Scala analysis: part7_12
Partial 7-limit half-octave temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 29.273 cents 29.273330 2: 130.559 cents 130.558590 3: 231.844 cents 231.843840 4: 314.972 cents 314.971540 5: 416.257 cents 416.256790 6: 600.000 cents 600.000000 7: 629.273 cents 629.273330 8: 730.559 cents 730.558590 9: 831.844 cents 831.843840 10: 914.972 cents 914.971540 11: 1016.257 cents 1016.256790 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 183.7432 cents 183.7432 1: 29.2733 cents 29.2733 2: 101.2853 cents 101.2853 3: 101.2853 cents 101.2853 4: 83.1277 cents 83.1277 5: 101.2853 cents 101.2853 6: 183.7432 cents 183.7432 7: 29.2733 cents 29.2733 8: 101.2853 cents 101.2853 9: 101.2853 cents 101.2853 10: 83.1277 cents 83.1277 11: 101.2853 cents 101.2853 12: 183.7432 cents 183.7432
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 29.27333 cents 1: 2 83.12770 cents 1: 6 101.28526 cents 1: 2 183.74321 cents 2: 2 130.55859 cents 2: 4 184.41295 cents 2: 2 202.57051 cents 2: 2 213.01654 cents 2: 2 285.02846 cents 3: 2 231.84384 cents 3: 4 285.69821 cents 3: 4 314.30179 cents 3: 2 368.15616 cents 4: 2 314.97154 cents 4: 2 386.98346 cents 4: 2 397.42949 cents 4: 4 415.58705 cents 4: 2 469.44141 cents 5: 2 416.25679 cents 5: 6 498.71474 cents 5: 2 516.87230 cents 5: 2 570.72667 cents 6: 12 600.00000 cents 7: 2 629.27333 cents 7: 2 683.12770 cents 7: 6 701.28526 cents 7: 2 783.74321 cents 8: 2 730.55859 cents 8: 4 784.41295 cents 8: 2 802.57051 cents 8: 2 813.01654 cents 8: 2 885.02846 cents 9: 2 831.84384 cents 9: 4 885.69821 cents 9: 4 914.30179 cents 9: 2 968.15616 cents 10: 2 914.97154 cents 10: 2 986.98346 cents 10: 2 997.42949 cents 10: 4 1015.58705 cents 10: 2 1069.44141 cents 11: 2 1016.25679 cents 11: 6 1098.71474 cents 11: 2 1116.87230 cents 11: 2 1170.72667 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.09091 = 45/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 29.3 130.6 231.8 315.0 416.3 600.0 629.3 730.6 831.8 915.0 1016.3 1200.0 29.3 : 101.3 202.6 285.7 387.0 570.7 600.0 701.3 802.6 885.7 987.0 1170.7 1200.0 130.6 : 101.3 184.4 285.7 469.4 498.7 600.0 701.3 784.4 885.7 1069.4 1098.7 1200.0 231.8 : 83.1 184.4 368.2 397.4 498.7 600.0 683.1 784.4 968.2 997.4 1098.7 1200.0 315.0 : 101.3 285.0 314.3 415.6 516.9 600.0 701.3 885.0 914.3 1015.6 1116.9 1200.0 416.3 : 183.7 213.0 314.3 415.6 498.7 600.0 783.7 813.0 914.3 1015.6 1098.7 1200.0 600.0 : 29.3 130.6 231.8 315.0 416.3 600.0 629.3 730.6 831.8 915.0 1016.3 1200.0 629.3 : 101.3 202.6 285.7 387.0 570.7 600.0 701.3 802.6 885.7 987.0 1170.7 1200.0 730.6 : 101.3 184.4 285.7 469.4 498.7 600.0 701.3 784.4 885.7 1069.4 1098.7 1200.0 831.8 : 83.1 184.4 368.2 397.4 498.7 600.0 683.1 784.4 968.2 997.4 1098.7 1200.0 915.0 : 101.3 285.0 314.3 415.6 516.9 600.0 701.3 885.0 914.3 1015.6 1116.9 1200.0 1016.3: 183.7 213.0 314.3 415.6 498.7 600.0 783.7 813.0 914.3 1015.6 1098.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.2733 .. 183.7432 cents 154.46988 cents 29.27333 cents 2: 130.5586 .. 285.0285 cents 154.46987 cents -53.18462 cents 3: 231.8438 .. 368.1562 cents 136.31232 cents -53.18462 cents 4: 314.9715 .. 469.4414 cents 154.46987 cents -53.18462 cents 5: 416.2568 .. 570.7267 cents 154.46988 cents -53.18462 cents 6: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 29.27333 cents 7: 629.2733 .. 