Scala analysis: Indonesia_Pengawesari
Pengawesari (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: 225.000 cents 225.000000 2: 476.000 cents 476.000000 3: 735.000 cents 735.000000 4: 968.000 cents 968.000000 5: 1223.000 cents 1223.000000
SHOW/INTERVAL
0: 255.0000 cents 255.0000 1: 225.0000 cents 225.0000 2: 251.0000 cents 251.0000 3: 259.0000 cents 259.0000 4: 233.0000 cents 233.0000 5: 255.0000 cents 255.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 225.00000 cents 1: 1 233.00000 cents 1: 1 251.00000 cents 1: 1 255.00000 cents 1: 1 259.00000 cents 2: 1 476.00000 cents 2: 1 480.00000 cents 2: 1 488.00000 cents 2: 1 492.00000 cents 2: 1 510.00000 cents 3: 1 713.00000 cents 3: 1 731.00000 cents 3: 1 735.00000 cents 3: 1 743.00000 cents 3: 1 747.00000 cents 4: 1 964.00000 cents 4: 1 968.00000 cents 4: 1 972.00000 cents 4: 1 990.00000 cents 4: 1 998.00000 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 : 225.0 476.0 735.0 968.0 1223.0 225.0 : 251.0 510.0 743.0 998.0 1223.0 476.0 : 259.0 492.0 747.0 972.0 1223.0 735.0 : 233.0 488.0 713.0 964.0 1223.0 968.0 : 255.0 480.0 731.0 990.0 1223.0 1223.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 225.0000 .. 259.0000 cents 34.00000 cents 225.00000 cents 2: 476.0000 .. 510.0000 cents 34.00000 cents 217.00000 cents 3: 713.0000 .. 747.0000 cents 34.00000 cents 203.00000 cents 4: 964.0000 .. 998.0000 cents 34.00000 cents 217.00000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 225.00000 cents, class 1 Average step (divided formal octave): 244.6000 cents Largest one step interval : 259.00000 cents Average / Smallest step : 1.087111 Largest / Average step : 1.058872 Largest / Smallest step : 1.151111 Median interval of one step : 251.00000 cents, amount: 1 Least squares average step : 243.07273 cents, oct.: 1215.36364 cents Scale is strictly proper Scale is a mode of a 1223-tone equal temperament with octave 1223.000 cents degrees: 225 476 735 968 1223 Least number of segments generator : 612 of 612.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 978 of 978.000 cents and inv. generated superset size: 53 = 48 more = 1060.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDE Step pattern size order : ACEBD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 203.00000 cents Scale diversity : 1.112967 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.888798 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 : 4.00000 cents Number of recognisable fifths : 1, average 713.0000 cents Number of recognisable fourths : 3, average 496.6667 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 = 20.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions with margin 34.0000 cents: 1 2 3 4 Limited inverse transpositions with margin 34.0000 cents: 1 2 3 4 -- Rational properties --
