Scala analysis: 12_lumma_7thcomma2262
1/7-comma SSSSLLSSLLLS temperament.
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 96.929 cents 96.929000 2: 197.208 cents 197.208000 3: 297.488 cents 297.488000 4: 394.415 cents 394.415000 5: 501.396 cents 501.396000 6: 598.325 cents 598.325000 7: 698.604 cents 698.604000 8: 795.533 cents 795.533000 9: 895.811 cents 895.811000 10: 999.442 cents 999.442000 11: 1096.370 cents 1096.370000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 103.6300 cents 103.6300 1: 96.9290 cents 96.9290 2: 100.2790 cents 100.2790 3: 100.2800 cents 100.2800 4: 96.9270 cents 96.9270 5: 106.9810 cents 106.9810 6: 96.9290 cents 96.9290 7: 100.2790 cents 100.2790 8: 96.9290 cents 96.9290 9: 100.2780 cents 100.2780 10: 103.6310 cents 103.6310 11: 96.9280 cents 96.9280 12: 103.6300 cents 103.6300
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 96.92700 cents 1: 1 96.92800 cents 1: 3 96.92900 cents 1: 1 100.27800 cents 1: 2 100.27900 cents 1: 1 100.28000 cents 1: 1 103.63000 cents 1: 1 103.63100 cents 1: 1 106.98100 cents 2: 2 197.20700 cents 2: 3 197.20800 cents 2: 1 200.55800 cents 2: 3 200.55900 cents 2: 1 203.90800 cents 2: 1 203.90900 cents 2: 1 203.91000 cents 3: 1 294.13700 cents 3: 2 297.48600 cents 3: 1 297.48700 cents 3: 1 297.48800 cents 3: 2 300.83700 cents 3: 2 300.83800 cents 3: 1 304.18800 cents 3: 2 304.18900 cents 4: 2 394.41500 cents 4: 2 397.76600 cents 4: 1 401.11600 cents 4: 2 401.11700 cents 4: 3 401.11800 cents 4: 2 404.46700 cents 5: 3 498.04500 cents 5: 2 498.04600 cents 5: 6 501.39600 cents 5: 1 501.39700 cents 6: 1 594.97300 cents 6: 1 594.97400 cents 6: 1 598.32300 cents 6: 3 598.32500 cents 6: 3 601.67500 cents 6: 1 601.67700 cents 6: 1 605.02600 cents 6: 1 605.02700 cents 7: 1 698.60300 cents 7: 6 698.60400 cents 7: 2 701.95400 cents 7: 3 701.95500 cents 8: 2 795.53300 cents 8: 3 798.88200 cents 8: 2 798.88300 cents 8: 1 798.88400 cents 8: 2 802.23400 cents 8: 2 805.58500 cents 9: 2 895.81100 cents 9: 1 895.81200 cents 9: 2 899.16200 cents 9: 2 899.16300 cents 9: 1 902.51200 cents 9: 1 902.51300 cents 9: 2 902.51400 cents 9: 1 905.86300 cents 10: 1 996.09000 cents 10: 1 996.09100 cents 10: 1 996.09200 cents 10: 3 999.44100 cents 10: 1 999.44200 cents 10: 3 1002.79200 cents 10: 2 1002.79300 cents 11: 1 1093.01900 cents 11: 1 1096.36900 cents 11: 1 1096.37000 cents 11: 1 1099.72000 cents 11: 2 1099.72100 cents 11: 1 1099.72200 cents 11: 3 1103.07100 cents 11: 1 1103.07200 cents 11: 1 1103.07300 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 6.90909 = 76/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 96.9 197.2 297.5 394.4 501.4 598.3 698.6 795.5 895.8 999.4 1096.4 1200.0 96.9 : 100.3 200.6 297.5 404.5 501.4 601.7 698.6 798.9 902.5 999.4 1103.1 1200.0 197.2 : 100.3 197.2 304.2 401.1 501.4 598.3 698.6 802.2 899.2 1002.8 1099.7 1200.0 297.5 : 96.9 203.9 300.8 401.1 498.0 598.3 702.0 798.9 902.5 999.4 1099.7 1200.0 394.4 : 107.0 203.9 304.2 401.1 501.4 605.0 702.0 805.6 902.5 1002.8 1103.1 1200.0 501.4 : 96.9 197.2 294.1 394.4 498.0 595.0 698.6 795.5 895.8 996.1 1093.0 1200.0 598.3 : 100.3 197.2 297.5 401.1 498.0 601.7 698.6 798.9 899.2 996.1 1103.1 1200.0 698.6 : 96.9 197.2 300.8 397.8 501.4 598.3 698.6 798.9 895.8 1002.8 1099.7 1200.0 795.5 : 100.3 203.9 300.8 404.5 501.4 601.7 702.0 798.9 905.9 1002.8 1103.1 1200.0 895.8 : 103.6 200.6 304.2 401.1 501.4 601.7 698.6 805.6 902.5 1002.8 1099.7 1200.0 999.4 : 96.9 200.6 297.5 397.8 498.0 595.0 702.0 798.9 899.2 996.1 1096.4 1200.0 1096.4: 103.6 200.6 300.8 401.1 498.0 605.0 702.0 802.2 899.2 999.4 1103.