Scala analysis: secoralternative10
George Secor "meantone alternative", {196/195, 676/675}-tempering in POTE tuning of 2.3.5.7.13 scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 140.004 cents 140.004410 2: 264.204 cents 264.203790 3: 388.403 cents 388.403160 4: 496.797 cents 496.797500 5: 594.808 cents 594.808160 6: 703.203 cents 703.202500 7: 843.207 cents 843.206910 8: 967.406 cents 967.406290 9: 1091.606 cents 1091.605660 10: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 108.3943 cents 108.3943 1: 140.0044 cents 140.0044 2: 124.1994 cents 124.1994 3: 124.1994 cents 124.1994 4: 108.3943 cents 108.3943 5: 98.0107 cents 98.0107 6: 108.3943 cents 108.3943 7: 140.0044 cents 140.0044 8: 124.1994 cents 124.1994 9: 124.1994 cents 124.1994 10: 108.3943 cents 108.3943
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 98.01066 cents 1: 3 108.39434 cents 1: 4 124.19938 cents 1: 2 140.00441 cents 2: 2 206.40500 cents 2: 2 232.59371 cents 2: 4 248.39875 cents 2: 2 264.20379 cents 3: 1 314.79934 cents 3: 1 330.60437 cents 3: 1 346.40941 cents 3: 2 356.79309 cents 3: 3 372.59813 cents 3: 2 388.40316 cents 4: 1 438.99871 cents 4: 2 454.80375 cents 4: 1 470.60879 cents 4: 6 496.79750 cents 5: 1 563.19809 cents 5: 2 579.00312 cents 5: 2 594.80816 cents 5: 2 605.19184 cents 5: 2 620.99688 cents 5: 1 636.80191 cents 6: 6 703.20250 cents 6: 1 729.39121 cents 6: 2 745.19625 cents 6: 1 761.00129 cents 7: 2 811.59684 cents 7: 3 827.40188 cents 7: 2 843.20691 cents 7: 1 853.59059 cents 7: 1 869.39563 cents 7: 1 885.20066 cents 8: 2 935.79621 cents 8: 4 951.60125 cents 8: 2 967.40629 cents 8: 2 993.59500 cents 9: 2 1059.99559 cents 9: 4 1075.80062 cents 9: 3 1091.60566 cents 9: 1 1101.98934 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 140.0 264.2 388.4 496.8 594.8 703.2 843.2 967.4 1091.6 1200.0 140.0 : 124.2 248.4 356.8 454.8 563.2 703.2 827.4 951.6 1060.0 1200.0 264.2 : 124.2 232.6 330.6 439.0 579.0 703.2 827.4 935.8 1075.8 1200.0 388.4 : 108.4 206.4 314.8 454.8 579.0 703.2 811.6 951.6 1075.8 1200.0 496.8 : 98.0 206.4 346.4 470.6 594.8 703.2 843.2 967.4 1091.6 1200.0 594.8 : 108.4 248.4 372.6 496.8 605.2 745.2 869.4 993.6 1102.0 1200.0 703.2 : 140.0 264.2 388.4 496.8 636.8 761.0 885.2 993.6 1091.6 1200.0 843.2 : 124.2 248.4 356.8 496.8 621.0 745.2 853.6 951.6 1060.0 1200.0 967.4 : 124.2 232.6 372.6 496.8 621.0 729.4 827.4 935.8 1075.8 1200.0 1091.6: 108.4 248.4 372.6 496.8 605.2 703.2 811.6 951.6 1075.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 98.0107 .. 140.0044 cents 41.99375 cents 98.01066 cents 2: 206.4050 .. 264.2038 cents 57.79879 cents 66.40059 cents 3: 314.7993 .. 388.4032 cents 73.60382 cents 50.59555 cents 4: 438.9987 .. 496.7975 cents 57.79879 cents 50.59555 cents 5: 563.1981 .. 636.8019 cents 73.60382 cents 66.40059 cents 6: 703.2025 .. 761.0013 cents 57.79879 cents 66.40059 cents 7: 811.5968 .. 885.2007 cents 73.60382 cents 50.59555 cents 8: 935.7962 .. 993.5950 cents 57.79879 cents 50.59555 cents 9: 1059.9956 .. 1101.9893 cents 41.99375 cents 66.40059 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 98.01066 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 140.00441 cents Average / Smallest step : 1.224357 Largest / Average step : 1.166703 Largest / Smallest step : 1.428461 Median interval of one step : 124.19938 cents, amount: 4 Most common interval of one step : 124.19938 cents, amount: 4 Least squares average step : 120.72784 cents, oct.: 1207.27836 cents Scale is strictly proper Step pattern alph. order: ABBCDCABBC Step pattern size order : DCCBABDCCB Scale is a Constant Structure, by a margin of 50.59555 cents Scale diversity : 1.407348 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.553338 Rothenberg efficiency : 0.351349 redundancy: 0.648651 Efficiency x scale size : 3.513492 Number of different interval sizes : 42 = 4.66667 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 10.38368 cents Most common intervals : 496.79750 cents & inv., amount: 6 Most common triad is 0.0 496.797 703.203 cents, amount: 2 Number of recognisable fifths : 6, average 703.2025 cents Scale contains two identical disjunct pentachords Formal octave complements present : 3 = 30.0000% Limited inverse transpositions with margin 73.6038 cents: 9 -- Rational properties --
