Scala analysis: sf4
sf4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 154.839 cents 154.838710 2: 348.387 cents 348.387097 3: 503.226 cents 503.225806 4: 658.065 cents 658.064516 5: 812.903 cents 812.903226 6: 1006.452 cents 1006.451613 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 193.5484 cents 193.5484 1: 154.8387 cents 154.8387 2: 193.5484 cents 193.5484 3: 154.8387 cents 154.8387 4: 154.8387 cents 154.8387 5: 154.8387 cents 154.8387 6: 193.5484 cents 193.5484 7: 193.5484 cents 193.5484
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 154.83871 cents 1: 3 193.54839 cents 2: 2 309.67742 cents 2: 4 348.38710 cents 2: 1 387.09677 cents 3: 1 464.51613 cents 3: 3 503.22581 cents 3: 3 541.93548 cents 4: 3 658.06452 cents 4: 3 696.77419 cents 4: 1 735.48387 cents 5: 1 812.90323 cents 5: 4 851.61290 cents 5: 2 890.32258 cents 6: 3 1006.45161 cents 6: 4 1045.16129 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.66667 = 8/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 154.8 348.4 503.2 658.1 812.9 1006.5 1200.0 154.8 : 193.5 348.4 503.2 658.1 851.6 1045.2 1200.0 348.4 : 154.8 309.7 464.5 658.1 851.6 1006.5 1200.0 503.2 : 154.8 309.7 503.2 696.8 851.6 1045.2 1200.0 658.1 : 154.8 348.4 541.9 696.8 890.3 1045.2 1200.0 812.9 : 193.5 387.1 541.9 735.5 890.3 1045.2 1200.0 1006.5: 193.5 348.4 541.9 696.8 851.6 1006.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 154.8387 .. 193.5484 cents 38.70968 cents 154.83871 cents 2: 309.6774 .. 387.0968 cents 77.41935 cents 116.12903 cents 3: 464.5161 .. 541.9355 cents 77.41936 cents 77.41936 cents 4: 658.0645 .. 735.4839 cents 77.41935 cents 116.12903 cents 5: 812.9032 .. 890.3226 cents 77.41935 cents 77.41936 cents 6: 1006.4516 .. 1045.1613 cents 38.70968 cents 116.12903 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 154.83871 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 193.54839 cents Average / Smallest step : 1.107143 Largest / Average step : 1.129032 Largest / Smallest step : 1.250000 Median interval of one step : 154.83871 cents, amount: 4 Most common interval of one step : 154.83871 cents, amount: 4 Least squares average step : 167.83410 cents, oct.: 1174.83871 cents Scale is strictly proper Scale is 3-distributional even Scale is a mode of a 31-tone equal temperament with octave 1200.000 cents degrees: 4 9 13 17 21 26 31 Least number of segments generator : 18 of 696.774 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 22 of 851.613 cents and inv. generated superset size: 10 = 3 more = 142.857% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAABB Step pattern size order : SLSSSLL Interval vector is [ 0 0 0 4 3 0 0 2 4 1 0 1 3 3 0 ] Scale is a Constant Structure, by a margin of 77.41935 cents Scale diversity : 1.297166 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.677419 Rothenberg efficiency : 0.521088 redundancy: 0.478912 Efficiency x scale size : 3.647619 Number of different interval sizes : 16 = 2.66667 / class Number of one step interval sizes : 2 Highest interval variety : 3 Mean interval variety : 2.66667 = 8/3 Median interval variety : 2.5 Lowest interval variety : 2 Smallest interval difference : 38.70968 cents Number of recognisable fifths : 3, average 696.7742 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 22.8006 c. M:-44.2396 c. Lebeng 13: 2 2 1 2 2 2 2 SP M ME S SD: 22.6772 c. M: 41.6873 c. Oukranian 16: 2 3 2 2 2 2 3 P D3 S SD: 19.3764 c. M: 31.4516 c. 17: 2 3 2 2 2 3 3 P D3 SD: 18.7770 c. M: 36.4326 c. Safi al-Din's maqam Rahawi 18: 2 3 2 3 2 3 3 SP M ME S SD: 18.1572 c. M: 36.5591 c. 20: 3 3 3 2 3 3 3 SP M ME I SD: 20.8458 c. M:-36.7742 c. 21: 3 3 3 3 2 4 3 SP T3 SD: 16.2499 c. M:-27.6498 c. 22: 3 3 3 3 3 3 4 SP M ME S SD: 13.7424 c. M: 24.6334 c. 24: 3 4 3 3 3 4 4 SP D3 SD: 6.6502 c. M: 12.9032 c. 31: 4 5 4 4 4 5 5 SP D3 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: 21.9452 cents 3 x x 4 x 5 x 6 S SD: 23.8810 cents 4 x 5 x 6 x 7:8 S SD: 17.2853 cents 5 x 6 x 7:8:9:10 S SD: 16.6196 cents 6 x 7:8:9:10:11:12 S SD: 20.7802 cents 7:8 x 9:10:11:13:14 SD: 21.9211 cents 8:9:10:11:12:13:14:16 S SD: 14.4734 cents 9:10:11:12:13:14:16:18 S SD: 8.6399 cents 13:14:16:17:19:21:23:26 SD: 7.8045 cents 17:19:21:23:25:27:30:34 SD: 7.6959 cents 18:20:22:24:26:29:32:36 SD: 5.5657 cents 22:24:27:29:32:35:39:44 SD: 4.7015 cents 23:25:28:31:34:37:41:46 SD: 4.1319 cents 30:33:37:40:44:48:54:60 SD: 3.1803 cents 32:35:39:43:47:51:57:64 SD: 2.2305 cents 45:49:55:60:66:72:80:90 SD: 2.0973 cents 50:55:61:67:73:80:89:100 SD: 2.0632 cents 53:58:65:71:78:85:95:106 SD: 1.9823 cents 54:59:66:72:79:86:97:108 SD: 1.6935 cents 62:68:76:83:91:99:111:124 SD: 1.3959 cents 63:69:77:84:92:101:113:126 SD: 1.3114 cents 75:82:92:100:110:120:134:150 SD: 1.3058 cents 77:84:94:103:113:123:138:154 SD: 1.2808 cents 85:93:104:114:124:136:152:170 SD: 0.9626 cents 95:104:116:127:139:152:170:190 SD: 0.5173 cents 160:175:196:214:234:256:286:320 SD: 0.4587 cents 180:197:220:241:263:288:322:360 SD: 0.4584 cents 184:201:225:246:269:294:329:368 SD: 0.3681 cents 225:246:275:301:329:360:402:450 SD: 0.3224 cents 255:279:312:341:373:408:456:510 SD: 0.2179 cents 279:305:341:373:408:446:499:558 SD: 0.2116 cents 394:431:482:527:576:630:705:788 SD: 0.2021 cents 417:456:510:558:610:667:746:834 SD: 0.1820 cents 439:480:537:587:642:702:785:878 SD: 0.0976 cents 534:584:653:714:781:854:955:1068 SD: 0.0544 cents