Scala analysis: 7_6-on-3_2-tempered
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 64.050 cents 64.049550 2: 165.988 cents 165.987920 3: 267.926 cents 267.926290 4: 331.976 cents 331.975850 5: 433.914 cents 433.914220 6: 497.964 cents 497.963770 7: 599.902 cents 599.902140 8: 701.841 cents 701.840510 9: 765.890 cents 765.890060 10: 867.828 cents 867.828430 11: 969.767 cents 969.766810 12: 1033.816 cents 1033.816360 13: 1135.755 cents 1135.754730 14: 1199.804 cents 1199.804280
SHOW/INTERVAL
0: 64.0495 cents 64.0495 1: 64.0496 cents 64.0496 2: 101.9384 cents 101.9384 3: 101.9384 cents 101.9384 4: 64.0496 cents 64.0496 5: 101.9384 cents 101.9384 6: 64.0496 cents 64.0496 7: 101.9384 cents 101.9384 8: 101.9384 cents 101.9384 9: 64.0496 cents 64.0496 10: 101.9384 cents 101.9384 11: 101.9384 cents 101.9384 12: 64.0496 cents 64.0496 13: 101.9384 cents 101.9384 14: 64.0495 cents 64.0495
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 64.04955 cents 1: 8 101.93837 cents 2: 1 128.09910 cents 2: 10 165.98792 cents 2: 3 203.87674 cents 3: 4 230.03748 cents 3: 10 267.92629 cents 4: 1 294.08702 cents 4: 8 331.97585 cents 4: 5 369.86467 cents 5: 3 396.02540 cents 5: 10 433.91422 cents 5: 1 471.80304 cents 6: 8 497.96377 cents 6: 6 535.85259 cents 7: 3 562.01332 cents 7: 8 599.90214 cents 7: 3 637.79096 cents 8: 6 663.95169 cents 8: 8 701.84051 cents 9: 1 728.00124 cents 9: 10 765.89006 cents 9: 3 803.77888 cents 10: 5 829.93961 cents 10: 8 867.82843 cents 10: 1 905.71726 cents 11: 10 931.87799 cents 11: 4 969.76681 cents 12: 3 995.92754 cents 12: 10 1033.81636 cents 12: 1 1071.70518 cents 13: 8 1097.86591 cents 13: 6 1135.75473 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.53846 = 33/13
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.0 : 64.0 166.0 267.9 332.0 433.9 498.0 599.9 701.8 765.9 867.8 969.8 1033.8 1135.8 1199.8 64.0 : 101.9 203.9 267.9 369.9 433.9 535.9 637.8 701.8 803.8 905.7 969.8 1071.7 1135.8 1199.8 166.0 : 101.9 166.0 267.9 332.0 433.9 535.9 599.9 701.8 803.8 867.8 969.8 1033.8 1097.9 1199.8 267.9 : 64.0 166.0 230.0 332.0 433.9 498.0 599.9 701.8 765.9 867.8 931.9 995.9 1097.9 1199.8 332.0 : 101.9 166.0 267.9 369.9 433.9 535.9 637.8 701.8 803.8 867.8 931.9 1033.8 1135.8 1199.8 433.9 : 64.0 166.0 267.9 332.0 433.9 535.9 599.9 701.8 765.9 829.9 931.9 1033.8 1097.9 1199.8 498.0 : 101.9 203.9 267.9 369.9 471.8 535.9 637.8 701.8 765.9 867.8 969.8 1033.8 1135.8 1199.8 599.9 : 101.9 166.0 267.9 369.9 433.9 535.9 599.9 664.0 765.9 867.8 931.9 1033.8 1097.9 1199.8 701.8 : 64.0 166.0 267.9 332.0 433.9 498.0 562.0 664.0 765.9 829.9 931.9 995.9 1097.9 1199.8 765.9 : 101.9 203.9 267.9 369.9 433.9 498.0 599.9 701.8 765.9 867.8 931.9 1033.8 1135.8 1199.8 867.8 : 101.9 166.0 267.9 332.0 396.0 498.0 599.9 664.0 765.9 829.9 931.9 1033.8 1097.9 1199.8 969.8 : 64.0 166.0 230.0 294.1 396.0 498.0 562.0 664.0 728.0 829.9 931.9 995.9 1097.9 1199.8 1033.8: 101.9 166.0 230.0 332.0 433.9 498.0 599.9 664.0 765.9 867.8 931.9 1033.8 1135.8 1199.8 1135.8: 64.0 128.1 230.0 332.0 396.0 498.0 562.0 664.0 765.9 829.9 931.9 1033.8 1097.9 1199.8 1199.8