783.7432 cents 154.46988 cents 29.27333 cents 8: 730.5586 .. 885.0285 cents 154.46987 cents -53.18462 cents 9: 831.8438 .. 968.1562 cents 136.31232 cents -53.18462 cents 10: 914.9715 .. 1069.4414 cents 154.46987 cents -53.18462 cents 11: 1016.2568 .. 1170.7267 cents 154.46988 cents -53.18462 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 29.27333 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 183.74321 cents Average / Smallest step : 3.416079 Largest / Average step : 1.837432 Largest / Smallest step : 6.276813 Median interval of one step : 101.28526 cents, amount: 6 Most common interval of one step : 101.28526 cents, amount: 6 Least squares average step : 92.91017 cents, oct.: 1114.92201 cents Scale is not proper Scale has 2 repeating blocks of 6 notes Step pattern alph. order: ABBCBDABBCBD Step pattern size order : ACCBCDACCBCD Scale is a Constant Structure, by a margin of 0.66974 cents Scale diversity : 1.375359 Lumma stability : 0.097578 Lumma impropriety factor : 0.354564 Rothenberg efficiency (ambiguous key): 0.232924 redundancy: 0.767076 Efficiency x scale size : 2.795094 Number of different interval sizes : 45 = 4.09091 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.09091 = 45/11 Median interval variety : 4 Lowest interval variety : 1 Smallest interval difference : 0.66974 cents Most common intervals : 600.00000 cents & inv., amount: 12 Number of recognisable fifths : 6, average 701.2853 cents Scale contains two identical disjunct hexachords Formal octave complements present : 2 = 16.6667% Limited transpositions : 6 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 0 1 1 1 1 2 0 1 1 1 1 2 N B D3 SD: 23.4280 c. M: 31.8438 c. 17: 0 2 1 1 2 2 1 1 2 1 1 3 N SD: 21.2218 c. M: 35.2941 c. 20: 0 2 2 1 2 3 0 2 2 1 2 3 N B SD: 14.5665 c. M: 29.2733 c. 23: 0 2 2 2 2 3 1 2 2 1 2 4 N SD: 18.6895 c. M: 29.2733 c. 26: 1 2 2 2 2 4 1 2 2 2 2 4 N B SD: 8.3169 c. M:-16.8805 c. 30: 1 2 3 2 2 5 1 2 3 2 2 5 N B SD: 9.8542 c. M: 16.2568 c. 34: 1 3 3 2 3 5 1 3 3 2 3 5 N B SD: 8.5687 c. M:-15.2150 c. 38: 1 3 3 3 3 6 1 3 3 3 3 6 N B SD: 5.3739 c. M: 10.7912 c. 46: 1 4 4 3 4 7 1 4 4 3 4 7 N B SD: 1.9920 c. M: 3.1864 c. 72: 2 6 6 5 6 11 2 6 6 5 6 11 N B SD: 2.2152 c. M:-4.0600 c. 84: 2 7 7 6 7 13 2 7 7 6 7 13 N B SD: 1.8030 c. M: 3.2724 c. 118: 3 10 10 8 10 18 3 10 10 8 10 18 N B SD: 1.2255 c. M:-2.0545 c. 130: 3 11 11 9 11 20 3 11 11 9 11 20 N B SD: 1.1139 c. M: 1.5810 c. 156: 4 13 13 11 13 24 4 13 13 11 13 24 N B SD: 0.8532 c. M:-1.4959 c. 202: 5 17 17 14 17 31 5 17 17 14 17 31 N B SD: 0.2631 c. M:-0.4296 c. 450: 11 38 38 31 38 69 11 38 38 31 38 69 N B SD: 0.1819 c. M: 0.3049 c. 948: 23 80 80 66 80 145 23 80 80 66 80 145 N B SD: 0.1751 c. M:-0.2183 c. 1020: 25 86 86 71 86 156 25 86 86 71 86 156 N B SD: 0.1713 c. M:-0.3226 c. 1066: 26 90 90 74 90 163 26 90 90 74 90 163 N B SD: 0.1404 c. M:-0.2535 c. 1150: 28 97 97 80 97 176 28 97 97 80 97 176 N B SD: 0.1216 c. M: 0.1917 c. 1196: 29 101 101 83 101 183 29 101 101 83 101 183 N B SD: 0.1117 c. M: 0.1763 c. 1268: 31 107 107 88 107 194 31 107 107 88 107 194 N B SD: 0.0972 c. M:-0.1704 c. 1352: 33 114 114 94 114 207 33 114 114 94 114 207 N B SD: 0.0970 c. M: 0.1870 c. 1398: 34 118 118 97 118 214 34 118 118 97 118 