Scala analysis: modmos12a
A 12-note modmos in 50-et meantone
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 24.000 cents 24.000000 2: 192.000 cents 192.000000 3: 264.000 cents 264.000000 4: 384.000 cents 384.000000 5: 456.000 cents 456.000000 6: 576.000 cents 576.000000 7: 696.000 cents 696.000000 8: 768.000 cents 768.000000 9: 840.000 cents 840.000000 10: 960.000 cents 960.000000 11: 1080.000 cents 1080.000000 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 120.0000 cents 120.0000 1: 24.0000 cents 24.0000 2: 168.0000 cents 168.0000 3: 72.0000 cents 72.0000 4: 120.0000 cents 120.0000 5: 72.0000 cents 72.0000 6: 120.0000 cents 120.0000 7: 120.0000 cents 120.0000 8: 72.0000 cents 72.0000 9: 72.0000 cents 72.0000 10: 120.0000 cents 120.0000 11: 120.0000 cents 120.0000 12: 120.0000 cents 120.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 24.00000 cents 1: 4 72.00000 cents 1: 6 120.00000 cents 1: 1 168.00000 cents 2: 2 144.00000 cents 2: 6 192.00000 cents 2: 4 240.00000 cents 3: 5 264.00000 cents 3: 5 312.00000 cents 3: 2 360.00000 cents 4: 8 384.00000 cents 4: 4 432.00000 cents 5: 3 456.00000 cents 5: 7 504.00000 cents 5: 2 552.00000 cents 6: 1 528.00000 cents 6: 5 576.00000 cents 6: 5 624.00000 cents 6: 1 672.00000 cents 7: 2 648.00000 cents 7: 7 696.00000 cents 7: 3 744.00000 cents 8: 4 768.00000 cents 8: 8 816.00000 cents 9: 2 840.00000 cents 9: 5 888.00000 cents 9: 5 936.00000 cents 10: 4 960.00000 cents 10: 6 1008.00000 cents 10: 2 1056.00000 cents 11: 1 1032.00000 cents 11: 6 1080.00000 cents 11: 4 1128.00000 cents 11: 1 1176.00000 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.09091 = 34/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 24.0 192.0 264.0 384.0 456.0 576.0 696.0 768.0 840.0 960.0 1080.0 1200.0 24.0 : 168.0 240.0 360.0 432.0 552.0 672.0 744.0 816.0 936.0 1056.0 1176.0 1200.0 192.0 : 72.0 192.0 264.0 384.0 504.0 576.0 648.0 768.0 888.0 1008.0 1032.0 1200.0 264.0 : 120.0 192.0 312.0 432.0 504.0 576.0 696.0 816.0 936.0 960.0 1128.0 1200.0 384.0 : 72.0 192.0 312.0 384.0 456.0 576.0 696.0 816.0 840.0 1008.0 1080.0 1200.0 456.0 : 120.0 240.0 312.0 384.0 504.0 624.0 744.0 768.0 936.0 1008.0 1128.0 1200.0 576.0 : 120.0 192.0 264.0 384.0 504.0 624.0 648.0 816.0 888.0 1008.0 1080.0 1200.0 696.0 : 72.0 144.0 264.0 384.0 504.0 528.0 696.0 768.0 888.0 960.0 1080.0 1200.0 768.0 : 72.0 192.0 312.0 432.0 456.0 624.0 696.0 816.0 888.0 1008.0 1128.0 1200.0 840.0 : 120.0 240.0 360.0 384.0 552.0 624.0 744.0 816.0 936.0 1056.0 1128.0 1200.0 960.0 : 120.0 240.0 264.0 432.0 504.0 624.0 696.0 816.0 936.0 1008.0 1080.0 1200.0 1080.0: 120.0 144.0 312.0 384.0 504.0 576.0 696.0 816.0 888.0 960.0 1080.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 24.0000 .. 168.0000 cents 144.00000 cents 24.00000 cents 2: 144.0000 .. 240.0000 cents 96.00000 cents -24.00000 cents 3: 264.0000 .. 360.0000 cents 96.00000 cents 24.00000 cents 4: 384.0000 .. 432.0000 cents 48.00000 cents 24.00000 cents 5: 456.0000 .. 552.0000 cents 96.00000 cents 24.00000 cents 6: 528.0000 .. 