Scala analysis: mean2-5
2/5-comma meantone, Eb-G#, C-C
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 53.467 cents 53.467400 2: 186.705 cents 186.704970 3: 319.943 cents 319.942540 4: 373.410 cents 373.409940 5: 506.648 cents 506.647510 6: 560.115 cents 560.114910 7: 693.352 cents 693.352490 8: 746.820 cents 746.819880 9: 880.057 cents 880.057460 10: 1013.295 cents 1013.295030 11: 1066.762 cents 1066.762430 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 133.2376 cents 133.2376 1: 53.4674 cents 53.4674 2: 133.2376 cents 133.2376 3: 133.2376 cents 133.2376 4: 53.4674 cents 53.4674 5: 133.2376 cents 133.2376 6: 53.4674 cents 53.4674 7: 133.2376 cents 133.2376 8: 53.4674 cents 53.4674 9: 133.2376 cents 133.2376 10: 133.2376 cents 133.2376 11: 53.4674 cents 53.4674 12: 133.2376 cents 133.2376
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 53.46740 cents 1: 7 133.23757 cents 2: 10 186.70497 cents 2: 2 266.47514 cents 3: 3 240.17237 cents 3: 9 319.94254 cents 4: 8 373.40994 cents 4: 4 453.18011 cents 5: 1 426.87734 cents 5: 11 506.64751 cents 6: 6 560.11491 cents 6: 6 639.88509 cents 7: 11 693.35249 cents 7: 1 773.12266 cents 8: 4 746.81988 cents 8: 8 826.59006 cents 9: 9 880.05746 cents 9: 3 959.82763 cents 10: 2 933.52486 cents 10: 10 1013.29503 cents 11: 7 1066.76243 cents 11: 5 1146.53260 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 53.5 186.7 319.9 373.4 506.6 560.1 693.4 746.8 880.1 1013.3 1066.8 1200.0 53.5 : 133.2 266.5 319.9 453.2 506.6 639.9 693.4 826.6 959.8 1013.3 1146.5 1200.0 186.7 : 133.2 186.7 319.9 373.4 506.6 560.1 693.4 826.6 880.1 1013.3 1066.8 1200.0 319.9 : 53.5 186.7 240.2 373.4 426.9 560.1 693.4 746.8 880.1 933.5 1066.8 1200.0 373.4 : 133.2 186.7 319.9 373.4 506.6 639.9 693.4 826.6 880.1 1013.3 1146.5 1200.0 506.6 : 53.5 186.7 240.2 373.4 506.6 560.1 693.4 746.8 880.1 1013.3 1066.8 1200.0 560.1 : 133.2 186.7 319.9 453.2 506.6 639.9 693.4 826.6 959.8 1013.3 1146.5 1200.0 693.4 : 53.5 186.7 319.9 373.4 506.6 560.1 693.4 826.6 880.1 1013.3 1066.8 1200.0 746.8 : 133.2 266.5 319.9 453.2 506.6 639.9 773.1 826.6 959.8 1013.3 1146.5 1200.0 880.1 : 133.2 186.7 319.9 373.4 506.6 639.9 693.4 826.6 880.1 1013.3 1066.8 1200.0 1013.3: 53.5 186.7 240.2 373.4 506.6 560.1 693.4 746.8 880.1 933.5 1066.8 1200.0 1066.8: 133.2 186.7 319.9 453.2 506.6 639.9 693.4 826.6 880.1 1013.3 1146.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 53.4674 .. 133.2376 cents 79.77017 cents 53.46740 cents 2: 186.7050 .. 266.4751 cents 79.77017 cents 53.46740 cents 3: 240.1724 .. 319.9425 cents 79.77017 cents -26.30277 cents 4: 373.4099 .. 453.1801 cents 79.77017 cents 53.46740 cents 5: 426.8773 .. 506.6475 cents 79.77017 cents -26.30277 cents 6: 560.1149 .. 639.8851 cents 79.77018 cents 53.46740 cents 7: 693.3525 .. 773.1227 cents 79.77017 cents 53.46740 cents 8: 746.8199 .. 826.5901 cents 79.77018 cents -26.30278 cents 9: 880.0575 .. 959.8276 cents 79.77017 cents 53.46740 cents 10: 933.5249 .. 1013.2950 cents 79.77017 cents -26.30277 cents 11: 1066.7624 .. 