Scala analysis: xen18-erlich-luna-13
6L 7s MOS for Luna, L=152.392, s=40.804
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40.804 cents 40.804000 2: 193.196 cents 193.196000 3: 234.000 cents 234.000000 4: 386.392 cents 386.392000 5: 427.196 cents 427.196000 6: 579.588 cents 579.588000 7: 620.392 cents 620.392000 8: 772.784 cents 772.784000 9: 813.588 cents 813.588000 10: 965.980 cents 965.980000 11: 1006.784 cents 1006.784000 12: 1159.176 cents 1159.176000 13: 1199.980 cents 1199.980000
SHOW/INTERVAL
0: 40.8040 cents 40.8040 1: 40.8040 cents 40.8040 2: 152.3920 cents 152.3920 3: 40.8040 cents 40.8040 4: 152.3920 cents 152.3920 5: 40.8040 cents 40.8040 6: 152.3920 cents 152.3920 7: 40.8040 cents 40.8040 8: 152.3920 cents 152.3920 9: 40.8040 cents 40.8040 10: 152.3920 cents 152.3920 11: 40.8040 cents 40.8040 12: 152.3920 cents 152.3920 13: 40.8040 cents 40.8040
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 40.80400 cents 1: 6 152.39200 cents 2: 1 81.60800 cents 2: 12 193.19600 cents 3: 8 234.00000 cents 3: 5 345.58800 cents 4: 2 274.80400 cents 4: 11 386.39200 cents 5: 9 427.19600 cents 5: 4 538.78400 cents 6: 3 468.00000 cents 6: 10 579.58800 cents 7: 10 620.39200 cents 7: 3 731.98000 cents 8: 4 661.19600 cents 8: 9 772.78400 cents 9: 11 813.58800 cents 9: 2 925.17600 cents 10: 5 854.39200 cents 10: 8 965.98000 cents 11: 12 1006.78400 cents 11: 1 1118.37200 cents 12: 6 1047.58800 cents 12: 7 1159.17600 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 13 0.0 : 40.8 193.2 234.0 386.4 427.2 579.6 620.4 772.8 813.6 966.0 1006.8 1159.2 1200.0 40.8 : 152.4 193.2 345.6 386.4 538.8 579.6 732.0 772.8 925.2 966.0 1118.4 1159.2 1200.0 193.2 : 40.8 193.2 234.0 386.4 427.2 579.6 620.4 772.8 813.6 966.0 1006.8 1047.6 1200.0 234.0 : 152.4 193.2 345.6 386.4 538.8 579.6 732.0 772.8 925.2 966.0 1006.8 1159.2 1200.0 386.4 : 40.8 193.2 234.0 386.4 427.2 579.6 620.4 772.8 813.6 854.4 1006.8 1047.6 1200.0 427.2 : 152.4 193.2 345.6 386.4 538.8 579.6 732.0 772.8 813.6 966.0 1006.8 1159.2 1200.0 579.6 : 40.8 193.2 234.0 386.4 427.2 579.6 620.4 661.2 813.6 854.4 1006.8 1047.6 1200.0 620.4 : 152.4 193.2 345.6 386.4 538.8 579.6 620.4 772.8 813.6 966.0 1006.8 1159.2 1200.0 772.8 : 40.8 193.2 234.0 386.4 427.2 468.0 620.4 661.2 813.6 854.4 1006.8 1047.6 1200.0 813.6 : 152.4 193.2 345.6 386.4 427.2 579.6 620.4 772.8 813.6 966.0 1006.8 1159.2 1200.0 966.0 : 40.8 193.2 234.0 274.8 427.2 468.0 620.4 661.2 813.6 854.4 1006.8 1047.6 1200.0 1006.8: 152.4 193.2 234.0 386.4 427.2 579.6 620.4 772.8 813.6 966.0 1006.8 1159.2 1200.0 1159.2: 40.8 81.6 234.0 274.8 427.2 468.0 620.4 661.2 813.6 854.4 1006.8 1047.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 40.8040 .. 152.3920 cents 111.58800 cents 40.80400 cents 2: 81.6080 .. 193.1960 cents 111.58800 cents -70.78400 cents 3: 234.0000 .. 345.5880 cents 111.58800 cents 40.80400 cents 4: 274.8040 .. 386.3920 cents 111.58800 cents -70.78400 cents 5: 427.1960 .. 538.7840 cents 111.58800 cents 40.80400 cents 6: 468.0000 .. 579.5880 cents 111.58800 cents -70.78400 cents 7: 620.3920 .. 731.9800 cents 111.58800 cents 40.80400 cents 8: 661.1960 .. 