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 96.9270 .. 106.9810 cents 10.05400 cents 96.92700 cents 2: 197.2070 .. 203.9100 cents 6.70300 cents 90.22600 cents 3: 294.1370 .. 304.1890 cents 10.05200 cents 90.22700 cents 4: 394.4150 .. 404.4670 cents 10.05200 cents 90.22600 cents 5: 498.0450 .. 501.3970 cents 3.35200 cents 93.57800 cents 6: 594.9730 .. 605.0270 cents 10.05400 cents 93.57600 cents 7: 698.6030 .. 701.9550 cents 3.35200 cents 93.57600 cents 8: 795.5330 .. 805.5850 cents 10.05200 cents 93.57800 cents 9: 895.8110 .. 905.8630 cents 10.05200 cents 90.22600 cents 10: 996.0900 .. 1002.7930 cents 6.70300 cents 90.22700 cents 11: 1093.0190 .. 1103.0730 cents 10.05400 cents 90.22600 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 96.92700 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 106.98100 cents Average / Smallest step : 1.031704 Largest / Average step : 1.069810 Largest / Smallest step : 1.103728 Median interval of one step : 100.27850 cents, amount: 0 Most common interval of one step : 96.92900 cents, amount: 3 Least squares average step : 99.73797 cents, oct.: 1196.85563 cents Scale is strictly proper Step pattern alph. order: ABCDEABAFGHI Step pattern size order : CEFAICECDHBG Scale is a Constant Structure, by a margin of 90.22600 cents Scale diversity : 1.061617 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.924600 Rothenberg efficiency : 0.248665 redundancy: 0.751335 Efficiency x scale size : 2.983983 Number of different interval sizes : 76 = 6.90909 / class Number of one step interval sizes : 9 Highest interval variety : 9 Mean interval variety : 6.90909 = 76/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 0.00100 cents Most common intervals : 501.39600 cents & inv., amount: 6 Most common triad is 0.0 501.396 698.604 cents, amount: 3 Number of recognisable fifths : 12, average 700.0000 cents Scale is a well-temperament. It has 4 different sizes of fifth Scale has monotonic third-sizes over circle of fifths Best fifths form a closed circle Formal octave complements present : 3 = 25.0000% Limited transpositions with margin 10.0520 cents: 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions with margin 10.0520 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: 3.0608 c. M:-5.5850 c. Twelve-tone Chromatic (1/11-comma) 98: 8 8 8 8 9 8 8 8 8 9 8 8 SP D3 S SD: 2.6397 c. M:-5.6708 c. 100: 8 8 9 8 9 8 8 8 9 8 8 9 SP D3 SD: 3.0842 c. M: 5.2080 c. 103: 8 9 8 9 9 8 9 8 9 9 8 9 SP M ME SD: 2.8004 c. M: 6.2259 c. 109: 9 9 9 9 10 8 9 9 9 10 9 9 SP D3 SD: 3.2361 c. M:-5.0260 c. 110: 9 9 9 9 10 9 9 9 9 10 9 9 SP D3 S SD: 2.3544 c. M:-5.4482 c. 112: 9 9 10 9 10 9 9 9 10 9 9 10 SP D3 SD: 2.7072 c. M: 4.3509 c. 113: 9 9 10 9 10 9 10 9 9 10 9 10 SP M ME SD: 2.7012 c. M: 6.0576 c. 115: 9 10 10 9 10 9 10 9 10 10 9 10 SP M ME SD: 2.3884 c. M:-5.1207 c. Meantone Chromatic (3/23-comma), Preston-12 