672.0000 cents 144.00000 cents -24.00000 cents 7: 648.0000 .. 744.0000 cents 96.00000 cents -24.00000 cents 8: 768.0000 .. 816.0000 cents 48.00000 cents 24.00000 cents 9: 840.0000 .. 936.0000 cents 96.00000 cents 24.00000 cents 10: 960.0000 .. 1056.0000 cents 96.00000 cents 24.00000 cents 11: 1032.0000 .. 1176.0000 cents 144.00000 cents -24.00000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 24.00000 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 168.00000 cents Average / Smallest step : 4.166667 Largest / Average step : 1.680000 Largest / Smallest step : 7.000000 Median interval of one step : 120.00000 cents, amount: 6 Most common interval of one step : 120.00000 cents, amount: 6 Least squares average step : 96.81231 cents, oct.: 1161.74769 cents Scale is not proper Scale is a mode of a 50-tone equal temperament with octave 1200.000 cents degrees: 1 8 11 16 19 24 29 32 35 40 45 50 Least number of segments generator : 47 of 1128.000 cents and inv. number of contiguous generator circle segments: 2 Shortest superset generator : 29 of 696.000 cents and inv. generated superset size: 20 = 8 more = 166.667% Number of contiguous 1-step segments: 1 Step pattern alph. order: ABCDCDDCCDDD Step pattern size order : ADBCBCCBBCCC Interval vector is [ 1 0 4 0 6 2 1 6 0 4 5 0 5 0 2 8 0 4 3 0 7 1 2 5 0 ] Scale is a Constant Structure, by a margin of 24.00000 cents Scale diversity : 1.385170 Lumma stability : 0.160000 Lumma impropriety factor : 0.080000 Rothenberg efficiency : 0.382095 redundancy: 0.617905 Efficiency x scale size : 4.585137 Number of different interval sizes : 34 = 3.09091 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.09091 = 34/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 24.00000 cents Most common intervals : 384.00000 cents & inv., amount: 8 Most common triad is 0.0 384.000 816.000 cents, amount: 4 Number of recognisable fifths : 7, average 696.0000 cents Formal octave complements present : 1 = 8.3333% -- Rational properties --
FIT/MODE
12: 0 2 1 1 1 1 1 1 1 1 1 1 N T3 SD: 30.7463 c. M:-60.0000 c. 13: 0 2 1 1 1 1 1 1 1 1 2 1 N D3 SD: 24.3408 c. M: 49.8462 c. 14: 0 2 1 1 1 2 1 1 1 1 2 1 N D3 SD: 22.2637 c. M: 41.1429 c. 17: 0 3 1 1 1 2 2 1 1 2 1 2 N SD: 20.2380 c. M: 32.4706 c. 19: 0 3 1 2 1 2 2 1 1 2 2 2 N SD: 11.7254 c. M: 24.0000 c. 26: 1 3 2 2 2 2 3 2 1 3 2 3 P D3 SD: 13.7018 c. M:-22.1538 c. 27: 1 3 2 3 1 3 3 1 2 3 2 3 P SD: 12.6387 c. M:-20.4444 c. 29: 1 4 1 3 2 3 3 2 1 3 3 3 N SD: 11.3423 c. M:-18.2069 c. 30: 1 4 2 3 1 3 3 2 2 3 3 3 P SD: 11.7757 c. M:-16.0000 c. 31: 1 4 2 3 2 3 3 2 2 3 3 3 P SD: 7.1865 c. M:-14.7097 c. 40: 1 5 3 4 2 4 4 3 2 4 4 4 P SD: 6.4807 c. M: 12.0000 c. 48: 1 7 3 4 3 5 5 3 3 4 5 5 N SD: 7.0356 c. M:-11.0000 c. 50: 1 7 3 5 3 5 5 3 3 5 5 5 N 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: 2.9775 cents 3 x x x x 4 x x x 5 x x 6 S SD: 20.3729 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 2.7239 cents 5 x x 6 x x 7 x x 8:9 x 10 S SD: 16.3939 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 