772.7840 cents 111.58800 cents -70.78400 cents 9: 813.5880 .. 925.1760 cents 111.58800 cents 40.80400 cents 10: 854.3920 .. 965.9800 cents 111.58800 cents -70.78400 cents 11: 1006.7840 .. 1118.3720 cents 111.58800 cents 40.80400 cents 12: 1047.5880 .. 1159.1760 cents 111.58800 cents -70.78400 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 40.80400 cents, class 1 Average step (divided formal octave): 92.3062 cents Largest one step interval : 152.39200 cents Average / Smallest step : 2.262184 Largest / Average step : 1.650941 Largest / Smallest step : 3.734732 Median interval of one step : 40.80400 cents, amount: 7 Most common interval of one step : 40.80400 cents, amount: 7 Least squares average step : 93.25990 cents, oct.: 1212.37867 cents Scale is not proper Scale has Myhill's property chromas: 111.58800 cents and 70.78400 cents, ratio: 1.576458 generators: 2 of 193.19600 cents and 11 of 1006.78400 cents ET pair of linear temperament : 25&31 Scale is distributional even Scale is a mode of a 1000-tone equal temperament with octave 1199.980 cents degrees: 34 161 195 322 356 483 517 644 678 805 839 966 1000 generators: 161 and 839 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABABABA Step pattern size order : SLSLSLSLSLSLS Scale is a Constant Structure, by a margin of 40.80400 cents Scale diversity : 1.228158 Lumma stability : 0.238027 Lumma impropriety factor : 0.353926 Rothenberg efficiency : 0.717949 redundancy: 0.282051 Efficiency x scale size : 9.333333 Number of different interval sizes : 24 = 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 : 40.80400 cents Most common intervals : 193.19600 cents & inv., amount: 12 Scale is a chain of 6 triads 0.0 193.196 386.392 cents Most common triad is 0.0 193.196 1006.784 cents, amount: 11 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Scale contains two identical disjunct hexachords Formal octave complements present : 13 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 6-7 -- Rational properties --
FIT/MODE
13: 0 2 0 2 0 2 0 2 0 2 0 2 1 N T3 SD: 49.0326 c. M: 83.7225 c. 14: 0 2 0 2 1 1 1 2 0 2 0 2 1 N T3 SD: 40.2445 c. M: 65.3109 c. 15: 0 2 0 2 1 2 0 2 1 2 0 2 1 N SD: 43.1093 c. M: 74.0027 c. 16: 0 2 1 2 0 2 1 2 0 2 1 2 1 N T3 SD: 40.1581 c. M: 65.9950 c. 17: 0 2 1 2 1 2 0 2 1 2 1 2 1 N T3 SD: 37.9754 c. M: 66.9134 c. 18: 0 2 1 2 1 2 1 2 1 2 1 2 1 N T3 SD: 35.1279 c. M: 59.8649 c. 19: 1 2 1 2 1 2 1 2 1 2 1 2 1 P M ME I SD: 13.9394 c. M:-22.3528 c. 25: 1 3 1 3 1 3 1 3 1 3 1 3 1 N M DE I SD: 4.4870 c. M:-7.1952 c. 31: 1 4 1 4 1 4 1 4 1 4 1 4 1 N M DE I SD: 1.3064 c. M: 2.0950 c. 56: 2 7 2 7 2 7 2 7 2 7 2 7 2 N M DE I SD: 1.2799 c. M:-2.0524 c. 87: 3 11 3 11 3 11 3 11 3 11 3 11 3 N M DE I SD: 0.3583 c. M:-0.5746 c. 118: 4 15 4 15 4 15 4 15 4 15 4 15 4 N M DE I SD: 0.0790 c. M:-0.1267 c. 323: 11 41 11 41 11 41 11 41 11 41 11 41 11 N M DE I SD: 0.0388 c. M:-0.0622 c. 441: 15 56 15 56 15 56 15 56 15 56 15 56 15 N M DE I SD: 0.0073 c. M:-0.0116 c. 1000: 34 127 34 127 34 127 34 127 34 127 34 127 34 N M DE I SD: 0.0029 c. M:-0.0047 c. 1441: 49 183 49 183 49 183 49 183 49 183 49 183 49 N M DE I SD: 0.0002 c. M:-0.0003 c.