122: 10 10 10 10 11 10 10 10 10 11 9 11 SP D3 SD: 2.0303 c. M: 4.5667 c. 124: 10 10 11 10 11 10 10 10 11 10 10 11 SP D3 SD: 2.4386 c. M:-4.1890 c. 125: 10 10 11 10 11 10 11 10 10 11 10 11 SP M ME SD: 2.3042 c. M: 5.2080 c. 127: 10 11 10 11 11 10 11 10 11 11 10 11 SP M ME SD: 2.1540 c. M: 4.5746 c. 134: 11 11 11 11 12 11 11 11 11 12 10 12 SP D3 SD: 1.8002 c. M: 3.8327 c. 137: 11 11 12 11 12 11 12 11 11 12 11 12 SP M ME SD: 2.0049 c. M: 4.5073 c. 139: 11 12 11 12 12 11 12 11 12 12 11 12 SP M ME SD: 1.9662 c. M: 3.9628 c. 146: 12 12 12 12 13 12 12 12 12 13 11 13 SP D3 SD: 1.6456 c. M:-3.2977 c. 158: 13 13 13 13 14 13 13 13 13 14 12 14 SP D3 SD: 1.5497 c. M:-3.0896 c. 162: 13 14 13 13 15 13 13 13 14 14 13 14 SP D3 SD: 1.7222 c. M: 2.9404 c. 165: 13 14 14 13 15 13 14 13 14 14 14 14 SP D3 SD: 1.7359 c. M: 3.0784 c. 170: 14 14 14 14 15 14 14 14 14 15 13 15 SP D3 SD: 1.4984 c. M:-2.9109 c. 174: 14 15 14 14 16 14 14 14 15 15 14 15 SP D3 SD: 1.5427 c. M:-2.7920 c. 177: 14 15 15 14 16 14 15 14 15 15 15 15 SP D3 SD: 1.5150 c. M: 2.8318 c. 182: 15 15 15 15 16 15 15 15 15 16 14 16 SP D3 SD: 1.4796 c. M:-2.7558 c. 185: 15 15 16 15 16 15 16 15 15 16 15 16 SP M ME SD: 1.4541 c. M: 2.6134 c. 186: 15 16 15 15 17 15 15 15 16 16 15 16 SP D3 SD: 1.4119 c. M:-2.7920 c. 189: 15 16 16 15 17 15 16 15 16 16 16 16 SP D3 SD: 1.3434 c. M: 2.6166 c. 196: 16 16 17 15 18 16 16 16 16 17 16 17 SP SD: 1.4608 c. M: 2.5783 c. 197: 16 16 17 16 17 16 17 16 16 17 16 17 SP M ME SD: 1.4208 c. M:-2.4365 c. 198: 16 17 16 16 18 16 16 16 17 17 16 17 SP D3 SD: 1.3226 c. M:-2.7920 c. 201: 16 17 17 16 18 16 17 16 17 17 17 17 SP D3 SD: 1.2159 c. M: 2.4271 c. 213: 17 18 18 17 19 17 18 17 18 18 18 18 SP D3 SD: 1.1276 c. M: 2.2589 c. 222: 18 19 18 18 20 18 18 18 19 19 18 19 SP D3 SD: 1.2410 c. M:-2.7920 c. 225: 18 19 19 18 20 18 19 18 19 19 19 19 SP D3 SD: 1.0735 c. M:-2.2967 c. 234: 19 20 19 19 21 19 19 19 20 20 19 20 SP D3 SD: 1.2357 c. M:-2.7920 c. 235: 19 20 19 19 21 19 20 19 19 21 19 20 SP SD: 1.2861 c. M: 2.1940 c. 237: 19 20 20 19 21 19 20 19 20 20 20 20 SP D3 SD: 1.0481 c. M:-2.3642 c. 246: 20 20 21 20 22 20 20 20 21 21 20 21 SP SD: 1.1254 c. M: 2.0860 c. 247: 20 21 20 20 22 20 21 20 20 22 20 21 SP SD: 1.2282 c. M:-1.9823 c. 249: 20 21 21 20 22 20 21 20 21 21 20 22 SP SD: 1.0394 c. M: 2.3941 c. 258: 21 21 22 21 23 21 21 21 22 22 21 22 SP SD: 1.1170 c. M:-1.8634 c. 261: 21 22 22 21 23 21 22 21 22 22 21 23 SP SD: 0.9919 c. M: 2.1171 c. 263: 21 22 22 21 24 21 22 21 22 23 21 23 SP SD: 1.1073 c. M: 2.0196 c. 268: 22 22 22 22 24 22 22 22 22 23 22 23 SP D3 SD: 1.0382 c. M: 1.9656 c. 269: 22 22 23 21 24 22 23 21 23 23 22 23 SP SD: 1.2333 c. M: 1.8499 c. 270: 22 22 23 22 24 22 22 22 23 23 22 23 SP SD: 1.1243 c. M:-1.9668 c. 273: 22 23 23 22 24 22 23 22 23 23 22 24 SP SD: 0.9675 c. M: 1.8645 c. 275: 22 23 23 22 25 22 23 22 23 24 22 24 SP SD: 0.9254 c. M: 1.6877 c. 285: 23 24 24 23 25 23 24 23 24 24 23 25 SP SD: 0.9622 c. M: 1.6332 c. 287: 23 24 24 23 26 23 24 23 24 25 23 25 SP SD: 0.7587 c. M: 1.3836 c. 299: 24 25 25 24 27 24 25 24 25 26 24 26 SP SD: 0.6054 c. M: 1.1040 c. 311: 25 26 26 25 28 25 26 25 26 27 25 27 SP SD: 0.4640 c. M: 0.8459 c. 323: 26 27 27 26 29 26 27 26 27 28 26 28 SP SD: 0.3330 c. M: 0.6070 c. 335: 27 28 