Scala analysis: tetra
{225/224, 385/384} tempering of two-tetrachord 12-note scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 85.315 cents 85.314685 2: 201.399 cents 201.398601 3: 317.483 cents 317.482517 4: 383.217 cents 383.216783 5: 468.531 cents 468.531469 6: 584.615 cents 584.615385 7: 700.699 cents 700.699301 8: 816.783 cents 816.783217 9: 882.517 cents 882.517483 10: 967.832 cents 967.832168 11: 1083.916 cents 1083.916084 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 116.0839 cents 116.0839 1: 85.3147 cents 85.3147 2: 116.0839 cents 116.0839 3: 116.0839 cents 116.0839 4: 65.7343 cents 65.7343 5: 85.3147 cents 85.3147 6: 116.0839 cents 116.0839 7: 116.0839 cents 116.0839 8: 116.0839 cents 116.0839 9: 65.7343 cents 65.7343 10: 85.3147 cents 85.3147 11: 116.0839 cents 116.0839 12: 116.0839 cents 116.0839
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 65.73427 cents 1: 3 85.31469 cents 1: 7 116.08392 cents 2: 2 151.04895 cents 2: 2 181.81818 cents 2: 4 201.39860 cents 2: 4 232.16783 cents 3: 4 267.13287 cents 3: 2 297.90210 cents 3: 5 317.48252 cents 3: 1 348.25175 cents 4: 7 383.21678 cents 4: 1 402.79720 cents 4: 1 413.98601 cents 4: 3 433.56643 cents 5: 2 468.53147 cents 5: 8 499.30070 cents 5: 1 518.88112 cents 5: 1 549.65035 cents 6: 1 565.03497 cents 6: 5 584.61538 cents 6: 5 615.38462 cents 6: 1 634.96503 cents 7: 1 650.34965 cents 7: 1 681.11888 cents 7: 8 700.69930 cents 7: 2 731.46853 cents 8: 3 766.43357 cents 8: 1 786.01399 cents 8: 1 797.20280 cents 8: 7 816.78322 cents 9: 1 851.74825 cents 9: 5 882.51748 cents 9: 2 902.09790 cents 9: 4 932.86713 cents 10: 4 967.83217 cents 10: 4 998.60140 cents 10: 2 1018.18182 cents 10: 2 1048.95105 cents 11: 7 1083.91608 cents 11: 3 1114.68531 cents 11: 2 1134.26573 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.81818 = 42/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 85.3 201.4 317.5 383.2 468.5 584.6 700.7 816.8 882.5 967.8 1083.9 1200.0 85.3 : 116.1 232.2 297.9 383.2 499.3 615.4 731.5 797.2 882.5 998.6 1114.7 1200.0 201.4 : 116.1 181.8 267.1 383.2 499.3 615.4 681.1 766.4 882.5 998.6 1083.9 1200.0 317.5 : 65.7 151.0 267.1 383.2 499.3 565.0 650.3 766.4 882.5 967.8 1083.9 1200.0 383.2 : 85.3 201.4 317.5 433.6 499.3 584.6 700.7 816.8 902.1 1018.2 1134.3 1200.0 468.5 : 116.1 232.2 348.3 414.0 499.3 615.4 731.5 816.8 932.9 1049.0 1114.7 1200.0 584.6 : 116.1 232.2 297.9 383.2 499.3 615.4 700.7 816.8 932.9 998.6 1083.9 1200.0 700.7 : 116.1 181.8 267.1 383.2 499.3 584.6 700.7 816.8 882.5 967.8 1083.9 1200.0 816.8 : 65.7 151.0 267.1 383.2 468.5 584.6 700.7 766.4 851.7 967.8 1083.9 1200.0 882.5 : 85.3 201.4 317.5 402.8 518.9 635.0 700.7 786.0 902.1 1018.2 1134.3 1200.0 967.8 : 116.1 232.2 317.5 433.6 549.7 615.4 700.7 816.8 932.9 1049.0 1114.7 1200.0 1083.9: 116.1 201.4 317.5 433.6 499.3 584.6 700.7 816.8 932.9 998.6 1083.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 65.7343 .. 116.0839 cents 50.34965 cents 65.73427 cents 2: 151.0490 .. 232.1678 cents 81.11888 cents 34.96503 cents 3: 267.1329 .. 