Scala analysis: pelog11i
George Secor's isopelogic scale with ~537.84194 generator and just 13/11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40.577 cents 40.577490 2: 164.894 cents 164.893610 3: 13/11 289.209719 tridecimal minor third 4: 413.526 cents 413.525830 5: 537.842 cents 537.841940 6: 662.158 cents 662.158060 7: 702.736 cents 702.735550 8: 827.052 cents 827.051660 9: 951.368 cents 951.367780 10: 1075.684 cents 1075.683890 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 124.3161 cents 124.3161 1: 40.5775 cents 40.5775 2: 124.3161 cents 124.3161 3: 124.3161 cents 124.3161 4: 124.3161 cents 124.3161 5: 124.3161 cents 124.3161 6: 124.3161 cents 124.3161 7: 40.5775 cents 40.5775 8: 124.3161 cents 124.3161 9: 124.3161 cents 124.3161 10: 124.3161 cents 124.3161 11: 124.3161 cents 124.3161
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 40.57749 cents 1: 9 124.31612 cents 2: 4 164.89361 cents 2: 7 248.63223 cents 3: 6 13/11 289.210 cents tridecimal minor third 3: 5 372.94834 cents 4: 8 413.52583 cents 4: 3 497.26445 cents 5: 10 537.84194 cents 5: 1 621.58057 cents 6: 1 578.41943 cents 6: 10 662.15806 cents 7: 3 702.73555 cents 7: 8 786.47417 cents 8: 5 827.05166 cents 8: 6 910.79029 cents 9: 7 951.36778 cents 9: 4 1035.10640 cents 10: 9 1075.68389 cents 10: 2 1159.42251 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 0.0 : 40.6 164.9 289.2 413.5 537.8 662.2 702.7 827.1 951.4 1075.7 1200.0 40.6 : 124.3 248.6 372.9 497.3 621.6 662.2 786.5 910.8 1035.1 1159.4 1200.0 164.9 : 124.3 248.6 372.9 497.3 537.8 662.2 786.5 910.8 1035.1 1075.7 1200.0 289.2 : 124.3 248.6 372.9 413.5 537.8 662.2 786.5 910.8 951.4 1075.7 1200.0 413.5 : 124.3 248.6 289.2 413.5 537.8 662.2 786.5 827.1 951.4 1075.7 1200.0 537.8 : 124.3 164.9 289.2 413.5 537.8 662.2 702.7 827.1 951.4 1075.7 1200.0 662.2 : 40.6 164.9 289.2 413.5 537.8 578.4 702.7 827.1 951.4 1075.7 1200.0 702.7 : 124.3 248.6 372.9 497.3 537.8 662.2 786.5 910.8 1035.1 1159.4 1200.0 827.1 : 124.3 248.6 372.9 413.5 537.8 662.2 786.5 910.8 1035.1 1075.7 1200.0 951.4 : 124.3 248.6 289.2 413.5 537.8 662.2 786.5 910.8 951.4 1075.7 1200.0 1075.7: 124.3 164.9 289.2 413.5 537.8 662.2 786.5 827.1 951.4 1075.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 40.5775 .. 124.3161 cents 83.73863 cents 40.57749 cents 2: 164.8936 .. 248.6322 cents 83.73862 cents 40.57749 cents 3: 289.2097 .. 372.9483 cents 83.73862 cents 40.57749 cents 4: 413.5258 .. 497.2644 cents 83.73862 cents 40.57749 cents 5: 537.8419 .. 621.5806 cents 83.73863 cents 40.57749 cents 6: 578.4194 .. 662.1581 cents 83.73863 cents -43.16114 cents 7: 702.7356 .. 786.4742 cents 83.73862 cents 40.57749 cents 8: 827.0517 .. 910.7903 cents 83.73863 cents 40.57749 cents 9: 951.3678 .. 1035.1064 cents 83.73862 cents 40.57749 cents 10: 1075.6839 .. 