Scala analysis: cauldron
Circulating temperament with two pure 9/7 thirds
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 86.506 cents 86.506118 2: 189.205 cents 189.204894 3: 308.096 cents 308.096331 4: 378.410 cents 378.409788 5: 505.398 cents 505.397553 6: 575.711 cents 575.711012 7: 694.602 cents 694.602447 8: 797.301 cents 797.301225 9: 883.807 cents 883.807341 10: 1010.795 cents 1010.795107 11: 1073.012 cents 1073.012235 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 126.9878 cents 126.9878 1: 86.5061 cents 86.5061 2: 102.6988 cents 102.6988 3: 118.8914 cents 118.8914 4: 70.3135 cents 70.3135 5: 126.9878 cents 126.9878 6: 70.3135 cents 70.3135 7: 118.8914 cents 118.8914 8: 102.6988 cents 102.6988 9: 86.5061 cents 86.5061 10: 126.9878 cents 126.9878 11: 62.2171 cents 62.2171 12: 126.9878 cents 126.9878
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 62.21713 cents 1: 2 70.31346 cents 1: 2 86.50612 cents 1: 2 102.69878 cents 1: 2 118.89144 cents 1: 3 126.98776 cents 2: 6 189.20489 cents 2: 2 197.30122 cents 2: 2 213.49388 cents 2: 2 221.59021 cents 3: 1 267.61468 cents 3: 2 275.71101 cents 3: 2 291.90367 cents 3: 2 308.09633 cents 3: 5 316.19266 cents 4: 4 378.40979 cents 4: 2 386.50612 cents 4: 2 402.69877 cents 4: 2 418.89144 cents 4: 2 435.08409 cents 5: 3 489.20489 cents 5: 2 497.30122 cents 5: 7 505.39755 cents 6: 2 567.61468 cents 6: 2 575.71101 cents 6: 2 591.90367 cents 6: 2 608.09633 cents 6: 2 624.28899 cents 6: 2 632.38532 cents 7: 7 694.60245 cents 7: 2 702.69878 cents 7: 3 710.79511 cents 8: 2 764.91590 cents 8: 2 781.10857 cents 8: 2 797.30123 cents 8: 2 813.49388 cents 8: 4 821.59021 cents 9: 5 883.80734 cents 9: 2 891.90367 cents 9: 2 908.09633 cents 9: 2 924.28899 cents 9: 1 932.38532 cents 10: 2 978.40979 cents 10: 2 986.50612 cents 10: 2 1002.69878 cents 10: 6 1010.79511 cents 11: 3 1073.01223 cents 11: 2 1081.10856 cents 11: 2 1097.30122 cents 11: 2 1113.49388 cents 11: 2 1129.68654 cents 11: 1 1137.78287 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.72727 = 52/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 86.5 189.2 308.1 378.4 505.4 575.7 694.6 797.3 883.8 1010.8 1073.0 1200.0 86.5 : 102.7 221.6 291.9 418.9 489.2 608.1 710.8 797.3 924.3 986.5 1113.5 1200.0 189.2 : 118.9 189.2 316.2 386.5 505.4 608.1 694.6 821.6 883.8 1010.8 1097.3 1200.0 308.1 : 70.3 197.3 267.6 386.5 489.2 575.7 702.7 764.9 891.9 978.4 1081.1 1200.0 378.4 : 127.0 197.3 316.2 418.9 505.4 632.4 694.6 821.6 908.1 1010.8 1129.7 1200.0 505.4 : 70.3 189.2 291.9 378.4 505.4 567.6 694.6 781.1 883.8 1002.7 1073.0 1200.0 575.7 : 118.9 221.6 308.1 435.1 497.3 624.3 710.8 813.5 932.4 1002.7 1129.7 1200.0 694.6 : 102.7 189.2 316.2 378.4 505.4 591.9 694.6 813.5 883.8 1010.8 1081.1 1200.0 797.3 : 86.5 213.5 275.7 402.7 489.2 591.9 710.8 781.1 908.1 978.4 1097.3 1200.0 883.8 : 127.0 189.2 316.2 402.7 505.4 624.3 694.6 821.6 891.9 1010.8 1113.5 1200.0 1010.8: 62.2 189.2 275.7 378.4 497.3 567.6 694.6 764.9 883.8 986.5 1073.0 1200.0 1073.0: 127.0 213.5 316.2 435.1 505.4 632.4 702.7 821.6 924.3 1010.8 1137.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.2171 .. 126.9878 cents 64.77064 cents 62.21713 cents 2: 189.2049 .. 