Scala analysis: starrb
12 note {126/125, 176/175} scale, 328-et version
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 80.488 cents 80.487805 2: 160.976 cents 160.975610 3: 267.073 cents 267.073171 4: 391.463 cents 391.463415 5: 471.951 cents 471.951220 6: 578.049 cents 578.048780 7: 702.439 cents 702.439024 8: 782.927 cents 782.926829 9: 889.024 cents 889.024390 10: 969.512 cents 969.512195 11: 1050.000 cents 1050.000000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 150.0000 cents 150.0000 1: 80.4878 cents 80.4878 2: 80.4878 cents 80.4878 3: 106.0976 cents 106.0976 4: 124.3902 cents 124.3902 5: 80.4878 cents 80.4878 6: 106.0976 cents 106.0976 7: 124.3902 cents 124.3902 8: 80.4878 cents 80.4878 9: 106.0976 cents 106.0976 10: 80.4878 cents 80.4878 11: 80.4878 cents 80.4878 12: 150.0000 cents 150.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 80.48780 cents 1: 3 106.09756 cents 1: 2 124.39024 cents 1: 1 150.00000 cents 2: 2 160.97561 cents 2: 4 186.58537 cents 2: 2 204.87805 cents 2: 4 230.48780 cents 3: 3 267.07317 cents 3: 9 310.97561 cents 4: 1 347.56098 cents 4: 6 391.46341 cents 4: 4 417.07317 cents 4: 1 435.36585 cents 5: 3 471.95122 cents 5: 6 497.56098 cents 5: 1 515.85366 cents 5: 2 541.46341 cents 6: 6 578.04878 cents 6: 6 621.95122 cents 7: 2 658.53659 cents 7: 1 684.14634 cents 7: 6 702.43902 cents 7: 3 728.04878 cents 8: 1 764.63415 cents 8: 4 782.92683 cents 8: 6 808.53659 cents 8: 1 852.43902 cents 9: 9 889.02439 cents 9: 3 932.92683 cents 10: 4 969.51220 cents 10: 2 995.12195 cents 10: 4 1013.41463 cents 10: 2 1039.02439 cents 11: 1 1050.00000 cents 11: 2 1075.60976 cents 11: 3 1093.90244 cents 11: 6 1119.51220 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.45455 = 38/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 80.5 161.0 267.1 391.5 472.0 578.0 702.4 782.9 889.0 969.5 1050.0 1200.0 80.5 : 80.5 186.6 311.0 391.5 497.6 622.0 702.4 808.5 889.0 969.5 1119.5 1200.0 161.0 : 106.1 230.5 311.0 417.1 541.5 622.0 728.0 808.5 889.0 1039.0 1119.5 1200.0 267.1 : 124.4 204.9 311.0 435.4 515.9 622.0 702.4 782.9 932.9 1013.4 1093.9 1200.0 391.5 : 80.5 186.6 311.0 391.5 497.6 578.0 658.5 808.5 889.0 969.5 1075.6 1200.0 472.0 : 106.1 230.5 311.0 417.1 497.6 578.0 728.0 808.5 889.0 995.1 1119.5 1200.0 578.0 : 124.4 204.9 311.0 391.5 472.0 622.0 702.4 782.9 889.0 1013.4 1093.9 1200.0 702.4 : 80.5 186.6 267.1 347.6 497.6 578.0 658.5 764.6 889.0 969.5 1075.6 1200.0 782.9 : 106.1 186.6 267.1 417.1 497.6 578.0 684.1 808.5 889.0 995.1 1119.5 1200.0 889.0 : 80.5 161.0 311.0 391.5 472.0 578.0 702.4 782.9 889.0 1013.4 1093.9 1200.0 969.5 : 80.5 230.5 311.0 391.5 497.6 622.0 702.4 808.5 932.9 1013.4 1119.5 1200.0 1050.0: 150.0 230.5 311.0 417.1 541.5 622.0 728.0 852.4 932.9 1039.0 1119.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.4878 .. 150.0000 cents 69.51220 cents 80.48780 cents 2: 160.9756 .. 230.4878 cents 69.51220 cents 10.97561 cents 3: 267.0732 .. 310.9756 cents 43.90244 cents 36.58537 cents 4: 347.5610 .. 435.3659 cents 87.80488 cents 36.58537 cents 5: 471.9512 .. 