Scala analysis: Ethiopia_AI_581_12_1939
AI 581/12 - 1939, Ethiopia
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 308.000 cents 308.000000 2: 482.000 cents 482.000000 3: 657.000 cents 657.000000 4: 999.000 cents 999.000000 5: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 201.0000 cents 201.0000 1: 308.0000 cents 308.0000 2: 174.0000 cents 174.0000 3: 175.0000 cents 175.0000 4: 342.0000 cents 342.0000 5: 201.0000 cents 201.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 174.00000 cents 1: 1 175.00000 cents 1: 1 201.00000 cents 1: 1 308.00000 cents 1: 1 342.00000 cents 2: 1 349.00000 cents 2: 1 482.00000 cents 2: 1 509.00000 cents 2: 1 517.00000 cents 2: 1 543.00000 cents 3: 1 657.00000 cents 3: 1 683.00000 cents 3: 1 691.00000 cents 3: 1 718.00000 cents 3: 1 851.00000 cents 4: 1 858.00000 cents 4: 1 892.00000 cents 4: 1 999.00000 cents 4: 1 1025.00000 cents 4: 1 1026.00000 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 308.0 482.0 657.0 999.0 1200.0 308.0 : 174.0 349.0 691.0 892.0 1200.0 482.0 : 175.0 517.0 718.0 1026.0 1200.0 657.0 : 342.0 543.0 851.0 1025.0 1200.0 999.0 : 201.0 509.0 683.0 858.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 174.0000 .. 342.0000 cents 168.00000 cents 174.00000 cents 2: 349.0000 .. 543.0000 cents 194.00000 cents 7.00000 cents 3: 657.0000 .. 851.0000 cents 194.00000 cents 114.00000 cents 4: 858.0000 .. 1026.0000 cents 168.00000 cents 7.00000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 174.00000 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 342.00000 cents Average / Smallest step : 1.379310 Largest / Average step : 1.425000 Largest / Smallest step : 1.965517 Median interval of one step : 201.00000 cents, amount: 1 Least squares average step : 240.70909 cents, oct.: 1203.54545 cents Scale is strictly proper Scale is a mode of a 1200-tone equal temperament with octave 1200.000 cents degrees: 308 482 657 999 1200 Least number of segments generator : 601 of 601.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1019 of 1019.000 cents and inv. generated superset size: 144 = 139 more = 2880.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDE Step pattern size order : DABEC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 7.00000 cents Scale diversity : 1.454757 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.396667 Rothenberg efficiency : 0.400000 redundancy: 0.600000 Efficiency x scale size : 2.000000 Number of different interval sizes : 20 = 5.00000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 5.00000 = 5 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 1.00000 cents Number of recognisable fifths : 2, average 704.5000 cents Number of appreciable fifths : 1, average 691.0000 cents Best fifths form a closed circle Formal octave complements present : 1 = 20.0000% Limited inverse transpositions with margin 194.0000 cents: 4 -- Rational properties --
