Scala analysis: testing
Two #15 chords in 72-ET.
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 383.333 cents 383.333333 2: 700.000 cents 700.000000 3: 1083.333 cents 1083.333333 4: 1400.000 cents 1400.000000 5: 1783.333 cents 1783.333333 6: 2100.000 cents 2100.000000 7: 2483.333 cents 2483.333333 8: 2500.000 cents 2500.000000
SHOW/INTERVAL
0: 16.6667 cents 16.6667 1: 383.3333 cents 383.3333 2: 316.6667 cents 316.6667 3: 383.3333 cents 383.3333 4: 316.6667 cents 316.6667 5: 383.3333 cents 383.3333 6: 316.6667 cents 316.6667 7: 383.3333 cents 383.3333 8: 16.6667 cents 16.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16.66667 cents 1: 3 316.66667 cents 1: 4 383.33333 cents 2: 2 400.00000 cents 2: 6 700.00000 cents 3: 2 716.66667 cents 3: 1 783.33333 cents 3: 2 1016.66667 cents 3: 3 1083.33333 cents 4: 4 1100.00000 cents 4: 4 1400.00000 cents 5: 3 1416.66667 cents 5: 2 1483.33333 cents 5: 1 1716.66667 cents 5: 2 1783.33333 cents 6: 6 1800.00000 cents 6: 2 2100.00000 cents 7: 4 2116.66667 cents 7: 3 2183.33333 cents 7: 1 2483.33333 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 2.85714 = 20/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 383.3 700.0 1083.3 1400.0 1783.3 2100.0 2483.3 2500.0 383.3 : 316.7 700.0 1016.7 1400.0 1716.7 2100.0 2116.7 2500.0 700.0 : 383.3 700.0 1083.3 1400.0 1783.3 1800.0 2183.3 2500.0 1083.3: 316.7 700.0 1016.7 1400.0 1416.7 1800.0 2116.7 2500.0 1400.0: 383.3 700.0 1083.3 1100.0 1483.3 1800.0 2183.3 2500.0 1783.3: 316.7 700.0 716.7 1100.0 1416.7 1800.0 2116.7 2500.0 2100.0: 383.3 400.0 783.3 1100.0 1483.3 1800.0 2183.3 2500.0 2483.3: 16.7 400.0 716.7 1100.0 1416.7 1800.0 2116.7 2500.0 2500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 16.6667 .. 383.3333 cents 366.66667 cents 16.66667 cents 2: 400.0000 .. 700.0000 cents 300.00000 cents 16.66667 cents 3: 716.6667 .. 1083.3333 cents 366.66667 cents 16.66667 cents 4: 1100.0000 .. 1400.0000 cents 300.00000 cents 16.66667 cents 5: 1416.6667 .. 1783.3333 cents 366.66667 cents 16.66667 cents 6: 1800.0000 .. 2100.0000 cents 300.00000 cents 16.66667 cents 7: 2116.6667 .. 2483.3333 cents 366.66667 cents 16.66667 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 16.66667 cents, class 1 Average step (divided formal octave): 312.5000 cents Largest one step interval : 383.33333 cents Average / Smallest step : 18.750000 Largest / Average step : 1.226667 Largest / Smallest step : 23.000000 Median interval of one step : 350.00000 cents, amount: 0 Most common interval of one step : 383.33333 cents, amount: 4 Least squares average step : 340.84967 cents, oct.: 2726.79739 cents Scale is strictly proper Scale is a mode of a 150-tone equal temperament with octave 2500.000 cents degrees: 23 42 65 84 107 126 149 150 Least number of segments generator : 77 of 1283.333 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 107 of 1783.333 cents and inv. generated superset size: 30 = 22 more = 375.000% Number of contiguous 1-step segments: 1 Step pattern alph. order: ABABABAC Step pattern size order : LMLMLMLS Interval vector is [ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 3 4 0 0 0 0 0 0 0 0 0 ] Scale is a Constant Structure, by a margin of 16.66667 cents Scale diversity :-0.119503 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.053333 Rothenberg efficiency : 0.546429 redundancy: 0.453571 Efficiency x scale size : 4.371429 Number of different interval sizes : 20 = 2.85714 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 2.85714 = 20/7 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 16.66667 cents Most common intervals : 700.00000 cents & inv., amount: 6 Most common triad is 0.0 700.000 1800.000 cents, amount: 4 Number of recognisable fifths : 8, average 704.1667 cents Number of appreciable fifths : 6, average 700.0000 cents Number of recognisable fourths : 0 Scale contains two identical disjunct "tetrachords" of 2 notes Formal octave complements present : 1 = 12.5000% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 7-8 -- Rational properties --