348.2517 cents 81.11888 cents 34.96503 cents 4: 383.2168 .. 433.5664 cents 50.34965 cents 34.96503 cents 5: 468.5315 .. 549.6503 cents 81.11888 cents 34.96503 cents 6: 565.0350 .. 634.9650 cents 69.93007 cents 15.38462 cents 7: 650.3497 .. 731.4685 cents 81.11888 cents 15.38462 cents 8: 766.4336 .. 816.7832 cents 50.34965 cents 34.96503 cents 9: 851.7483 .. 932.8671 cents 81.11888 cents 34.96503 cents 10: 967.8322 .. 1048.9510 cents 81.11888 cents 34.96503 cents 11: 1083.9161 .. 1134.2657 cents 50.34965 cents 34.96504 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 65.73427 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 116.08392 cents Average / Smallest step : 1.521277 Largest / Average step : 1.160839 Largest / Smallest step : 1.765957 Median interval of one step : 116.08392 cents, amount: 7 Most common interval of one step : 116.08392 cents, amount: 7 Least squares average step : 98.77999 cents, oct.: 1185.35987 cents Scale is strictly proper Scale is a mode of a 858-tone equal temperament with octave 2/1 degrees: 61 144 227 274 335 418 501 584 631 692 775 858 Least number of segments generator : 431 of 602.797 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 527 of 737.063 cents and inv. generated superset size: 207 = 195 more = 1725.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBCABBBCABB Step pattern size order : MLLSMLLLSMLL Scale is a Constant Structure, by a margin of 15.38462 cents Scale diversity : 1.455256 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.368298 Rothenberg efficiency : 0.363261 redundancy: 0.636739 Efficiency x scale size : 4.359127 Number of different interval sizes : 42 = 3.81818 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.81818 = 42/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 11.18881 cents Most common intervals : 499.30070 cents & inv., amount: 8 Most common triad is 0.0 499.301 700.699 cents, amount: 4 Number of recognisable fifths : 8, average 700.6993 cents Best fifths form a closed circle Formal octave complements present : 5 = 41.6667% -- 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: 18.0581 c. M:-32.1678 c. Twelve-tone Chromatic (1/11-comma) 16: 1 2 1 1 1 2 1 2 1 1 1 2 P B D3 SD: 17.9164 c. M: 33.9161 c. 19: 1 2 2 1 1 2 2 2 1 1 2 2 P D3 SD: 13.5244 c. M: 26.4262 c. 20: 1 2 2 1 2 2 2 2 1 1 2 2 N D3 SD: 17.3336 c. M: 25.3147 c. 22: 2 2 2 1 2 2 2 2 1 2 2 2 P D3 I SD: 13.2129 c. M:-23.7762 c. 23: 2 2 2 1 2 2 2 3 1 2 2 2 P D3 SD: 14.1735 c. M:-23.4722 c. 25: 2 2 3 1 2 2 3 2 1 2 3 2 N SD: 12.6902 c. M:-20.0839 c. 26: 2 2 3 1 2 3 2 3 1 2 2 3 P SD: 11.7015 c. M: 22.3776 c. 28: 2 3 2 2 2 3 2 3 2 2 2 3 SP B D3 SD: 12.0254 c. M:-17.8821 c. 29: 2 3 3 1 2 3 3 3 1 2 3 3 N SD: 9.8994 c. M: 16.1080 c. 31: 2 3 3 2 2 3 3 3 2 2 3 3 SP D3 SD: 5.1898 c. M: 7.8953 c. 41: 3 4 4 2 3 4 4 4 2 3 4 4 P SD: 2.6090 c. M:-4.4687 c. 72: 5 7 7 4 5 7 7 7 4 5 7 7 SP SD: 1.1011 c. M: 1.9814 c. 113: 8 11 11 6 8 11 11 11 6 8 11 11 SP SD: 0.8657 c. M: 1.4605 c. 166: 12 16 16 9 12 16 16 16 9 12 16 16 SP SD: 0.7960 c. M:-1.4323 c. 