1146.5326 cents 79.77017 cents 53.46740 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 53.46739 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 133.23757 cents Average / Smallest step : 1.870299 Largest / Average step : 1.332376 Largest / Smallest step : 2.491941 Median interval of one step : 133.23757 cents, amount: 7 Most common interval of one step : 133.23757 cents, amount: 7 Least squares average step : 98.13870 cents, oct.: 1177.66435 cents Scale is not proper Scale has Myhill's property chromas: 79.77017 cents and 26.30277 cents, ratio: 3.032767 generators: 5 of 506.64751 cents and 7 of 693.35249 cents ET pair of linear temperament : 19&45 Scale is distributional even Scale is a mode of a 1369-tone equal temperament with octave 2/1 degrees: 61 213 365 426 578 639 791 852 1004 1156 1217 1369 generators: 578 and 791 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABABABBAB Step pattern size order : SLLSLSLSLLSL Scale is a Constant Structure, by a margin of 26.30277 cents Ratio Whole / Half tone : 1.401294 Scale diversity : 1.230963 Lumma stability : 0.356449 Lumma impropriety factor : 0.087676 Rothenberg efficiency : 0.722222 redundancy: 0.277778 Efficiency x scale size : 8.666667 Number of different interval sizes : 22 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 26.30277 cents Most common intervals : 506.64751 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 133.238 693.352 cents Most common triad is 0.0 506.648 693.352 cents, amount: 10 Number of recognisable fifths : 11, average 693.3525 cents Scale contains two identical disjunct hexachords Formal octave complements present : 7 = 58.3333% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- 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: 28.3333 c. M:-53.1801 c. Twelve-tone Chromatic (1/11-comma) 15: 1 1 2 1 1 1 2 0 2 2 0 2 N D3 SD: 21.7812 c. M: 26.8199 c. 16: 1 1 2 1 2 0 2 1 2 1 1 2 P D3 SD: 22.8640 c. M: 38.2950 c. 18: 1 2 2 1 2 0 2 1 2 2 1 2 N T3 SD: 18.0666 c. M: 26.7816 c. 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 5.9005 c. M:-11.0749 c. Meantone Chromatic (1/3-comma) 26: 1 3 3 1 3 1 3 1 3 3 1 3 N M DE SD: 4.4532 c. M: 8.3583 c. Meantone Chromatic (4/9-comma) 45: 2 5 5 2 5 2 5 2 5 5 2 5 N M DE SD: 0.0816 c. M: 0.1532 c. Meantone Chromatic (2/5-comma) 739: 33 82 82 33 82 33 82 33 82 82 33 82 N M DE SD: 0.0722 c. M:-0.1355 c. 784: 35 87 87 35 87 35 87 35 87 87 35 87 N M DE SD: 0.0633 c. M:-0.1189 c. 829: 37 92 92 37 92 37 92 37 92 92 37 92 N M DE SD: 0.0555 c. M:-0.1041 c. 874: 39 97 97 39 97 39 97 39 97 97 39 97 N M DE SD: 0.0484 c. M:-0.0909 c. 919: 41 102 102 41 102 41 102 41 102 102 41 102 N M DE SD: 0.0420 c. M:-0.0789 c. 964: 43 107 107 43 107 43 107 43 107 107 43 107 N M DE SD: 0.0363 c. M:-0.0681 c. 1009: 45 112 112 45 112 45 112 45 112 112 45 112 N M DE SD: 0.0310 c. M:-0.0582 c. 1054: 47 117 117 47 117 47 117 47 117 117 47 117 N M DE SD: 0.0262 c. M:-0.0492 c. 1099: 49 122 122 49 122 49 122 49 122 122 49 122 N M DE SD: 0.0218 c. M:-0.0409 c. 1144: 51 127 127 51 127 51 127 51 127 127 51 127 N M DE SD: 0.0177 c. M:-0.0333 c. 1189: 53 132 132 53 132 53 132 53 132 132 53 132 N M DE SD: 0.0140 c. M:-0.0262 c. 1234: 55 137 137 55 137 55 137 55 137 137 55 137 N M DE SD: 0.0105 c. M:-0.0197 c. 1279: 57 142 142 57 142 57 142 57 142 142 57 142 N M DE SD: 0.0072 c. M:-0.0136 c. 1324: 59 147 147 59 147 59 147 59 147 147 59 147 N M DE SD: 0.0042 c. M:-0.0079 c. 1369: 61 152 152 61 152 61 152 61 152 152 61 152 N M DE SD: 0.0014 c. M:-0.0026 c. 1414: 63 157 157 63 157 63 157 63 157 157 63 157 N M DE SD: 0.0012 c. M: 0.0023 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: 4.3013 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.2060 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 