28 27 30 27 28 27 28 29 27 29 SP SD: 0.2115 c. M: 0.3851 c. 347: 28 29 29 28 31 28 29 28 29 30 28 30 SP SD: 0.0983 c. M: 0.1787 c. 359: 29 30 30 29 32 29 30 29 30 31 29 31 SP SD: 0.0073 c. M:-0.0140 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: 1.6755 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.9775 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.9616 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.0391 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.5753 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.4453 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.1506 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.8631 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.2487 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.9305 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.2635 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.8699 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.4772 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.0784 cents 16:17:18:19:20:21:23:24:25:27:29:30:32 SD: 5.0138 cents 19:20:21:23:24:25:27:28:30:32:34:36:38 SD: 5.0103 cents 20:21:22:24:25:27:28:30:32:34:36:38:40 SD: 4.9852 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.2909 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.7745 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.3559 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.8598 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.1253 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 2.0528 cents 48:51:54:57:60:64:68:72:76:81:86:90:96 SD: 1.8417 cents 50:53:56:59:63:67:71:75:79:84:89:94:100 SD: 1.4828 cents 65:69:73:77:82:87:92:97:103:109:116:122:130 SD: 1.2885 cents 68:72:76:81:85:91:96:102:108:114:121:128:136 SD: 1.1109 cents 74:78:83:88:93:99:105:111:117:124:132:139:148 SD: 1.0458 cents 75:79:84:89:94:100:106:112:119:126:134:141:150 SD: 1.0304 cents 86:91:96:102:108:115:122:129:136:144:153:162:172 SD: 0.9688 cents 90:95:101:107:113:120:127:135:142:151:160:170:180 SD: 0.9057 cents 101:107:113:120:127:135:143:151:160:169:180:190:202 SD: 0.7027 cents 118:125:132:140:148:158:167:177:187:198:210:222:236 SD: 0.7002 cents 122:129:137:145:153:163:172:183:193:205:217:230:244 SD: 0.6615 cents 133:141:149:158:167:178:188:199:211:223:237:251:266 SD: 0.6095 cents 140:148:157:166:176:187:198:210:222:235:249:264:280 SD: 0.5499 cents 155:164:174:184:195:207:219:232:245:260:276:292:310 SD: 0.4438 cents 175:185:196:208:220:234:247:262:277:294:312:330:350 SD: 0.4089 cents 191:202:214:227:240:255:270:286:302:320:340:360:382 SD: 0.3610 cents 208:220:233:247:261:278:294:311:329:349:370:392:416 SD: 0.3503 cents 223:236:250:265:280:298:315:334:353:374:397:420:446 SD: 0.2036 cents 298:315:334:354:374:398:421:446:472:500:531:561:596 SD: 0.1895 cents 348:368:390:413:437:465:492:521:551:584:620:656:696 SD: 0.1725 cents 422:446:473:501:530:564:596:632:668:708:752:795:844 SD: 0.1605 cents 449:475:503:533:564:600:634:672:711:753:800:846:898 SD: 0.1565 cents 453:479:508:538:569:605:640:678:717:760:807:853:906 SD: 0.1441 cents 465:492:521:552:584:621:657:696:736:780:828:876:930 SD: 0.1252 cents 571:604:640:678:717:763:807:855:904:958:1017:1076:1142 SD: 0.0930 cents