Scala analysis: starra
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: 204.878 cents 204.878049 3: 310.976 cents 310.975610 4: 391.463 cents 391.463415 5: 471.951 cents 471.951220 6: 621.951 cents 621.951219 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: 1093.902 cents 1093.902439 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 106.0976 cents 106.0976 1: 80.4878 cents 80.4878 2: 124.3902 cents 124.3902 3: 106.0976 cents 106.0976 4: 80.4878 cents 80.4878 5: 80.4878 cents 80.4878 6: 150.0000 cents 150.0000 7: 80.4878 cents 80.4878 8: 80.4878 cents 80.4878 9: 106.0976 cents 106.0976 10: 80.4878 cents 80.4878 11: 124.3902 cents 124.3902 12: 106.0976 cents 106.0976
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 : 80.5 204.9 311.0 391.5 472.0 622.0 702.4 782.9 889.0 969.5 1093.9 1200.0 80.5 : 124.4 230.5 311.0 391.5 541.5 622.0 702.4 808.5 889.0 1013.4 1119.5 1200.0 204.9 : 106.1 186.6 267.1 417.1 497.6 578.0 684.1 764.6 889.0 995.1 1075.6 1200.0 311.0 : 80.5 161.0 311.0 391.5 472.0 578.0 658.5 782.9 889.0 969.5 1093.9 1200.0 391.5 : 80.5 230.5 311.0 391.5 497.6 578.0 702.4 808.5 889.0 1013.4 1119.5 1200.0 472.0 : 150.0 230.5 311.0 417.1 497.6 622.0 728.0 808.5 932.9 1039.0 1119.5 1200.0 622.0 : 80.5 161.0 267.1 347.6 472.0 578.0 658.5 782.9 889.0 969.5 1050.0 1200.0 702.4 : 80.5 186.6 267.1 391.5 497.6 578.0 702.4 808.5 889.0 969.5 1119.5 1200.0 782.9 : 106.1 186.6 311.0 417.1 497.6 622.0 728.0 808.5 889.0 1039.0 1119.5 1200.0 889.0 : 80.5 204.9 311.0 391.5 515.9 622.0 702.4 782.9 932.9 1013.4 1093.9 1200.0 969.5 : 124.4 230.5 311.0 435.4 541.5 622.0 702.4 852.4 932.9 1013.4 1119.5 1200.0 1093.9: 106.1 186.6 311.0 417.1 497.6 578.0 728.0 808.5 889.0 995.1 1075.6 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 69.51220 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 : 99.06191 cents, oct.: 1188.74296 cents Scale is strictly proper Scale is a mode of a 328-tone equal temperament with octave 2/1 degrees: 22 56 85 107 129 170 192 214 243 265 299 328 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: ABCAADAACABC Step pattern size order : ACBAADAABACB 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 : 3 = 25.0000% -- 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: 16.4597 c. M:-30.4878 c. Twelve-tone Chromatic (1/11-comma) 15: 1 2 1 1 1 2 1 1 1 1 2 1 P D3 SD: 16.4102 c. M:-35.1220 c. Twelve-tone Chromatic 19: 1 2 2 1 1 3 1 1 2 1 2 2 N D3 SD: 16.6061 c. M: 29.8460 c. 22: 1 3 2 1 2 2 2 1 2 2 2 2 P D3 SD: 15.5248 c. M: 25.9424 c. 23: 2 2 2 2 1 3 2 1 2 2 2 2 P D3 SD: 14.5754 c. M:-27.9958 c. 24: 2 2 2 2 1 3 2 2 2 1 3 2 P T3 SD: 14.1344 c. M: 21.9512 c. 25: 2 2 2 2 2 3 2 1 3 1 3 2 P D3 SD: 13.8761 c. M:-22.9756 c. 27: 2 3 2 2 2 3 2 2 2 2 3 2 SP D3 SD: 11.0394 c. M:-17.3442 c. 31: 2 3 3 2 2 4 2 2 3 2 3 3 P D3 SD: 6.0164 c. M: 11.3297 c. 41: 3 4 4 2 3 5 3 3 3 3 4 4 P SD: 7.4680 c. M: 10.9756 c. 43: 3 4 4 3 3 5 3 3 4 3 4 4 SP D3 SD: 5.0975 c. M: 9.5292 c. 46: 3 5 4 3 3 6 3 3 4 3 5 4 P SD: 2.5193 c. M: 4.2948 c. 58: 4 6 5 4 4 7 4 4 5 4 6 5 SP SD: 2.1760 c. M:-3.9108 c. 89: 6 9 8 6 6 11 6 6 8 6 9 8 SP SD: 1.2604 c. M: 2.6309 c. 104: 7 11 9 7 7 13 7 7 9 7 11 9 SP SD: 1.3497 c. M:-2.8143 c. 135: 9 14 12 9 9 17 9 9 12 9 14 12 SP SD: 0.4674 c. M: 0.8401 c. 193: 13 20 17 13 13 