Scala analysis: xen15-chalmers-stretched-14-1
Least-Squares Stretched 14-Tone Equal Temperament, Table 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 86.680 cents 86.680000 2: 173.360 cents 173.360000 3: 260.040 cents 260.040000 4: 346.720 cents 346.720000 5: 433.400 cents 433.400000 6: 520.080 cents 520.080000 7: 606.760 cents 606.760000 8: 693.440 cents 693.440000 9: 780.120 cents 780.120000 10: 866.800 cents 866.800000 11: 953.480 cents 953.480000 12: 1040.160 cents 1040.160000 13: 1126.830 cents 1126.830000 14: 1213.510 cents 1213.510000
SHOW/INTERVAL
0: 86.6800 cents 86.6800 1: 86.6800 cents 86.6800 2: 86.6800 cents 86.6800 3: 86.6800 cents 86.6800 4: 86.6800 cents 86.6800 5: 86.6800 cents 86.6800 6: 86.6800 cents 86.6800 7: 86.6800 cents 86.6800 8: 86.6800 cents 86.6800 9: 86.6800 cents 86.6800 10: 86.6800 cents 86.6800 11: 86.6800 cents 86.6800 12: 86.6800 cents 86.6800 13: 86.6700 cents 86.6700 14: 86.6800 cents 86.6800
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 86.67000 cents 1: 13 86.68000 cents 2: 2 173.35000 cents 2: 12 173.36000 cents 3: 3 260.03000 cents 3: 11 260.04000 cents 4: 4 346.71000 cents 4: 10 346.72000 cents 5: 5 433.39000 cents 5: 9 433.40000 cents 6: 6 520.07000 cents 6: 8 520.08000 cents 7: 7 606.75000 cents 7: 7 606.76000 cents 8: 8 693.43000 cents 8: 6 693.44000 cents 9: 9 780.11000 cents 9: 5 780.12000 cents 10: 10 866.79000 cents 10: 4 866.80000 cents 11: 11 953.47000 cents 11: 3 953.48000 cents 12: 12 1040.15000 cents 12: 2 1040.16000 cents 13: 13 1126.83000 cents 13: 1 1126.84000 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 12 13 14 0.0 : 86.7 173.4 260.0 346.7 433.4 520.1 606.8 693.4 780.1 866.8 953.5 1040.2 1126.8 1213.5 86.7 : 86.7 173.4 260.0 346.7 433.4 520.1 606.8 693.4 780.1 866.8 953.5 1040.2 1126.8 1213.5 173.4 : 86.7 173.4 260.0 346.7 433.4 520.1 606.8 693.4 780.1 866.8 953.5 1040.2 1126.8 1213.5 260.0 : 86.7 173.4 260.0 346.7 433.4 520.1 606.8 693.4 780.1 866.8 953.5 1040.2 1126.8 1213.5 346.7 : 86.7 173.4 260.0 346.7 433.4 520.1 606.8 693.4 780.1 866.8 953.5 1040.2 1126.8 1213.5 433.4 : 86.7 173.4 260.0 346.7 433.4 520.1 606.8 693.4 780.1 866.8 953.5 1040.2 1126.8 1213.5 520.1 : 86.7 173.4 260.0 346.7 433.4 520.1 606.8 693.4 780.1 866.8 953.5 1040.2 1126.8 1213.5 606.8 : 86.7 173.4 260.0 346.7 433.4 520.1 606.8 693.4 780.1 866.8 953.5 1040.2 1126.8 1213.5 693.4 : 86.7 173.4 260.0 346.7 433.4 520.1 606.8 693.4 780.1 866.8 953.5 1040.2 1126.8 1213.5 780.1 : 86.7 173.4 260.0 346.7 433.4 520.1 606.8 693.4 780.1 866.8 953.5 1040.2 1126.8 1213.5 866.8 : 86.7 173.4 260.0 346.7 433.4 520.1 606.8 693.4 780.1 866.8 953.5 1040.2 1126.8 1213.5 953.5 : 86.7 173.4 260.0 346.7 433.4 520.1 606.8 693.4 780.1 866.8 953.5 1040.2 1126.8 1213.5 1040.2: 86.7 173.4 260.0 346.7 433.4 520.1 606.8 693.4 780.1 866.8 953.5 1040.2 1126.8 1213.5 1126.8: 86.7 173.4 260.0 346.7 433.4 520.1 606.8 693.4 780.1 866.8 953.5 1040.2 1126.8 1213.5 1213.5