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 64.0496 .. 101.9384 cents 37.88882 cents 64.04955 cents 2: 128.0991 .. 203.8767 cents 75.77764 cents 26.16073 cents 3: 230.0375 .. 267.9263 cents 37.88881 cents 26.16074 cents 4: 294.0870 .. 369.8647 cents 75.77765 cents 26.16073 cents 5: 396.0254 .. 471.8030 cents 75.77764 cents 26.16073 cents 6: 497.9638 .. 535.8526 cents 37.88882 cents 26.16073 cents 7: 562.0133 .. 637.7910 cents 75.77764 cents 26.16073 cents 8: 663.9517 .. 701.8405 cents 37.88882 cents 26.16073 cents 9: 728.0012 .. 803.7789 cents 75.77764 cents 26.16073 cents 10: 829.9396 .. 905.7173 cents 75.77765 cents 26.16073 cents 11: 931.8780 .. 969.7668 cents 37.88882 cents 26.16073 cents 12: 995.9275 .. 1071.7052 cents 75.77764 cents 26.16073 cents 13: 1097.8659 .. 1135.7547 cents 37.88882 cents 26.16073 cents
SHOW DATA
Number of notes : 14 -- Interval properties -- Smallest interval : 64.04955 cents, class 1 Average step (divided formal octave): 85.7003 cents Largest one step interval : 101.93837 cents Average / Smallest step : 1.338031 Largest / Average step : 1.189475 Largest / Smallest step : 1.591555 Median interval of one step : 101.93837 cents, amount: 8 Most common interval of one step : 101.93837 cents, amount: 8 Least squares average step : 86.40955 cents, oct.: 1209.73376 cents Scale is strictly proper Scale is 3-distributional even Scale is a mode of a 1330-tone equal temperament with octave 1199.804 cents degrees: 71 184 297 368 481 552 665 778 849 962 1075 1146 1259 1330 Least number of segments generator : 667 of 601.706 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 849 of 765.890 cents and inv. generated superset size: 672 = 658 more = 4800.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABABBABBABA Step pattern size order : SLLSLSLLSLLSLS Scale is a Constant Structure, by a margin of 26.16073 cents Scale diversity : 1.312253 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.368417 Number of different interval sizes : 33 = 2.53846 / class Number of one step interval sizes : 2 Highest interval variety : 3 Mean interval variety : 2.53846 = 33/13 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 26.16073 cents Number of recognisable fifths : 8, average 701.8405 cents Number of recognisable fourths : 8, average 497.9638 cents Scale contains two identical disjunct heptachords Formal octave complements present : 12 = 85.7143% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
14: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 13.7997 c. M: 27.0634 c. 22: 1 2 2 1 2 1 2 2 1 2 2 1 2 1 P D3 SD: 6.0634 c. M:-11.8912 c. 36: 2 3 3 2 3 2 3 3 2 3 3 2 3 2 SP D3 SD: 1.6612 c. M: 3.2578 c. 58: 3 5 5 3 5 3 5 5 3 5 5 3 5 3 SP D3 SD: 1.2688 c. M:-2.4884 c. 94: 5 8 8 5 8 5 8 8 5 8 8 5 8 5 SP D3 SD: 0.1467 c. M:-0.2877 c. 224: 12 19 19 12 19 12 19 19 12 19 19 12 19 12 SP D3 SD: 0.1438 c. M: 0.2821 c. 318: 17 27 27 17 27 17 27 27 17 27 27 17 27 17 SP D3 SD: 0.0580 c. M: 0.1137 c. 412: 22 35 35 22 35 22 35 35 22 35 35 22 35 22 SP D3 SD: 0.0113 c. M: 0.0221 c. 918: 49 78 78 49 78 49 78 78 49 78 78 49 78 49 SP D3 SD: 0.0049 c. M:-0.0096 c. 1330: 71 113 113 71 113 71 113 113 71 113 113 71 113 71 SP D3 SD: 0.0001 c. M: 0.0002 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x 2 S SD: 0.1957 