Scala analysis: mts12
Meantone with stretched octaves
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 191.962 cents 191.962060 3: 313.252 cents 313.251700 4: 383.924 cents 383.924130 5: 505.214 cents 505.213760 6: 575.886 cents 575.886190 7: 697.176 cents 697.175830 8: 767.848 cents 767.848250 9: 889.138 cents 889.137890 10: 1010.428 cents 1010.427520 11: 1081.100 cents 1081.099950 12: 1202.390 cents 1202.389590
SHOW/INTERVAL
0: 121.2896 cents 121.2896 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 121.2896 cents 121.2896 3: 121.2896 cents 121.2896 4: 70.6724 cents 70.6724 5: 121.2896 cents 121.2896 6: 70.6724 cents 70.6724 7: 121.2896 cents 121.2896 8: 70.6724 cents 70.6724 9: 121.2896 cents 121.2896 10: 121.2896 cents 121.2896 11: 70.6724 cents 70.6724 12: 121.2896 cents 121.2896
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 7 121.28963 cents 2: 10 191.96206 cents 2: 2 242.57927 cents 3: 3 262.63449 cents 3: 9 313.25170 cents 4: 8 383.92413 cents 4: 4 434.54133 cents 5: 1 454.59655 cents 5: 11 505.21376 cents 6: 6 575.88619 cents 6: 6 626.50340 cents 7: 11 697.17583 cents 7: 1 747.79304 cents 8: 4 767.84825 cents 8: 8 818.46546 cents 9: 9 889.13789 cents 9: 3 939.75509 cents 10: 2 959.81032 cents 10: 10 1010.42752 cents 11: 7 1081.09995 cents 11: 5 1131.71716 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 : 70.7 192.0 313.3 383.9 505.2 575.9 697.2 767.8 889.1 1010.4 1081.1 1202.4 70.7 : 121.3 242.6 313.3 434.5 505.2 626.5 697.2 818.5 939.8 1010.4 1131.7 1202.4 192.0 : 121.3 192.0 313.3 383.9 505.2 575.9 697.2 818.5 889.1 1010.4 1081.1 1202.4 313.3 : 70.7 192.0 262.6 383.9 454.6 575.9 697.2 767.8 889.1 959.8 1081.1 1202.4 383.9 : 121.3 192.0 313.3 383.9 505.2 626.5 697.2 818.5 889.1 1010.4 1131.7 1202.4 505.2 : 70.7 192.0 262.6 383.9 505.2 575.9 697.2 767.8 889.1 1010.4 1081.1 1202.4 575.9 : 121.3 192.0 313.3 434.5 505.2 626.5 697.2 818.5 939.8 1010.4 1131.7 1202.4 697.2 : 70.7 192.0 313.3 383.9 505.2 575.9 697.2 818.5 889.1 1010.4 1081.1 1202.4 767.8 : 121.3 242.6 313.3 434.5 505.2 626.5 747.8 818.5 939.8 1010.4 1131.7 1202.4 889.1 : 121.3 192.0 313.3 383.9 505.2 626.5 697.2 818.5 889.1 1010.4 1081.1 1202.4 1010.4: 70.7 192.0 262.6 383.9 505.2 575.9 697.2 767.8 889.1 959.8 1081.1 1202.4 1081.1: 121.3 192.0 313.3 434.5 505.2 626.5 697.2 818.5 889.1 1010.4 1131.7 1202.4 1202.4
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 121.2896 cents 50.61721 cents 25/24, 70.6724 cents 2: 191.9621 .. 242.5793 cents 50.61721 cents 70.67243 cents 3: 262.6345 .. 313.2517 cents 50.61721 cents 20.05522 cents 4: 383.9241 .. 434.5413 cents 50.61720 cents 70.67243 cents 5: 454.5965 .. 505.2138 cents 50.61721 cents 20.05522 cents 6: 575.8862 .. 626.5034 cents 50.61721 cents 70.67243 cents 7: 697.1758 .. 747.7930 cents 50.61721 cents 70.67243 cents 8: 767.8482 .. 818.4655 cents 50.61721 cents 20.05521 cents 9: 889.1379 .. 939.7551 cents 50.61720 cents 70.67243 cents 10: 959.8103 .. 1010.4275 cents 50.61720 cents 20.05522 cents 11: 1081.1000 .. 1131.7172 cents 50.61721 cents 70.67243 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 70.67242 cents, class 1 Average step (divided formal octave): 100.1991 cents Largest one step interval : 121.28963 cents Average / Smallest step : 1.417797 Largest / Average step : 1.210486 Largest / Smallest step : 1.716223 Median interval of one step : 121.28963 cents, amount: 7 Most common interval of one step : 121.28963 cents, amount: 7 Least squares average step : 99.01806 cents, oct.: 1188.21677 cents Scale is strictly proper Scale has Myhill's property chromas: 50.61721 cents and 20.05522 cents, ratio: 2.523892 generators: 5 of 505.21376 cents and 7 of 697.17583 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 1259-tone equal temperament with octave 1202.390 cents degrees: 74 201 328 402 529 603 730 804 931 1058 1132 1259 generators: 529 and 730 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABABABBAB Step pattern size order : SLLSLSLSLLSL Scale is a Constant Structure, by a margin of 20.05521 cents Scale diversity : 1.217976 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.536931 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 : 20.05521 cents Most common intervals : 505.21376 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 121.290 697.176 cents Most common triad is 0.0 505.214 697.176 cents, amount: 10 Number of recognisable fifths : 11, average 697.1758 cents Number of recognisable fourths : 11, average 505.2138 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 7 = 58.