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 86.6700 .. 86.6800 cents 0.01000 cents 86.67000 cents 2: 173.3500 .. 173.3600 cents 0.01000 cents 86.67000 cents 3: 260.0300 .. 260.0400 cents 0.01000 cents 86.67000 cents 4: 346.7100 .. 346.7200 cents 0.01000 cents 86.67000 cents 5: 433.3900 .. 433.4000 cents 0.01000 cents 86.67000 cents 6: 520.0700 .. 520.0800 cents 0.01000 cents 86.67000 cents 7: 606.7500 .. 606.7600 cents 0.01000 cents 86.67000 cents 8: 693.4300 .. 693.4400 cents 0.01000 cents 86.67000 cents 9: 780.1100 .. 780.1200 cents 0.01000 cents 86.67000 cents 10: 866.7900 .. 866.8000 cents 0.01000 cents 86.67000 cents 11: 953.4700 .. 953.4800 cents 0.01000 cents 86.67000 cents 12: 1040.1500 .. 1040.1600 cents 0.01000 cents 86.67000 cents 13: 1126.8300 .. 1126.8400 cents 0.01000 cents 86.67000 cents
SHOW DATA
Number of notes : 14 -- Interval properties -- Smallest interval : 86.67000 cents, class 1 Average step (divided formal octave): 86.6793 cents Largest one step interval : 86.68000 cents Average / Smallest step : 1.000107 Largest / Average step : 1.000008 Largest / Smallest step : 1.000115 Median interval of one step : 86.68000 cents, amount: 13 Most common interval of one step : 86.68000 cents, amount: 13 Least squares average step : 86.67973 cents, oct.: 1213.51628 cents Scale is strictly proper Scale has Myhill's property chromas: 0.01000 cents and 86.66000 cents, ratio: 8666.000000 generators: 1 of 86.68000 cents and 13 of 1126.83000 cents ET pair of linear temperament : 13&14 Scale is maximally even for L / S <= 2 Scale is distributional even Step pattern alph. order: AAAAAAAAAAAABA Step pattern size order : LLLLLLLLLLLLSL Scale is a Constant Structure, by a margin of 86.67000 cents Scale diversity : 0.990986 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.999893 Rothenberg efficiency : 0.714286 redundancy: 0.285714 Efficiency x scale size : 10.000000 Number of different interval sizes : 26 = 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 : 0.01000 cents Most common intervals : 86.68000 cents & inv., amount: 13 Scale is a chain of 7 triads 0.0 520.080 1126.830 cents Most common triad is 0.0 86.680 1126.830 cents, amount: 12 Number of recognisable fifths : 14, average 693.4343 cents Number of recognisable fourths : 0 Scale contains two identical conjunct heptachords Formal octave complements present : 3 = 21.4286% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 1 2 3 4 5 6 7 8 9 10 11 12 13 Limited inverse transpositions : 1 2 3 4 5 6 7 8 9 10 11 12 13 Inversional symmetry on degrees : 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Inversional symmetry on intervals : 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 -- Rational properties --
FIT/MODE
14: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 0.0049 c. M: 0.0086 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x 2 S SD: 13.5100 cents 2 x x x x x x x 3 x x x x x 4 S SD: 7.9848 cents 3 x x x x x 4 x x x 5 x x x 6 S SD: 10.4156 cents 4 x x x 5 x x x 6 x x 7 x x 8 S SD: 11.3418 cents 5 x x x 6 x x 7 x 8 x x 9 x 10 S SD: 11.6141 cents 6 x x 7 x x 8 x 9 x 10 x 11 x 12 S SD: 5.7257 cents 7 x x 8 x 9 x 10 x 11 x 12:13 x 14 S SD: 7.2116 cents 8 x 9 x 10 x 11 x 12 x 13:14 x 15:16 S SD: 9.7984 cents 9 x 10 x 11 x 12:13 x 14:15:16 x 17:18 S SD: 7.5863 cents 10 x 11 x 12:13 x 14:15:16 