541.4634 cents 69.51220 cents 36.58537 cents 6: 578.0488 .. 621.9512 cents 43.90244 cents 36.58537 cents 7: 658.5366 .. 728.0488 cents 69.51219 cents 36.58537 cents 8: 764.6341 .. 852.4390 cents 87.80488 cents 36.58537 cents 9: 889.0244 .. 932.9268 cents 43.90244 cents 36.58537 cents 10: 969.5122 .. 1039.0244 cents 69.51220 cents 36.58537 cents 11: 1050.0000 .. 1119.5122 cents 69.51220 cents 10.97561 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 80.48780 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 150.00000 cents Average / Smallest step : 1.242424 Largest / Average step : 1.500000 Largest / Smallest step : 1.863636 Median interval of one step : 93.29268 cents, amount: 0 Most common interval of one step : 80.48780 cents, amount: 6 Least squares average step : 97.57598 cents, oct.: 1170.91182 cents Scale is strictly proper Scale is a mode of a 328-tone equal temperament with octave 2/1 degrees: 22 44 73 107 129 158 192 214 243 265 287 328 Least number of segments generator : 165 of 603.659 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 311 of 1137.805 cents and inv. generated superset size: 42 = 30 more = 350.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: AABCABCABAAD Step pattern size order : AABCABCABAAD Scale is a Constant Structure, by a margin of 10.97561 cents Scale diversity : 1.391140 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.396341 Rothenberg efficiency : 0.410510 redundancy: 0.589490 Efficiency x scale size : 4.926118 Number of different interval sizes : 38 = 3.45455 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.45455 = 38/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 10.97561 cents Most common intervals : 310.97561 cents & inv., amount: 9 Most common triad is 0.0 310.976 889.024 cents, amount: 6 Number of recognisable fifths : 6, average 702.4390 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 26.1034 c. M:-50.0000 c. Twelve-tone Chromatic (1/11-comma) 15: 1 1 1 2 1 1 2 1 1 1 1 2 P D3 SD: 13.1319 c. M: 27.0732 c. 21: 1 2 2 2 1 2 2 2 2 1 1 3 N D3 SD: 15.8375 c. M:-25.2613 c. 22: 1 2 2 2 2 2 2 1 2 2 1 3 P D3 SD: 14.9044 c. M: 25.9424 c. 23: 1 2 2 2 2 2 2 2 2 1 2 3 P D3 SD: 16.1405 c. M: 30.3818 c. 26: 2 1 3 2 2 2 3 2 2 2 2 3 P D3 SD: 13.8962 c. M: 24.2026 c. 27: 2 2 2 3 2 2 3 2 2 2 2 3 SP D3 SD: 10.8999 c. M:-17.0732 c. 31: 2 2 3 3 2 3 3 2 3 2 2 4 P D3 SD: 4.8298 c. M: 8.7333 c. 46: 3 3 4 5 3 4 5 3 4 3 3 6 P SD: 3.5952 c. M: 6.5217 c. 58: 4 4 5 6 4 5 6 4 5 4 4 7 SP SD: 2.8327 c. M:-5.1724 c. 89: 6 6 8 9 6 8 9 6 8 6 6 11 SP SD: 1.2415 c. M:-2.5898 c. 104: 7 7 9 11 7 9 11 7 9 7 7 13 SP SD: 0.9883 c. M: 1.6886 c. 135: 9 9 12 14 9 12 14 9 12 9 9 17 SP SD: 0.6085 c. M: 1.1111 c. 193: 13 13 17 20 13 17 20 13 17 13 13 24 SP SD: 0.4256 c. M:-0.7772 c. 328: 22 22 29 34 22 29 34 22 29 22 22 41 SP SD: 0.0000 c. M:-0.0000 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 3 x x x x 4 S SD: 0.2420 cents 3 x x x x 4 x x x 5 x x 6 S SD: 8.8359 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 1.3044 cents 5 x x 6 x x 7 x 8 x x 9:10 S SD: 13.2286 