11.4477 cents 7 x x 8 x 9:10 x 11 x 12:13:14 S SD: 9.2991 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 3.8292 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 11.3571 cents 10 x 11:12 x 13:14:15 x 16:17:19:20 SD: 9.1981 cents 11 x 12:13:14 x 15:16:17:18:19:21:22 SD: 9.6674 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 8.6931 cents 13 x x 15:16:17:18:19:20:21:23:24:26 SD: 6.5739 cents 14 x x 16:17:18:20:21:22:23:24:26:28 S SD: 8.3321 cents 15 x 17 x 19:20:21:22:23:24:26:28:30 SD: 7.5359 cents 20:21:22:23:25:26:28:30:31:32:35:37:40 SD: 6.4752 cents 23:24:26:27:29:30:32:34:36:37:40:43:46 SD: 5.3549 cents 24:25:27:28:30:31:33:36:37:39:42:45:48 SD: 5.0265 cents 27:28:30:31:34:35:38:40:42:44:47:50:54 SD: 4.7146 cents 29:30:32:34:36:38:40:43:45:47:50:54:58 SD: 4.5452 cents 30:31:34:35:37:39:42:45:47:49:52:56:60 SD: 4.1196 cents 31:32:35:36:39:40:43:46:48:50:54:58:62 SD: 3.9633 cents 32:33:36:37:40:42:45:48:50:52:56:60:64 SD: 3.5242 cents 35:36:39:41:44:46:49:52:55:57:61:65:70 SD: 3.3658 cents 36:37:40:42:45:47:50:54:56:58:63:67:72 SD: 2.7496 cents 40:41:45:47:50:52:56:60:62:65:70:75:80 SD: 2.6916 cents 41:42:46:48:51:53:57:61:64:67:71:77:82 SD: 2.6858 cents 43:44:48:50:54:56:60:64:67:70:75:80:86 SD: 1.8180 cents 50:51:56:58:62:65:70:75:78:81:87:93:100 SD: 1.7639 cents 53:54:59:62:66:69:74:79:83:86:92:99:106 SD: 1.4918 cents 59:60:66:69:74:77:82:88:92:96:103:110:118 SD: 1.3350 cents 61:62:68:71:76:79:85:91:95:99:106:114:122 SD: 1.0280 cents 77:78:86:90:96:100:107:115:120:125:134:144:154 SD: 0.9006 cents 93:94:104:108:116:121:130:139:145:151:162:174:186 SD: 0.8278 cents 109:111:122:127:136:142:152:163:170:177:190:203:218 SD: 0.7850 cents 120:122:134:140:150:156:167:179:187:195:209:224:240 SD: 0.6880 cents 127:129:142:148:159:165:177:190:198:206:221:237:254 SD: 0.6306 cents 129:131:144:150:161:168:180:193:201:210:225:241:258 SD: 0.5825 cents 136:138:152:158:170:177:190:203:212:221:237:254:272 SD: 0.5694 cents 145:147:162:169:181:189:202:217:226:236:252:271:290 SD: 0.5613 cents 152:154:170:177:190:198:212:227:237:247:265:284:304 SD: 0.4367 cents 170:172:190:198:212:221:237:254:265:276:296:317:340 SD: 0.4166 cents 202:205:226:235:252:263:282:302:315:328:352:377:404 SD: 0.3810 cents 206:209:230:240:257:268:287:308:321:335:359:384:412 SD: 0.3455 cents 213:216:238:248:266:277:297:318:332:346:371:397:426 SD: 0.2904 cents 274:278:306:319:342:357:382:410:427:445:477:511:548 SD: 0.2842 cents 279:283:312:325:348:363:389:417:435:453:486:521:558 SD: 0.2524 cents 299:303:334:348:373:389:417:447:466:486:521:558:598 SD: 0.2236 cents 351:356:392:409:438:457:490:525:547:570:611:655:702 SD: 0.2132 cents 358:363:400:417:447:466:499:535:558:582:623:668:716 SD: 0.1740 cents 418:424:467:487:522:544:583:625:651:679:728:780:836 SD: 0.1358 cents 487:494:544:567:608:634:679:728:759:791:848:909:974 SD: 0.1270 cents 564:572:630:657:704:734:787:843:879:916:982:1052:1128 SD: 0.1142 cents 588:596:657:685:734:765:820:879:916:955:1024:1097:1176 SD: 0.1021 cents