x 17:18:19:20 S SD: 7.3524 cents 11 x 12:13 x 14:15:16 x 17:18:19:20:21:22 S SD: 6.3517 cents 12 x 13:14:15 x 16:17:18:19:20:21:22:23:24 S SD: 5.5567 cents 13:14 x 15:16:17:18 x 19:20:21:23:24:25:26 SD: 8.5651 cents 14:15 x 16:17:18:19:20:21:22:23:24:26:27:28 S SD: 4.8886 cents 15:16:17 x 18:19:20:21:22:24:25:26:27:29:30 SD: 7.0455 cents 16:17:18:19:20:21:22:23:24:25:26:28:29:31:32 SD: 6.6836 cents 17:18:19:20:21:22:23:24:25:27:28:29:31:33:34 SD: 4.6260 cents 18:19:20:21:22:23:24:26:27:28:30:31:33:35:36 SD: 4.0800 cents 23:24:25:27:28:30:31:33:34:36:38:40:42:44:46 SD: 3.8713 cents 26:27:29:30:32:33:35:37:39:41:43:45:47:50:52 SD: 3.2768 cents 31:33:34:36:38:40:42:44:46:49:51:54:57:59:62 SD: 2.9103 cents 35:37:39:41:43:45:47:50:52:55:58:61:64:67:71 SD: 2.4041 cents 37:39:41:43:45:48:50:53:55:58:61:64:67:71:75 SD: 2.2137 cents 38:40:42:44:46:49:51:54:57:60:63:66:69:73:77 SD: 2.1097 cents 45:47:50:52:55:58:61:64:67:71:74:78:82:86:91 SD: 1.7481 cents 49:52:54:57:60:63:66:70:73:77:81:85:89:94:99 SD: 1.6575 cents 55:58:61:64:67:71:74:78:82:86:91:95:100:105:111 SD: 1.4610 cents 57:60:63:66:70:73:77:81:85:89:94:99:104:109:115 SD: 1.1516 cents 74:78:82:86:90:95:100:105:110:116:122:128:135:142:149 SD: 0.9831 cents 85:89:94:99:104:109:115:121:127:133:140:147:155:163:171 SD: 0.9774 cents 86:90:95:100:105:110:116:122:128:135:142:149:157:165:173 SD: 0.9425 cents 94:99:104:109:115:121:127:133:140:148:155:163:171:180:189 SD: 0.9334 cents 95:100:105:110:116:122:128:135:142:149:157:165:173:182:191 SD: 0.7489 cents 112:118:124:130:137:144:151:159:167:176:185:194:204:215:226 SD: 0.6073 cents 131:138:145:152:160:168:177:186:196:206:216:227:239:251:264 SD: 0.5926 cents 134:141:148:156:164:172:181:190:200:210:221:232:244:257:270 SD: 0.5209 cents 140:147:155:163:171:180:189:199:209:220:231:243:255:268:282 SD: 0.5113 cents 154:162:170:179:188:198:208:219:230:242:254:267:281:295:310 SD: 0.4229 cents 172:181:190:200:210:221:232:244:257:270:284:298:314:330:347 SD: 0.3862 cents 191:201:211:222:233:245:258:271:285:300:315:331:348:366:385 SD: 0.3671 cents 197:207:218:229:241:253:266:280:294:309:325:342:359:378:397 SD: 0.3255 cents 217:228:240:252:265:279:293:308:324:341:358:376:396:416:437 SD: 0.3240 cents 229:241:253:266:280:294:309:325:342:359:378:397:418:439:462 SD: 0.3175 cents 248:261:274:288:303:319:335:352:370:389:409:430:452:475:500 SD: 0.3027 cents 253:266:280:294:309:325:342:359:378:397:417:439:461:485:510 SD: 0.2961 cents 257:270:284:299:314:330:347:365:384:403:424:446:469:493:518 SD: 0.2720 cents 274:288:303:318:335:352:370:389:409:430:452:475:500:525:552 SD: 0.2445 cents 314:330:347:365:384:403:424:446:469:493:518:545:573:602:633 SD: 0.2361 cents 334:351:369:388:408:429:451:474:499:524:551:579:609:640:673 SD: 0.1933 cents 351:369:388:408:429:451:474:498:524:551:579:609:640:673:707 SD: 0.1548 cents 388:408:429:451:474:498:524:551:579:609:640:673:708:744:782 SD: 0.1464 cents 505:531:558:587:617:649:682:717:754:792:833:876:921:968:1018 SD: 0.1268 cents 531:558:587:617:649:682:717:754:793:833:876:921:968:1018:1070 SD: 0.1267 cents 562:591:621:653:687:722:759:798:839:882:927:975:1025:1077:1133 SD: 0.1179 cents