Scala analysis: 5151
5151 temperament III (1197/709.5/696).
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 97.500 cents 97.500000 2: 195.000 cents 195.000000 3: 292.500 cents 292.500000 4: 390.000 cents 390.000000 5: 487.500 cents 487.500000 6: 598.500 cents 598.500000 7: 696.000 cents 696.000000 8: 793.500 cents 793.500000 9: 891.000 cents 891.000000 10: 988.500 cents 988.500000 11: 1086.000 cents 1086.000000 12: 1197.000 cents 1197.000000
SHOW/INTERVAL
0: 111.0000 cents 111.0000 1: 97.5000 cents 97.5000 2: 97.5000 cents 97.5000 3: 97.5000 cents 97.5000 4: 97.5000 cents 97.5000 5: 97.5000 cents 97.5000 6: 111.0000 cents 111.0000 7: 97.5000 cents 97.5000 8: 97.5000 cents 97.5000 9: 97.5000 cents 97.5000 10: 97.5000 cents 97.5000 11: 97.5000 cents 97.5000 12: 111.0000 cents 111.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 10 97.50000 cents 1: 2 111.00000 cents 2: 8 195.00000 cents 2: 4 208.50000 cents 3: 6 292.50000 cents 3: 6 306.00000 cents 4: 4 390.00000 cents 4: 8 403.50000 cents 5: 2 487.50000 cents 5: 10 501.00000 cents 6: 12 598.50000 cents 7: 10 696.00000 cents 7: 2 709.50000 cents 8: 8 793.50000 cents 8: 4 807.00000 cents 9: 6 891.00000 cents 9: 6 904.50000 cents 10: 4 988.50000 cents 10: 8 1002.00000 cents 11: 2 1086.00000 cents 11: 10 1099.50000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.90909 = 21/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 97.5 195.0 292.5 390.0 487.5 598.5 696.0 793.5 891.0 988.5 1086.0 1197.0 97.5 : 97.5 195.0 292.5 390.0 501.0 598.5 696.0 793.5 891.0 988.5 1099.5 1197.0 195.0 : 97.5 195.0 292.5 403.5 501.0 598.5 696.0 793.5 891.0 1002.0 1099.5 1197.0 292.5 : 97.5 195.0 306.0 403.5 501.0 598.5 696.0 793.5 904.5 1002.0 1099.5 1197.0 390.0 : 97.5 208.5 306.0 403.5 501.0 598.5 696.0 807.0 904.5 1002.0 1099.5 1197.0 487.5 : 111.0 208.5 306.0 403.5 501.0 598.5 709.5 807.0 904.5 1002.0 1099.5 1197.0 598.5 : 97.5 195.0 292.5 390.0 487.5 598.5 696.0 793.5 891.0 988.5 1086.0 1197.0 696.0 : 97.5 195.0 292.5 390.0 501.0 598.5 696.0 793.5 891.0 988.5 1099.5 1197.0 793.5 : 97.5 195.0 292.5 403.5 501.0 598.5 696.0 793.5 891.0 1002.0 1099.5 1197.0 891.0 : 97.5 195.0 306.0 403.5 501.0 598.5 696.0 793.5 904.5 1002.0 1099.5 1197.0 988.5 : 97.5 208.5 306.0 403.5 501.0 598.5 696.0 807.0 904.5 1002.0 1099.5 1197.0 1086.0: 111.0 208.5 306.0 403.5 501.0 598.5 709.5 807.0 904.5 1002.0 1099.5 1197.0 1197.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 97.5000 .. 111.0000 cents 13.50000 cents 97.50000 cents 2: 195.0000 .. 208.5000 cents 13.50000 cents 84.00000 cents 3: 292.5000 .. 306.0000 cents 13.50000 cents 84.00000 cents 4: 390.0000 .. 403.5000 cents 13.50000 cents 84.00000 cents 5: 487.5000 .. 501.0000 cents 13.50000 cents 84.00000 cents 6: 598.5000 .. 598.5000 cents 1/1, 0.0000 cents 97.50000 cents 7: 696.0000 .. 709.5000 cents 13.50000 cents 97.50000 cents 8: 793.5000 .. 807.0000 cents 13.50000 cents 84.00000 cents 9: 891.0000 .. 904.5000 cents 13.50000 cents 84.00000 cents 10: 988.5000 .. 1002.0000 cents 13.50000 cents 84.00000 cents 11: 1086.0000 .. 1099.5000 cents 13.50000 cents 84.00000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 97.50000 cents, class 1 Average step (divided formal octave): 99.7500 cents Largest one step interval : 111.00000 cents Average / Smallest step : 1.023077 Largest / Average step : 1.112782 Largest / Smallest step : 1.138462 Median interval of one step : 97.50000 cents, amount: 10 Most common interval of one step : 97.50000 cents, amount: 10 Least squares average step : 99.05769 cents, oct.: 1188.69231 cents Scale is strictly proper Scale has 2 repeating blocks of 6 notes Blocks have Myhill's property chromas: 13.50000 cents and 84.00000 cents, ratio: 6.222222 generators: 1 of 97.50000 cents and 501.00000 cents ET pair of linear temperament : 86&356 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 798-tone equal temperament with octave 1197.000 cents degrees: 65 130 195 260 325 399 464 529 594 659 724 798 Least number of segments generator : 401 of 601.500 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 733 of 1099.500 cents and inv. generated superset size: 405 = 393 more = 3375.