Scala analysis: sf5
sf5
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: 696.774 cents 696.774194 5: 851.613 cents 851.612903 6: 1045.161 cents 1045.161290 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 154.8387 cents 154.8387 1: 154.8387 cents 154.8387 2: 193.5484 cents 193.5484 3: 154.8387 cents 154.8387 4: 193.5484 cents 193.5484 5: 154.8387 cents 154.8387 6: 193.5484 cents 193.5484 7: 154.8387 cents 154.8387
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 154.83871 cents 1: 3 193.54839 cents 2: 1 309.67742 cents 2: 6 348.38710 cents 3: 5 503.22581 cents 3: 2 541.93548 cents 4: 2 658.06452 cents 4: 5 696.77419 cents 5: 6 851.61290 cents 5: 1 890.32258 cents 6: 3 1006.45161 cents 6: 4 1045.16129 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 154.8 348.4 503.2 696.8 851.6 1045.2 1200.0 154.8 : 193.5 348.4 541.9 696.8 890.3 1045.2 1200.0 348.4 : 154.8 348.4 503.2 696.8 851.6 1006.5 1200.0 503.2 : 193.5 348.4 541.9 696.8 851.6 1045.2 1200.0 696.8 : 154.8 348.4 503.2 658.1 851.6 1006.5 1200.0 851.6 : 193.5 348.4 503.2 696.8 851.6 1045.2 1200.0 1045.2: 154.8 309.7 503.2 658.1 851.6 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 .. 348.3871 cents 38.70968 cents 116.12903 cents 3: 503.2258 .. 541.9355 cents 38.70968 cents 154.83871 cents 4: 658.0645 .. 696.7742 cents 38.70968 cents 116.12903 cents 5: 851.6129 .. 890.3226 cents 38.70968 cents 154.83871 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 : 171.98157 cents, oct.: 1203.87097 cents Scale is strictly proper Scale has Myhill's property chromas: 38.70968 cents and 116.12903 cents, ratio: 3.000000 generators: 2 of 348.38710 cents and 5 of 851.61290 cents Scale is maximally even in 31-tone equal temperament ET pair of linear temperament : 24&31 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 31-tone equal temperament with octave 1200.000 cents degrees: 4 9 13 18 22 27 31 generators: 9 and 22 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABA Step pattern size order : SLSLSLS Interval vector is [ 0 0 0 4 3 0 0 1 6 0 0 0 5 2 0 ] Scale is a Constant Structure, by a margin of 116.12903 cents Scale diversity : 1.178504 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.806452 Rothenberg efficiency : 0.761905 redundancy: 0.238095 Efficiency x scale size : 5.333333 Number of different interval sizes : 12 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 38.70968 cents Most common intervals : 348.38710 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 348.387 696.774 cents Most common triad is 0.0 348.387 851.613 cents, amount: 5 Number of recognisable fifths : 5, average 696.7742 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 7 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 11.0599 c. M:-16.5899 c. Lebeng 17: 2 3 2 3 2 3 2 SP M ME I SD: 9.1082 c. M:-13.6622 c. Neutral Dorian, Maqamic-7 24: 3 4 3 4 3 4 3 SP M ME I SD: 3.2258 c. M:-4.8387 c. Neutral Dorian, Misaelides 2nd Byzantine mode, Iced Fridgian, Maqam Sikah Baladi, Maqamic-7 31: 4 5 4 5 4 5 4 SP M ME I SD: 0.0000 c. M: 0.0000 c. Neutral Dorian, Maqamic-7
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: 2.5904 cents 3 x x 4 x 5 x 6 S SD: 11.0510 cents 4 x 5 x 6 x 7:8 S SD: 21.3488 cents 5 x 6:7 x 8:9:10 S SD: 19.5519 cents 6 x 7:8:9:10:11:12 S SD: 14.7088 cents 7:8 x 9:10:11:13:14 SD: 24.8545 cents 8:9:10:11:12:13:15:16 SD: 12.9104 cents 9:10:11:12:13:15:16:18 SD: 12.6867 cents 10:11:12:13:15:16:18:20 SD: 10.8824 cents 12:13:15:16:18:20:22:24 SD: 7.6220 cents 14:15:17:19:21:23:26:28 SD: 7.6185 cents 18:20:22:24:27:29:33:36 SD: 5.5426 cents 22:24:27:29:33:36:40:44 SD: 4.0659 cents 30:33:37:40:45:49:55:60 SD: 2.8406 cents 36:39:44:48:54:59:66:72 SD: 2.6733 cents 41:45:50:55:61:67:75:82 SD: 1.8840 cents 53:58:65:71:79:87:97:106 SD: 1.5014 cents 63:69:77:84:94:103:115:126 SD: 1.1260 cents 77:84:94:103:115:126:141:154 SD: 0.8809 cents 95:104:116:127:142:155:174:190 SD: 0.8432 cents 107:117:131:143:160:175:196:214 SD: 0.5087 cents 139:152:170:186:208:227:254:278 SD: 0.4624 cents 192:210:235:257:287:314:351:384 SD: 0.3490 cents 216:236:264:289:323:353:395:432 SD: 0.3380 cents 234:256:286:313:350:383:428:468 SD: 0.2721 cents 246:269:301:329:368:402:450:492 SD: 0.2529 cents 323:353:395:432:483:528:591:646 SD: 0.2259 cents 341:373:417:456:510:558:624:682 SD: 0.2080 cents 373:408:456:499:558:610:682:746 SD: 0.1665 cents 480:525:587:642:718:785:878:960 SD: 0.0836 cents