1159.4225 cents 83.73862 cents 40.57749 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 40.57749 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 124.31612 cents Average / Smallest step : 2.688459 Largest / Average step : 1.139564 Largest / Smallest step : 3.063672 Median interval of one step : 124.31612 cents, amount: 9 Most common interval of one step : 124.31612 cents, amount: 9 Least squares average step : 105.94657 cents, oct.: 1165.41231 cents Scale is not proper Scale has Myhill's property chromas: 83.73863 cents and 43.16114 cents, ratio: 1.940139 generators: 5 of 537.84194 cents and 6 of 662.15806 cents ET pair of linear temperament : 29&444 Scale is distributional even Scale is a mode of a 1390-tone equal temperament with octave 2/1 degrees: 47 191 335 479 623 767 814 958 1102 1246 1390 generators: 623 and 767 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBBBBABBBB Step pattern size order : SLLLLLSLLLL Scale is a Constant Structure, by a margin of 40.57749 cents Scale diversity : 1.217445 Lumma stability : 0.338146 Lumma impropriety factor : 0.035968 Rothenberg efficiency : 0.727273 redundancy: 0.272727 Efficiency x scale size : 8.000000 Number of different interval sizes : 20 = 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 : 40.57749 cents Most common intervals : 537.84194 cents & inv., amount: 10 Scale is a chain of 5 triads 0.0 537.842 1075.684 cents Most common triad is 0.0 537.842 662.158 cents, amount: 9 Number of recognisable fifths : 3, average 702.7356 cents Scale contains two identical disjunct hexachords Best minor thirds form a closed circle Formal octave complements present : 3 = 27.2727% Limited inverse transpositions : 7 Inversional symmetry on degrees : 9 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 13 (not all pitches rational)
FIT/MODE
11: 0 1 1 1 1 1 1 1 1 1 2 N T3 SD: 75.3787 c. M: 116.7035 c. 12: 0 1 1 2 1 1 1 1 1 1 2 N D3 SD: 50.8122 c. M: 89.2097 c. 13: 0 2 1 1 2 1 1 1 1 2 1 N D3 SD: 26.5875 c. M: 44.2951 c. 17: 1 1 2 2 2 1 1 2 1 2 2 N D3 SD: 21.0737 c. M: 33.7207 c. 18: 0 2 2 2 2 2 0 2 2 2 2 N M DE S SD: 22.9895 c. M: 40.5775 c. 20: 1 2 2 2 2 2 1 2 2 2 2 P M ME S SD: 11.0040 c. M:-19.4225 c. Balzano Eleven-tone inverse 29: 1 3 3 3 3 3 1 3 3 3 3 N M DE S SD: 0.4543 c. M:-0.8018 c. Isopelogic-11 241: 8 25 25 25 25 25 8 25 25 25 25 N M DE S SD: 0.4212 c. M: 0.7435 c. 270: 9 28 28 28 28 28 9 28 28 28 28 N M DE S SD: 0.3272 c. M: 0.5775 c. 299: 10 31 31 31 31 31 10 31 31 31 31 N M DE S SD: 0.2514 c. M: 0.4437 c. 328: 11 34 34 34 34 34 11 34 34 34 34 N M DE S SD: 0.1890 c. M: 0.3336 c. 357: 12 37 37 37 37 37 12 37 37 37 37 N M DE S SD: 0.1367 c. M: 0.2414 c. 386: 13 40 40 40 40 40 13 40 40 40 40 N M DE S SD: 0.0923 c. M: 0.1630 c. 415: 14 43 43 43 43 43 14 43 43 43 43 N M DE S SD: 0.0541 c. M: 0.0956 c. 444: 15 46 46 46 46 46 15 46 46 46 46 N M DE S SD: 0.0209 c. M: 0.0369 c. 473: 16 49 49 49 49 49 16 49 49 49 49 N M DE S SD: 0.0082 c. M:-0.0145 