Scala analysis: xen15-chalmers-stretched-14-2
Least-Squares Stretched 14-Tone Equal Temperament, Table 6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 86.390 cents 86.390000 2: 172.790 cents 172.790000 3: 259.180 cents 259.180000 4: 345.580 cents 345.580000 5: 431.970 cents 431.970000 6: 518.360 cents 518.360000 7: 604.760 cents 604.760000 8: 691.150 cents 691.150000 9: 777.550 cents 777.550000 10: 863.940 cents 863.940000 11: 950.330 cents 950.330000 12: 1036.730 cents 1036.730000 13: 1123.120 cents 1123.120000 14: 1209.520 cents 1209.520000
SHOW/INTERVAL
0: 86.4000 cents 86.4000 1: 86.3900 cents 86.3900 2: 86.4000 cents 86.4000 3: 86.3900 cents 86.3900 4: 86.4000 cents 86.4000 5: 86.3900 cents 86.3900 6: 86.3900 cents 86.3900 7: 86.4000 cents 86.4000 8: 86.3900 cents 86.3900 9: 86.4000 cents 86.4000 10: 86.3900 cents 86.3900 11: 86.3900 cents 86.3900 12: 86.4000 cents 86.4000 13: 86.3900 cents 86.3900 14: 86.4000 cents 86.4000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 8 86.39000 cents 1: 6 86.40000 cents 2: 2 172.78000 cents 2: 12 172.79000 cents 3: 10 259.18000 cents 3: 4 259.19000 cents 4: 4 345.57000 cents 4: 10 345.58000 cents 5: 12 431.97000 cents 5: 2 431.98000 cents 6: 6 518.36000 cents 6: 8 518.37000 cents 7: 1 604.75000 cents 7: 12 604.76000 cents 7: 1 604.77000 cents 8: 8 691.15000 cents 8: 6 691.16000 cents 9: 2 777.54000 cents 9: 12 777.55000 cents 10: 10 863.94000 cents 10: 4 863.95000 cents 11: 4 950.33000 cents 11: 10 950.34000 cents 12: 12 1036.73000 cents 12: 2 1036.74000 cents 13: 6 1123.12000 cents 13: 8 1123.13000 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.07692 = 27/13
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.0 : 86.4 172.8 259.2 345.6 432.0 518.4 604.8 691.1 777.5 863.9 950.3 1036.7 1123.1 1209.5 86.4 : 86.4 172.8 259.2 345.6 432.0 518.4 604.8 691.2 777.6 863.9 950.3 1036.7 1123.1 1209.5 172.8 : 86.4 172.8 259.2 345.6 432.0 518.4 604.8 691.1 777.5 863.9 950.3 1036.7 1123.1 1209.5 259.2 : 86.4 172.8 259.2 345.6 432.0 518.4 604.8 691.1 777.6 863.9 950.3 1036.7 1123.1 1209.5 345.6 : 86.4 172.8 259.2 345.6 432.0 518.4 604.8 691.1 777.5 863.9 950.3 1036.7 1123.1 1209.5 432.0 : 86.4 172.8 259.2 345.6 432.0 518.4 604.8 691.1 777.6 863.9 950.3 1036.7 1123.1 1209.5 518.4 : 86.4 172.8 259.2 345.6 432.0 518.4 604.8 691.2 777.5 863.9 950.3 1036.7 1123.1 1209.5 604.8 : 86.4 172.8 259.2 345.6 432.0 518.4 604.8 691.1 777.5 863.9 950.3 1036.7 1123.1 1209.5 691.1 : 86.4 172.8 259.2 345.6 432.0 518.4 604.8 691.2 777.5 863.9 950.3 1036.7 1123.1 1209.5 777.5 : 86.4 172.8 259.2 345.6 432.0 518.4 604.8 691.1 777.6 863.9 950.3 1036.7 1123.1 1209.5 863.9 : 86.4 172.8 259.2 345.6 432.0 518.4 604.8 691.2 777.5 863.9 950.3 1036.7 1123.1 1209.5 950.3 : 86.4 172.8 259.2 345.6 432.0 518.4 604.8 691.2 777.6 864.0 950.3 1036.7 1123.1 1209.5 1036.7: 86.4 172.8 259.2 345.6 432.0 518.4 604.8 691.2 777.6 863.9 950.3 1036.7 1123.1 1209.5 1123.1: 86.4 172.8 259.2 345.6 432.0 518.4 604.8 691.2 777.6 864.0 950.3 1036.7 1123.1 1209.5 1209.5