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 16.0743 c. M: 28.4032 c. 19: 2 2 2 2 1 2 2 2 2 2 SP M ME SD: 15.6966 c. M: 26.3871 c. 21: 2 3 2 2 1 2 3 2 2 2 P D3 SD: 16.3157 c. M: 25.7187 c. 22: 3 2 2 2 2 2 2 3 2 2 P D3 S SD: 12.6698 c. M: 25.0251 c. 24: 3 2 3 2 2 2 3 2 3 2 SP D3 SD: 9.5037 c. M: 17.4063 c. 29: 3 3 3 3 2 3 3 3 3 3 SP M ME SD: 13.1879 c. M: 15.9894 c. 31: 4 3 3 3 2 3 4 3 3 3 SP SD: 8.2544 c. M:-14.8343 c. 33: 4 3 4 3 2 3 4 4 3 3 P SD: 9.9171 c. M:-14.4119 c. 34: 4 3 4 3 3 3 4 3 4 3 SP D3 SD: 7.5303 c. M: 17.1450 c. 36: 4 4 4 3 3 3 4 4 4 3 SP SD: 6.3326 c. M:-11.5968 c. 37: 4 4 4 3 3 4 4 4 4 3 SP D3 SD: 7.8549 c. M:-11.0970 c. 41: 5 4 4 4 3 4 5 4 4 4 SP SD: 5.5005 c. M: 9.4423 c. 46: 5 5 5 4 4 4 5 5 5 4 SP SD: 4.8252 c. M: 9.5696 c. 53: 6 6 5 5 4 5 6 6 5 5 SP SD: 4.6687 c. M:-7.4943 c. 58: 7 6 6 5 5 5 7 6 6 5 SP SD: 4.1272 c. M:-5.1918 c. 67: 8 7 7 6 5 6 8 7 7 6 SP SD: 3.5132 c. M:-5.6267 c. 68: 8 7 7 6 6 6 8 7 7 6 SP SD: 2.7248 c. M:-5.1918 c. 77: 9 8 8 7 6 7 9 8 8 7 SP SD: 1.4369 c. M: 2.6004 c. 87: 10 9 9 8 7 8 10 9 9 8 SP SD: 1.6559 c. M: 2.1963 c. 145: 17 15 15 13 12 13 17 15 15 13 SP SD: 0.6843 c. M:-1.0539 c. 222: 26 23 23 20 18 20 26 23 23 20 SP SD: 0.4469 c. M:-0.7860 c. 232: 27 24 24 21 19 21 27 24 24 21 SP SD: 0.2690 c. M: 0.4721 c. 377: 44 39 39 34 31 34 44 39 39 34 SP SD: 0.2176 c. M:-0.4173 c. 454: 53 47 47 41 37 41 53 47 47 41 SP SD: 0.0891 c. M:-0.1431 c. 686: 80 71 71 62 56 62 80 71 71 62 SP SD: 0.0510 c. M: 0.0650 c. 1140: 133 118 118 103 93 103 133 118 118 103 SP SD: 0.0374 c. M: 0.0713 c. 1517: 177 157 157 137 124 137 177 157 157 137 SP SD: 0.0261 c. M:-0.0501 c. 1971: 230 204 204 178 161 178 230 204 204 178 SP SD: 0.0201 c. M:-0.0291 c. 2203: 257 228 228 199 180 199 257 228 228 199 SP SD: 0.0151 c. M: 0.0237 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 0.6237 cents 3 x x x 4 x x 5 x x 6 S SD: 13.7236 cents 4 x x 5 x x 6 x 7 x 8 S SD: 0.7043 cents 5 x 6 x x 7 x 8:9 x 10 S SD: 15.7321 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 9.8434 cents 7 x 8:9 x 10 x 11:12:13:14 S SD: 13.5841 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 9.3148 cents 9:10 x 11:12:13:14:15:16:17:18 S SD: 11.9886 cents 10:11:12 x 13:14:15:16:17:19:20 SD: 10.4647 cents 11:12:13:14:15:16:17:18:19:21:22 SD: 9.9789 cents 12:13:14:15:16:17:18:20:21:23:24 SD: 5.4629 cents 20:22:23:25:27:28:30:33:35:38:40 SD: 5.2390 cents 22:24:26:28:29:31:33:36:38:41:44 SD: 5.1594 cents 23:25:27:29:31:32:35:37:40:43:46 SD: 4.9183 cents 24:26:28:30:32:34:36:39:42:45:48 S SD: 1.0202 cents 84:91:98:105:112:118:126:137:147:158:168 SD: 0.8820 cents 96:104:112:120:128:135:144:156:168:180:192 SD: 0.7615 cents 108:117:126:135:144:152:162:176:189:203:216 SD: 0.5879 cents 132:143:154:165:176:186:198:215:231:248:264 SD: 0.4658 cents 156:169:182:195:208:220:234:254:273:293:312 SD: 0.4411 cents 175:190:204:219:233:247:263:285:306:329:350 SD: 0.4352 cents 190:206:221:238:253:268:285:309:332:357:380 SD: 0.3886 cents 214:232:249:268:285:302:321:348:374:402:428 SD: 0.3538 cents 247:268:288:309:329:348:371:402:432:464:494 SD: 0.2862 cents 271:294:316:339:361:382:407:441:474:509:542 SD: 0.2518 cents 274:297:319:343:365:386:411:446:479:515:548 SD: 0.2484 cents 298:323:347:373:397:420:447:485:521:560:596 SD: 0.1796 cents 322:349:375:403:429:454:483:524:563:605:644 SD: 0.1489 cents 437:474:509:547:582:616:656:711:764:821:874 SD: 0.1317 cents 461:500:537:577:614:650:692:750:806:866:922 SD: 0.1118 cents 569:617:663:712:758:802:854:926:995:1069:1138 SD: 0.0939 cents 593:643:691:742:790:836:890:965:1037:1114:1186 SD: 0.0851 cents