Scala analysis: 10_serpent1
Two pentatonic chains of 7:4's rooted a 5:4 apart, tuned in 31-tet.
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 154.839 cents 154.839000 2: 232.258 cents 232.258000 3: 387.097 cents 387.097000 4: 464.516 cents 464.516000 5: 619.355 cents 619.355000 6: 696.774 cents 696.774000 7: 851.613 cents 851.613000 8: 967.742 cents 967.742000 9: 1083.871 cents 1083.871000 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 116.1290 cents 116.1290 1: 154.8390 cents 154.8390 2: 77.4190 cents 77.4190 3: 154.8390 cents 154.8390 4: 77.4190 cents 77.4190 5: 154.8390 cents 154.8390 6: 77.4190 cents 77.4190 7: 154.8390 cents 154.8390 8: 116.1290 cents 116.1290 9: 116.1290 cents 116.1290 10: 116.1290 cents 116.1290
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 77.41900 cents 1: 3 116.12900 cents 1: 4 154.83900 cents 2: 8 232.25800 cents 2: 2 270.96800 cents 3: 2 309.67700 cents 3: 3 348.38700 cents 3: 5 387.09700 cents 4: 6 464.51600 cents 4: 4 503.22600 cents 5: 1 541.93500 cents 5: 4 580.64500 cents 5: 4 619.35500 cents 5: 1 658.06500 cents 6: 4 696.77400 cents 6: 6 735.48400 cents 7: 5 812.90300 cents 7: 3 851.61300 cents 7: 2 890.32300 cents 8: 2 929.03200 cents 8: 8 967.74200 cents 9: 4 1045.16100 cents 9: 3 1083.87100 cents 9: 3 1122.58100 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 2.66667 = 8/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 154.8 232.3 387.1 464.5 619.4 696.8 851.6 967.7 1083.9 1200.0 154.8 : 77.4 232.3 309.7 464.5 541.9 696.8 812.9 929.0 1045.2 1200.0 232.3 : 154.8 232.3 387.1 464.5 619.4 735.5 851.6 967.7 1122.6 1200.0 387.1 : 77.4 232.3 309.7 464.5 580.6 696.8 812.9 967.7 1045.2 1200.0 464.5 : 154.8 232.3 387.1 503.2 619.4 735.5 890.3 967.7 1122.6 1200.0 619.4 : 77.4 232.3 348.4 464.5 580.6 735.5 812.9 967.7 1045.2 1200.0 696.8 : 154.8 271.0 387.1 503.2 658.1 735.5 890.3 967.7 1122.6 1200.0 851.6 : 116.1 232.3 348.4 503.2 580.6 735.5 812.9 967.7 1045.2 1200.0 967.7 : 116.1 232.3 387.1 464.5 619.4 696.8 851.6 929.0 1083.9 1200.0 1083.9: 116.1 271.0 348.4 503.2 580.6 735.5 812.9 967.7 1083.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 77.4190 .. 154.8390 cents 77.42000 cents 77.41900 cents 2: 232.2580 .. 270.9680 cents 38.71000 cents 77.41900 cents 3: 309.6770 .. 387.0970 cents 77.42000 cents 38.70900 cents 4: 464.5160 .. 503.2260 cents 38.71000 cents 77.41900 cents 5: 541.9350 .. 658.0650 cents 116.13000 cents 38.70900 cents 6: 696.7740 .. 735.4840 cents 38.71000 cents 38.70900 cents 7: 812.9030 .. 890.3230 cents 77.42000 cents 77.41900 cents 8: 929.0320 .. 967.7420 cents 38.71000 cents 38.70900 cents 9: 1045.1610 .. 1122.5810 cents 77.42000 cents 77.41900 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 77.41900 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 154.83900 cents Average / Smallest step : 1.550007 Largest / Average step : 1.290325 Largest / Smallest step : 2.000013 Median interval of one step : 116.12900 cents, amount: 3 Most common interval of one step : 154.83900 cents, amount: 4 Least squares average step : 120.45245 cents, oct.: 1204.52455 cents Scale is strictly proper Scale is a mode of a 31-tone equal temperament with octave 2/1 degrees: 4 6 10 12 16 18 22 25 28 31 Least number of segments generator : 25 of 967.742 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 28 of 1083.871 cents and inv. generated superset size: 16 = 6 more = 160.