cents 2 x x x x x x x 3 x x x x x 4 S SD: 0.1134 cents 3 x x x x x 4 x x x 5 x x x 6 S SD: 5.5105 cents 4 x x x x 5 x x 6 x x 7 x x 8 S SD: 11.9026 cents 5 x x x 6 x x 7 x 8 x x 9 x 10 S SD: 11.1657 cents 6 x x 7 x x 8 x 9 x 10 x 11 x 12 S SD: 3.7864 cents 7 x x 8 x 9 x 10 x 11 x 12:13 x 14 S SD: 9.8090 cents 8 x 9 x x 10 x 11:12 x 13:14 x 15:16 S SD: 11.9016 cents 9 x 10 x 11 x 12:13 x 14:15:16 x 17:18 S SD: 7.0514 cents 10 x 11 x 12:13 x 14:15:16:17 x 18:19:20 S SD: 8.1944 cents 11 x 12:13 x 14:15:16 x 17:18:19:20:21:22 S SD: 7.0781 cents 12 x 13:14 x 15:16:17:18:19:20:21:22:23:24 S SD: 5.5984 cents 13 x 14:15:16:17 x 18 x 20:21:23:24:25:26 SD: 8.0103 cents 14 x 15:16:17:18:19:20:21:22:23 x 25:27:28 SD: 6.4751 cents 15:16:17 x 18:19:20:21 x 23:25:26:27:29:30 SD: 7.2483 cents 16:17:18:19 x x 21:23:24:25:26:28:29:31:32 SD: 6.6804 cents 17:18:19:20:21:22:23:24 x 26:28:30:31:33:34 SD: 5.6381 cents 18:19:20:21:22:23:24:25:27:28:30:32:33:35:36 SD: 4.4574 cents 20:21:22:23:24:26:27:28:30:31:33:35:36:39:40 SD: 4.0860 cents 21:22:23 x 25:27:28:30:32:33:35:37:38:40:42 SD: 4.5094 cents 22:23:24:26:27:28:29:31:33:34:36:39:40:42:44 SD: 4.0200 cents 24:25:26:28:29:31:32:34:36:37:40:42:44:46:48 SD: 3.0189 cents 28:29:31:33:34:36:37:40:42:44:46:49:51:54:56 SD: 2.5965 cents 29:30:32:34:35:37:39:41:43:45:48:51:53:56:58 SD: 2.4032 cents 32:33:35:37:39:41:43:45:48:50:53:56:58:62:64 SD: 2.3720 cents 42:44:46:49:51:54:56:59:63:65:69:74:76:81:84 SD: 2.0597 cents 48:50:53:56:58:62:64:68:72:75:79:84:87:93:96 SD: 1.3673 cents 60:62:66:70:73:77:80:85:90:93:99:105:109:116:120 SD: 1.0346 cents 72:75:79:84:87:93:96:102:108:112:119:126:131:139:144 SD: 1.0287 cents 77:80:85:90:93:99:103:109:115:120:127:135:140:148:154 SD: 0.9799 cents 80:83:88:93:97:103:107:113:120:125:132:140:145:154:160 SD: 0.9362 cents 84:87:92:98:102:108:112:119:126:131:139:147:153:162:168 SD: 0.9090 cents 99:103:109:116:120:127:132:140:148:154:163:173:180:191:198 SD: 0.8522 cents 102:106:112:119:124:131:136:144:153:159:168:179:185:197:204 SD: 0.8231 cents 106:110:117:124:128:136:141:150:159:165:175:186:193:204:212 SD: 0.7941 cents 108:112:119:126:131:139:144:153:162:168:178:189:196:208:216 SD: 0.4769 cents 138:143:152:161:167:177:184:195:207:215:228:242:251:266:276 SD: 0.4405 cents 162:168:178:189:196:208:216:229:243:252:267:284:294:312:324 SD: 0.4290 cents 180:187:198:210:218:231:240:255:270:280:297:315:327:347:360 SD: 0.3428 cents 208:216:229:243:252:267:277:294:312:324:343:364:378:401:416 SD: 0.3030 cents 246:255:271:287:298:316:328:348:369:383:406:431:447:474:492 SD: 0.2177 cents 288:299:317:336:349:370:384:407:432:448:475:504:523:555:576 SD: 0.2127 cents 316:328:348:369:383:406:421:447:474:492:522:553:574:609:632 SD: 0.1898 cents 369:383:406:431:447:474:492:522:553:574:609:646:670:711:738 SD: 0.1854 cents 370:384:407:432:448:475:493:523:555:576:611:648:672:713:740 SD: 0.1849 cents 426:442:469:497:516:547:568:602:639:663:703:746:774:821:852 SD: 0.1531 cents 449:466:494:524:544:577:599:635:673:699:741:786:816:865:898 SD: 0.1519 cents 478:496:526:558:579:614:637:676:717:744:789:837:868:921:956 SD: 0.1063 cents 586:608:645:684:710:753:781:829:879:912:967:1026:1065:1129:1172 SD: 0.1033 cents