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 5 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 17.9785 c. M:-33.7448 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 4.4990 c. M: 8.4443 c. Meantone Chromatic (1/3-comma) 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 4.2020 c. M:-7.8870 c. Meantone Chromatic (53/220-comma) 50: 3 5 5 3 5 3 5 3 5 5 3 5 SP M DE SD: 0.8956 c. M:-1.6811 c. Meantone Chromatic (5/18-comma), Eair-12 69: 4 7 7 4 7 4 7 4 7 7 4 7 SP M DE SD: 0.5898 c. M: 1.1071 c. Meantone Chromatic (5/17-comma), Synch-Meantone-12 119: 7 12 12 7 12 7 12 7 12 12 7 12 SP M DE SD: 0.0343 c. M:-0.0644 c. Meantone Chromatic (2/7-comma), Zarlino 664: 39 67 67 39 67 39 67 39 67 67 39 67 SP M DE SD: 0.0305 c. M: 0.0573 c. 783: 46 79 79 46 79 46 79 46 79 79 46 79 SP M DE SD: 0.0207 c. M: 0.0388 c. 902: 53 91 91 53 91 53 91 53 91 91 53 91 SP M DE SD: 0.0134 c. M: 0.0252 c. 1021: 60 103 103 60 103 60 103 60 103 103 60 103 SP M DE SD: 0.0079 c. M: 0.0147 c. 1140: 67 115 115 67 115 67 115 67 115 115 67 115 SP M DE SD: 0.0035 c. M: 0.0065 c. 1259: 74 127 127 74 127 74 127 74 127 127 74 127 SP M DE SD: 0.0001 c. M:-0.0002 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 2.3896 cents 2 x x x x x x 3 x x x x 4 S SD: 2.6716 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.9803 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 10.5028 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 9.3975 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.5178 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.8804 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.7729 cents 9 x 10:11 x 12 x 13:14:15:16:17:18 S SD: 8.3276 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.5644 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.1937 cents 12 x 13:14:15:16:17:18:19:20 x 22:24 S SD: 8.7295 cents 13:14:15 x 16:17:18:19:20:22:23:24:26 S SD: 10.0937 cents 14:15:16:17 x 19:20:21:22:23:25:26:28 SD: 8.1199 cents 15:16:17:18:19:20:21:22:23:25:27:28:30 SD: 5.9274 cents 16:17:18:19:20:21:22:24:25:27:29:30:32 SD: 5.3424 cents 18:19:20:22 x 24:25:27:28:30:32:34:36 SD: 4.5907 cents 20:21:22:24:25:27:28:30:31:33:36:37:40 SD: 3.8109 cents 24:25:27:29:30:32:33:36:37:40:43:45:48 SD: 3.1779 cents 25:26:28:30:31:33:35:37:39:42:45:47:50 SD: 3.1550 cents 32:33:36:38:40:43:45:48:50:53:57:60:64 SD: 3.1308 cents 36:38:40:43:45:48:50:54:56:60:65:67:72 SD: 2.6436 cents 40:42:45:48:50:54:56:60:62:67:72:75:80 SD: 2.3913 cents 41:43:46:49:51:55:57:61:64:69:73:77:82 SD: 2.3204 cents 43:45:48:52:54:58:60:64:67:72:77:80:86 SD: 2.2430 cents 44:46:49:53:55:59:61:66:69:74:79:82:88 SD: 1.9698 cents 45:47:50:54:56:60:63:67:70:75:81:84:90 SD: 1.6589 cents 52:54:58:62:65:70:73:78:81:87:93:97:104 SD: 1.6413 cents 61:64:68:73:76:82:85:91:95:102:109:114:122 SD: 1.4408 cents 66:69:74:79:82:88:92:99:103:110:118:123:132 SD: 1.4178 cents 68:71:76:81:85:91:95:102:106:114:122:127:136 SD: 1.1797 cents 76:79:85:91:95:102:106:114:118:127:136:142:152 SD: 0.9081 cents 91:95:102:109:114:122:127:136:142:152:163:170:182 SD: 0.8708 cents 97:101:108:116:121:130:135:145:151:162:174:181:194 SD: 0.7487 cents 101:105:113:121:126:135:141:151:157:169:181:189:202 SD: 0.7094 cents 121:126:135:145:151:162:169:181:189:202:217:226:242 SD: 0.5322 cents 145:151:162:174:181:194:202:217:226:242:260:271:290 SD: 0.4265 cents 197:205:220:236:246:264:275:295:307:329:353:368:395 SD: 0.3681 cents 213:222:238:255:266:285:297:319:332:356:382:398:427 SD: 0.3247 cents 238:248:266:285:297:319:332:356:371:398:427:444:477 SD: 0.3135 cents 262:273:293:314:327:351:365:392:408:438:470:489:525 SD: 0.2929 cents 283:295:316:339:353:379:395:423:441:473:507:528:567 SD: 0.2892 cents 289:301:323:346:361:387:403:432:450:483:518:540:579 SD: 0.2542 cents 307:320:343:368:383:411:428:459:478:513:550:573:615 SD: 0.2245 cents 357:372:399:428:446:478:498:534:556:597:640:667:715 SD: 0.2093 cents 383:399:428:459:478:513:534:573:597:640:687:715:767 SD: 0.1444 cents 484:504:541:580:604:648:675:724:754:809:868:904:969 SD: 0.1341 cents 555:578:620:665:693:743:774:830:865:928:995:1036:1112 SD: 0.1302 cents