11.7739 cents 5 x x 6 x x 7 x x 8:9 x 10 S SD: 14.0624 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.5537 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 16.4045 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.4931 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 8.4654 cents 10 x 11:12 x 13:14:15 x 17:18:19:20 SD: 9.4909 cents 11 x 12:13:14 x 15:16:17:18:20 x 22 S SD: 9.9342 cents 12 x 13:14:15:16:17:18 x 20 x 22:24 S SD: 9.6917 cents 13 x 14 x 16:17:18:19:20:22:23:24:26 S SD: 9.1368 cents 14:15:16:17 x 19 x 21:22:23:25:26:28 SD: 9.4677 cents 15:16:17:18:19:20:21:22:23:25:27:28:30 SD: 7.1511 cents 16:17:18:19:20:21:22:24:25:27:29:30:32 SD: 7.0288 cents 17:18:19:20:21:23 x 25:26:28 x 31:34 SD: 7.5416 cents 18:19:20 x 22:24:25:27:28:30:32:33:36 SD: 5.3569 cents 20:21:22:24:25:27:28:30:31:33:36:37:40 SD: 4.3251 cents 24:25:27:29:30:32:33:36:37:40:43:44:48 SD: 3.1009 cents 26:27:29:31:32:35:36:39:40:43:47:48:52 SD: 2.6024 cents 29:30:32:35:36:39:40:43:45:48:52:54:58 SD: 2.4325 cents 33:34:37:40:41:44:46:49:51:55:59:61:66 SD: 2.3795 cents 34:35:38:41:42:46:47:51:52:57:61:63:68 SD: 2.3723 cents 35:36:39:42:43:47:48:52:54:58:63:65:70 SD: 2.1650 cents 44:45:49:53:55:59:61:66:68:73:79:81:88 SD: 2.1303 cents 45:46:50:54:56:60:62:67:69:75:81:83:90 SD: 1.9607 cents 50:52:56:60:62:67:69:75:77:83:90:93:100 SD: 1.8295 cents 53:55:59:64:66:71:73:79:82:88:95:98:106 SD: 1.5246 cents 59:61:66:71:73:79:82:88:91:98:106:109:118 SD: 1.2541 cents 63:65:70:76:78:84:87:94:97:105:113:117:126 SD: 1.1121 cents 87:90:97:105:108:117:120:130:134:145:156:161:174 SD: 0.9973 cents 88:91:98:106:109:118:122:131:135:146:158:163:176 SD: 0.9683 cents 89:92:99:107:110:119:123:133:137:148:160:165:178 SD: 0.8055 cents 97:100:108:117:120:130:134:145:149:161:174:180:194 SD: 0.8018 cents 104:107:116:125:129:139:144:155:160:173:187:193:208 SD: 0.7648 cents 121:125:135:146:150:162:167:181:186:201:217:224:242 SD: 0.7465 cents 123:127:137:148:153:165:170:184:189:204:221:228:246 SD: 0.7170 cents 124:128:138:149:154:166:171:185:191:206:223:230:248 SD: 0.5686 cents 133:137:148:160:165:178:184:199:205:221:239:246:266 SD: 0.5625 cents 157:162:175:189:195:210:217:234:242:261:282:291:314 SD: 0.4607 cents 167:172:186:201:207:224:231:249:257:278:300:309:334 SD: 0.4245 cents 183:189:204:220:227:245:253:273:282:304:329:339:366 SD: 0.3983 cents 191:197:213:230:237:256:264:285:294:318:343:354:382 SD: 0.3336 cents 217:224:242:261:269:291:300:324:334:361:390:402:434 SD: 0.3316 cents 254:262:283:306:315:340:351:379:391:422:456:470:508 SD: 0.3109 cents 256:264:285:308:318:343:354:382:394:426:460:474:512 SD: 0.2737 cents 282:291:314:339:350:378:390:421:434:469:506:522:564 SD: 0.2287 cents 291:300:324:350:361:390:402:434:448:484:523:539:582 SD: 0.2214 cents 317:327:353:381:393:425:438:473:488:527:569:587:634 SD: 0.2082 cents 353:364:393:425:438:473:488:527:543:587:634:654:706 SD: 0.2035 cents 385:397:429:463:478:516:532:575:593:640:691:713:770 SD: 0.1883 cents 412:425:459:496:511:552:569:615:634:685:740:763:824 SD: 0.1746 cents 424:437:472:510:526:568:586:633:653:705:761:785:848 SD: 0.1729 cents 445:459:496:535:552:596:615:664:685:740:799:824:890 SD: 0.1610 cents 473:488:527:569:587:634:654:706:728:786:849:876:946 SD: 0.1399 cents 536:553:597:645:665:718:741:800:825:891:962:993:1072 SD: 0.1296 cents 573:591:638:689:711:768:792:855:882:953:1029:1061:1146 SD: 0.1226 cents