Scala analysis: Indonesia_Madukusuma
Madukusuma (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: 121.000 cents 121.000000 2: 251.000 cents 251.000000 3: 554.000 cents 554.000000 4: 690.000 cents 690.000000 5: 796.000 cents 796.000000 6: 937.000 cents 937.000000 7: 1216.000 cents 1216.000000
SHOW/INTERVAL
0: 279.0000 cents 279.0000 1: 121.0000 cents 121.0000 2: 130.0000 cents 130.0000 3: 303.0000 cents 303.0000 4: 136.0000 cents 136.0000 5: 106.0000 cents 106.0000 6: 141.0000 cents 141.0000 7: 279.0000 cents 279.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 106.00000 cents 1: 1 121.00000 cents 1: 1 130.00000 cents 1: 1 136.00000 cents 1: 1 141.00000 cents 1: 1 279.00000 cents 1: 1 303.00000 cents 2: 1 242.00000 cents 2: 1 247.00000 cents 2: 1 251.00000 cents 2: 1 400.00000 cents 2: 1 420.00000 cents 2: 1 433.00000 cents 2: 1 439.00000 cents 3: 1 383.00000 cents 3: 1 526.00000 cents 3: 1 530.00000 cents 3: 1 541.00000 cents 3: 1 545.00000 cents 3: 1 554.00000 cents 3: 1 569.00000 cents 4: 1 647.00000 cents 4: 1 662.00000 cents 4: 1 671.00000 cents 4: 1 675.00000 cents 4: 1 686.00000 cents 4: 1 690.00000 cents 4: 1 833.00000 cents 5: 1 777.00000 cents 5: 1 783.00000 cents 5: 1 796.00000 cents 5: 1 816.00000 cents 5: 1 965.00000 cents 5: 1 969.00000 cents 5: 1 974.00000 cents 6: 1 913.00000 cents 6: 1 937.00000 cents 6: 1 1075.00000 cents 6: 1 1080.00000 cents 6: 1 1086.00000 cents 6: 1 1095.00000 cents 6: 1 1110.00000 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 : 121.0 251.0 554.0 690.0 796.0 937.0 1216.0 121.0 : 130.0 433.0 569.0 675.0 816.0 1095.0 1216.0 251.0 : 303.0 439.0 545.0 686.0 965.0 1086.0 1216.0 554.0 : 136.0 242.0 383.0 662.0 783.0 913.0 1216.0 690.0 : 106.0 247.0 526.0 647.0 777.0 1080.0 1216.0 796.0 : 141.0 420.0 541.0 671.0 974.0 1110.0 1216.0 937.0 : 279.0 400.0 530.0 833.0 969.0 1075.0 1216.0 1216.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 106.0000 .. 303.0000 cents 197.00000 cents 106.00000 cents 2: 242.0000 .. 439.0000 cents 197.00000 cents -61.00000 cents 3: 383.0000 .. 569.0000 cents 186.00000 cents -56.00000 cents 4: 647.0000 .. 833.0000 cents 186.00000 cents 78.00000 cents 5: 777.0000 .. 974.0000 cents 197.00000 cents -56.00000 cents 6: 913.0000 .. 1110.0000 cents 197.00000 cents -61.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 106.00000 cents, class 1 Average step (divided formal octave): 173.7143 cents Largest one step interval : 303.00000 cents Average / Smallest step : 1.638814 Largest / Average step : 1.744243 Largest / Smallest step : 2.858491 Median interval of one step : 136.00000 cents, amount: 1 Least squares average step : 165.42143 cents, oct.: 1157.95000 cents Scale is not proper Scale is a mode of a 1216-tone equal temperament with octave 1216.000 cents degrees: 121 251 554 690 796 937 1216 Least number of segments generator : 609 of 609.