FIT/MODE
8: 1 1 1 1 1 1 2 0 N T3 SD: 138.7803 c. M: 225.0000 c. 9: 1 2 1 1 1 2 1 0 N D3 SD: 85.6169 c. M:-133.3333 c. 11: 2 1 2 1 2 1 2 0 P D3 SD: 41.8385 c. M:-71.2121 c. 13: 2 2 2 1 2 2 2 0 P D3 SD: 44.6423 c. M:-70.5128 c. 14: 2 2 2 2 2 2 2 0 P M DE SD: 22.2718 c. M:-42.8571 c. 18: 3 2 3 2 3 2 3 0 P SD: 19.6419 c. M:-33.3333 c. 25: 4 3 4 3 4 3 4 0 P SD: 11.7851 c. M:-16.6667 c. 32: 5 4 5 4 5 4 5 0 P SD: 9.7439 c. M:-16.6667 c. 75: 11 10 11 10 11 10 11 1 SP SD: 11.7851 c. M: 16.6667 c. 76: 12 9 12 10 11 10 11 1 P SD: 9.8073 c. M: 16.2281 c. 77: 12 10 11 10 12 10 11 1 P SD: 9.7703 c. M: 15.8009 c. 79: 12 10 12 10 12 10 12 1 SP SD: 8.7940 c. M: 14.9789 c. 86: 13 11 13 11 13 11 13 1 SP SD: 7.2513 c. M: 12.4031 c. 93: 14 12 14 12 14 12 14 1 SP SD: 6.3043 c. M: 10.2151 c. 100: 15 13 15 13 15 13 15 1 SP SD: 5.8926 c. M: 8.3333 c. 104: 16 13 16 13 16 13 16 1 SP SD: 4.9394 c. M: 8.6538 c. 111: 17 14 17 14 17 14 17 1 SP SD: 3.5611 c. M: 5.8559 c. 118: 18 15 18 15 18 15 18 1 SP SD: 2.6424 c. M: 4.5198 c. 125: 19 16 19 16 19 16 19 1 SP SD: 2.3570 c. M: 3.3333 c. 136: 21 17 21 17 21 17 21 1 SP SD: 2.2927 c. M: 4.4118 c. 143: 22 18 22 18 22 18 22 1 SP SD: 1.0902 c. M: 2.0979 c. 150: 23 19 23 19 23 19 23 1 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x 2 x 3 x 4 x S SD: 62.0275 cents 2 x 3:4:5:6:7:8 x S SD: 45.3628 cents 3:4:5:6:7:8:10 x 13 SD: 38.9233 cents 4:5:6:7:9:11:13 x 17 SD: 19.0201 cents 5:6:8:9:11:14:17:21 x SD: 21.8540 cents 6:8:9:11:13:17:20:25 x SD: 19.6301 cents 7:9:11:13:16:20:24:29:30 SD: 14.6534 cents 8:10:12:15:18:22:27 x 34 SD: 4.8156 cents 9:11:13:17:20:25:30 x 38 SD: 11.4558 cents 10:12:15:19:22:28:34:42 x SD: 11.8981 cents 11:14:16:21:25:31:37:46:47 SD: 9.6101 cents 12:15:18:22:27:34:40:50:51 SD: 5.5878 cents 13:16:19:24:29:36:44 x 55 SD: 8.5024 cents 14:17:21:26:31:39:47:59 x SD: 7.9374 cents 15:19:22:28:34:42:50:63:64 SD: 6.5038 cents 16:20:24:30:36:45:54:67:68 SD: 1.6536 cents 18:22:27:34:40:50:61 x 76 SD: 6.9115 cents 19:24:28:36:43:53:64:80:81 SD: 5.8534 cents 20:25:30:37:45:56:67:84:85 SD: 2.6179 cents 23:29:34:43:52:64:77:97 x SD: 5.1237 cents 24:30:36:45:54:67:81:101:102 SD: 1.6198 cents 36:45:54:67:81:101:121:151:153 SD: 1.3993 cents 40:50:60:75:90:112:135:168:170 SD: 1.3303 cents 44:55:66:82:99:123:148:185:186 SD: 1.2512 cents 52:65:78:97:117:146:175:218:220 SD: 1.0647 cents 56:70:84:105:126:157:188:235:237 SD: 1.0522 cents 60:75:90:112:135:168:202:252:254 SD: 0.8252 cents 76:95:114:142:171:213:256:319:322 SD: 0.7533 cents 85:106:127:159:191:238:286:357:360 SD: 0.7019 cents 101:126:151:189:227:283:340:424:428 SD: 0.5989 cents 121:151:181:226:272:339:407:508:513 SD: 0.5188 cents 122:152:183:228:274:342:410:512:517 SD: 0.5008 cents 130:162:195:243:292:364:437:546:551 SD: 0.4603 cents 146:182:219:273:328:409:491:613:619 SD: 0.3874 cents 177:221:265:331:397:496:595:743:750 SD: 0.3243 cents 193:241:289:361:433:541:649:810:818 SD: 0.2981 cents 201:251:301:376:451:563:676:844:852 SD: 0.2736 cents 237:296:355:443:532:664:797:995:1004 SD: 0.2350 cents 253:316:379:473:568:709:851:1062:1072 SD: 0.2251 cents 275:343:412:514:617:770:925:1154:1165 SD: 0.2204 cents 283:353:424:529:635:793:952:1188:1199 SD: 0.1726 cents 291:363:436:544:653:815:979:1221:1233 SD: 0.1590 cents 299:373:448:559:671:838:1006:1255:1267 SD: 0.1571 cents 307:383:460:574:689:860:1033:1289:1301 SD: 0.1349 cents 323:403:484:604:725:905:1086:1356:1369 SD: 0.1258 cents 331:413:496:619:743:927:1113:1389:1403 SD: 0.1242 cents 383:478:574:716:860:1073:1288:1608:1623 SD: 0.1151 cents 468:584:701:875:1051:1311:1574:1964:1983 SD: 0.1138 cents 528:659:791:987:1185:1479:1776:2216:2238 SD: 0.0993 cents 544:679:815:1017:1221:1524:1830:2283:2305 SD: 0.0921 cents 584:729:875:1092:1311:1636:1964:2451:2475 SD: 0.0898 cents