Scala analysis: United_Kingdom_Bagpipe_04
Bagpipe 4 (Bagpipes), United Kingdom
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 197.000 cents 197.000000 2: 341.000 cents 341.000000 3: 495.000 cents 495.000000 4: 703.000 cents 703.000000 5: 853.000 cents 853.000000 6: 1009.000 cents 1009.000000 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 191.0000 cents 191.0000 1: 197.0000 cents 197.0000 2: 144.0000 cents 144.0000 3: 154.0000 cents 154.0000 4: 208.0000 cents 208.0000 5: 150.0000 cents 150.0000 6: 156.0000 cents 156.0000 7: 191.0000 cents 191.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 144.00000 cents 1: 1 150.00000 cents 1: 1 154.00000 cents 1: 1 156.00000 cents 1: 1 191.00000 cents 1: 1 197.00000 cents 1: 1 208.00000 cents 2: 1 298.00000 cents 2: 1 306.00000 cents 2: 1 341.00000 cents 2: 1 347.00000 cents 2: 1 358.00000 cents 2: 1 362.00000 cents 2: 1 388.00000 cents 3: 1 495.00000 cents 3: 1 497.00000 cents 3: 1 506.00000 cents 3: 1 512.00000 cents 3: 1 514.00000 cents 3: 1 532.00000 cents 3: 1 544.00000 cents 4: 1 656.00000 cents 4: 1 668.00000 cents 4: 1 686.00000 cents 4: 1 688.00000 cents 4: 1 694.00000 cents 4: 1 703.00000 cents 4: 1 705.00000 cents 5: 1 812.00000 cents 5: 1 838.00000 cents 5: 1 842.00000 cents 5: 1 853.00000 cents 5: 1 859.00000 cents 5: 1 894.00000 cents 5: 1 902.00000 cents 6: 1 992.00000 cents 6: 1 1003.00000 cents 6: 1 1009.00000 cents 6: 1 1044.00000 cents 6: 1 1046.00000 cents 6: 1 1050.00000 cents 6: 1 1056.00000 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 : 197.0 341.0 495.0 703.0 853.0 1009.0 1200.0 197.0 : 144.0 298.0 506.0 656.0 812.0 1003.0 1200.0 341.0 : 154.0 362.0 512.0 668.0 859.0 1056.0 1200.0 495.0 : 208.0 358.0 514.0 705.0 902.0 1046.0 1200.0 703.0 : 150.0 306.0 497.0 694.0 838.0 992.0 1200.0 853.0 : 156.0 347.0 544.0 688.0 842.0 1050.0 1200.0 1009.0: 191.0 388.0 532.0 686.0 894.0 1044.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 144.0000 .. 208.0000 cents 64.00000 cents 144.00000 cents 2: 298.0000 .. 388.0000 cents 90.00000 cents 90.00000 cents 3: 495.0000 .. 544.0000 cents 49.00000 cents 107.00000 cents 4: 656.0000 .. 705.0000 cents 49.00000 cents 112.00000 cents 5: 812.0000 .. 902.0000 cents 90.00000 cents 107.00000 cents 6: 992.0000 .. 1056.0000 cents 64.00000 cents 90.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 144.00000 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 208.00000 cents Average / Smallest step : 1.190476 Largest / Average step : 1.213333 Largest / Smallest step : 1.444444 Median interval of one step : 156.00000 cents, amount: 1 Least squares average step : 170.67857 cents, oct.: 1194.75000 cents Scale is strictly proper Scale is a mode of a 1200-tone equal temperament with octave 1200.000 cents degrees: 197 341 495 703 853 1009 1200 Least number of segments generator : 601 of 601.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 857 of 857.000 cents and inv. generated superset size: 317 = 310 more = 4528.571% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFG Step pattern size order : FACGBDE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.00000 cents Scale diversity : 1.363276 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.661667 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 : 5, average 695.2000 cents Number of appreciable fifths : 3, average 700.6667 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 = 