Scala analysis: Indonesia_Udanarum
Udanarum (Saron Demung or Gender Barung), Indonesia
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 140.000 cents 140.000000 2: 264.000 cents 264.000000 3: 513.000 cents 513.000000 4: 678.000 cents 678.000000 5: 787.000 cents 787.000000 6: 967.000 cents 967.000000 7: 1218.000 cents 1218.000000
SHOW/INTERVAL
0: 251.0000 cents 251.0000 1: 140.0000 cents 140.0000 2: 124.0000 cents 124.0000 3: 249.0000 cents 249.0000 4: 165.0000 cents 165.0000 5: 109.0000 cents 109.0000 6: 180.0000 cents 180.0000 7: 251.0000 cents 251.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 109.00000 cents 1: 1 124.00000 cents 1: 1 140.00000 cents 1: 1 165.00000 cents 1: 1 180.00000 cents 1: 1 249.00000 cents 1: 1 251.00000 cents 2: 1 264.00000 cents 2: 1 274.00000 cents 2: 1 289.00000 cents 2: 1 373.00000 cents 2: 1 391.00000 cents 2: 1 414.00000 cents 2: 1 431.00000 cents 3: 1 454.00000 cents 3: 1 513.00000 cents 3: 1 515.00000 cents 3: 1 523.00000 cents 3: 1 538.00000 cents 3: 1 540.00000 cents 3: 1 571.00000 cents 4: 1 647.00000 cents 4: 1 678.00000 cents 4: 1 680.00000 cents 4: 1 695.00000 cents 4: 1 703.00000 cents 4: 1 705.00000 cents 4: 1 764.00000 cents 5: 1 787.00000 cents 5: 1 804.00000 cents 5: 1 827.00000 cents 5: 1 845.00000 cents 5: 1 929.00000 cents 5: 1 944.00000 cents 5: 1 954.00000 cents 6: 1 967.00000 cents 6: 1 969.00000 cents 6: 1 1038.00000 cents 6: 1 1053.00000 cents 6: 1 1078.00000 cents 6: 1 1094.00000 cents 6: 1 1109.00000 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 140.0 264.0 513.0 678.0 787.0 967.0 1218.0 140.0 : 124.0 373.0 538.0 647.0 827.0 1078.0 1218.0 264.0 : 249.0 414.0 523.0 703.0 954.0 1094.0 1218.0 513.0 : 165.0 274.0 454.0 705.0 845.0 969.0 1218.0 678.0 : 109.0 289.0 540.0 680.0 804.0 1053.0 1218.0 787.0 : 180.0 431.0 571.0 695.0 944.0 1109.0 1218.0 967.0 : 251.0 391.0 515.0 764.0 929.0 1038.0 1218.0 1218.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 109.0000 .. 251.0000 cents 142.00000 cents 109.00000 cents 2: 264.0000 .. 431.0000 cents 167.00000 cents 13.00000 cents 3: 454.0000 .. 571.0000 cents 117.00000 cents 23.00000 cents 4: 647.0000 .. 764.0000 cents 117.00000 cents 76.00000 cents 5: 787.0000 .. 954.0000 cents 167.00000 cents 23.00000 cents 6: 967.0000 .. 1109.0000 cents 142.00000 cents 13.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 109.00000 cents, class 1 Average step (divided formal octave): 174.0000 cents Largest one step interval : 251.00000 cents Average / Smallest step : 1.596330 Largest / Average step : 1.442529 Largest / Smallest step : 2.302752 Median interval of one step : 165.00000 cents, amount: 1 Least squares average step : 165.58571 cents, oct.: 1159.10000 cents Scale is strictly proper Scale is a mode of a 1218-tone equal temperament with octave 1218.000 cents degrees: 140 264 513 678 787 967 1218 Least number of segments generator : 611 of 611.