Scala analysis: starrc
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: 310.976 cents 310.975610 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: 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: 80.4878 cents 80.4878 3: 150.0000 cents 150.0000 4: 80.4878 cents 80.4878 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: 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: 8 391.46341 cents 4: 4 417.07317 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: 4 782.92683 cents 8: 8 808.53659 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: 3.09091 = 34/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 80.5 161.0 311.0 391.5 472.0 578.0 702.4 782.9 889.0 969.5 1093.9 1200.0 80.5 : 80.5 230.5 311.0 391.5 497.6 622.0 702.4 808.5 889.0 1013.4 1119.5 1200.0 161.0 : 150.0 230.5 311.0 417.1 541.5 622.0 728.0 808.5 932.9 1039.0 1119.5 1200.0 311.0 : 80.5 161.0 267.1 391.5 472.0 578.0 658.5 782.9 889.0 969.5 1050.0 1200.0 391.5 : 80.5 186.6 311.0 391.5 497.6 578.0 702.4 808.5 889.0 969.5 1119.5 1200.0 472.0 : 106.1 230.5 311.0 417.1 497.6 622.0 728.0 808.5 889.0 1039.0 1119.5 1200.0 578.0 : 124.4 204.9 311.0 391.5 515.9 622.0 702.4 782.9 932.9 1013.4 1093.9 1200.0 702.4 : 80.5 186.6 267.1 391.5 497.6 578.0 658.5 808.5 889.0 969.5 1075.6 1200.0 782.9 : 106.1 186.6 311.0 417.1 497.6 578.0 728.0 808.5 889.0 995.1 1119.5 1200.0 889.0 : 80.5 204.9 311.0 391.5 472.0 622.0 702.4 782.9 889.0 1013.4 1093.9 1200.0 969.5 : 124.4 230.5 311.0 391.5 541.5 622.0 702.4 808.5 932.9 1013.4 1119.5 1200.0 1093.9: 106.1 186.6 267.1 417.1 497.6 578.0 684.1 808.5 889.0 995.1 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: 391.4634 .. 417.0732 cents 25.60976 cents 80.48780 cents 5: 471.9512 .. 541.4634 cents 69.51220 cents 54.87805 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: 782.9268 .. 808.5366 cents 25.60976 cents 54.87805 cents 9: 889.0244 .. 932.9268 cents 43.90244 cents 80.48780 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 : 98.52158 cents, oct.: 1182.25891 cents Scale is strictly proper Scale is a mode of a 328-tone equal temperament with octave 2/1 degrees: 22 44 85 107 129 158 192 214 243 265 299 328 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: AABAACDACADC Step pattern size order : AADAABCABACB Scale is a Constant Structure, by a margin of 10.97561 cents Scale diversity : 1.317610 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.500000 Rothenberg efficiency : 0.439743 redundancy: 0.560257 Efficiency x scale size : 5.276912 Number of different interval sizes : 34 = 3.09091 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.09091 = 34/11 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% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 8-9 -- 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: 19.8959 c. M:-39.0244 c. Twelve-tone Chromatic (1/11-comma) 15: 1 1 2 1 1 1 2 1 1 1 2 1 P B ME SD: 12.9065 c. M:-26.0976 c. Augene-12 22: 1 2 3 1 2 2 2 1 2 2 2 2 P D3 SD: 15.0619 c. M: 25.9424 c. 23: 2 1 3 2 1 2 3 1 2 2 2 2 P D3 SD: 14.5904 c. M:-27.9958 c. 26: 2 1 4 1 2 2 3 2 2 2 3 2 N SD: 14.2118 c. M: 24.2026 c. 27: 2 2 3 2 2 2 3 2 2 2 3 2 SP B ME SD: 10.9693 c. M:-17.2087 c. Augene-12 31: 2 2 4 2 2 3 3 2 3 2 3 3 P D3 SD: 5.3515 c. M: 10.0315 c. 43: 3 3 5 3 3 4 4 3 4 3 4 4 SP D3 SD: 4.6799 c. M:-7.9977 c. 46: 3 3 6 3 3 4 5 3 4 3 5 4 P SD: 2.6048 c. M: 4.4539 c. 58: 4 4 7 4 4 5 6 4 5 4 6 5 SP SD: 2.4727 c. M:-4.5416 c. 89: 6 6 11 6 6 8 9 6 8 6 9 8 SP SD: 1.0336 c. M: 1.7676 c. 104: 7 7 13 7 7 9 11 7 9 7 11 9 SP SD: 1.0900 c. M:-2.2514 c. 135: 9 