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABACCC Step pattern size order : LSLSLSLMMM Interval vector is [ 0 3 3 4 0 8 2 2 3 5 0 6 4 1 4 ] Scale is a Constant Structure, by a margin of 38.70900 cents Scale diversity : 1.349256 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.516125 Rothenberg efficiency : 0.530317 redundancy: 0.469683 Efficiency x scale size : 5.303175 Number of different interval sizes : 24 = 2.66667 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 2.66667 = 8/3 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 38.70900 cents Most common intervals : 232.25800 cents & inv., amount: 8 Most common triad is 0.0 232.258 967.742 cents, amount: 6 Number of recognisable fifths : 4, average 696.7740 cents Best major thirds form a closed circle Formal octave complements present : 3 = 30.0000% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 8-9 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.3618 c. M: 34.8390 c. 15: 2 1 2 1 2 1 2 1 2 1 SP B ME SD: 19.0514 c. M:-36.1290 c. Archytas Clan-10 16: 2 1 2 1 2 1 2 2 1 2 P D3 SD: 17.8607 c. M: 33.8710 c. 20: 3 1 2 2 2 2 2 2 2 2 P T3 SD: 16.7059 c. M: 27.0970 c. 21: 3 1 3 1 3 1 3 2 2 2 P SD: 8.7435 c. M:-16.5896 c. 31: 4 2 4 2 4 2 4 3 3 3 SP SD: 0.0002 c. M: 0.0003 c. Lumma Decatonic
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 2.5905 cents 3 x x x 4 x x 5 x x 6 S SD: 15.6222 cents 4 x x 5 x x 6 x 7 x 8 S SD: 1.3377 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 20.3835 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 11.3188 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 11.9478 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 9.3571 cents 9:10 x 11:12:13 x 15:16:17:18 SD: 9.6243 cents 10:11 x x 13:14:15:16:17:19:20 SD: 9.8344 cents 11:12:13:14 x 16 x 18:19:21:22 SD: 10.2911 cents 12:13:14:15:16:17:18:20:21:22:24 S SD: 7.1736 cents 13:14:15:16:17:19 x 21:23:24:26 SD: 7.4398 cents 14:15:16 x 18:20:21:23:24:26:28 SD: 6.6278 cents 16 x 18:20:21:23:24:26:28:30:32 SD: 3.6738 cents 17:19 x 21:22:24:25:28:30:32:34 SD: 7.0876 cents 19:21:22:24:25:27:28:31:33:36:38 SD: 5.1518 cents 20:22:23:25:26:29:30:33:35:37:40 SD: 3.8657 cents 28:31:32:35:37:40:42:46:49:52:56 SD: 3.1993 cents 32:35:37:40:42:46:48:52:56:60:64 SD: 2.5574 cents 40:44:46:50:52:57:60:65:70:75:80 SD: 2.2648 cents 44:48:50:55:58:63:66:72:77:82:88 SD: 1.9945 cents 49:54:56:61:64:70:73:80:86:92:98 SD: 1.9645 cents 52:57:59:65:68:74:78:85:91:97:104 SD: 1.8021 cents 55:60:63:69:72:79:82:90:96:103:110 SD: 1.2752 cents 63:69:72:79:82:90:94:103:110:118:126 SD: 1.1485 cents 75:82:86:94:98:107:112:123:131:140:150 SD: 1.0087 cents 84:92:96:105:110:120:126:137:147:157:168 SD: 0.8344 cents 107:117:122:134:140:153:160:175:187:200:214 SD: 0.5980 cents 139:152:159:174:182:199:208:227:243:260:278 SD: 0.4339 cents 160:175:183:200:209:229:239:262:280:299:320 SD: 0.4324 cents 172:188:197:215:225:246:257:281:301:322:344 SD: 0.4315 cents 195:213:223:244:255:279:292:319:341:365:390 SD: 0.3580 cents 224:245:256:280:293:320:335:366:392:419:448 SD: 0.3050 cents 244:267:279:305:319:349:365:399:427:456:488 SD: 0.2298 cents 279:305:319:349:365:399:417:456:488:522:558 SD: 0.1952 cents 299:327:342:374:391:428:447:489:523:559:598 SD: 0.1927 cents 363:397:415:454:475:519:543:594:635:679:726 SD: 0.1704 cents 426:466:487:533:557:609:637:697:745:797:852 SD: 0.1687 cents 439:480:502:549:574:628:657:718:768:821:878 SD: 0.1495 cents 523:572:598:654:684:748:782:855:915:978:1046 SD: 0.1076 cents 579:633:662:724:757:828:866:947:1013:1083:1158 SD: 0.1048 cents