Scala analysis: xen18-erlich-meantone-12
7L 5s MOS for Meantone, L=117.25, s=76.19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 117.250 cents 117.250000 2: 193.440 cents 193.440000 3: 310.690 cents 310.690000 4: 386.880 cents 386.880000 5: 504.130 cents 504.130000 6: 580.320 cents 580.320000 7: 697.570 cents 697.570000 8: 814.820 cents 814.820000 9: 891.010 cents 891.010000 10: 1008.260 cents 1008.260000 11: 1084.450 cents 1084.450000 12: 1201.700 cents 1201.700000
SHOW/INTERVAL
0: 117.2500 cents 117.2500 1: 117.2500 cents 117.2500 2: 76.1900 cents 76.1900 3: 117.2500 cents 117.2500 4: 76.1900 cents 76.1900 5: 117.2500 cents 117.2500 6: 76.1900 cents 76.1900 7: 117.2500 cents 117.2500 8: 117.2500 cents 117.2500 9: 76.1900 cents 76.1900 10: 117.2500 cents 117.2500 11: 76.1900 cents 76.1900 12: 117.2500 cents 117.2500
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 76.19000 cents 1: 7 117.25000 cents 2: 10 193.44000 cents 2: 2 234.50000 cents 3: 3 269.63000 cents 3: 9 310.69000 cents 4: 8 386.88000 cents 4: 4 427.94000 cents 5: 1 463.07000 cents 5: 11 504.13000 cents 6: 6 580.32000 cents 6: 6 621.38000 cents 7: 11 697.57000 cents 7: 1 738.63000 cents 8: 4 773.76000 cents 8: 8 814.82000 cents 9: 9 891.01000 cents 9: 3 932.07000 cents 10: 2 967.20000 cents 10: 10 1008.26000 cents 11: 7 1084.45000 cents 11: 5 1125.51000 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 : 117.3 193.4 310.7 386.9 504.1 580.3 697.6 814.8 891.0 1008.3 1084.5 1201.7 117.3 : 76.2 193.4 269.6 386.9 463.1 580.3 697.6 773.8 891.0 967.2 1084.4 1201.7 193.4 : 117.3 193.4 310.7 386.9 504.1 621.4 697.6 814.8 891.0 1008.3 1125.5 1201.7 310.7 : 76.2 193.4 269.6 386.9 504.1 580.3 697.6 773.8 891.0 1008.3 1084.4 1201.7 386.9 : 117.3 193.4 310.7 427.9 504.1 621.4 697.6 814.8 932.1 1008.3 1125.5 1201.7 504.1 : 76.2 193.4 310.7 386.9 504.1 580.3 697.6 814.8 891.0 1008.3 1084.4 1201.7 580.3 : 117.3 234.5 310.7 427.9 504.1 621.4 738.6 814.8 932.1 1008.3 1125.5 1201.7 697.6 : 117.3 193.4 310.7 386.9 504.1 621.4 697.6 814.8 891.0 1008.3 1084.4 1201.7 814.8 : 76.2 193.4 269.6 386.9 504.1 580.3 697.6 773.8 891.0 967.2 1084.4 1201.7 891.0 : 117.2 193.4 310.7 427.9 504.1 621.4 697.6 814.8 891.0 1008.3 1125.5 1201.7 1008.3: 76.2 193.4 310.7 386.9 504.1 580.3 697.6 773.8 891.0 1008.3 1084.5 1201.7 1084.5: 117.2 234.5 310.7 427.9 504.1 621.4 697.6 814.8 932.1 1008.3 1125.5 1201.7 1201.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.1900 .. 117.2500 cents 41.06000 cents 76.19000 cents 2: 193.4400 .. 234.5000 cents 41.06000 cents 76.19000 cents 3: 269.6300 .. 310.6900 cents 41.06000 cents 35.13000 cents 4: 386.8800 .. 427.9400 cents 41.06000 cents 76.19000 cents 5: 463.0700 .. 504.1300 cents 41.06000 cents 35.13000 cents 6: 580.3200 .. 621.3800 cents 41.06000 cents 76.19000 cents 7: 697.5700 .. 738.6300 cents 41.06000 cents 76.19000 cents 8: 773.7600 .. 814.8200 cents 41.06000 cents 35.13000 cents 9: 891.0100 .. 932.0700 cents 41.06000 cents 76.19000 cents 10: 967.2000 .. 1008.2600 cents 41.06000 cents 35.13000 cents 11: 1084.4500 .. 1125.5100 cents 41.06000 cents 76.19000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 76.19000 cents, class 1 Average step (divided formal octave): 100.1417 cents Largest one step interval : 117.25000 cents Average / Smallest step : 1.314368 Largest / Average step : 1.170841 Largest / Smallest step : 1.538916 Median interval of one step : 117.25000 cents, amount: 7 Most common interval of one step : 117.25000 cents, amount: 7 Least squares average step : 99.75212 cents, oct.: 1197.02548 cents Scale is strictly proper Scale has Myhill's property chromas: 41.06000 cents and 35.13000 cents, ratio: 1.168802 generators: 5 of 504.13000 cents and 7 of 697.57000 cents ET pair of linear temperament : 12&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 2019-tone equal temperament with octave 1201.700 cents degrees: 197 325 522 650 847 975 1172 1369 1497 1694 1822 2019 generators: 847 and 1172 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABAABABA Step pattern size order : LSLSLSLLSLSL Scale is a Constant Structure, by a margin of 35.13000 cents Scale diversity : 1.216995 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.624149 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 : 35.13000 cents Most common intervals : 504.13000 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 117.250 697.570 cents Most common triad