24 13 13 17 13 20 17 SP SD: 0.3270 c. M:-0.5876 c. 328: 22 34 29 22 22 41 22 22 29 22 34 29 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 9 x 10 S SD: 13.9075 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 11.3430 cents 7 x 8 x x 9:10 x 11 x 12:13:14 S SD: 8.9070 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 10.7536 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 6.8781 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.8975 cents 11 x 12:13:14 x 16 x 17:18:19:21:22 SD: 10.0560 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 7.9349 cents 13:14:15 x 16:17:19 x 20:22:23:24:26 SD: 9.8340 cents 14:15:16:17 x 18:20:21:22:23:25:26:28 SD: 7.4770 cents 15:16:17:18:19:20:21:23:24:25:26:28:30 SD: 6.7417 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 2.9707 cents 32:34:36:38:40:42:46:48:50:53:56:60:64 SD: 2.9204 cents 35:37:39:42:44:46:50:53:55:58:61:66:70 SD: 2.8439 cents 39:41:44:47:49:51:56:59:61:65:68:73:78 SD: 2.2181 cents 40:42:45:48:50:53:57:60:63:67:70:75:80 SD: 1.7383 cents 56:59:63:67:70:74:80:84:88:94:98:105:112 SD: 1.5539 cents 60:63:68:72:75:79:86:90:94:100:105:113:120 SD: 1.4016 cents 64:67:72:77:80:84:92:96:101:107:112:120:128 SD: 1.2781 cents 70:73:79:84:88:92:100:105:110:117:123:132:140 SD: 1.1963 cents 80:84:90:96:100:105:115:120:126:134:140:150:160 SD: 1.0763 cents 82:86:92:98:103:108:117:123:129:137:144:154:164 SD: 1.0483 cents 86:90:97:103:108:113:123:129:135:144:151:162:172 SD: 0.7456 cents 102:107:115:122:128:134:146:153:160:170:179:192:204 SD: 0.7042 cents 122:128:137:146:153:160:175:183:192:204:214:229:244 SD: 0.6900 cents 127:133:143:152:159:167:182:191:200:212:222:239:254 SD: 0.5904 cents 143:150:161:171:179:188:205:215:225:239:250:269:286 SD: 0.5374 cents 152:159:171:182:191:200:218:228:239:254:266:286:304 SD: 0.5302 cents 166:174:187:199:208:218:238:249:261:277:291:312:332 SD: 0.4573 cents 168:176:189:201:211:221:241:252:264:281:294:316:336 SD: 0.4478 cents 182:191:205:218:228:239:261:273:286:304:319:342:364 SD: 0.4432 cents 185:194:208:221:232:243:265:278:291:309:324:348:370 SD: 0.4339 cents 189:198:213:226:237:248:271:284:297:316:331:356:378 SD: 0.4246 cents 192:201:216:230:241:252:275:288:302:321:336:361:384 SD: 0.3122 cents 208:218:234:249:261:273:298:312:327:348:364:391:416 SD: 0.2873 cents 252:264:284:302:316:331:361:378:396:421:441:474:504 SD: 0.2819 cents 268:281:302:321:336:352:384:402:421:448:469:504:536 SD: 0.2723 cents 280:293:315:335:351:368:401:420:440:468:490:527:560 SD: 0.2386 cents 294:308:331:352:369:386:421:441:462:491:515:553:588 SD: 0.2281 cents 296:310:333:354:371:389:424:444:465:495:518:557:592 SD: 0.2259 cents 310:325:349:371:389:407:444:465:487:518:543:583:620 SD: 0.2167 cents 380:398:428:455:476:499:544:570:597:635:665:715:760 SD: 0.2151 cents 382:400:430:457:479:502:547:573:600:638:669:719:764 SD: 0.2122 cents 398:417:448:476:499:523:570:597:626:665:697:749:796 SD: 0.1806 cents 421:441:474:504:528:553:603:632:662:704:737:792:842 SD: 0.1521 cents 437:458:492:523:548:574:626:656:687:730:765:822:874 SD: 0.1257 cents 462:484:520:553:579:607:662:693:726:772:809:869:924 SD: 0.1218 cents 565:592:636:676:708:742:809:848:888:944:989:1063:1130 SD: 0.1153 cents 590:618:664:706:740:775:845:885:927:986:1033:1110:1180 SD: 0.1041 cents