Scala analysis: rain123
Raintree scale tuned to 123-et
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 97.561 cents 97.560976 2: 204.878 cents 204.878049 3: 302.439 cents 302.439024 4: 400.000 cents 400.000000 5: 497.561 cents 497.560976 6: 604.878 cents 604.878049 7: 702.439 cents 702.439024 8: 800.000 cents 800.000000 9: 897.561 cents 897.560976 10: 995.122 cents 995.121951 11: 1102.439 cents 1102.439024 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 97.5610 cents 97.5610 1: 97.5610 cents 97.5610 2: 107.3171 cents 107.3171 3: 97.5610 cents 97.5610 4: 97.5610 cents 97.5610 5: 97.5610 cents 97.5610 6: 107.3171 cents 107.3171 7: 97.5610 cents 97.5610 8: 97.5610 cents 97.5610 9: 97.5610 cents 97.5610 10: 97.5610 cents 97.5610 11: 107.3171 cents 107.3171 12: 97.5610 cents 97.5610
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 97.56098 cents 1: 3 107.31707 cents 2: 6 195.12195 cents 2: 6 204.87805 cents 3: 3 292.68293 cents 3: 9 302.43902 cents 4: 1 390.24390 cents 4: 10 400.00000 cents 4: 1 409.75610 cents 5: 9 497.56098 cents 5: 3 507.31707 cents 6: 6 595.12195 cents 6: 6 604.87805 cents 7: 3 692.68293 cents 7: 9 702.43902 cents 8: 1 790.24390 cents 8: 10 800.00000 cents 8: 1 809.75610 cents 9: 9 897.56098 cents 9: 3 907.31707 cents 10: 6 995.12195 cents 10: 6 1004.87805 cents 11: 3 1092.68293 cents 11: 9 1102.43902 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.18182 = 24/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 97.6 204.9 302.4 400.0 497.6 604.9 702.4 800.0 897.6 995.1 1102.4 1200.0 97.6 : 107.3 204.9 302.4 400.0 507.3 604.9 702.4 800.0 897.6 1004.9 1102.4 1200.0 204.9 : 97.6 195.1 292.7 400.0 497.6 595.1 692.7 790.2 897.6 995.1 1092.7 1200.0 302.4 : 97.6 195.1 302.4 400.0 497.6 595.1 692.7 800.0 897.6 995.1 1102.4 1200.0 400.0 : 97.6 204.9 302.4 400.0 497.6 595.1 702.4 800.0 897.6 1004.9 1102.4 1200.0 497.6 : 107.3 204.9 302.4 400.0 497.6 604.9 702.4 800.0 907.3 1004.9 1102.4 1200.0 604.9 : 97.6 195.1 292.7 390.2 497.6 595.1 692.7 800.0 897.6 995.1 1092.7 1200.0 702.4 : 97.6 195.1 292.7 400.0 497.6 595.1 702.4 800.0 897.6 995.1 1102.4 1200.0 800.0 : 97.6 195.1 302.4 400.0 497.6 604.9 702.4 800.0 897.6 1004.9 1102.4 1200.0 897.6 : 97.6 204.9 302.4 400.0 507.3 604.9 702.4 800.0 907.3 1004.9 1102.4 1200.0 995.1 : 107.3 204.9 302.4 409.8 507.3 604.9 702.4 809.8 907.3 1004.9 1102.4 1200.0 1102.4: 97.6 195.1 302.4 400.0 497.6 595.1 702.4 800.0 897.6 995.1 1092.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 97.5610 .. 107.3171 cents 9.75610 cents 97.56098 cents 2: 195.1220 .. 204.8780 cents 9.75610 cents 87.80488 cents 3: 292.6829 .. 302.4390 cents 9.75610 cents 87.80488 cents 4: 390.2439 .. 409.7561 cents 19.51220 cents 87.80488 cents 5: 497.5610 .. 507.3171 cents 9.75610 cents 87.80488 cents 6: 595.1220 .. 604.8780 cents 9.75610 cents 87.80488 cents 7: 692.6829 .. 702.4390 cents 9.75610 cents 87.80488 cents 8: 790.2439 .. 809.7561 cents 19.51220 cents 87.80488 cents 9: 897.5610 .. 907.3171 cents 9.75610 cents 87.80488 cents 10: 995.1220 .. 1004.8780 cents 9.75610 cents 87.80488 cents 11: 1092.6829 .. 1102.4390 cents 9.75610 cents 87.80488 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 97.56098 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 107.31707 cents Average / Smallest step : 1.025000 Largest / Average step : 1.073171 Largest / Smallest step : 1.100000 Median interval of one step : 97.56098 cents, amount: 9 Most common interval of one step : 97.56098 cents, amount: 9 Least squares average step : 100.00750 cents, oct.: 1200.09006 cents Scale is strictly proper Scale is 3-distributional even Scale is a mode of a 123-tone equal temperament with octave 1200.000 cents degrees: 10 21 31 41 51 62 72 82 92 102 113 123 Least number of segments generator : 62 of 604.878 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 92 of 897.561 cents and inv. generated superset size: 85 = 73 more = 708.