9 17 9 9 12 14 9 12 9 14 12 SP SD: 0.5312 c. M: 0.9756 c. 193: 13 13 24 13 13 17 20 13 17 13 20 17 SP SD: 0.3715 c. M:-0.6824 c. 239: 16 16 30 16 16 21 25 16 21 16 25 21 SP SD: 0.3849 c. M:-0.6582 c. 328: 22 22 41 22 22 29 34 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: 11.4890 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: 14.0402 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.8112 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.2970 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.9335 cents 11 x 12:13:14 x 15 x 17:18:19:21:22 SD: 8.8403 cents 12 x 13:14:15:16:17:18:19:20:21:23:24 SD: 6.4347 cents 13 x 14 x 16:17:18 x 20:22:23:24:26 S SD: 8.3172 cents 14:15 x 17 x 18:20:21:22:23:25:26:28 SD: 8.7227 cents 15:16 x 18:19:20:21:23:24:25:26:28:30 SD: 6.3440 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.1288 cents 19:20:21:23:24:25:27:29:30:32:33:36:38 SD: 4.6947 cents 20:21:22:24:25:26:28:30:31:33:35:38:40 SD: 3.5233 cents 28:29:31:34:35:37:39:42:44:47:49:53:56 SD: 3.3202 cents 32:34:35:38:40:42:45:48:50:53:56:60:64 SD: 3.0839 cents 35:37:38:42:44:46:49:53:55:58:61:66:70 SD: 2.8906 cents 36:38:40:43:45:47:50:54:57:60:63:68:72 SD: 2.7593 cents 39:41:43:47:49:51:54:59:61:65:68:73:78 SD: 2.5734 cents 40:42:44:48:50:53:56:60:63:67:70:75:80 SD: 1.6519 cents 58:61:64:69:73:76:81:87:91:97:102:109:116 SD: 1.6240 cents 60:63:66:72:75:79:84:90:94:100:105:113:120 SD: 1.1116 cents 80:84:88:96:100:105:112:120:126:134:140:150:160 SD: 1.0609 cents 82:86:90:98:103:108:115:123:129:137:144:154:164 SD: 0.9819 cents 86:90:94:103:108:113:120:129:135:144:151:162:172 SD: 0.8830 cents 101:106:111:121:127:133:141:152:159:169:177:190:202 SD: 0.8678 cents 102:107:112:122:128:134:142:153:160:170:179:192:204 SD: 0.7950 cents 103:108:113:123:129:135:144:155:162:172:180:194:206 SD: 0.7477 cents 121:127:133:145:152:159:169:182:190:202:212:228:242 SD: 0.7025 cents 122:128:134:146:153:160:170:183:192:204:214:229:244 SD: 0.6466 cents 134:140:147:160:168:176:187:201:211:224:235:252:268 SD: 0.6362 cents 142:149:156:170:178:187:198:213:223:237:249:267:284 SD: 0.6200 cents 143:150:157:171:179:188:200:215:225:239:250:269:286 SD: 0.5710 cents 146:153:160:175:183:192:204:219:229:244:256:275:292 SD: 0.5645 cents 152:159:167:182:191:200:212:228:239:254:266:286:304 SD: 0.5404 cents 162:170:178:194:203:213:226:243:255:271:284:305:324 SD: 0.5172 cents 166:174:182:199:208:218:232:249:261:277:291:312:332 SD: 0.4572 cents 182:191:200:218:228:239:254:273:286:304:319:342:364 SD: 0.4445 cents 185:194:203:221:232:243:258:278:291:309:324:348:370 SD: 0.4416 cents 192:201:211:230:241:252:268:288:302:321:336:361:384 SD: 0.3660 cents 194:203:213:232:243:255:271:291:305:324:340:365:388 SD: 0.3350 cents 229:240:251:274:287:301:320:344:360:383:401:431:458 SD: 0.3347 cents 249:261:273:298:312:327:348:374:391:416:436:468:498 SD: 0.3303 cents 252:264:277:302:316:331:352:378:396:421:441:474:504 SD: 0.3227 cents 255:267:280:305:320:335:356:383:401:426:446:480:510 SD: 0.3102 cents 268:281:294:321:336:352:374:402:421:448:469:504:536 SD: 0.2387 cents 310:325:340:371:389:407:433:465:487:518:543:583:620 SD: 0.2360 cents 316:331:347:378:396:415:441:474:497:528:553:594:632 SD: 0.2195 cents 320:335:351:383:401:420:447:480:503:535:560:602:640 SD: 0.2023 cents 401:420:440:480:503:527:560:602:630:670:702:754:802 SD: 0.1786 cents 402:421:441:481:504:528:561:603:632:672:704:756:804 SD: 0.1485 cents 441:462:484:528:553:579:616:662:693:737:772:830:882 SD: 0.1446 cents 462:484:507:553:579:607:645:693:726:772:809:869:924 SD: 0.1071 cents