FIT/HARMONIC
1 x x x x x x x x x x x x 2 S SD: 0.0200 cents 2 x x x x x x x 3 x x x x 4 S SD: 35.4145 cents 3 x x x x 4 x x x 5 x x x 6 S SD: 33.3801 cents 4 x x x 5 x x x 6 x 7 x x 8 S SD: 17.7215 cents 5 x x x 6 x 7 x x 8 x 9 x 10 S SD: 14.3264 cents 6 x x 7 x 8 x x 9:10 x 11 x 12 S SD: 22.3223 cents 7 x x 8 x 9 x 10:11 x 12:13 x 14 S SD: 10.5621 cents 8 x 9 x 10 x 11 x x 13:14 x x 16 SD: 6.7656 cents 9 x 10 x 11:12 x 13:14 x x 16 x 18 S SD: 12.0334 cents 10 x 11 x x 13:14 x x 16:17:18 x 20 SD: 8.9113 cents 11 x 12:13 x 14:15:16:17:18:19:20:21:22 S SD: 10.0511 cents 12 x 13:14:15 x x 17 x 19:21 x 23:24 SD: 9.5028 cents 13 x x 15:16:17:18:19:20:21 x 23:25:26 SD: 7.7483 cents 14 x x 16 x 18 x 20:22 x 24:25:27:28 SD: 5.2306 cents 15:16 x 17 x 19:21 x 23:24:26:27:29:30 SD: 8.5791 cents 16:17:18 x 20 x 22:23:25:26:28:29:31:32 SD: 7.3546 cents 17:18:19 x 21:22:24 x x 27:30 x 33:34 SD: 7.8994 cents 18:19:20:21 x 23:25:26:28:29:31:32:35:36 SD: 6.1108 cents 19:20:21:22:24 x x 27:30 x 33:34:37:38 SD: 6.3405 cents 20:21:22:23:25:26:28:29:31:32:35:36:39:40 SD: 5.0781 cents 22:23 x 25 x 28:31 x 34:35:38:39:43:44 SD: 5.3479 cents 23:24:26 x 29 x 32:33:36:37:40:41:45:46 SD: 4.0187 cents 24:25:27 x 30:31 x 34 x 38:42:43:47:48 SD: 4.3838 cents 25:26:28:29:31:32:35:36:39:40:44:45:49:50 SD: 3.3652 cents 26:27:29:30 x 33:36:37:41:42:45:47:51:52 SD: 4.2040 cents 27:28:30:31:34:35:38:39:42:43:47:48:53:54 SD: 3.4766 cents 28:29:31:32:35:36:39:40:44:45:49:50:55:56 SD: 2.5106 cents 30:31 x 34 x 38:42:43:47:48:52:54:59:60 SD: 3.3477 cents 31:32:35 x 39:40:43:44:48:50:54:55:61:62 SD: 3.7398 cents 32:33:36:37:40:41:45:46:50:51:56:57:63:64 SD: 2.4806 cents 35:36:39:40:44:45:49:50:55:56:61:63:68:70 SD: 1.8801 cents 43:44:48:49:54:55:60:62:67:69:75:77:84:86 SD: 1.4963 cents 60:61:67:69:75:77:84:86:94:96:105:107:117:120 SD: 1.3764 cents 67:69:75:77:84:86:94:96:105:107:117:120:131:134 SD: 1.3239 cents 68:70:76:78:85:87:95:97:106:109:119:122:133:136 SD: 1.0867 cents 75:77:84:86:94:96:105:107:117:120:131:134:147:150 SD: 0.9225 cents 83:85:93:95:104:106:116:119:130:133:145:148:162:166 SD: 0.8127 cents 111:114:124:127:139:142:155:159:173:178:194:199:217:222 SD: 0.7721 cents 118:121:132:135:148:151:165:169:184:189:206:211:231:236 SD: 0.6831 cents 125:128:140:143:156:160:175:179:195:200:218:224:244:250 SD: 0.5852 cents 128:131:143:147:160:164:179:183:200:205:224:229:250:256 SD: 0.5551 cents 151:155:169:173:189:193:211:216:236:242:264:270:295:302 SD: 0.5267 cents 153:157:171:175:191:196:214:219:239:245:267:274:299:306 SD: 0.4780 cents 160:164:179:183:200:205:224:229:250:256:280:286:313:320 SD: 0.4575 cents 167:171:187:191:209:214:233:239:261:267:292:299:326:334 SD: 0.4487 cents 171:175:191:196:214:219:239:245:267:274:299:306:334:342 SD: 0.4167 cents 208:213:233:238:260:266:291:298:325:333:363:372:406:416 SD: 0.4042 cents 212:217:237:243:265:271:296:303:331:339:370:379:414:424 SD: 0.3842 cents 213:218:238:244:266:273:298:305:333:341:372:381:416:426 SD: 0.3342 cents 236:242:264:270:295:302:330:338:369:378:412:422:461:472 SD: 0.3342 cents 255:261:285:292:319:326:356:365:398:408:446:456:498:510 SD: 0.3320 cents 256:262:286:293:320:328:358:366:400:410:447:458:500:512 SD: 0.2844 cents 297:304:332:340:371:380:415:425:464:475:519:531:580:594 SD: 0.1545 cents 332:340:371:380:415:425:464:475:519:531:580:594:649:664 SD: 0.1496 cents 455:466:509:521:569:582:636:651:711:728:795:814:889:910 SD: 0.1399 cents 540:553:604:618:675:691:755:773:844:864:943:966:1055:1080 SD: 0.1246 cents