Scala analysis: 12_lumma_7thcomma2343
1/7-comma SSSSSLSLLSLL temperament.
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 96.927 cents 96.927000 2: 197.207 cents 197.207000 3: 297.486 cents 297.486000 4: 394.414 cents 394.414000 5: 501.396 cents 501.396000 6: 594.972 cents 594.972000 7: 698.603 cents 698.603000 8: 798.882 cents 798.882000 9: 895.810 cents 895.810000 10: 999.441 cents 999.441000 11: 1096.369 cents 1096.369000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 103.6310 cents 103.6310 1: 96.9270 cents 96.9270 2: 100.2800 cents 100.2800 3: 100.2790 cents 100.2790 4: 96.9280 cents 96.9280 5: 106.9820 cents 106.9820 6: 93.5760 cents 93.5760 7: 103.6310 cents 103.6310 8: 100.2790 cents 100.2790 9: 96.9280 cents 96.9280 10: 103.6310 cents 103.6310 11: 96.9280 cents 96.9280 12: 103.6310 cents 103.6310
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 93.57600 cents 1: 1 96.92700 cents 1: 3 96.92800 cents 1: 2 100.27900 cents 1: 1 100.28000 cents 1: 3 103.63100 cents 1: 1 106.98200 cents 2: 4 197.20700 cents 2: 2 200.55800 cents 2: 4 200.55900 cents 2: 2 203.91000 cents 3: 4 297.48600 cents 3: 2 297.48700 cents 3: 3 300.83800 cents 3: 2 304.18900 cents 3: 1 304.19000 cents 4: 2 394.41400 cents 4: 1 397.76500 cents 4: 2 397.76600 cents 4: 3 401.11700 cents 4: 1 401.11800 cents 4: 1 404.46800 cents 4: 2 404.46900 cents 5: 5 498.04500 cents 5: 4 501.39600 cents 5: 3 501.39700 cents 6: 1 594.97200 cents 6: 2 594.97300 cents 6: 2 598.32400 cents 6: 1 598.32500 cents 6: 1 601.67500 cents 6: 2 601.67600 cents 6: 2 605.02700 cents 6: 1 605.02800 cents 7: 3 698.60300 cents 7: 4 698.60400 cents 7: 5 701.95500 cents 8: 2 795.53100 cents 8: 1 795.53200 cents 8: 1 798.88200 cents 8: 3 798.88300 cents 8: 2 802.23400 cents 8: 1 802.23500 cents 8: 2 805.58600 cents 9: 1 895.81000 cents 9: 2 895.81100 cents 9: 3 899.16200 cents 9: 2 902.51300 cents 9: 4 902.51400 cents 10: 2 996.09000 cents 10: 4 999.44100 cents 10: 2 999.44200 cents 10: 4 1002.79300 cents 11: 1 1093.01800 cents 11: 3 1096.36900 cents 11: 1 1099.72000 cents 11: 2 1099.72100 cents 11: 3 1103.07200 cents 11: 1 1103.07300 cents 11: 1 1106.42400 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 5.45455 = 60/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 96.9 197.2 297.5 394.4 501.4 595.0 698.6 798.9 895.8 999.4 1096.4 1200.0 96.9 : 100.3 200.6 297.5 404.5 498.0 601.7 702.0 798.9 902.5 999.4 1103.1 1200.0 197.2 : 100.3 197.2 304.2 397.8 501.4 601.7 698.6 802.2 899.2 1002.8 1099.7 1200.0 297.5 : 96.9 203.9 297.5 401.1 501.4 598.3 702.0 798.9 902.5 999.4 1099.7 1200.0 394.4 : 107.0 200.6 304.2 404.5 501.4 605.0 702.0 805.6 902.5 1002.8 1103.1 1200.0 501.4 : 93.6 197.2 297.5 394.4 498.0 595.0 698.6 795.5 895.8 996.1 1093.0 1200.0 595.0 : 103.6 203.9 300.8 404.5 501.4 605.0 702.0 802.2 902.5 999.4 1106.4 1200.0 698.6 : 100.3 197.2 300.8 397.8 501.4 598.3 698.6 798.9 895.8 1002.8 1096.4 1200.0 798.9 : 96.9 200.6 297.5 401.1 498.0 598.3 698.6 795.5 902.5 996.1 1099.7 1200.0 895.8 : 103.6 200.6 304.2 401.1 501.4 601.7 698.6 805.6 899.2 1002.8 1103.1 1200.0 999.4 : 96.9 200.6 297.5 397.8 498.0 595.0 702.0 795.5 899.2 999.4 1096.4 1200.0 1096.4: 103.6 200.6 300.8 401.1 498.0 605.0 698.6 802.2 902.5 999.4 1103.