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 4.4201 cents 7 x x 8 x 9:10 x 11 x 12:13:14 S SD: 11.0641 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 10.0012 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 11.2048 cents 10 x 11:12 x 13:14:15:16:17 x 18:20 S SD: 8.3023 cents 11 x 12:13:14 x 15 x 17:18:19:20:22 SD: 8.5478 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 4.0801 cents 13 x 14:15:16:17:18 x 20:22:23:24:26 S SD: 7.1084 cents 14:15 x 16 x 18:20:21:22:23:25:26:28 SD: 9.0790 cents 15:16 x 18:19:20:21:23:24:25:26:28:30 SD: 8.1121 cents 16:17:18:19:20:21:22:24:25:27:28:29:32 SD: 5.8443 cents 18:19:20:21:23:24:25:27:28:30:32:33:36 SD: 4.9545 cents 19:20:21:22:24:25:27:29:30:32:33:35:38 SD: 4.4569 cents 20:21:22:23:25:26:28:30:31:33:35:37:40 SD: 4.0166 cents 23:24:25:27:29:30:32:35:36:38:40:42:46 SD: 3.6724 cents 28:29:31:33:35:37:39:42:44:47:49:51:56 SD: 2.9842 cents 35:37:38:41:44:46:49:53:55:58:61:64:70 SD: 2.9308 cents 36:38:40:42:45:47:50:54:57:60:63:66:72 SD: 2.6802 cents 38:40:42:44:48:50:53:57:60:64:67:70:76 SD: 2.6754 cents 40:42:44:47:50:53:56:60:63:67:70:73:80 SD: 1.9702 cents 42:44:46:49:53:55:59:63:66:70:74:77:84 SD: 1.7010 cents 48:50:53:56:60:63:67:72:75:80:84:88:96 SD: 1.5932 cents 60:63:66:70:75:79:84:90:94:100:105:110:120 SD: 1.0288 cents 83:87:91:97:104:109:116:125:130:139:145:152:166 SD: 0.9399 cents 84:88:92:98:105:110:117:126:132:140:147:154:168 SD: 0.8623 cents 102:107:112:119:128:134:142:153:160:170:179:187:204 SD: 0.7868 cents 103:108:113:120:129:135:144:155:162:172:180:189:206 SD: 0.6930 cents 121:127:133:141:152:159:169:182:190:202:212:222:242 SD: 0.6603 cents 126:132:138:147:158:165:176:189:198:211:221:231:252 SD: 0.6590 cents 131:137:144:153:164:172:183:197:206:219:229:240:262 SD: 0.6063 cents 143:150:157:167:179:188:200:215:225:239:250:262:286 SD: 0.5913 cents 144:151:158:168:181:189:201:216:226:241:252:264:288 SD: 0.5204 cents 162:170:178:189:203:213:226:243:255:271:284:297:324 SD: 0.4971 cents 166:174:182:194:208:218:232:249:261:277:291:304:332 SD: 0.4823 cents 173:181:190:202:217:227:242:260:272:289:303:317:346 SD: 0.4751 cents 185:194:203:216:232:243:258:278:291:309:324:339:370 SD: 0.3878 cents 192:201:211:224:241:252:268:288:302:321:336:352:384 SD: 0.3364 cents 204:214:224:238:256:268:285:306:321:341:357:374:408 SD: 0.3210 cents 252:264:277:294:316:331:352:378:396:421:441:462:504 SD: 0.2607 cents 288:302:316:336:361:378:402:432:453:481:504:528:576 SD: 0.2455 cents 316:331:347:369:396:415:441:474:497:528:553:580:632 SD: 0.2412 cents 318:333:349:371:399:418:444:477:500:531:557:583:636 SD: 0.2377 cents 336:352:369:392:421:441:469:504:528:562:588:616:672 SD: 0.2359 cents 338:354:371:394:424:444:472:507:531:565:592:620:676 SD: 0.2048 cents 378:396:415:441:474:496:528:567:594:632:662:693:756 SD: 0.1936 cents 401:420:440:468:503:527:560:602:630:670:702:735:802 SD: 0.1891 cents 402:421:441:469:504:528:561:603:632:672:704:737:804 SD: 0.1506 cents 462:484:507:539:579:607:645:693:726:772:809:847:924 SD: 0.1177 cents 565:592:620:659:708:742:789:848:888:944:989:1036:1130 SD: 0.1169 cents