185: 13 18 18 10 13 18 18 18 10 13 18 18 SP SD: 0.7695 c. M: 1.5044 c. 197: 14 19 19 11 14 19 19 19 11 14 19 19 SP SD: 0.4761 c. M:-0.7312 c. 238: 17 23 23 13 17 23 23 23 13 17 23 23 SP SD: 0.2221 c. M:-0.3996 c. 310: 22 30 30 17 22 30 30 30 17 22 30 30 SP SD: 0.0852 c. M: 0.1534 c. 548: 39 53 53 30 39 53 53 53 30 39 53 53 SP SD: 0.0482 c. M:-0.0868 c. 858: 61 83 83 47 61 83 83 83 47 61 83 83 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: 0.6279 cents 3 x x x x 4 x x x 5 x x 6 S SD: 9.8570 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 0.8716 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 9.9877 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 11.3425 cents 7 x 8 x x 9:10 x 11 x 12:13:14 S SD: 10.7050 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 5.1689 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 10.3143 cents 10 x 11:12 x 13:14:15:16:17 x 19:20 SD: 6.6647 cents 11 x 12:13:14 x 15:16 x 18:19:21:22 SD: 12.2510 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 8.2657 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 8.5381 cents 14:15:16:17 x 18:20:21:22:23:24:26:28 S SD: 7.9573 cents 15:16:17:18:19:20:21:22:24:25:26:28:30 S SD: 5.3827 cents 16:17:18:19:20:21:22:24:26:27:28:30:32 S SD: 4.5982 cents 18:19:20:22 x 24:25:27:29:30:31:34:36 SD: 5.4084 cents 20:21:22:24:25:26:28:30:32:33:35:37:40 SD: 3.8717 cents 24:25:27:29:30:31:34:36:38:40:42:45:48 SD: 3.5299 cents 25:26:28:30:31:33:35:37:40:42:44:47:50 SD: 3.2673 cents 32:34:36:38:40:42:45:48:51:53:56:60:64 SD: 2.6838 cents 35:37:39:42:44:46:49:52:56:58:61:65:70 SD: 2.6467 cents 36:38:40:43:45:47:50:54:58:60:63:67:72 SD: 2.6285 cents 38:40:43:46:47:50:53:57:61:63:66:71:76 SD: 2.5098 cents 39:41:44:47:49:51:55:58:63:65:68:73:78 SD: 2.2956 cents 40:42:45:48:50:52:56:60:64:67:70:75:80 SD: 1.6035 cents 55:58:62:66:69:72:77:82:88:92:96:103:110 SD: 1.5808 cents 60:63:67:72:75:79:84:90:96:100:105:112:120 SD: 1.2138 cents 74:78:83:89:92:97:104:111:119:123:129:138:148 SD: 1.1939 cents 78:82:88:94:97:102:109:117:125:130:136:146:156 SD: 1.1836 cents 80:84:90:96:100:105:112:120:128:133:140:150:160 SD: 0.6811 cents 120:126:135:144:150:157:168:180:192:200:210:224:240 SD: 0.6554 cents 138:145:155:166:172:181:193:207:221:230:241:258:276 SD: 0.5281 cents 154:162:173:185:192:202:216:231:247:256:269:288:308 SD: 0.4168 cents 179:188:201:215:223:235:251:268:287:298:313:335:358 SD: 0.3860 cents 194:204:218:233:242:254:272:291:311:323:339:363:388 SD: 0.2936 cents 219:230:246:263:273:287:307:328:351:365:383:410:438 SD: 0.2850 cents 254:267:285:305:317:333:356:381:407:423:444:475:508 SD: 0.2522 cents 299:314:336:359:373:392:419:448:479:498:523:559:598 SD: 0.1696 cents 431:453:484:518:538:565:604:646:691:718:754:806:862 SD: 0.1656 cents 453:476:509:544:565:594:635:679:726:754:792:847:906 SD: 0.1314 cents 493:518:554:592:615:646:691:739:790:821:862:922:986 SD: 0.1205 cents 537:564:603:645:670:704:753:805:861:894:939:1004:1074 SD: 0.1195 cents 577:606:648:693:720:756:809:865:925:961:1009:1079:1154 SD: 0.1187 cents