Scala analysis: xen18-erlich-helmholtz-12
5L 7s MOS for Helmholtz, L=112.25, s=91.26
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 91.260 cents 91.260000 2: 203.510 cents 203.510000 3: 294.770 cents 294.770000 4: 407.020 cents 407.020000 5: 498.280 cents 498.280000 6: 589.540 cents 589.540000 7: 701.790 cents 701.790000 8: 793.050 cents 793.050000 9: 905.300 cents 905.300000 10: 996.560 cents 996.560000 11: 1108.810 cents 1108.810000 12: 1200.070 cents 1200.070000
SHOW/INTERVAL
0: 91.2600 cents 91.2600 1: 91.2600 cents 91.2600 2: 112.2500 cents 112.2500 3: 91.2600 cents 91.2600 4: 112.2500 cents 112.2500 5: 91.2600 cents 91.2600 6: 91.2600 cents 91.2600 7: 112.2500 cents 112.2500 8: 91.2600 cents 91.2600 9: 112.2500 cents 112.2500 10: 91.2600 cents 91.2600 11: 112.2500 cents 112.2500 12: 91.2600 cents 91.2600
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 91.26000 cents 1: 5 112.25000 cents 2: 2 182.52000 cents 2: 10 203.51000 cents 3: 9 294.77000 cents 3: 3 315.76000 cents 4: 4 386.03000 cents 4: 8 407.02000 cents 5: 11 498.28000 cents 5: 1 519.27000 cents 6: 6 589.54000 cents 6: 6 610.53000 cents 7: 1 680.80000 cents 7: 11 701.79000 cents 8: 8 793.05000 cents 8: 4 814.04000 cents 9: 3 884.31000 cents 9: 9 905.30000 cents 10: 10 996.56000 cents 10: 2 1017.55000 cents 11: 5 1087.82000 cents 11: 7 1108.81000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 91.3 203.5 294.8 407.0 498.3 589.5 701.8 793.1 905.3 996.6 1108.8 1200.1 91.3 : 112.3 203.5 315.8 407.0 498.3 610.5 701.8 814.0 905.3 1017.6 1108.8 1200.1 203.5 : 91.3 203.5 294.8 386.0 498.3 589.5 701.8 793.0 905.3 996.6 1087.8 1200.1 294.8 : 112.3 203.5 294.8 407.0 498.3 610.5 701.8 814.0 905.3 996.6 1108.8 1200.1 407.0 : 91.3 182.5 294.8 386.0 498.3 589.5 701.8 793.0 884.3 996.6 1087.8 1200.1 498.3 : 91.3 203.5 294.8 407.0 498.3 610.5 701.8 793.0 905.3 996.6 1108.8 1200.1 589.5 : 112.3 203.5 315.8 407.0 519.3 610.5 701.8 814.0 905.3 1017.5 1108.8 1200.1 701.8 : 91.3 203.5 294.8 407.0 498.3 589.5 701.8 793.0 905.3 996.6 1087.8 1200.1 793.1 : 112.3 203.5 315.8 407.0 498.3 610.5 701.8 814.0 905.3 996.6 1108.8 1200.1 905.3 : 91.3 203.5 294.8 386.0 498.3 589.5 701.8 793.0 884.3 996.6 1087.8 1200.1 996.6 : 112.3 203.5 294.8 407.0 498.3 610.5 701.8 793.0 905.3 996.6 1108.8 1200.1 1108.8: 91.3 182.5 294.8 386.0 498.3 589.5 680.8 793.0 884.3 996.6 1087.8 1200.1 1200.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 91.2600 .. 112.2500 cents 20.99000 cents 91.26000 cents 2: 182.5200 .. 203.5100 cents 20.99000 cents 70.27000 cents 3: 294.7700 .. 315.7600 cents 20.99000 cents 91.26000 cents 4: 386.0300 .. 407.0200 cents 20.99000 cents 70.27000 cents 5: 498.2800 .. 519.2700 cents 20.99000 cents 91.26000 cents 6: 589.5400 .. 610.5300 cents 20.99000 cents 70.27000 cents 7: 680.8000 .. 701.7900 cents 20.99000 cents 70.27000 cents 8: 793.0500 .. 814.0400 cents 20.99000 cents 91.26000 cents 9: 884.3100 .. 905.3000 cents 20.99000 cents 70.27000 cents 10: 996.5600 .. 1017.5500 cents 20.99000 cents 91.26000 cents 11: 1087.8200 .. 1108.8100 cents 20.99000 cents 70.27000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 91.26000 cents, class 1 Average step (divided formal octave): 100.0058 cents Largest one step interval : 112.25000 cents Average / Smallest step : 1.095834 Largest / Average step : 1.122435 Largest / Smallest step : 1.230002 Median interval of one step : 91.26000 cents, amount: 7 Most common interval of one step : 91.26000 cents, amount: 7 Least squares average step : 100.01122 cents, oct.: 1200.13458 cents Scale is strictly proper Scale has Myhill's property chromas: 20.99000 cents and 70.27000 cents, ratio: 3.347785 generators: 5 of 498.28000 cents and 7 of 701.79000 cents ET pair of linear temperament : 12&53 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1144-tone equal temperament with octave 1200.070 cents degrees: 87 194 281 388 475 562 669 756 863 950 1057 1144 generators: 475 and 669 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABAABABABA Step pattern size order : SLSLSSLSLSLS Scale is a Constant Structure, by a margin of 70.27000 cents Ratio Whole / Half tone : 2.230002 Scale diversity : 1.141401 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.807603 Rothenberg efficiency : 0.722222 redundancy: 0.277778 Efficiency x scale size : 8.666667 Number of different interval sizes : 22 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 20.99000 cents Most common intervals : 498.28000 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 91.260 701.790 cents Most common triad is 0.0 498.280 701.790 cents, amount: 10 Number of recognisable fifths : 11, average 701.7900 cents Number of recognisable fourths : 11, average 498.2800 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 11 = 91.6667% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 8-9 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 6.1012 c. M:-10.4950 c. Twelve-tone Chromatic (1/11-comma) 29: 2 3 2 3 2 2 3 2 3 2 3 2 SP M ME SD: 5.9273 c. M: 10.1959 c. 41: 3 4 3 4 3 3 4 3 4 3 4 3 SP M ME SD: 2.4068 c. M: 4.1400 c. 53: 4 5 4 5 4 4 5 4 5 4 5 4 SP M ME SD: 0.4804 c. M: 0.8264 c. 118: 9 11 9 11 9 9 11 9 11 9 11 9 SP M DE SD: 0.1889 c. M:-0.3249 c. 171: 13 16 13 16 13 13 16 13 16 13 16 13 SP M DE SD: 0.0186 c. M: 0.0319 c. 802: 61 75 61 75 61 61 75 61 75 61 75 61 SP M DE SD: 0.0120 c. M:-0.0206 c. 973: 74 91 74 91 74 74 91 74 91 74 91 74 SP M DE SD: 0.0066 c. M:-0.0113 c. 1144: 87 107 87 107 87 87 107 87 107 87 107 87 SP M DE SD: 0.0028 c. M:-0.0049 c. 1315: 100 123 100 123 100 100 123 100 123 100 123 100 SP M DE SD: 0.0001 c. M:-0.0001 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0700 cents 2 x x x x x x 3 x x x x 4 S SD: 0.0896 cents 3 x x x x 4 x x x 5 x x 6 S SD: 6.9809 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.6529 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.3577 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.5477 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.6858 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.1302 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.1105 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0439 cents 11 x 12:13:14:15 x x 17:19:20:21:22 SD: 10.6854 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.5223 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 9.7018 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 7.2163 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.6815 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.5588 cents 18:19:20:21:23:24:25:27:28:30:32:34:36 SD: 4.7539 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 3.0812 cents 32:34:36:38:40:43:45:48:51:54:57:61:64 SD: 2.7206 cents 38:40:43:45:48:51:53:57:60:64:68:72:76 SD: 1.9925 cents 42:44:47:50:53:56:59:63:66:71:75:80:84 SD: 1.8338 cents 48:51:54:57:61:64:67:72:76:81:85:91:96 SD: 1.8019 cents 50:53:56:59:63:67:70:75:79:84:89:95:100 SD: 1.7526 cents 54:57:61:64:68:72:76:81:85:91:96:102:108 SD: 1.3227 cents 71:75:80:84:90:95:100:106:112:120:126:135:142 SD: 1.2079 cents 72:76:81:85:91:96:101:108:114:121:128:137:144 SD: 1.0206 cents 86:91:97:102:109:115:121:129:136:145:153:163:172 SD: 0.8686 cents 96:101:108:114:121:128:135:144:152:162:171:182:192 SD: 0.7302 cents 114:120:128:135:144:152:160:171:180:192:203:216:228 SD: 0.6335 cents 128:135:144:152:162:171:180:192:202:216:228:243:256 SD: 0.5235 cents 144:152:162:171:182:192:202:216:228:243:256:273:288 SD: 0.5103 cents 150:158:169:178:190:200:211:225:237:253:267:285:300 SD: 0.4506 cents 162:171:182:192:205:216:228:243:256:273:288:307:324 SD: 0.4027 cents 200:211:225:237:253:267:281:300:316:337:356:379:400 SD: 0.3764 cents 222:234:250:263:281:296:312:333:351:375:395:421:444 SD: 0.3194 cents 242:255:272:287:306:323:340:363:383:408:430:459:484 SD: 0.2931 cents 264:278:297:313:334:352:371:396:417:445:469:501:528 SD: 0.2806 cents 279:294:314:331:353:372:392:418:441:471:496:529:558 SD: 0.2722 cents 294:310:331:349:372:392:413:441:465:496:523:558:588 SD: 0.2676 cents 298:314:335:353:377:397:419:447:471:503:530:565:596 SD: 0.2605 cents 312:329:351:370:395:416:439:468:493:526:555:592:624 SD: 0.2336 cents 313:330:352:371:396:417:440:469:495:528:557:594:626 SD: 0.2322 cents 351:370:395:416:444:468:493:526:555:592:624:666:702 SD: 0.2024 cents 370:390:416:439:468:493:520:555:585:624:658:702:740 SD: 0.1760 cents 392:413:441:465:496:523:551:588:620:661:697:744:784 SD: 0.1665 cents 441:465:496:523:558:588:620:661:697:744:784:837:882 SD: 0.1416 cents 480:506:540:569:607:640:675:720:759:810:854:911:960 SD: 0.1341 cents 554:584:623:657:701:739:779:831:876:935:985:1051:1108 SD: 0.1146 cents