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 929 of 929.000 cents and inv. generated superset size: 416 = 409 more = 5942.857% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFG Step pattern size order : CBFDAEG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 13.00000 cents Scale diversity : 1.540956 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.300493 Rothenberg efficiency : 0.285714 redundancy: 0.714286 Efficiency x scale size : 2.000000 Number of different interval sizes : 42 = 7.00000 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 7.00000 = 7 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 2.00000 cents Number of recognisable fifths : 3, average 701.0000 cents Number of recognisable fourths : 1, average 513.0000 cents Number of appreciable fourths : 0 Best fifths form a closed circle Formal octave complements present : 1 = 14.2857% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 157.0000 cents: 2 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 55.3366 c. M:-84.0000 c. Lebeng 9: 1 1 2 1 1 1 2 P M ME S SD: 16.3993 c. M:-28.3333 c. Pseudo Pelog, Pelogic-7, Antiionian 14: 2 1 3 2 1 2 3 P T3 SD: 15.5196 c. M:-34.0000 c. 19: 2 2 4 2 2 3 4 P SD: 16.4991 c. M: 36.9474 c. 20: 2 2 4 3 2 3 4 P S SD: 14.9069 c. M: 25.8000 c. 23: 3 2 5 3 2 3 5 P T3 SD: 11.8558 c. M:-18.8696 c. 26: 3 3 5 4 2 4 5 SP S SD: 13.5025 c. M:-24.6923 c. 27: 3 3 5 4 2 4 6 P SD: 12.7656 c. M: 20.1111 c. 28: 3 3 6 4 2 4 6 P S SD: 9.4131 c. M:-18.0000 c. 29: 3 3 6 4 3 4 6 P S SD: 9.0947 c. M: 14.0000 c. 33: 4 3 7 4 3 5 7 P SD: 8.3322 c. M: 13.6364 c. 34: 4 3 7 5 3 5 7 P SD: 6.8234 c. M: 13.2353 c. 40: 5 4 8 5 4 6 8 SP SD: 7.7011 c. M:-12.2500 c. 42: 5 4 9 5 4 6 9 P SD: 7.0912 c. M: 11.0000 c. 43: 5 4 9 6 4 6 9 P SD: 4.6432 c. M: 9.0698 c. 45: 5 5 9 6 4 7 9 SP SD: 4.2868 c. M:-7.4000 c. 54: 6 6 11 7 5 8 11 SP SD: 4.0656 c. M:-6.6667 c. 59: 7 6 12 8 5 9 12 SP SD: 3.3110 c. M:-4.5085 c. 68: 8 7 14 9 6 10 14 SP SD: 3.4335 c. M:-6.4412 c. 79: 9 8 16 11 7 12 16 SP SD: 2.4545 c. M:-4.3165 c. 88: 10 9 18 12 8 13 18 SP SD: 1.2878 c. M:-1.9318 c. 147: 17 15 30 20 13 22 30 SP SD: 1.2253 c. M:-2.4286 c. 156: 18 16 32 21 14 23 32 SP SD: 1.3722 c. M:-2.3077 c. 180: 21 18 37 24 16 27 37 SP SD: 1.3349 c. M:-2.1000 c. 183: 21 19 37 25 16 27 38 SP SD: 1.3298 c. M:-2.2295 c. 189: 22 19 39 25 17 28 39 SP SD: 1.3220 c. M:-2.5556 c. 190: 22 19 39 26 17 28 39 SP SD: 1.0667 c. M:-1.5158 c. 209: 24 21 43 28 19 31 43 SP SD: 1.0186 c. M: 1.9809 c. 235: 27 24 48 32 21 35 48 SP SD: 0.9742 c. M:-2.2170 c. 244: 28 25 50 33 22 36 50 SP SD: 1.0272 c. M:-1.7049 c. 252: 29 26 51 34 23 37 52 SP SD: 0.9574 c. M:-1.8333 c. 262: 30 27 53 36 23 39 54 SP SD: 0.9443 c. M: 1.6260 c. 268: 31 