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.5760 .. 106.9820 cents 13.40600 cents 93.57600 cents 2: 197.2070 .. 203.9100 cents 6.70300 cents 90.22500 cents 3: 297.4860 .. 304.1900 cents 6.70400 cents 93.57600 cents 4: 394.4140 .. 404.4690 cents 10.05500 cents 90.22400 cents 5: 498.0450 .. 501.3970 cents 3.35200 cents 93.57600 cents 6: 594.9720 .. 605.0280 cents 10.05600 cents 93.57500 cents 7: 698.6030 .. 701.9550 cents 3.35200 cents 93.57500 cents 8: 795.5310 .. 805.5860 cents 10.05500 cents 93.57600 cents 9: 895.8100 .. 902.5140 cents 6.70400 cents 90.22400 cents 10: 996.0900 .. 1002.7930 cents 6.70300 cents 93.57600 cents 11: 1093.0180 .. 1106.4240 cents 13.40600 cents 90.22500 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 93.57600 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 106.98200 cents Average / Smallest step : 1.068650 Largest / Average step : 1.069820 Largest / Smallest step : 1.143263 Median interval of one step : 100.27900 cents, amount: 2 Least squares average step : 99.74816 cents, oct.: 1196.97790 cents Scale is strictly proper Step pattern alph. order: ABCDEFGCDGDG Step pattern size order : BEDCGAFDCFCF Scale is a Constant Structure, by a margin of 90.22400 cents Scale diversity : 1.061803 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.924587 Rothenberg efficiency : 0.262963 redundancy: 0.737037 Efficiency x scale size : 3.155556 Number of different interval sizes : 60 = 5.45455 / class Number of one step interval sizes : 7 Highest interval variety : 8 Mean interval variety : 5.45455 = 60/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 0.00100 cents Most common intervals : 498.04500 cents & inv., amount: 5 Number of recognisable fifths : 12, average 700.0000 cents Scale is a well-temperament. It has 3 different sizes of fifth Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited transpositions with margin 10.0560 cents: 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions with margin 10.0550 cents: 1 2 3 4 5 6 7 8 9 10 11 -- 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: 3.1125 c. M:-5.5860 c. Twelve-tone Chromatic (1/11-comma) 91: 7 8 8 7 8 7 8 8 7 8 7 8 SP M ME SD: 2.9122 c. M:-5.8107 c. 103: 8 9 9 8 9 8 9 9 8 9 8 9 SP M ME SD: 2.6193 c. M:-5.4266 c. 107: 9 9 9 8 10 8 9 9 9 9 9 9 SP D3 SD: 3.0170 c. M:-5.3177 c. 110: 9 9 9 9 10 9 9 9 9 10 9 9 SP D3 S SD: 2.8085 c. M:-5.4492 c. 113: 9 9 10 9 10 9 10 9 9 10 9 10 SP M ME SD: 2.5723 c. M: 6.0566 c. 115: 9 10 10 9 10 9 10 10 9 10 9 10 SP M ME SD: 2.4306 c. M:-5.1227 c. 117: 9 10 10 9 11 9 10 10 9 10 10 10 SP D3 SD: 2.6906 c. M: 4.6704 c. 124: 10 10 11 10 11 9 11 11 10 10 10 11 SP D3 SD: 2.9595 c. M: 4.6494 c. 125: 10 10 11 10 11 10 11 10 10 11 10 11 SP M ME SD: 2.1738 c. M: 5.2070 c. 126: 10 11 10 10 12 9 11 11 10 11 10 11 SP SD: 2.5371 c. M: 4.4958 c. 127: 10 11 11 10 11 10 11 11 10 11 10 11 SP M ME SD: 2.3126 c. M:-4.8762 c. 129: 10 11 11 10 12 10 11 11 10 11 11 11 SP D3 SD: 2.2707 c. M: 4.0922 c. 137: 11 11 12 11 12 11 12 11 11 12 11 12 SP M ME SD: 1.8748 c. M: 4.5063 c. 