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 11.5585 c. M:-19.6000 c. 23: 4 5 5 4 5 SP M ME S SD: 8.5456 c. M: 12.3043 c. 28: 5 6 6 5 6 SP M ME S SD: 5.8374 c. M:-7.5357 c. 33: 6 7 7 6 7 SP M ME S SD: 4.4410 c. M:-6.2121 c. 38: 7 8 8 7 8 SP M ME S SD: 3.9842 c. M:-6.7632 c. 43: 8 9 9 8 9 SP M ME S SD: 4.0976 c. M:-7.5116 c. 48: 9 10 10 9 10 SP M ME S SD: 4.4609 c. M:-8.1042 c. 62: 11 13 13 12 13 SP T3 SD: 4.4599 c. M: 8.0161 c. 67: 12 14 14 13 14 SP T3 SD: 3.5005 c. M: 5.9552 c. 72: 13 15 15 14 15 SP T3 SD: 2.7859 c. M: 4.5972 c. 77: 14 16 16 15 16 SP T3 SD: 2.3283 c. M: 4.3766 c. 82: 15 17 17 16 17 SP T3 SD: 2.1378 c. M: 4.1829 c. 87: 16 18 18 17 18 SP T3 SD: 2.1808 c. M: 4.0115 c. 92: 17 19 19 18 19 SP T3 SD: 2.3801 c. M: 3.8587 c. 97: 18 20 20 19 20 SP T3 SD: 2.6600 c. M: 3.7216 c. 98: 18 20 21 19 20 SP SD: 2.6159 c. M:-5.4082 c. 100: 18 21 21 19 21 SP T3 SD: 2.4228 c. M: 4.8600 c. 102: 19 21 21 20 21 SP T3 SD: 2.9718 c. M:-3.6078 c. 103: 19 21 22 20 21 SP SD: 2.6370 c. M:-5.6505 c. 105: 19 22 22 20 22 SP T3 SD: 1.9525 c. M: 3.6952 c. 110: 20 23 23 21 23 SP T3 SD: 1.6273 c. M: 2.6364 c. 115: 21 24 24 22 24 SP T3 SD: 1.4740 c. M:-2.5652 c. 168: 31 34 36 32 35 SP SD: 1.3029 c. M: 2.8155 c. 173: 32 35 37 33 36 SP SD: 1.2100 c. M: 2.3526 c. 178: 33 36 38 34 37 SP SD: 1.2103 c. M: 1.9157 c. 185: 34 38 39 35 39 SP SD: 1.3752 c. M: 2.8216 c. 190: 35 39 40 36 40 SP SD: 1.2449 c. M: 2.4737 c. 195: 36 40 41 37 41 SP SD: 1.1901 c. M: 2.1436 c. 196: 36 40 42 37 41 SP SD: 1.0638 c. M: 1.7755 c. 201: 37 41 43 38 42 SP SD: 0.8732 c. M: 1.4030 c. 206: 38 42 44 39 43 SP SD: 0.7647 c. M:-1.1748 c. 211: 39 43 45 40 44 SP SD: 0.7569 c. M:-1.1185 c. 216: 40 44 46 41 45 SP SD: 0.8394 c. M:-1.4815 c. 268: 49 55 57 51 56 SP SD: 0.9266 c. M: 1.4030 c. 273: 50 56 58 52 57 SP SD: 0.7100 c. M: 1.1355 c. 278: 51 57 59 53 58 SP SD: 0.5105 c. M: 0.8777 c. 283: 52 58 60 54 59 SP SD: 0.3426 c. M: 0.6290 c. 288: 53 59 61 55 60 SP SD: 0.2538 c. M: 0.3889 c. 321: 59 66 68 61 67 SP SD: 0.2376 c. M:-0.3240 c. 326: 60 67 69 62 68 SP SD: 0.2480 c. M:-0.4448 c. 599: 110 123 127 114 125 SP SD: 0.2412 c. M: 0.4090 c. 604: 111 124 128 115 126 SP SD: 0.1435 c. M: 0.2434 c. 609: 112 125 129 116 127 SP SD: 0.0474 c. M: 0.0805 c. 614: 113 126 130 117 128 SP SD: 0.0471 c. M:-0.0798 c. 1223: 225 251 259 233 255 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x 2 S SD: 23.0000 cents 2 x x 3 x 4 S SD: 20.1306 cents 3 x 4 x 5:6 S SD: 29.8344 cents 4 x 5:6:7:8 S SD: 24.5780 cents 6:7:8:9:11:12 SD: 20.4744 cents 7:8:9:11:12:14 SD: 15.1165 cents 9:10:12:14:16:18 S SD: 13.4364 cents 12:14:16:18:21:24 S SD: 12.4271 cents 13:15:17:20:23:26 SD: 8.2130 cents 15:17:20:23:26:30 SD: 7.3673 cents 21:24:28:32:37:43 SD: 6.4186 cents 23:26:30:35:40:47 SD: 5.6093 cents 28:32:37:43:49:57 SD: 2.8203 cents 44:50:58:67:77:89 SD: 1.7931 cents 51:58:67:78:89:103 SD: 1.7009 cents 64:73:84:98:112:130 SD: 1.5164 cents 72:82:95:110:126:146 SD: 0.8592 cents 79:90:104:121:138:160 SD: 0.8221 cents 108:123:142:165:189:219 SD: 0.5591 cents 123:140:162:188:215:249 SD: 0.5345 cents 151:172:199:231:264:306 SD: 0.4646 cents 180:205:237:275:315:365 SD: 0.3569 cents 187:213:246:286:327:379 SD: 0.3030 cents 231:263:304:353:404:468 SD: 0.2648 cents 259:295:341:396:453:525 SD: 0.0917 cents