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 86.3900 .. 86.4000 cents 0.01000 cents 86.39000 cents 2: 172.7800 .. 172.7900 cents 0.01000 cents 86.38000 cents 3: 259.1800 .. 259.1900 cents 0.01000 cents 86.39000 cents 4: 345.5700 .. 345.5800 cents 0.01000 cents 86.38000 cents 5: 431.9700 .. 431.9800 cents 0.01000 cents 86.39000 cents 6: 518.3600 .. 518.3700 cents 0.01000 cents 86.38000 cents 7: 604.7500 .. 604.7700 cents 0.02000 cents 86.38000 cents 8: 691.1500 .. 691.1600 cents 0.01000 cents 86.38000 cents 9: 777.5400 .. 777.5500 cents 0.01000 cents 86.38000 cents 10: 863.9400 .. 863.9500 cents 0.01000 cents 86.39000 cents 11: 950.3300 .. 950.3400 cents 0.01000 cents 86.38000 cents 12: 1036.7300 .. 1036.7400 cents 0.01000 cents 86.39000 cents 13: 1123.1200 .. 1123.1300 cents 0.01000 cents 86.38000 cents
SHOW DATA
Number of notes : 14 -- Interval properties -- Smallest interval : 86.39000 cents, class 1 Average step (divided formal octave): 86.3943 cents Largest one step interval : 86.40000 cents Average / Smallest step : 1.000050 Largest / Average step : 1.000066 Largest / Smallest step : 1.000116 Median interval of one step : 86.39000 cents, amount: 8 Most common interval of one step : 86.39000 cents, amount: 8 Least squares average step : 86.39403 cents, oct.: 1209.51641 cents Scale is strictly proper Scale is 3-distributional even Step pattern alph. order: ABABAABABAABAB Step pattern size order : SLSLSSLSLSSLSL Scale is a Constant Structure, by a margin of 86.38000 cents Scale diversity : 0.993793 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.999884 Number of different interval sizes : 27 = 2.07692 / class Number of one step interval sizes : 2 Highest interval variety : 3 Mean interval variety : 2.07692 = 27/13 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 0.01000 cents Number of recognisable fifths : 14, average 691.1543 cents Number of recognisable fourths : 0 Formal octave complements present : 8 = 57.1429% 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: 0.0036 c. M:-0.0071 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x 2 S SD: 9.5200 cents 2 x x x x x x x 3 x x x x x 4 S SD: 7.2003 cents 3 x x x x x 4 x x x 5 x x x 6 S SD: 10.1119 cents 4 x x x 5 x x x 6 x x 7 x x 8 S SD: 11.7492 cents 5 x x x 6 x x 7 x 8 x x 9 x 10 S SD: 11.2318 cents 6 x x 7 x x 8 x 9 x 10 x 11 x 12 S SD: 5.9061 cents 7 x x 8 x 9 x 10 x 11 x 12:13 x 14 S SD: 7.2703 cents 8 x 9 x 10 x 11 x 12 x 13:14 x 15:16 S SD: 9.7035 cents 9 x 10 x 11 x 12:13 x 14:15 x 16:17:18 S SD: 7.3109 cents 10 x 11 x 12:13 x 14:15:16 x 17:18:19:20 S SD: 7.0514 cents 11 x 12:13 x 14:15 x 16:17:18:19:20:21:22 S SD: 6.1493 cents 12 x 13:14:15 x 16:17:18:19:20:21:22:23:24 S SD: 5.7527 cents 13:14 x 15:16:17 x 18:19:20:21:23:24:25:26 SD: 8.4730 