221.5902 cents 32.38532 cents 62.21713 cents 3: 267.6147 .. 316.1927 cents 48.57798 cents 46.02447 cents 4: 378.4098 .. 435.0841 cents 56.67431 cents 62.21713 cents 5: 489.2049 .. 505.3976 cents 16.19266 cents 54.12080 cents 6: 567.6147 .. 632.3853 cents 64.77064 cents 62.21713 cents 7: 694.6024 .. 710.7951 cents 16.19266 cents 62.21713 cents 8: 764.9159 .. 821.5902 cents 56.67431 cents 54.12080 cents 9: 883.8073 .. 932.3853 cents 48.57798 cents 62.21713 cents 10: 978.4098 .. 1010.7951 cents 32.38532 cents 46.02447 cents 11: 1073.0122 .. 1137.7829 cents 64.77064 cents 62.21713 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 62.21713 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 126.98776 cents Average / Smallest step : 1.607274 Largest / Average step : 1.269878 Largest / Smallest step : 2.041042 Median interval of one step : 102.69878 cents, amount: 2 Most common interval of one step : 126.98776 cents, amount: 3 Least squares average step : 99.06166 cents, oct.: 1188.73987 cents Scale is strictly proper Step pattern alph. order: ABCDEDCBAEFE Step pattern size order : CDEBFBEDCFAF Scale is a Constant Structure, by a margin of 46.02447 cents Scale diversity : 1.369753 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.581690 Rothenberg efficiency : 0.281602 redundancy: 0.718398 Efficiency x scale size : 3.379221 Number of different interval sizes : 52 = 4.72727 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 4.72727 = 52/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 8.09633 cents Most common intervals : 505.39755 cents & inv., amount: 7 Most common triad is 0.0 505.398 694.602 cents, amount: 6 Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 5 = 41.6667% Limited transpositions with margin 64.7706 cents: 5 7 Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 10-11 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 14.6995 c. M:-26.9878 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 2 1 2 1 2 P M ME SD: 10.0941 c. M:-23.7514 c. 23: 2 2 2 1 3 1 2 2 2 2 2 2 P D3 SD: 14.5840 c. M:-22.6399 c. 26: 2 2 3 1 3 1 3 2 2 3 1 3 P D3 SD: 10.0542 c. M: 21.8649 c. 27: 2 2 3 2 2 2 3 2 2 3 1 3 SP D3 SD: 10.6645 c. M:-21.5902 c. 28: 2 2 3 2 3 1 3 3 2 3 1 3 P SD: 12.2729 c. M: 18.5682 c. 29: 2 2 3 2 3 2 3 2 2 3 2 3 SP M ME SD: 12.1967 c. M: 23.6877 c. 30: 2 3 3 1 4 1 3 3 2 3 2 3 P SD: 11.1801 c. M: 18.4098 c. 31: 2 3 3 2 3 2 3 3 2 3 2 3 SP M ME SD: 7.2791 c. M:-15.6020 c. 38: 3 3 4 2 4 2 4 3 3 4 2 4 SP D3 SD: 4.4947 c. M:-8.2307 c. 50: 4 4 5 3 5 3 5 4 4 5 3 5 SP D3 SD: 4.5712 c. M:-9.4939 c. 57: 4 5 6 3 6 3 6 5 4 6 3 6 SP SD: 3.2399 c. M:-7.6931 c. 69: 5 6 7 4 7 4 7 6 5 7 4 7 SP SD: 2.9056 c. M:-5.2486 c. 83: 6 7 8 5 9 5 8 7 6 9 4 9 SP SD: 2.1402 c. M: 4.4819 c. 102: 7 9 10 6 11 6 10 9 7 11 5 11 SP SD: 1.9173 c. M: 4.1532 c. 110: 8 9 11 7 11 7 11 9 8 12 5 12 SP SD: 2.8185 c. M: 3.9213 c. 113: 8 10 11 7 12 6 11 10 8 12 6 12 SP SD: 2.4913 c. M: 4.3370 c. 114: 8 10 11 7 12 7 11 10 8 12 6 12 SP SD: 1.6365 c. M:-3.2364 c. 121: 9 10 12 7 13 7 12 10 9 13 6 13 SP SD: 1.6476 c. M: 3.9128 c. 133: 10 11 13 8 14 8 13 11 10 14 7 14 SP SD: 1.5991 c. M:-3.7194 c. 140: 10 12 14 8 15 8 14 12 10 15 7 15 SP SD: 0.8626 c. M: 