27 55 36 24 40 55 SP SD: 0.7166 c. M:-1.0373 c. 271: 31 28 55 37 24 40 56 SP SD: 0.6931 c. M:-1.1734 c. 314: 36 32 64 43 28 46 65 SP SD: 0.6843 c. M: 1.1338 c. 354: 41 36 72 48 32 52 73 SP SD: 0.6574 c. M:-1.0678 c. 356: 41 36 73 48 32 53 73 SP SD: 0.5737 c. M:-1.2416 c. 359: 41 37 73 49 32 53 74 SP SD: 0.5361 c. M: 0.8969 c. 365: 42 37 75 49 33 54 75 SP SD: 0.5511 c. M:-0.8959 c. 384: 44 39 79 52 34 57 79 SP SD: 0.5821 c. M:-0.8438 c. 392: 45 40 80 53 35 58 81 SP SD: 0.5096 c. M: 0.8929 c. 460: 53 47 94 62 41 68 95 SP SD: 0.5154 c. M:-0.7826 c. 461: 53 47 94 63 41 68 95 SP SD: 0.4442 c. M:-1.0152 c. 480: 55 49 98 65 43 71 99 SP SD: 0.3392 c. M: 0.4875 c. 539: 62 55 110 73 48 80 111 SP SD: 0.2857 c. M: 0.6104 c. 548: 63 56 112 74 49 81 113 SP SD: 0.2662 c. M:-0.4927 c. 582: 67 59 119 79 52 86 120 SP SD: 0.1886 c. M: 0.3093 c. 636: 73 65 130 86 57 94 131 SP SD: 0.1726 c. M:-0.2830 c. 1028: 118 105 210 139 92 152 212 SP SD: 0.1972 c. M: 0.2802 c. 1062: 122 108 217 144 95 157 219 SP SD: 0.2016 c. M: 0.3390 c. 1071: 123 109 219 145 96 158 221 SP SD: 0.1682 c. M: 0.3333 c. 1116: 128 114 228 151 100 165 230 SP SD: 0.1585 c. M: 0.3011 c. 1130: 130 115 231 153 101 167 233 SP SD: 0.1003 c. M: 0.1504 c. 1218: 140 124 249 165 109 180 251 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 18.0000 cents 2 x x x 3 x x 4 S SD: 14.9820 cents 3 x x 4 x x 5:6 S SD: 28.6303 cents 4 x 5 x 6 x 7:8 S SD: 31.4859 cents 5 x 6:7 x 8:9:10 S SD: 21.0665 cents 6 x 7:8:9 x 11:12 SD: 17.7914 cents 7 x 8:9:10:11:12:14 S SD: 18.4855 cents 8 x 9:11:12:13:14:16 SD: 15.6751 cents 9:10 x 12:13:14:16:18 S SD: 12.2386 cents 11:12:13:15:16:17:19:22 SD: 9.0934 cents 12:13:14:16:18:19:21:24 SD: 4.9659 cents 23:25:27:31:34:36:40:46 SD: 3.9201 cents 35:38:41:47:52:55:61:71 SD: 2.2881 cents 47:51:55:63:70:74:82:95 SD: 2.2585 cents 48:52:56:65:71:76:84:97 SD: 2.1581 cents 50:54:58:67:74:79:87:101 SD: 2.1482 cents 56:61:65:75:83:88:98:113 SD: 1.9902 cents 59:64:69:79:87:93:103:119 SD: 1.7978 cents 61:66:71:82:90:96:107:123 SD: 1.3557 cents 73:79:85:98:108:115:128:148 SD: 1.2677 cents 84:91:98:113:124:132:147:170 SD: 1.0531 cents 92:100:107:124:136:145:161:186 SD: 0.9624 cents 96:104:112:129:142:151:168:194 SD: 0.7015 cents 139:151:162:187:206:219:243:281 SD: 0.6780 cents 151:164:176:203:223:238:264:305 SD: 0.6575 cents 163:177:190:219:241:257:285:329 SD: 0.6256 cents 165:179:192:222:244:260:288:333 SD: 0.5945 cents 177:192:206:238:262:279:309:358 SD: 0.4934 cents 188:204:219:253:278:296:329:380 SD: 0.4189 cents 200:217:233:269:296:315:350:404 SD: 0.3635 cents 238:258:277:320:352:375:416:481 SD: 0.2157 cents 334:362:389:449:494:526:584:675 SD: 0.1926 cents 426:462:496:573:630:671:745:861 SD: 0.1846 cents 438:475:510:589:648:690:766:885 SD: 0.1491 cents 559:606:651:752:827:881:977:1130 SD: 0.1437 cents