138: 11 12 11 11 13 10 12 12 11 12 11 12 SP SD: 2.1493 c. M: 3.6677 c. 141: 11 12 12 11 13 11 12 12 11 12 12 12 SP D3 SD: 1.9460 c. M: 3.6963 c. 146: 12 12 12 12 13 11 13 12 12 13 11 13 SP D3 S SD: 1.8148 c. M:-3.2987 c. 149: 12 12 13 12 13 12 13 12 12 13 12 13 SP M ME SD: 1.6561 c. M: 3.9184 c. 150: 12 13 12 12 14 11 13 13 12 13 12 13 SP SD: 1.8444 c. M: 2.9720 c. 153: 12 13 13 12 14 12 13 13 12 13 13 13 SP D3 SD: 1.6990 c. M: 3.3626 c. 158: 13 13 13 13 14 12 14 13 13 14 12 14 SP D3 S SD: 1.6037 c. M:-3.0906 c. 161: 13 13 14 13 14 13 14 13 13 14 13 14 SP M ME SD: 1.5037 c. M: 3.4182 c. 162: 13 14 13 13 15 12 14 14 13 14 13 14 SP SD: 1.6084 c. M:-2.7930 c. 165: 13 14 14 13 15 13 14 14 13 14 14 14 SP D3 SD: 1.5168 c. M: 3.0774 c. 170: 14 14 14 14 15 13 15 14 14 15 13 15 SP D3 S SD: 1.4528 c. M:-2.9119 c. 173: 14 14 15 14 15 14 15 14 14 15 14 15 SP M ME SD: 1.4054 c. M: 2.9873 c. 177: 14 15 15 14 16 14 15 15 14 15 15 15 SP D3 SD: 1.3896 c. M: 2.8308 c. 182: 15 15 15 15 16 14 16 15 15 16 14 16 SP D3 S SD: 1.3523 c. M:-2.7568 c. 185: 15 15 16 15 16 15 16 15 15 16 15 16 SP M ME SD: 1.3503 c. M: 2.6124 c. 186: 15 16 15 15 17 14 16 16 15 16 15 16 SP SD: 1.3056 c. M:-2.7930 c. 194: 16 16 16 16 17 15 17 16 16 17 15 17 SP D3 S SD: 1.2933 c. M:-2.6209 c. 197: 16 16 17 16 17 16 17 16 16 17 16 17 SP M ME SD: 1.3285 c. M: 2.2831 c. 198: 16 17 16 16 18 15 17 17 16 17 16 17 SP SD: 1.2236 c. M:-2.7930 c. 209: 17 17 18 17 18 17 18 17 17 18 17 18 SP M ME SD: 1.3309 c. M:-2.1572 c. 210: 17 18 17 17 19 16 18 18 17 18 17 18 SP SD: 1.1782 c. M:-2.7930 c. 222: 18 19 18 18 20 17 19 19 18 19 18 19 SP SD: 1.1618 c. M:-2.7930 c. 234: 19 20 19 19 21 18 20 20 19 20 19 20 SP SD: 1.1674 c. M:-2.7930 c. 244: 20 20 20 20 22 19 21 20 20 21 20 21 SP SD: 1.1414 c. M: 2.4040 c. 246: 20 20 21 20 22 19 21 21 20 21 20 21 SP SD: 1.0607 c. M: 2.0850 c. 256: 21 21 21 21 23 20 22 21 21 22 21 22 SP SD: 1.0514 c. M: 2.1735 c. 258: 21 21 22 21 23 20 22 22 21 22 21 22 SP SD: 1.0619 c. M:-1.8644 c. 263: 21 22 22 21 24 20 23 22 21 23 21 23 SP SD: 1.1244 c. M: 2.0186 c. 268: 22 22 22 22 24 21 23 22 22 23 22 23 SP SD: 0.9881 c. M: 1.9636 c. 269: 22 22 23 21 24 21 24 22 22 23 22 23 SP SD: 1.2472 c. M: 1.8489 c. 270: 22 22 23 22 24 21 23 23 22 23 22 23 SP SD: 1.0787 c. M:-1.9678 c. 275: 22 23 23 22 25 21 24 23 22 24 22 24 SP SD: 0.9395 c. M: 1.6867 c. 285: 23 24 24 23 25 22 25 24 23 24 23 25 SP SD: 1.0713 c. M: 1.6322 c. 287: 23 24 24 23 26 22 25 24 23 25 23 25 SP SD: 0.7701 c. M: 1.3826 c. 299: 24 25 25 24 27 23 26 25 24 26 24 26 SP SD: 0.6143 c. M: 1.1030 c. 311: 25 26 26 25 28 24 27 26 25 27 25 27 SP SD: 0.4705 c. M: 0.8449 c. 323: 26 27 27 26 29 25 28 27 26 28 26 28 SP SD: 0.3374 c. M: 0.6060 c. 335: 27 28 28 27 30 26 29 28 27 29 27 29 SP SD: 0.2138 c. M: 0.3841 c. 347: 28 29 29 28 31 27 30 29 28 30 28 30 SP SD: 0.0987 c. M: 0.1777 c. 359: 29 30 30 29 32 28 31 30 29 31 29 31 SP SD: 0.0086 c. M:-0.0150 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: 1.6760 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.9772 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.9614 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.4301 