .. 905.8650 cents 19.55000 cents 74.58500 cents 10: 996.0900 .. 1015.6400 cents 19.55000 cents 90.22500 cents 11: 1090.2250 .. 1109.7750 cents 19.55000 cents 74.58500 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 109.77500 cents Average / Smallest step : 1.108340 Largest / Average step : 1.097750 Largest / Smallest step : 1.216681 Median interval of one step : 94.13500 cents, amount: 5 Least squares average step : 100.78200 cents, oct.: 1209.38400 cents Scale is strictly proper Scale is 3-distributional even Step pattern alph. order: ABABCABABACB Step pattern size order : LMLMSLMLMLSM Scale is a Constant Structure, by a margin of 74.58500 cents Scale diversity : 1.138469 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.824050 Rothenberg efficiency : 0.514153 redundancy: 0.485847 Efficiency x scale size : 6.169841 Number of different interval sizes : 32 = 2.90909 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.90909 = 32/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 3.91000 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 10 Most common triad is 0.0 498.045 701.955 cents, amount: 8 Number of recognisable fifths : 11, average 701.5995 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 Formal octave complements present : 3 = 25.0000% Limited transpositions with margin 19.5500 cents: 6 11 Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 7-8 -- Rational properties -- Prime limit : 3 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 8.5589 c. M: 15.6400 c. Twelve-tone Chromatic (1/11-comma) 33: 3 3 3 2 3 3 2 3 3 3 2 3 SP D3 SD: 9.9141 c. M: 14.9559 c. 34: 3 3 3 3 2 3 3 3 3 3 2 3 SP B ME SD: 8.0125 c. M:-15.7094 c. 37: 3 3 4 3 2 4 3 3 3 3 3 3 SP D3 SD: 9.1491 c. M:-13.8016 c. 38: 3 3 4 3 3 3 3 4 3 3 3 3 SP D3 S SD: 8.2844 c. M: 15.0382 c. 39: 4 3 3 3 3 4 3 3 3 4 3 3 SP D3 SD: 8.4337 c. M: 13.5573 c. 41: 4 3 4 3 3 4 3 4 3 4 3 3 SP M ME SD: 5.4198 c. M:-8.7502 c. 53: 5 4 5 4 4 5 4 5 4 5 4 4 SP M ME SD: 2.4070 c. M:-3.5690 c. 65: 6 5 6 5 5 6 5 6 5 6 5 5 SP M ME SD: 1.0050 c. M:-1.8273 c. 142: 13 11 13 11 11 13 11 13 11 13 11 11 SP M DE SD: 1.1069 c. M: 2.1862 c. 164: 15 13 15 13 12 15 13 15 13 15 12 13 SP D3 SD: 0.9858 c. M:-1.9361 c. 176: 16 14 16 14 13 16 14 16 14 16 13 14 SP D3 SD: 0.7389 c. M: 1.3195 c. 229: 21 18 21 18 17 21 18 21 18 21 17 18 SP D3 SD: 0.5331 c. M:-0.9539 c. 241: 22 19 22 19 18 22 19 22 19 22 18 19 SP D3 SD: 0.2695 c. M:-0.4788 c. 306: 28 24 28 24 23 28 24 28 24 28 23 24 SP D3 SD: 0.0253 c. M:-0.0463 c. 2154: 197 169 197 169 162 197 169 197 169 197 162 169 SP D3 SD: 0.0225 c. M: 0.0411 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: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 7.1688 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 12.8794 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 5.1067 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.2623 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.4171 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 10.1789 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.2317 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.5410 cents 11:12 x 13:14:15:16:17:18:19:20:21:22 S SD: 9.9888 cents 12:13 x 14:15:16:17:18:19:20:22:23:24 S SD: 6.9152 cents 13:14:15:16 x 17:18:20:21:22:23:25:26 SD: 9.6297 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 6.3609 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 4.8390 cents 16:17:18:19:20:21:23:24:26:27:29:30:32 SD: 4.7450 cents 24:26:27:29:30:32:34:36:38:41:43:45:48 SD: 4.2235 cents 26:28:29:31:33:35:37:39:42:44:47:49:52 SD: 3.2133 cents 30:32:34:36:38:40:43:45:48:51:54:57:60 SD: 2.0587 cents 45:48:51:54:57:60:64:68:72:76:81:85:90 SD: 1.6092 cents 48:51:54:58:61:64:68:72:77:81:86:91:96 SD: 1.6078 cents 57:61:64:68:72:76:81:86:91:96:102:108:114 SD: 1.5205 cents 60:64:68:72:76:80:85:90:96:101:108:114:120 SD: 1.3191 cents 64:68:72:77:81:85:91:96:102:108:115:121:128 SD: 1.0137 cents 80:85:90:96:101:107:114:120:128:135:144:152:160 SD: 0.9829 cents 90:96:101:108:114:120:128:135:144:152:162:170:180 SD: 0.6705 cents 105:112:118:126:133:140:149:158:168:177:189:199:210 SD: 0.6390 cents 135:144:152:162:171:180:192:203:216:228:243:256:270 SD: 0.5730 cents 150:160:169:180:190:200:213:225:240:253:270:284:300 SD: 0.4230 cents 192:205:216:230:243:256:273:288:307:324:345:364:384 SD: 0.3810 cents 216:230:243:259:273:288:307:324:345:365:388:409:432 SD: 0.3485 cents 226:241:254:271:286:301:321:339:361:381:406:428:452 SD: 0.3260 cents 246:262:277:295:311:328:349:369:393:415:442:466:492 SD: 0.3204 cents 256:273:288:307:324:341:364:384:409:432:460:485:512 SD: 0.2611 cents 302:322:340:362:382:403:429:453:483:510:543:572:604 SD: 0.2552 cents 306:326:344:367:387:408:435:459:489:516:550:580:612 SD: 0.2477 cents 321:342:361:385:406:428:456:482:513:542:577:608:642 SD: 0.2236 cents 336:358:378:403:425:448:477:504:537:567:604:636:672 SD: 0.1895 cents 366:390:412:439:463:488:520:549:585:618:658:693:732 SD: 0.1823 cents 368:392:414:441:466:491:523:552:588:621:662:697:736 SD: 0.1680 cents 426:454:479:511:539:568:605:639:681:719:766:807:852 SD: 0.1559 cents 474:505:533:568:600:632:673:711:758:800:852:898:948 SD: 0.1534 cents 490:522:551:587:620:653:696:735:783:827:881:928:980 SD: 0.1418 cents 504:537:567:604:638:672:716:756:805:851:906:955:1008 SD: 0.1413 cents 528:563:594:633:668:704:750:792:844:891:949:1000:1056 SD: 0.1407 cents 538:573:605:645:681:717:764:807:860:908:967:1019:1076 SD: 0.1368 cents 550:586:619:659:696:733:781:825:879:928:989:1042:1100 SD: 0.1291 cents 568:605:639:681:719:757:807:852:908:959:1021:1076:1136 SD: 0.1285 cents 594:633:668:712:752:792:844:891:949:1002:1068:1125:1188 SD: 0.1082 cents