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1081 of 1081.000 cents and inv. generated superset size: 304 = 297 more = 4342.857% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFG Step pattern size order : BCGDAEF Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 17.00000 cents Scale diversity : 1.456821 Lumma stability : 0.238487 Lumma impropriety factor : 0.192434 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 : 4.00000 cents Number of recognisable fifths : 2, average 688.0000 cents Number of appreciable fifths : 1, average 690.0000 cents Number of recognisable 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 188.0000 cents: 2 -- Rational properties --
FIT/MODE
7: 0 1 2 1 0 1 2 N T3 SD: 72.3381 c. M: 121.0000 c. 8: 0 1 2 1 1 1 2 N D3 SD: 78.0943 c. M: 121.0000 c. 9: 1 1 2 1 1 1 2 P M ME S SD: 13.3800 c. M:-19.2222 c. Pseudo Pelog, Pelogic-7, Antiionian 20: 2 2 5 2 2 2 5 N M DE S SD: 13.1651 c. M: 25.0000 c. Pelogic-7, Antiionian 25: 2 3 6 3 2 3 6 N T3 SD: 14.8563 c. M: 23.7200 c. 26: 3 2 7 3 2 3 6 N SD: 11.0578 c. M:-19.3077 c. 28: 3 3 7 3 2 4 6 N SD: 11.0640 c. M:-18.4286 c. 29: 3 3 7 3 3 3 7 N M DE S SD: 9.8462 c. M: 19.1034 c. 30: 3 3 8 3 3 3 7 N T3 SD: 8.2889 c. M:-14.6667 c. 35: 3 4 9 4 3 4 8 N SD: 7.3670 c. M: 16.7714 c. 38: 4 4 9 5 3 4 9 N SD: 8.1679 c. M:-14.0000 c. 39: 4 4 10 4 4 4 9 N T3 SD: 6.5758 c. M:-14.6667 c. 40: 4 4 10 5 3 5 9 N SD: 6.0071 c. M:-9.2000 c. 44: 4 5 11 5 4 5 10 N SD: 4.6845 c. M: 10.4545 c. 49: 5 5 12 6 4 6 11 N SD: 4.5601 c. M: 8.0408 c. 53: 5 6 13 6 5 6 12 N SD: 4.1116 c. M:-7.0189 c. 60: 6 6 15 7 5 7 14 N SD: 4.8118 c. M: 7.8000 c. 61: 6 7 15 7 5 7 14 N SD: 4.5815 c. M:-8.1475 c. 64: 6 7 16 7 6 7 15 N SD: 4.6291 c. M: 7.0000 c. 69: 7 7 17 8 6 8 16 N SD: 3.9224 c. M: 7.6812 c. 70: 7 7 18 8 6 8 16 N SD: 3.7605 c. M: 7.8000 c. 77: 8 8 19 9 6 9 18 N SD: 4.2258 c. M: 6.3896 c. 78: 8 8 20 8 7 9 18 N SD: 3.5542 c. M:-7.2308 c. 79: 8 8 20 9 7 9 18 N SD: 2.8562 c. M: 4.7215 c. 83: 8 9 21 9 7 10 19 N SD: 2.7177 c. M: 4.8675 c. 92: 9 10 23 10 8 11 21 N SD: 1.8337 c. M: 2.9565 c. 127: 13 13 32 14 11 15 29 N SD: 1.7683 c. M:-3.4724 c. 130: 13 14 32 15 11 15 30 N SD: 1.4888 c. M:-2.1846 c. 160: 16 17 40 18 14 18 37 N SD: 1.3331 c. M: 2.2000 c. 171: 17 18 43 19 15 20 39 N SD: 1.0649 c. M: 2.1111 c. 180: 18 19 45 20 16 21 41 N SD: 1.0521 c. M:-2.0222 c. 208: 21 22 52 23 18 24 48 N SD: 1.1136 