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: AAAAABAAAAAB Step pattern size order : SSSSSLSSSSSL Scale is a Constant Structure, by a margin of 84.00000 cents Scale diversity : 1.088957 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.887218 Rothenberg efficiency (ambiguous key): 0.505556 redundancy: 0.494444 Efficiency x scale size : 6.066667 Number of different interval sizes : 21 = 1.90909 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.90909 = 21/11 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 13.50000 cents Most common intervals : 598.50000 cents & inv., amount: 12 Number of recognisable fifths : 12, average 698.2500 cents Number of recognisable fourths : 12, average 498.7500 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 2 = 16.6667% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 6 Limited inverse transpositions : 5 11 Inversional symmetry on intervals : 2-3 5-6 8-9 11-12 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 6.8122 c. M:-11.2500 c. Twelve-tone Chromatic (1/11-comma) 50: 4 4 4 4 4 5 4 4 4 4 4 5 SP B ME SD: 5.2681 c. M: 8.7000 c. Injera-12 62: 5 5 5 5 5 6 5 5 5 5 5 6 SP B ME SD: 2.9300 c. M: 4.8387 c. Injera-12 74: 6 6 6 6 6 7 6 6 6 6 6 7 SP B ME SD: 1.3502 c. M: 2.2297 c. Injera-12 86: 7 7 7 7 7 8 7 7 7 7 7 8 SP B ME SD: 0.2112 c. M: 0.3488 c. Injera-12 270: 22 22 22 22 22 25 22 22 22 22 22 25 SP B DE SD: 0.1009 c. M:-0.1667 c. 356: 29 29 29 29 29 33 29 29 29 29 29 33 SP B DE SD: 0.0255 c. M:-0.0421 c. 442: 36 36 36 36 36 41 36 36 36 36 36 41 SP B DE SD: 0.0205 c. M: 0.0339 c. 798: 65 65 65 65 65 74 65 65 65 65 65 74 SP B DE 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: 3.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 3.3340 cents 3 x x x x 4 x x x 5 x x 6 S SD: 4.2727 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 5.2745 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 9.0647 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 7.8154 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.8901 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.8100 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.6101 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.4138 cents 11 x 12:13:14:15 x 16:17:18:19:21:22 SD: 11.5770 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 5.9689 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 8.8735 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.0721 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.5076 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.1105 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 3.9946 cents 24:25:27:28:30:32:34:36:38:40:42:45:48 SD: 3.8061 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.5510 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.4635 cents 34:36:38:40:43:45:48:51:54:57:60:64:68 SD: 2.0986 cents 43:45:48:51:54:57:61:64:68:72:76:81:86 SD: 2.0892 cents 48:51:54:57:60:64:68:72:76:80:85:90:96 S SD: 1.6745 cents 53:56:59:63:66:70:75:79:84:89:94:99:106 SD: 1.6709 cents 55:58:62:65:69:73:78:82:87:92:97:103:110 SD: 1.4878 cents 65:69:73:77:81:86:92:97:103:109:115:122:130 SD: 1.2667 cents 67:71:75:79:84:89:95:100:106:112:119:125:134 SD: 1.2115 cents 70:74:78:83:88:93:99:105:111:117:124:131:140 SD: 1.1720 cents 82:87:92:97:103:109:116:123:130:137:145:154:164 SD: 1.1686 cents 83:88:93:98:104:110:117:124:131:139:147:155:166 SD: 0.8619 cents 107:113:120:127:134:142:151:160:169:179:189:200:214 SD: 0.7752 cents 119:126:133:141:149:158:168:178:188:199:211:223:238 SD: 0.5767 cents 135:143:151:160:169:179:191:202:213:226:239:253:270 SD: 0.5705 cents 157:166:176:186:197:208:222:235:248:263:278:294:313 SD: 0.5312 cents 158:167:177:187:198:209:223:236:250:264:280:296:315 SD: 0.5224 cents 169:179:189:200:212:224:239:253:267:283:299:316:337 SD: 0.5157 cents 170:180:190:201:213:225:240:254:269:284:301:318:339 SD: 0.5141 cents 174:184:195:206:218:231:246:260:275:291:308:326:347 SD: 0.4011 cents 206:218:231:244:258:273:291:308:326:345:365:386:411 SD: 0.3940 cents 210:222:235:249:263:278:297:314:332:351:372:393:419 SD: 0.3854 cents 218:231:244:258:273:289:308:326:345:365:386:408:435 SD: 0.3208 cents 244:258:273:289:306:323:345:365:386:408:432:457:487 SD: 0.3096 cents 261:276:292:309:327:346:369:390:413:437:462:489:521 SD: 0.2154 cents 344:364:385:407:431:456:486:514:544:576:609:644:687 SD: 0.1933 cents 446:472:499:528:559:591:630:667:705:746:789:835:890 SD: 0.1905 cents 452:478:506:535:566:599:639:676:715:756:800:846:902 SD: 0.1809 cents 479:507:536:567:600:635:677:716:758:801:848:897:956 SD: 0.1699 cents 487:515:545:577:610:645:688:728:770:815:862:912:972 SD: 0.1584 cents 495:524:554:586:620:656:699:740:783:828:876:927:988 SD: 0.1464 cents 535:566:599:633:670:709:756:800:846:895:947:1002:1068 SD: 0.1402 cents 538:569:602:637:674:713:760:804:851:900:952:1007:1074 SD: 0.1146 cents 554:586:620:656:694:734:783:828:876:927:981:1037:1106 SD: 0.1082 cents