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 44.9844 c. M: 68.0000 c. 7: 2 1 1 2 1 P M ME S SD: 28.1296 c. M:-34.8571 c. Thai mode 6 11: 3 1 2 3 2 P T3 SD: 23.4749 c. M: 45.6364 c. 12: 3 2 2 3 2 SP M ME S SD: 21.1566 c. M:-43.0000 c. Minor Pentatonic, Blues Pentatonic, Raga Dhani (Suddha Dhanyasi), Abheri, Udhayaravi Chandrika, Qing Shang, Gu Xian, Jia Zhong, Yu: China, P'yongjo-kyemyonjo: Korea, Minyo: Japan, Lai Yai, Lai Noi: Laos, Nam, Northern Sa mac: Vietnam, Peruvian Pentatonic 2, Batti Minor: Ethiopia 13: 3 2 2 4 2 P T3 SD: 18.8178 c. M: 31.0769 c. 17: 4 3 2 5 3 P SD: 16.6831 c. M: 25.6471 c. 18: 5 2 3 5 3 P T3 SD: 13.9380 c. M:-25.3333 c. 20: 5 3 3 6 3 P T3 SD: 10.1784 c. M:-21.0000 c. 22: 6 3 3 6 4 P T3 S SD: 12.2642 c. M:-19.2727 c. 23: 6 3 4 6 4 SP T3 SD: 11.7585 c. M:-21.2609 c. 24: 6 4 3 7 4 P SD: 9.3595 c. M:-18.0000 c. 28: 7 4 4 8 5 P SD: 10.5099 c. M: 14.1429 c. 30: 8 4 4 9 5 N SD: 9.3595 c. M: 17.0000 c. 31: 8 4 5 9 5 P SD: 8.5459 c. M: 17.4839 c. 35: 9 5 5 10 6 P SD: 3.3939 c. M: 5.5714 c. 42: 11 6 6 12 7 P SD: 3.2963 c. M:-6.2857 c. 55: 14 8 8 16 9 P SD: 2.7568 c. M:-4.6364 c. 77: 20 11 11 22 13 P SD: 2.1646 c. M:-3.6883 c. 82: 21 12 12 23 14 SP SD: 1.9352 c. M: 3.8780 c. 89: 23 13 13 25 15 SP SD: 2.4912 c. M:-3.6742 c. 90: 23 13 13 26 15 P SD: 2.0111 c. M: 3.6667 c. 97: 25 14 14 28 16 P SD: 1.6126 c. M:-3.0619 c. 102: 26 15 15 29 17 SP SD: 1.3367 c. M: 2.1176 c. 132: 34 19 19 38 22 P SD: 1.2844 c. M: 2.4545 c. 137: 35 20 20 39 23 SP SD: 0.6818 c. M: 1.4307 c. 144: 37 21 21 41 24 SP SD: 0.9661 c. M:-1.3333 c. 172: 44 25 25 49 29 SP SD: 0.9567 c. M: 1.3256 c. 179: 46 26 26 51 30 SP SD: 0.3530 c. M:-0.6816 c. 281: 72 41 41 80 47 SP SD: 0.4692 c. M:-0.6512 c. 316: 81 46 46 90 53 SP SD: 0.2505 c. M: 0.4051 c. 495: 127 72 72 141 83 SP SD: 0.2194 c. M:-0.4242 c. 550: 141 80 80 157 92 SP SD: 0.2506 c. M: 0.3636 c. 650: 167 94 95 185 109 SP SD: 0.2121 c. M:-0.3077 c. 705: 181 102 103 201 118 SP SD: 0.1540 c. M: 0.2979 c. 787: 202 114 115 224 132 SP SD: 0.1639 c. M: 0.2706 c. 807: 207 117 118 230 135 SP SD: 0.2058 c. M:-0.2565 c. 829: 213 120 121 236 139 SP SD: 0.1893 c. M:-0.3233 c. 842: 216 122 123 240 141 SP SD: 0.1501 c. M: 0.2898 c. 849: 218 123 124 242 142 SP SD: 0.1801 c. M:-0.2933 c. 877: 225 127 128 250 147 SP SD: 0.2058 c. M: 0.3580 c. 884: 227 128 129 252 148 SP SD: 0.0895 c. M:-0.1448 c. 1021: 262 148 149 291 171 SP SD: 0.0619 c. M: 0.1195 c. 1200: 308 174 175 342 201 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x 2 S SD: 0.0000 cents 2 x x 3 x 4 S SD: 22.4775 cents 3 x 4 x 5:6 S SD: 38.5862 cents 4:5 x 6:7:8 S SD: 23.8019 cents 5:6 x 7:9:10 SD: 19.2883 cents 6:7:8:9:11:12 SD: 16.1325 cents 9:11:12:13:16:18 SD: 9.4538 cents 15:18:20:22:27:30 SD: 5.2849 cents 22:26:29:32:39:44 SD: 4.4616 cents 26:31:34:38:46:52 SD: 4.2314 cents 31:37:41:45:55:62 SD: 2.7386 cents 37:44:49:54:66:74 SD: 1.9769 cents 41:49:54:60:73:82 SD: 1.1367 cents 72:86:95:105:128:144 SD: 1.0492 cents 78:93:103:114:139:156 SD: 0.7540 cents 87:104:115:127:155:174 SD: 0.5377 cents 128:153:169:187:228:256 SD: 0.3091 cents 206:246:272:301:367:412 SD: 0.2911 cents 277:331:366:405:493:554 SD: 0.2502 cents 314:375:415:459:559:628 SD: 0.2377 cents 355:424:469:519:632:710 SD: 0.1725 cents 405:484:535:592:721:810 SD: 0.1493 cents 442:528:584:646:787:884 SD: 0.0863 cents 483:577:638:706:860:966 SD: 0.0711 cents 570:681:753:833:1015:1140 SD: 0.0381 cents