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAABAAAABA Step pattern size order : SLSSSLSSSSLS Interval vector is [ 0 0 0 0 0 0 0 0 0 9 3 0 0 0 0 0 0 0 0 6 6 0 0 0 0 0 0 0 0 3 9 0 0 0 0 0 0 0 0 1 10 1 0 0 0 0 0 0 0 0 9 3 0 0 0 0 0 0 0 0 6 ] Scale is a Constant Structure, by a margin of 87.80488 cents Scale diversity : 1.084095 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.894309 Rothenberg efficiency : 0.564881 redundancy: 0.435119 Efficiency x scale size : 6.778571 Number of different interval sizes : 24 = 2.18182 / class Number of one step interval sizes : 2 Highest interval variety : 3 Mean interval variety : 2.18182 = 24/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 9.75610 cents Most common intervals : 400.00000 cents & inv., amount: 10 Most common triad is 0.0 400.000 800.000 cents, amount: 9 Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 11 = 91.6667% Limited transpositions with margin 9.7561 cents: 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions with margin 9.7561 cents: 1 2 3 4 5 6 7 8 9 10 11 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 2.9872 c. M: 4.8780 c. Twelve-tone Chromatic (1/11-comma) 63: 5 6 5 5 5 6 5 5 5 5 6 5 SP D3 SD: 2.8449 c. M:-4.6458 c. 75: 6 7 6 6 6 7 6 6 6 6 7 6 SP D3 SD: 1.9118 c. M:-3.1220 c. 87: 7 8 7 7 7 8 7 7 7 7 8 7 SP D3 SD: 1.2361 c. M:-2.0185 c. 99: 8 9 8 8 8 9 8 8 8 8 9 8 SP D3 SD: 0.7242 c. M:-1.1826 c. 111: 9 10 9 9 9 10 9 9 9 9 10 9 SP D3 SD: 0.3229 c. M:-0.5274 c. 123: 10 11 10 10 10 11 10 10 10 10 11 10 SP D3 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: 0.2420 cents 3 x x x x 4 x x x 5 x x 6 S SD: 4.4037 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.4121 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.3944 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 10.8742 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.6867 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.3474 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 7.8118 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.3193 cents 11:12 x 13:14:15:16 x 17:18:20:21:22 S SD: 11.3227 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.1618 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 9.5984 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.0985 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.1756 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.7452 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 3.7264 cents 30:32:34:36:38:40:43:45:48:50:53:57:60 SD: 3.1994 cents 31:33:35:37:39:41:44:47:49:52:55:59:62 SD: 2.4652 cents 36:38:41:43:45:48:51:54:57:60:64:68:72 SD: 2.4176 cents 38:40:43:45:48:51:54:57:60:64:68:72:76 SD: 2.2111 cents 46:49:52:55:58:61:65:69:73:77:82:87:92 SD: 1.7264 cents 48:51:54:57:60:64:68:72:76:81:85:91:96 SD: 1.7042 cents 53:56:60:63:67:71:75:80:84:89:94:100:106 SD: 1.6059 cents 54:57:61:64:68:72:77:81:86:91:96:102:108 SD: 1.3994 cents 66:70:74:79:83:88:94:99:105:111:117:125:132 SD: 1.3294 cents 70:74:79:83:88:93:99:105:111:118:124:132:140 SD: 1.2923 cents 72:76:81:86:91:96:102:108:114:121:128:136:144 SD: 0.8371 cents 88:93:99:105:111:117:125:132:140:148:156:166:176 SD: 0.8214 cents 100:106:113:119:126:133:142:150:159:168:178:189:200 SD: 0.8158 cents 104:110:117:124:131:139:147:156:165:175:185:197:208 SD: 0.7882 cents 119:126:134:142:150:159:169:179:189:200:211:225:238 SD: 0.7081 cents 120:127:135:143:151:160:170:180:190:202:213:227:240 SD: 0.5987 cents 126:133:142:150:159:168:179:189:200:212:224:238:252 SD: 0.5905 cents 136:144:153:162:171:181:193:204:216:228:242:257:272 SD: 0.5362 cents 153:162:172:182:193:204:217:230:243:257:272:289:306 SD: 0.4555 cents 174:184:196:207:219:232:247:261:276:292:309:329:348 SD: 0.3340 cents 240:254:270:286:302:320:340:360:381:403:426:454:480 SD: 0.3310 cents 246:260:277:293:310:328:349:369:391:413:437:465:492 SD: 0.2603 cents 277:293:312:330:349:369:393:416:440:465:492:524:554 SD: 0.2581 cents 294:311:331:350:370:392:417:441:467:494:522:556:588 SD: 0.2483 cents 327:346:368:389:412:436:464:491:519:549:581:618:654 SD: 0.2200 cents 342:362:385:407:431:456:485:513:543:574:608:647:684 SD: 0.2161 cents 358:379:403:426:451:477:508:537:568:601:636:677:716 SD: 0.2128 cents 366:387:412:436:461:488:519:549:581:615:650:692:732 SD: 0.1580 cents 430:455:484:512:542:573:610:645:683:722:764:813:860 SD: 0.1391 cents 502:531:565:598:632:669:712:753:797:843:892:949:1004 SD: 0.1356 cents 519:549:584:618:654:692:736:779:824:872:922:981:1038 SD: 0.1166 cents 550:582:619:655:693:733:780:825:873:924:977:1040:1100 SD: 0.0942 cents