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.5749 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.6757 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.6284 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.2344 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.1058 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.0631 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.2988 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.6819 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.5872 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.9362 cents 20:21:22:24:25:27:28:30:32:34:36:38:40 SD: 4.8402 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.2387 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.8235 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.2613 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.9733 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 1.9408 cents 48:51:54:57:60:64:68:72:76:81:86:90:96 SD: 1.9403 cents 50:53:56:59:63:67:71:75:79:84:89:94:100 SD: 1.7118 cents 51:54:57:61:64:68:72:76:81:86:91:96:102 SD: 1.5703 cents 58:61:65:69:73:77:82:87:92:97:103:109:116 SD: 1.5373 cents 59:62:66:70:74:79:83:88:94:99:105:111:118 SD: 1.3858 cents 65:69:73:77:82:87:92:97:103:109:116:122:130 SD: 1.3765 cents 66:70:74:78:83:88:93:99:105:111:118:124:132 SD: 1.2593 cents 68:72:76:81:85:91:96:102:108:114:121:128:136 SD: 1.0384 cents 75:79:84:89:94:100:106:112:119:126:134:141:150 SD: 1.0367 cents 86:91:96:102:108:115:121:129:136:144:153:162:172 SD: 0.9341 cents 90:95:101:107:113:120:127:135:143:151:160:170:180 SD: 0.7723 cents 102:108:114:121:128:136:144:153:162:171:182:192:204 SD: 0.7155 cents 117:124:131:139:147:156:165:175:186:196:208:220:234 SD: 0.7089 cents 122:129:137:145:153:163:172:183:194:205:217:230:244 SD: 0.6688 cents 133:141:149:158:167:178:188:199:211:223:237:251:266 SD: 0.6375 cents 137:145:154:163:172:183:193:205:217:230:244:258:274 SD: 0.6100 cents 140:148:157:166:176:187:197:210:222:235:249:264:280 SD: 0.5736 cents 149:158:167:177:187:199:210:223:236:250:265:281:298 SD: 0.5419 cents 155:164:174:184:195:207:219:232:246:260:276:292:310 SD: 0.4729 cents 173:183:194:205:217:231:244:259:274:290:308:326:346 SD: 0.4651 cents 175:185:196:208:220:234:247:262:278:294:312:330:350 SD: 0.4501 cents 191:202:214:227:240:255:269:286:303:320:340:360:382 SD: 0.3421 cents 223:236:250:265:280:298:314:334:354:374:397:420:446 SD: 0.3044 cents 239:253:268:284:300:319:337:358:379:401:426:450:478 SD: 0.2853 cents 266:281:298:316:334:355:375:398:422:446:474:501:532 SD: 0.2713 cents 273:289:306:324:343:365:385:409:433:458:486:514:546 SD: 0.2620 cents 292:309:327:347:367:390:412:437:463:490:520:550:584 SD: 0.2452 cents 298:315:334:354:374:398:420:446:473:500:531:561:596 SD: 0.2113 cents 348:368:390:413:437:465:491:521:552:584:620:656:696 SD: 0.1657 cents 438:463:491:520:550:585:618:656:695:735:780:825:876 SD: 0.1543 cents 449:475:503:533:564:600:633:672:712:753:800:846:898 SD: 0.1464 cents 507:536:568:602:637:677:715:759:804:851:903:955:1014 SD: 0.1445 cents 539:570:604:640:677:720:760:807:855:904:960:1015:1078 SD: 0.0785 cents