Scala analysis: pelog_pb
"Primitive" Pelog, step of blown semi-fourths, von Hornbostel, type b.
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 105.000 cents 105.000000 2: 261.000 cents 261.000000 3: 522.000 cents 522.000000 4: 678.000 cents 678.000000 5: 783.000 cents 783.000000 6: 939.000 cents 939.000000 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 261.0000 cents 261.0000 1: 105.0000 cents 105.0000 2: 156.0000 cents 156.0000 3: 261.0000 cents 261.0000 4: 156.0000 cents 156.0000 5: 105.0000 cents 105.0000 6: 156.0000 cents 156.0000 7: 261.0000 cents 261.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 105.00000 cents 1: 3 156.00000 cents 1: 2 261.00000 cents 2: 3 261.00000 cents 2: 1 366.00000 cents 2: 3 417.00000 cents 3: 1 417.00000 cents 3: 5 522.00000 cents 3: 1 573.00000 cents 4: 1 627.00000 cents 4: 5 678.00000 cents 4: 1 783.00000 cents 5: 3 783.00000 cents 5: 1 834.00000 cents 5: 3 939.00000 cents 6: 2 939.00000 cents 6: 3 1044.00000 cents 6: 2 1095.00000 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 105.0 261.0 522.0 678.0 783.0 939.0 1200.0 105.0 : 156.0 417.0 573.0 678.0 834.0 1095.0 1200.0 261.0 : 261.0 417.0 522.0 678.0 939.0 1044.0 1200.0 522.0 : 156.0 261.0 417.0 678.0 783.0 939.0 1200.0 678.0 : 105.0 261.0 522.0 627.0 783.0 1044.0 1200.0 783.0 : 156.0 417.0 522.0 678.0 939.0 1095.0 1200.0 939.0 : 261.0 366.0 522.0 783.0 939.0 1044.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 105.0000 .. 261.0000 cents 156.00000 cents 105.00000 cents 2: 261.0000 .. 417.0000 cents 156.00000 cents 1/1, 0.0000 cents 3: 417.0000 .. 573.0000 cents 156.00000 cents 1/1, 0.0000 cents 4: 627.0000 .. 783.0000 cents 156.00000 cents 54.00000 cents 5: 783.0000 .. 939.0000 cents 156.00000 cents 1/1, 0.0000 cents 6: 939.0000 .. 1095.0000 cents 156.00000 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 105.00000 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 261.00000 cents Average / Smallest step : 1.632653 Largest / Average step : 1.522500 Largest / Smallest step : 2.485714 Median interval of one step : 156.00000 cents, amount: 3 Most common interval of one step : 156.00000 cents, amount: 3 Least squares average step : 163.24286 cents, oct.: 1142.70000 cents Scale is proper Scale has trivalence property Scale is a mode of a 400-tone equal temperament with octave 2/1 degrees: 35 87 174 226 261 313 400 Least number of segments generator : 201 of 603.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 313 of 939.000 cents and inv. generated superset size: 8 = 1 more = 114.286% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCBABC Step pattern size order : SMLMSML Scale is not a Constant Structure Scale diversity : 1.337251 Rothenberg stability : 0.571429 = 4/7 Lumma stability : 0.220000 Rothenberg efficiency : 0.609524 redundancy: 0.390476 Efficiency x scale size : 4.266667 Number of different interval sizes : 14 = 2.33333 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 51.00000 cents Scale is a chain of 3 triads 0.0 417.000 678.000 cents Most common triad is 0.0 261.000 522.000 cents, amount: 4 Number of recognisable fifths : 0 Scale contains two identical disjunct tetrachords Best fifths form a closed circle Formal octave complements present : 5 = 71.4286% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
7: 0 1 2 0 1 1 2 N T3 SD: 94.1693 c. M: 163.7143 c. 8: 0 1 2 1 1 1 2 N D3 SD: 72.9227 c. M: 111.0000 c. 9: 1 1 2 1 1 1 2 P M ME S SD: 14.2071 c. M:-28.3333 c. Pseudo Pelog, Pelogic-7, Antiionian 14: 1 2 3 2 1 2 3 P T3 SD: 9.6704 c. M: 19.2857 c. Superpelog-Pelog 23: 2 3 5 3 2 3 5 P T3 SD: 0.3270 c. M: 0.6522 c. Superpelog-Pelog 216: 19 28 47 28 19 28 47 P T3 SD: 0.2786 c. M:-0.5556 c. 239: 21 31 52 31 21 31 52 P T3 SD: 0.2203 c. M:-0.4393 c. 262: 23 34 57 34 23 34 57 P T3 SD: 0.1722 c. M:-0.3435 c. 285: 25 37 62 37 25 37 62 P T3 SD: 0.1320 c. M:-0.2632 c. 308: 27 40 67 40 27 40 67 P T3 SD: 0.0977 c. M:-0.1948 c. 331: 29 43 72 43 29 43 72 P T3 SD: 0.0682 c. M:-0.1360 c. 354: 31 46 77 46 31 46 77 P T3 SD: 0.0425 c. M:-0.0847 c. 377: 33 49 82 49 33 49 82 P T3 SD: 0.0200 c. M:-0.0398 c. 400: 35 52 87 52 35 52 87 P T3 SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 11.9775 cents 3 x x 4 x x 5:6 S SD: 19.8872 cents 4 x 5 x 6 x 7:8 S SD: 32.7557 cents 5 x 6:7 x 8:9:10 S SD: 23.4661 cents 6 x 7:8:9 x 10:12 S SD: 12.9117 cents 7 x 8:9:10:11:12:14 S SD: 18.3639 cents 8 x 9:11:12:13:14:16 SD: 15.7159 cents 9:10 x 12:13:14:15:18 S SD: 17.9431 cents 10:11:12:14:15:16:17:20 SD: 15.7648 cents 11:12:13:15:16:17:19:22 SD: 9.9750 cents 12:13:14:16:18:19:21:24 SD: 8.2766 cents 14:15:16:19:21:22:24:28 SD: 5.9786 cents 17:18:20:23:25:27:29:34 SD: 4.7097 cents 29:31:34:39:43:46:50:58 SD: 3.7175 cents 31:33:36:42:46:49:53:62 SD: 2.3028 cents 48:51:56:65:71:75:83:96 SD: 2.1812 cents 49:52:57:66:72:77:84:98 SD: 2.1115 cents 54:57:63:73:80:85:93:108 SD: 1.9201 cents 60:64:70:81:89:94:103:120 SD: 1.7628 cents 61:65:71:82:90:96:105:122 SD: 1.7601 cents 63:67:73:85:93:99:108:126 SD: 1.4185 cents 68:72:79:92:101:107:117:136 SD: 1.3656 cents 79:84:92:107:117:124:136:158 SD: 0.7994 cents 110:117:128:149:163:173:189:220 SD: 0.7718 cents 128:136:149:173:189:201:220:256 SD: 0.6397 cents 142:151:165:192:210:223:244:284 SD: 0.4400 cents 190:202:221:257:281:299:327:380 SD: 0.3888 cents 196:208:228:265:290:308:337:392 SD: 0.3513 cents 271:288:315:366:401:426:466:542 SD: 0.2809 cents 290:308:337:392:429:456:499:580 SD: 0.2133 cents 350:372:407:473:518:550:602:700 SD: 0.1748 cents 369:392:429:499:546:580:635:738 SD: 0.1489 cents 497:528:578:672:735:781:855:994 SD: 0.1390 cents 511:543:594:691:756:803:879:1022 SD: 0.1166 cents 528:561:614:714:781:830:908:1056 SD: 0.1031 cents