is 0.0 504.130 697.570 cents, amount: 10 Number of recognisable fifths : 11, average 697.5700 cents Number of recognisable fourths : 11, average 504.1300 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 : 7 Inversional symmetry on intervals : 3-4 9-10 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 11.9350 c. M:-20.5300 c. Twelve-tone Chromatic (1/11-comma) 19: 2 1 2 1 2 1 2 2 1 2 1 2 P M ME SD: 6.4493 c. M: 11.0937 c. Genus diatonico-chromaticum, Yasser's Supradiatonic inverse 31: 3 2 3 2 3 2 3 3 2 3 2 3 SP M ME SD: 0.6672 c. M:-1.1477 c. Genus diatonico-chromaticum 112: 11 7 11 7 11 7 11 11 7 11 7 11 SP M DE SD: 0.5400 c. M: 0.9289 c. 143: 14 9 14 9 14 9 14 14 9 14 9 14 SP M DE SD: 0.2783 c. M: 0.4787 c. 174: 17 11 17 11 17 11 17 17 11 17 11 17 SP M DE SD: 0.1099 c. M: 0.1890 c. 205: 20 13 20 13 20 13 20 20 13 20 13 20 SP M DE SD: 0.0077 c. M:-0.0132 c. 1404: 137 89 137 89 137 89 137 137 89 137 89 137 SP M DE SD: 0.0069 c. M: 0.0119 c. 1609: 157 102 157 102 157 102 157 157 102 157 102 157 SP M DE SD: 0.0051 c. M: 0.0087 c. 1814: 177 115 177 115 177 115 177 177 115 177 115 177 SP M DE SD: 0.0036 c. M: 0.0062 c. 2019: 197 128 197 128 197 128 197 197 128 197 128 197 SP M DE SD: 0.0025 c. M: 0.0042 c. 2224: 217 141 217 141 217 141 217 217 141 217 141 217 SP M DE SD: 0.0015 c. M: 0.0026 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 1.7000 cents 2 x x x x x x 3 x x x x 4 S SD: 2.3515 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.0579 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.9294 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 2.1969 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.5082 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.8678 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.0751 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.7103 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0137 cents 11:12 x 13:14:15 x 16:18 x 20:21:22 S SD: 10.7449 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 7.1293 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 8.5837 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.7414 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.1498 cents 24:26:27:29:30:32:34:36:38:40:43:45:48 SD: 3.5905 cents 25:27:28:30:31:33:35:37:40:42:45:47:50 SD: 3.3565 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.3332 cents 30:32:34:36:38:40:42:45:48:50:54:56:60 SD: 3.0131 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.6149 cents 40:43:45:48:50:54:56:60:64:67:72:75:80 SD: 1.9886 cents 45:48:50:54:56:60:63:67:72:75:81:84:90 SD: 1.8817 cents 52:56:58:62:65:70:73:78:83:87:93:97:104 SD: 1.7021 cents 56:60:63:67:70:75:78:84:90:94:100:105:112 SD: 1.4285 cents 60:64:67:72:75:80:84:90:96:100:107:112:120 SD: 1.2679 cents 68:73:76:81:85:91:95:102:109:114:122:127:136 SD: 1.0429 cents 76:81:85:91:95:102:106:114:122:127:136:142:152 SD: 1.0189 cents 83:89:93:99:104:111:116:124:133:139:149:155:166 SD: 0.8986 cents 85:91:95:102:106:114:119:127:136:142:152:159:170 SD: 0.7894 cents 100:107:112:120:125:134:140:150:160:167:179:187:200 SD: 0.7365 cents 101:108:113:121:126:135:141:151:162:169:181:189:202 SD: 0.5952 cents 128:137:143:153:160:171:179:192:205:214:229:239:256 SD: 0.5941 cents 143:153:160:171:179:191:200:214:229:239:256:268:286 SD: 0.4632 cents 153:164:171:183:191:205:214:229:245:256:274:286:306 SD: 0.4547 cents 168:180:188:201:210:225:235:251:269:281:301:314:336 SD: 0.4075 cents 228:244:255:273:285:305:319:341:365:381:408:427:456 SD: 0.3211 cents 254:272:284:304:318:340:355:380:407:425:455:475:508 SD: 0.3119 cents 286:306:320:342:358:383:400:428:458:479:512:535:573 SD: 0.3058 cents 296:317:331:354:370:396:414:443:474:495:530:554:593 SD: 0.2124 cents 331:354:370:396:414:443:463:495:530:554:593:619:663 SD: 0.2074 cents 371:397:415:444:464:496:519:555:594:621:664:694:743 SD: 0.1825 cents 432:462:483:517:540:578:604:646:692:723:773:808:865 SD: 0.1801 cents 447:478:500:535:559:598:625:669:716:748:800:836:895 SD: 0.1602 cents 459:491:513:549:574:614:642:687:735:768:822:859:919 SD: 0.1500 cents 514:550:575:615:643:688:719:769:823:860:920:962:1029 SD: 0.1385 cents 524:561:586:627:655:701:733:784:839:877:938:980:1049 SD: 0.1340 cents 544:582:608:651:680:728:761:814:871:910:974:1018:1089 SD: 0.1271 cents 559:598:625:669:699:748:782:836:895:935:1001:1046:1119 SD: 0.1245 cents 600:642:671:718:750:803:839:898:961:1004:1074:1123:1201 SD: 0.1197 cents