1.5837 c. 152: 11 13 15 9 16 9 15 13 11 16 8 16 SP SD: 0.3660 c. M:-0.6720 c. 292: 21 25 29 17 31 17 29 25 21 31 15 31 SP SD: 0.2230 c. M: 0.4095 c. 444: 32 38 44 26 47 26 44 38 32 47 23 47 SP SD: 0.0214 c. M: 0.0393 c. 1484: 107 127 147 87 157 87 147 127 107 157 77 157 SP SD: 0.0183 c. M:-0.0336 c. 1928: 139 165 191 113 204 113 191 165 139 204 100 204 SP SD: 0.0092 c. M:-0.0168 c. 2372: 171 203 235 139 251 139 235 203 171 251 123 251 SP SD: 0.0034 c. M:-0.0063 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: 3.6763 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.4577 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 10.8338 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 4.0886 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.1091 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 13.8301 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.6517 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 8.9407 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.9681 cents 11 x 12:13:14:15 x 16:17:18:20 x 22 S SD: 11.0798 cents 12 x 13:14:15:16:17:18:19:20 x 22:24 S SD: 7.5770 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 9.6452 cents 14:15:16:17 x 19:20:21:22:23:25:26:28 SD: 7.5170 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.1822 cents 18:19:20 x 22:24:25:27:29:30:32:33:36 SD: 4.8064 cents 20:21:22:24:25:27:28:30:32:33:36:37:40 SD: 3.4077 cents 32:34:36:38:40:43:45:48:51:53:57:59:64 SD: 3.2825 cents 33:35:37:39:41:44:46:49:52:55:59:61:66 SD: 2.7013 cents 35:37:39:42:44:47:49:52:55:58:63:65:70 SD: 2.6102 cents 36:38:40:43:45:48:50:54:57:60:65:67:72 SD: 1.8118 cents 41:43:46:49:51:55:57:61:65:68:74:76:82 SD: 1.7015 cents 53:56:59:63:66:71:74:79:84:88:95:99:106 SD: 1.4448 cents 61:64:68:73:76:82:85:91:97:102:109:113:122 SD: 1.2240 cents 77:81:86:92:96:103:107:115:122:128:138:143:154 SD: 0.7264 cents 114:120:127:136:142:153:159:170:181:190:204:212:228 SD: 0.6783 cents 132:139:147:158:164:177:184:197:209:220:237:245:264 SD: 0.6290 cents 135:142:151:161:168:181:188:202:214:225:242:251:270 SD: 0.6142 cents 139:146:155:166:173:186:194:208:220:232:249:258:278 SD: 0.5224 cents 154:162:172:184:192:206:215:230:244:257:276:286:308 SD: 0.4928 cents 156:164:174:186:194:209:218:233:247:260:280:290:312 SD: 0.4925 cents 174:183:194:208:217:233:243:260:276:290:312:323:348 SD: 0.4642 cents 180:189:201:215:224:241:251:269:285:300:323:335:360 SD: 0.3710 cents 200:210:223:239:249:268:279:299:317:333:359:372:400 SD: 0.3477 cents 233:245:260:278:290:312:325:348:369:388:418:433:466 SD: 0.2692 cents 251:264:280:300:312:336:350:375:398:418:450:466:502 SD: 0.2577 cents 294:309:328:351:366:394:410:439:466:490:527:546:588 SD: 0.2234 cents 348:366:388:416:433:466:485:520:552:580:624:647:696 SD: 0.2105 cents 390:410:435:466:485:522:544:583:618:650:699:725:780 SD: 0.1811 cents 405:426:452:484:504:542:565:605:642:675:726:753:810 SD: 0.1738 cents 425:447:474:508:529:569:593:635:674:708:762:790:850 SD: 0.1713 cents 431:453:481:515:536:577:601:644:683:718:773:801:862 SD: 0.1363 cents 528:555:589:631:657:707:736:789:837:880:947:981:1056 SD: 0.1292 cents 545:573:608:651:678:730:760:814:864:908:977:1013:1090 SD: 0.0840 cents