cents 14:15 x 16:17:18:19:20:21:22:23:24:25:27:28 SD: 4.9076 cents 15:16 x 17:18:19:20:21:22:24:25:26:27:29:30 SD: 6.9111 cents 16:17:18:19:20:21:22:23:24:25:26:28:29:31:32 SD: 6.8663 cents 17:18:19:20:21:22:23:24:25:27:28:29:31:33:34 SD: 4.6494 cents 18:19:20:21:22:23:24:26:27:28:30:31:33:34:36 SD: 4.0456 cents 22:23:24:26:27:28:30:31:33:34:36:38:40:42:44 SD: 4.0280 cents 23:24:25:27:28:30:31:33:34:36:38:40:42:44:46 SD: 3.8838 cents 26:27:29:30:32:33:35:37:39:41:43:45:47:50:52 SD: 3.2330 cents 31:33:34:36:38:40:42:44:46:49:51:54:56:59:62 SD: 2.8365 cents 32:34:35:37:39:41:43:45:48:50:53:55:58:61:64 SD: 2.8286 cents 35:37:39:41:43:45:47:50:52:55:58:61:64:67:70 SD: 2.6085 cents 36:38:40:42:44:46:49:51:54:56:59:62:66:69:72 SD: 2.4757 cents 37:39:41:43:45:47:50:52:55:58:61:64:67:71:74 SD: 2.1253 cents 45:47:50:52:55:58:61:64:67:71:74:78:82:86:90 SD: 1.8939 cents 49:52:54:57:60:63:66:69:73:77:81:85:89:94:99 SD: 1.8424 cents 55:58:61:64:67:71:74:78:82:86:91:95:100:105:111 SD: 1.3682 cents 57:60:63:66:70:73:77:81:85:89:94:99:104:109:115 SD: 1.2185 cents 67:70:74:78:82:86:90:95:100:105:110:116:122:128:135 SD: 1.1408 cents 74:78:82:86:90:95:100:105:110:116:122:128:135:142:149 SD: 0.9604 cents 77:81:85:89:94:99:104:109:115:121:127:133:140:147:155 SD: 0.9479 cents 94:99:104:109:115:121:127:133:140:147:155:163:171:180:189 SD: 0.7600 cents 112:118:124:130:137:144:151:159:167:175:184:194:204:214:225 SD: 0.7444 cents 113:119:125:131:138:145:152:160:168:177:186:196:206:216:227 SD: 0.7280 cents 117:123:129:136:143:150:158:166:174:183:193:203:213:224:235 SD: 0.6346 cents 134:141:148:156:164:172:181:190:200:210:221:232:244:256:269 SD: 0.5874 cents 141:148:156:164:172:181:190:200:210:221:232:244:257:270:284 SD: 0.4891 cents 155:163:171:180:189:199:209:220:231:243:255:268:282:297:312 SD: 0.4384 cents 172:181:190:200:210:221:232:244:256:270:283:298:313:329:346 SD: 0.4169 cents 173:182:191:201:211:222:233:245:258:271:285:300:315:331:348 SD: 0.3950 cents 194:204:214:225:237:249:262:275:289:304:320:336:353:371:390 SD: 0.3855 cents 198:208:219:230:242:254:267:281:295:310:326:343:360:379:398 SD: 0.3123 cents 249:262:275:289:304:320:336:353:371:390:410:431:453:476:501 SD: 0.2863 cents 272:286:301:316:332:349:367:386:405:426:448:471:495:520:547 SD: 0.2801 cents 275:289:304:319:336:353:371:390:410:431:453:476:501:526:553 SD: 0.2373 cents 332:349:367:386:405:426:448:471:495:520:547:575:604:635:668 SD: 0.2161 cents 335:352:370:389:409:430:452:475:499:525:552:580:610:641:674 SD: 0.1600 cents 448:471:495:520:547:575:604:635:668:702:738:776:815:857:901 SD: 0.1570 cents 476:500:526:553:581:611:642:675:710:746:784:824:866:911:957 SD: 0.1535 cents 507:533:560:589:619:651:684:719:756:794:835:878:923:970:1020 SD: 0.1318 cents 533:560:589:619:651:684:719:756:795:835:878:923:970:1020:1072 SD: 0.1237 cents 589:619:651:684:719:756:795:835:878:923:970:1020:1072:1127:1184 SD: 0.1118 cents