c. 917: 31 95 95 95 95 95 31 95 95 95 95 N M DE S SD: 0.0059 c. M: 0.0104 c. 1390: 47 144 144 144 144 144 47 144 144 144 144 N M DE S SD: 0.0011 c. M: 0.0020 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x 4 S SD: 0.3903 cents 3 x x x x 4 x x 5 x x 6 S SD: 23.2568 cents 4 x x x 5 x x 6 x 7 x 8 S SD: 8.0851 cents 5 x x 6 x 7 x x 8 x 9:10 S SD: 15.8074 cents 6 x x 7 x 8 x 9:10 x 11:12 S SD: 12.9747 cents 7 x x 8:9 x 10 x 11:12:13:14 S SD: 12.9066 cents 8 x 9 x 10:11 x 12:13:14:15:16 S SD: 6.9482 cents 9 x 10:11 x 12:13 x 15:16:17:18 SD: 13.6113 cents 10 x 11:12:13:14 x 15:16:17:19:20 SD: 9.2036 cents 11 x 12:13:14:15:16:17:18:19:20:22 S SD: 7.2987 cents 12 x 13:14:15:16 x 18:19:21:22:24 SD: 8.2448 cents 13 x 14:15:17:18:19:20:21:23:24:26 SD: 9.8586 cents 14 x 15:17:18:19 x 21:23:24:26:28 SD: 8.7591 cents 15 x 17:18:19:20:22:23:24:26:28:30 SD: 8.1094 cents 16 x 18:19:20:22:23:24:26:28:30:32 S SD: 6.5626 cents 20:21:22:24:25:27:29:30:32:35:37:40 SD: 6.2022 cents 21:22:23:25:27:29:31:32:34:36:39:42 SD: 5.7222 cents 22:23:24:26:28:30:32:33:35:38:41:44 SD: 4.3562 cents 26:27:29:31:33:35:38:39:42:45:48:52 SD: 4.2780 cents 28:29:31:33:36:38:41:42:45:49:52:56 SD: 3.4774 cents 30:31:33:35:38:41:44:45:48:52:56:60 SD: 2.8644 cents 34:35:37:40:43:46:50:51:55:59:63:68 SD: 2.7106 cents 38:39:42:45:48:52:56:57:61:66:71:76 SD: 1.8539 cents 49:50:54:58:62:67:72:74:79:85:91:98 SD: 1.4654 cents 60:61:66:71:76:82:88:90:97:104:112:120 SD: 1.3543 cents 71:73:78:84:90:97:104:107:114:123:132:142 SD: 1.2593 cents 77:79:85:91:98:105:113:116:124:133:143:154 SD: 1.1707 cents 78:80:86:92:99:106:114:117:126:135:145:156 SD: 1.0450 cents 82:84:90:97:104:112:120:123:132:142:153:164 SD: 0.7083 cents 122:125:134:144:155:166:179:183:197:211:227:244 SD: 0.6699 cents 131:134:144:155:166:179:192:197:211:227:244:262 SD: 0.6093 cents 137:140:151:162:174:187:201:206:221:237:255:274 SD: 0.6075 cents 159:163:175:188:202:217:233:239:256:275:296:318 SD: 0.5144 cents 160:164:176:189:203:218:235:240:258:277:298:320 SD: 0.4741 cents 170:174:187:201:216:232:249:255:274:295:316:340 SD: 0.3978 cents 208:213:229:246:264:284:305:312:335:360:387:416 SD: 0.3528 cents 247:253:272:292:314:337:362:371:398:428:460:494 SD: 0.3399 cents 252:258:277:298:320:344:369:378:406:437:469:504 SD: 0.3209 cents 253:259:278:299:321:345:371:380:408:438:471:506 SD: 0.2879 cents 258:264:284:305:328:352:378:387:416:447:480:516 SD: 0.2757 cents 292:299:321:345:371:398:428:438:471:506:544:584 SD: 0.2675 cents 330:338:363:390:419:450:484:495:532:572:614:660 SD: 0.1924 cents 341:349:375:403:433:465:500:512:550:591:635:682 SD: 0.1672 cents 423:433:465:500:537:577:620:635:682:733:787:846 SD: 0.1492 cents 500:512:550:591:635:682:733:750:806:866:931:1000 SD: 0.1240 cents 511:523:562:604:649:697:749:767:824:885:951:1022 SD: 0.0978 cents 549:562:604:649:697:749:805:824:885:951:1022:1098 SD: 0.0909 cents