214 N B SD: 0.0679 c. M: 0.0888 c. 1470: 36 124 124 102 124 225 36 124 124 102 124 225 N B SD: 0.0795 c. M:-0.1305 c. 1516: 37 128 128 105 128 232 37 128 128 105 128 232 N B SD: 0.0637 c. M:-0.1020 c. 1600: 39 135 135 111 135 245 39 135 135 111 135 245 N B SD: 0.0477 c. M: 0.0938 c. 1718: 42 145 145 119 145 263 42 145 145 119 145 263 N B SD: 0.0485 c. M:-0.0631 c. 1848: 45 156 156 128 156 283 45 156 156 128 156 283 N B SD: 0.0337 c. M: 0.0526 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 x 3 x x x 4 S SD: 14.3018 cents 3 x x x x 4 x x x x 5 x 6 S SD: 29.1099 cents 4 x x x x 5 x x 6 x x 7:8 S SD: 15.7410 cents 5 x x x 6 x 7 x x 8 x 9:10 S SD: 5.0508 cents 6 x x 7 x 8 x x 9 x 10:11:12 S SD: 17.2945 cents 7 x x 8 x 9 x 10 x 11:12:13:14 S SD: 11.3688 cents 8 x x 9 x 10:11 x 12:13 x 14:16 S SD: 12.1135 cents 9 x x 10:11 x x 13:14 x 15:16:18 SD: 11.1343 cents 10 x 11 x 12:13:14 x 15:16:17:18:20 S SD: 7.1117 cents 11 x 12 x 13:14 x 16:17:18:19:20:22 S SD: 6.7898 cents 12 x 13:14 x 15:17 x 18:19:20:22:24 SD: 8.8643 cents 13 x 14:15:16:17:18:19:20:21:22:23:26 SD: 7.9939 cents 14 x 15:16:17:18 x 20:21:23:24:25:28 SD: 5.5947 cents 15 x 16:17:18:19:21:22:23:24:25:27:30 SD: 5.3307 cents 16 x 17:18:19:20 x 23:24:26:27:29:32 SD: 6.1580 cents 17 x 18:19:20:22:24 x 26:27:29:31:34 SD: 7.8931 cents 18 x 19:21:22:23:25:26:27:29:31:32:36 SD: 7.4357 cents 19 x 20:22:23:24:27 x 29:31:32:34:38 SD: 5.6270 cents 20 x 22:23:24:25:28:29:31:32:34:36:40 SD: 5.6228 cents 21 x 23:24:25:27 x 30:32:34:36:38:42 SD: 4.2874 cents 23:24:25:26:28:29 x 33:35:37:39:41:46 SD: 5.5839 cents 25:26:27:29:30:32:35:36:38:40:42:45:50 SD: 4.7213 cents 26:27:28:30:31:33:37 x 40:42:44:47:52 SD: 4.1909 cents 28:29:30:32:34:36 x 40:43:45:48:50:56 SD: 4.8079 cents 29:30:31:33:35:37:41:42:44:47:49:52:58 SD: 3.3491 cents 33:34:36:38:40:42:47 x 50:53:56:59:66 SD: 3.9675 cents 34:35:37:39:41:43:48:49:52:55:58:61:68 SD: 2.7080 cents 36:37:39:41:43:46:51:52:55:58:61:65:72 SD: 2.2336 cents 41:42:44:47:49:52:58:59:63:66:70:74:82 SD: 2.2041 cents 48:49:52:55:58:61:68:69:73:78:81:86:96 SD: 1.8956 cents 49:50:53:56:59:62:69:70:75:79:83:88:98 SD: 1.7778 cents 50:51:54:57:60:64:71:72:76:81:85:90:100 SD: 1.4288 cents 55:56:59:63:66:70:78:79:84:89:93:99:110 SD: 1.0827 cents 89:91:96:102:107:113:126:128:136:144:151:160:178 SD: 1.0008 cents 99:101:107:113:119:126:140:142:151:160:168:178:198 SD: 0.7970 cents 114:116:123:130:137:145:161:164:174:184:193:205:228 SD: 0.6532 cents 125:127:135:143:150:159:177:180:191:202:212:225:250 SD: 0.4954 cents 166:169:179:190:199:211:235:239:253:268:282:299:332 SD: 0.4922 cents 169:172:182:193:203:215:239:243:258:273:287:304:338 SD: 0.4253 cents 181:184:195:207:217:230:256:260:276:293:307:326:362 SD: 0.3876 cents 217:221:234:248:260:276:307:312:331:351:368:390:434 SD: 0.3061 cents 280:285:302:320:336:356:396:403:427:453:475:504:560 SD: 0.2272 cents 342:348:369:391:410:435:484:492:522:553:580:615:684 SD: 0.2200 cents 356:362:384:407:427:453:503:512:543:576:604:640:712 SD: 0.2041 cents 406:413:438:464:487:516:574:584:619:656:689:730:812 SD: 0.1894 cents 411:418:443:470:493:523:581:591:627:665:697:739:822 SD: 0.1827 cents 461:469:497:527:553:586:652:663:703:745:782:829:922 SD: 0.1233 cents 577:587:622:660:692:734:816:830:880:933:979:1038:1154 SD: 0.1106 cents