c. M:-1.7692 c. 213: 21 23 53 24 18 25 49 N SD: 1.1041 c. M: 2.4601 c. 222: 22 24 55 25 19 26 51 N SD: 0.8488 c. M: 1.7658 c. 231: 23 25 57 26 20 27 53 N SD: 0.9153 c. M:-1.6753 c. 241: 24 26 60 27 21 28 55 N SD: 1.0659 c. M:-1.4896 c. 243: 24 26 61 27 21 28 56 N SD: 0.8881 c. M:-1.4568 c. 252: 25 27 63 28 22 29 58 N SD: 0.5052 c. M:-0.9206 c. 261: 26 28 65 29 23 30 60 N SD: 0.4668 c. M:-0.6897 c. 301: 30 32 75 34 26 35 69 N SD: 0.4405 c. M:-0.8173 c. 393: 39 42 98 44 34 46 90 N SD: 0.4129 c. M: 0.8041 c. 402: 40 43 100 45 35 47 92 N SD: 0.3833 c. M:-0.7114 c. 432: 43 46 108 48 38 50 99 N SD: 0.3967 c. M:-0.5926 c. 483: 48 52 120 54 42 56 111 N SD: 0.3869 c. M:-0.7598 c. 553: 55 59 138 62 48 64 127 N SD: 0.2403 c. M:-0.4593 c. 562: 56 60 140 63 49 65 129 N SD: 0.1501 c. M:-0.2420 c. 654: 65 70 163 73 57 76 150 N SD: 0.1290 c. M: 0.2080 c. 955: 95 102 238 107 83 111 219 N SD: 0.1276 c. M: 0.1885 c. 1207: 120 129 301 135 105 140 277 N SD: 0.0998 c. M: 0.1433 c. 1216: 121 130 303 136 106 141 279 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 16.0000 cents 2 x x x 3 x x 4 S SD: 9.9865 cents 3 x x 4 x x 5:6 S SD: 26.1578 cents 4 x 5 x 6 x 7:8 S SD: 35.1084 cents 5 x 6:7 x 8:9:10 S SD: 21.9600 cents 6 x 7:8:9 x 10:12 S SD: 16.1900 cents 7 x 8:10 x 11:12:14 S SD: 13.9674 cents 8 x 9:11:12:13:14:16 SD: 12.4935 cents 9:10 x 12:13:14:15:18 S SD: 19.5394 cents 10:11:12:14:15:16:17:20 SD: 12.7588 cents 11:12:13:15:16:17:19:22 SD: 11.4921 cents 12:13:14:17:18:19:21:24 SD: 9.4477 cents 13:14:15:18:19:21:22:26 SD: 8.2785 cents 14:15:16:19:21:22:24:28 SD: 5.7722 cents 24:26:28:33:36:38:41:48 SD: 4.6617 cents 26:28:30:36:39:41:45:52 SD: 3.9583 cents 31:33:36:43:46:49:53:63 SD: 3.6352 cents 32:34:37:44:48:51:55:65 SD: 3.6271 cents 37:40:43:51:55:59:64:75 SD: 3.5677 cents 38:41:44:52:57:60:65:77 SD: 3.2359 cents 39:42:45:54:58:62:67:79 SD: 2.2130 cents 43:46:50:59:64:68:74:87 SD: 1.9870 cents 45:48:52:62:67:71:77:91 SD: 1.9713 cents 53:57:61:73:79:84:91:107 SD: 1.3314 cents 82:88:95:113:122:130:141:166 SD: 1.0281 cents 96:103:111:132:143:152:165:194 SD: 0.5030 cents 178:191:206:245:265:282:306:359 SD: 0.4562 cents 180:193:208:248:268:285:309:363 SD: 0.3800 cents 223:239:258:307:332:353:383:450 SD: 0.3451 cents 249:267:288:343:371:394:428:503 SD: 0.3443 cents 262:281:303:361:390:415:450:529 SD: 0.2740 cents 276:296:319:380:411:437:474:557 SD: 0.1797 cents 443:475:512:610:660:702:761:894 SD: 0.1789 cents 480:515:555:661:715:760:825:969 SD: 0.1731 cents 525:563:607:723:782:831:902:1060 SD: 0.1560 cents 539:578:623:742:803:854:926:1088 SD: 0.1475 cents 596:639:689:821:888:944:1024:1203 SD: 0.1028 cents