Scala analysis: rain159
Raintree scale tuned to 159-edo
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 98.113 cents 98.113208 2: 203.774 cents 203.773585 3: 301.887 cents 301.886792 4: 400.000 cents 400.000000 5: 498.113 cents 498.113208 6: 603.774 cents 603.773585 7: 701.887 cents 701.886792 8: 800.000 cents 800.000000 9: 898.113 cents 898.113208 10: 996.226 cents 996.226415 11: 1101.887 cents 1101.886792 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 98.1132 cents 98.1132 1: 98.1132 cents 98.1132 2: 105.6604 cents 105.6604 3: 98.1132 cents 98.1132 4: 98.1132 cents 98.1132 5: 98.1132 cents 98.1132 6: 105.6604 cents 105.6604 7: 98.1132 cents 98.1132 8: 98.1132 cents 98.1132 9: 98.1132 cents 98.1132 10: 98.1132 cents 98.1132 11: 105.6604 cents 105.6604 12: 98.1132 cents 98.1132
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 98.11321 cents 1: 3 105.66038 cents 2: 6 196.22642 cents 2: 6 203.77359 cents 3: 3 294.33962 cents 3: 9 301.88679 cents 4: 1 392.45283 cents 4: 10 400.00000 cents 4: 1 407.54717 cents 5: 9 498.11321 cents 5: 3 505.66038 cents 6: 6 596.22641 cents 6: 6 603.77359 cents 7: 3 694.33962 cents 7: 9 701.88679 cents 8: 1 792.45283 cents 8: 10 800.00000 cents 8: 1 807.54717 cents 9: 9 898.11321 cents 9: 3 905.66038 cents 10: 6 996.22642 cents 10: 6 1003.77358 cents 11: 3 1094.33962 cents 11: 9 1101.88679 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 : 98.1 203.8 301.9 400.0 498.1 603.8 701.9 800.0 898.1 996.2 1101.9 1200.0 98.1 : 105.7 203.8 301.9 400.0 505.7 603.8 701.9 800.0 898.1 1003.8 1101.9 1200.0 203.8 : 98.1 196.2 294.3 400.0 498.1 596.2 694.3 792.5 898.1 996.2 1094.3 1200.0 301.9 : 98.1 196.2 301.9 400.0 498.1 596.2 694.3 800.0 898.1 996.2 1101.9 1200.0 400.0 : 98.1 203.8 301.9 400.0 498.1 596.2 701.9 800.0 898.1 1003.8 1101.9 1200.0 498.1 : 105.7 203.8 301.9 400.0 498.1 603.8 701.9 800.0 905.7 1003.8 1101.9 1200.0 603.8 : 98.1 196.2 294.3 392.5 498.1 596.2 694.3 800.0 898.1 996.2 1094.3 1200.0 701.9 : 98.1 196.2 294.3 400.0 498.1 596.2 701.9 800.0 898.1 996.2 1101.9 1200.0 800.0 : 98.1 196.2 301.9 400.0 498.1 603.8 701.9 800.0 898.1 1003.8 1101.9 1200.0 898.1 : 98.1 203.8 301.9 400.0 505.7 603.8 701.9 800.0 905.7 1003.8 1101.9 1200.0 996.2 : 105.7 203.8 301.9 407.5 505.7 603.8 701.9 807.5 905.7 1003.8 1101.9 1200.0 1101.9: 98.1 196.2 301.9 400.0 498.1 596.2 701.9 800.0 898.1 996.2 1094.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 98.1132 .. 105.6604 cents 7.54717 cents 98.11321 cents 2: 196.2264 .. 203.7736 cents 7.54717 cents 90.56604 cents 3: 294.3396 .. 301.8868 cents 7.54717 cents 90.56604 cents 4: 392.4528 .. 407.5472 cents 15.09434 cents 90.56604 cents 5: 498.1132 .. 505.6604 cents 7.54717 cents 90.56604 cents 6: 596.2264 .. 603.7736 cents 7.54717 cents 90.56604 cents 7: 694.3396 .. 701.8868 cents 7.54717 cents 90.56604 cents 8: 792.4528 .. 807.5472 cents 15.09434 cents 90.56604 cents 9: 898.1132 .. 905.6604 cents 7.54717 cents 90.56604 cents 10: 996.2264 .. 1003.7736 cents 7.54717 cents 90.56604 cents 11: 1094.3396 .. 1101.8868 cents 7.54717 cents 90.56604 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 98.11321 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 105.66038 cents Average / Smallest step : 1.019231 Largest / Average step : 1.056604 Largest / Smallest step : 1.076923 Median interval of one step : 98.11321 cents, amount: 9 Most common interval of one step : 98.11321 cents, amount: 9 Least squares average step : 100.00581 cents, oct.: 1200.06967 cents Scale is strictly proper Scale is 3-distributional even Scale is a mode of a 159-tone equal temperament with octave 1200.000 cents degrees: 13 27 40 53 66 80 93 106 119 132 146 159 Least number of segments generator : 80 of 603.774 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 119 of 898.113 cents and inv. generated superset size: 109 = 97 more = 908.333% 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 0 0 0 9 3 0 0 0 0 0 0 0 0 0 0 0 6 6 0 0 0 0 0 0 0 0 0 0 0 3 9 0 0 0 0 0 0 0 0 0 0 0 1 10 1 0 0 0 0 0 0 0 0 0 0 0 9 3 0 0 0 0 0 0 0 0 0 0 0 6 ] Scale is a Constant Structure, by a margin of 90.56604 cents Scale diversity : 1.065343 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.918239 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 : 7.54717 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 Scale is a well-temperament. It has 2 different sizes of fifth Scale has monotonic third-sizes over circle of fifths Best fifths form a closed circle Formal octave complements present : 11 = 91.6667% Limited transpositions with margin 7.5472 cents: 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions with margin 7.5472 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: 2.3108 c. M: 3.7736 c. Twelve-tone Chromatic (1/11-comma) 87: 7 8 7 7 7 8 7 7 7 7 8 7 SP D3 SD: 1.9124 c. M:-3.1230 c. 99: 8 9 8 8 8 9 8 8 8 8 9 8 SP D3 SD: 1.4005 c. M:-2.2870 c. 111: 9 10 9 9 9 10 9 9 9 9 10 9 SP D3 SD: 0.9993 c. M: 1.6318 c. 123: 10 11 10 10 10 11 10 10 10 10 11 10 SP D3 SD: 0.6763 c. M:-1.1045 c. 135: 11 12 11 11 11 12 11 11 11 11 12 11 SP D3 SD: 0.4108 c. M:-0.6709 c. 147: 12 13 12 12 12 13 12 12 12 12 13 12 SP D3 SD: 0.1886 c. M: 0.3080 c. 159: 13 14 13 13 13 14 13 13 13 13 14 13 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: 0.0341 cents 3 x x x x 4 x x x 5 x x 6 S SD: 4.5849 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.6571 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.1700 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 10.7678 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.7033 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.2851 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 7.8790 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.2274 cents 11:12 x 13:14:15:16 x 17:18:20:21:22 S SD: 11.3070 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.1709 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 9.6384 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.0874 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.1506 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.8205 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 3.7919 cents 26:28:29:31:33:35:37:39:41:44:46:49:52 SD: 3.7322 cents 27:29:30:32:34:36:38:41:43:45:48:51:54 SD: 3.7230 cents 30:32:34:36:38:40:43:45:48:50:53:57:60 SD: 3.3231 cents 31:33:35:37:39:41:44:47:49:52:55:59:62 SD: 2.5595 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.5281 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 2.5101 cents 38:40:43:45:48:51:54:57:60:64:68:72:76 SD: 2.1959 cents 46:49:52:55:58:61:65:69:73:77:82:87:92 SD: 1.7393 cents 48:51:54:57:60:64:68:72:76:81:85:91:96 SD: 1.6912 cents 53:56:60:63:67:71:75:79:84:89:94:100:106 SD: 1.6522 cents 54:57:61:64:68:72:77:81:86:91:96:102:108 SD: 1.4570 cents 62:66:70:74:78:83:88:93:98:104:110:117:124 SD: 1.4512 cents 63:67:71:75:79:84:89:94:100:106:112:119:126 SD: 1.3731 cents 69:73:78:82:87:92:98:103:110:116:123:130:138 SD: 1.3710 cents 70:74:79:83:88:93:99:105:111:118:124:132:140 SD: 1.3016 cents 72:76:81:86:91:96:102:108:114:121:128:136:144 SD: 0.8505 cents 104:110:117:124:131:139:147:156:165:175:185:197:208 SD: 0.7112 cents 120:127:135:143:151:160:170:180:190:202:213:227:240 SD: 0.5952 cents 135:143:152:161:170:180:191:202:214:227:240:255:270 SD: 0.5945 cents 136:144:153:162:171:181:193:204:216:228:242:257:272 SD: 0.5627 cents 138:146:155:164:174:184:196:207:219:232:245:261:276 SD: 0.5371 cents 153:162:172:182:193:204:217:229:243:257:272:289:306 SD: 0.4176 cents 184:195:207:219:232:245:261:276:292:309:327:348:368 SD: 0.3601 cents 216:229:243:257:272:288:306:324:343:363:384:408:432 SD: 0.3043 cents 240:254:270:286:302:320:340:360:381:403:427:454:480 SD: 0.3040 cents 242:256:272:288:305:323:343:363:384:407:430:457:484 SD: 0.3017 cents 257:272:289:306:324:343:364:385:408:432:457:486:514 SD: 0.2971 cents 262:277:295:312:330:349:371:393:416:440:466:495:524 SD: 0.2964 cents 273:289:307:325:344:364:387:409:433:459:485:516:546 SD: 0.2737 cents 288:305:324:343:363:384:408:432:457:484:512:544:576 SD: 0.1760 cents 378:400:425:450:476:504:536:567:600:635:672:714:756 SD: 0.1467 cents 446:472:502:531:562:595:632:669:708:749:793:843:892 SD: 0.1306 cents 546:578:614:650:688:728:774:819:867:917:971:1032:1092 SD: 0.1045 cents