14.2857% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 15.7130 c. M: 25.5714 c. Lebeng 17: 3 2 2 3 2 2 3 SP D3 I SD: 10.9293 c. M: 20.7647 c. Safi al-Din's maqam Rast 20: 3 3 2 4 2 3 3 SP D3 I SD: 14.4123 c. M:-19.0000 c. 24: 4 3 3 4 3 3 4 SP D3 I SD: 5.5291 c. M: 9.0000 c. Miha'il Musaqa's mode: Egypt, Neutral Diatonic Hypodorian, Dastgah-e Sehgah, Maqam Nairuz 31: 5 4 4 5 4 4 5 SP D3 I SD: 5.0896 c. M:-8.2258 c. Neutral Diatonic Hypodorian 49: 8 6 6 9 6 6 8 SP I SD: 4.2250 c. M:-7.2041 c. 56: 9 7 7 10 7 7 9 SP I SD: 2.9995 c. M:-4.1429 c. 75: 12 9 10 13 9 10 12 SP SD: 3.3381 c. M: 5.0000 c. 77: 13 9 10 13 10 10 12 SP SD: 3.4730 c. M:-5.5974 c. 80: 13 10 10 14 10 10 13 SP I SD: 2.5071 c. M: 4.0000 c. 87: 14 11 11 15 11 11 14 SP I SD: 2.4374 c. M: 3.8966 c. 92: 15 11 12 16 11 12 15 SP SD: 2.8276 c. M: 5.1739 c. 99: 16 12 13 17 12 13 16 SP SD: 2.5313 c. M: 4.5152 c. 109: 18 13 14 19 14 14 17 SP SD: 2.7143 c. M:-5.7156 c. 111: 18 14 14 19 14 14 18 SP I SD: 2.6631 c. M:-4.9459 c. 114: 19 13 15 20 14 15 18 SP SD: 2.2021 c. M: 4.1579 c. 121: 20 14 16 21 15 16 19 SP SD: 1.8892 c. M: 3.8099 c. 126: 21 15 16 22 16 16 20 SP SD: 2.1728 c. M:-4.1429 c. 127: 21 15 16 22 16 17 20 SP SD: 2.4313 c. M: 3.7874 c. 128: 21 15 17 22 16 17 20 SP SD: 2.0022 c. M: 3.5000 c. 133: 22 16 17 23 17 17 21 SP SD: 1.9747 c. M:-4.1429 c. 138: 23 16 18 24 17 18 22 SP SD: 1.4886 c. M:-3.0000 c. 145: 24 17 19 25 18 19 23 SP SD: 1.1252 c. M: 1.6897 c. 194: 32 23 25 34 24 25 31 SP SD: 1.0080 c. M:-2.1546 c. 201: 33 24 26 35 25 26 32 SP SD: 0.7056 c. M:-1.4776 c. 208: 34 25 27 36 26 27 33 SP SD: 0.7780 c. M:-1.1538 c. 225: 37 27 29 39 28 29 36 SP SD: 0.6901 c. M:-1.0000 c. 232: 38 28 30 40 29 30 37 SP SD: 0.6864 c. M:-1.5517 c. 328: 54 39 42 57 41 43 52 SP SD: 0.6858 c. M: 1.0976 c. 352: 58 42 45 61 44 46 56 SP SD: 0.5436 c. M: 0.7273 c. 359: 59 43 46 62 45 47 57 SP SD: 0.5153 c. M: 1.0501 c. 391: 64 47 50 68 49 51 62 SP SD: 0.5096 c. M: 0.8824 c. 408: 67 49 52 71 51 53 65 SP SD: 0.3487 c. M: 0.8824 c. 415: 68 50 53 72 52 54 66 SP SD: 0.2981 c. M: 0.5422 c. 553: 91 66 71 96 69 72 88 SP SD: 0.2458 c. M:-0.4684 c. 560: 92 67 72 97 70 73 89 SP SD: 0.1791 c. M: 0.2857 c. 584: 96 70 75 101 73 76 93 SP SD: 0.1941 c. M:-0.2603 c. 616: 101 74 79 107 77 80 98 SP SD: 0.1841 c. M:-0.2468 c. 640: 105 77 82 111 80 83 102 SP SD: 0.1567 c. M: 0.2500 c. 785: 129 94 101 136 98 102 125 SP SD: 0.1576 c. M:-0.2866 c. 975: 160 117 125 169 122 127 155 SP SD: 0.1592 c. M:-0.2308 c. 999: 164 120 128 173 125 130 159 SP SD: 0.1420 c. M: 0.2973 c. 1144: 188 137 147 198 143 149 182 SP SD: 0.1468 c. M: 0.2028 c. 1169: 192 140 150 203 146 152 186 SP SD: 0.1350 c. M: 0.2181 c. 1176: 193 141 151 204 147 153 187 SP SD: 0.1128 c. M: 0.1837 c. 1193: 196 143 153 207 149 155 190 SP SD: 0.0922 c. M:-0.1500 c. 1200: 197 144 154 208 150 156 191 SP SD: 0.0000 c. M:-0.0000 c.
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: 0.5225 cents 3 x x 4 x 5 x 6 S SD: 10.5021 cents 4 x 5 x 6 x 7:8 S SD: 15.1418 cents 5 x 6:7 x 8:9:10 S SD: 19.9208 cents 6:7 x 8:9:10:11:12 S SD: 14.4384 cents 7:8 x 9 x 11:13:14 SD: 23.3758 cents 8:9:10:11:12:13:14:16 S SD: 11.9893 cents 9:10:11:12:14:15:16:18 S SD: 10.3480 cents 10:11:12:13:15:16:18:20 SD: 10.0518 cents 14:16:17:19:21:23:25:28 SD: 6.9929 cents 18:20:22:24:27:29:32:36 SD: 4.9036 cents 24:27:29:32:36:39:43:48 SD: 2.8319 cents 33:37:40:44:50:54:59:66 SD: 2.6765 cents 42:47:51:56:63:69:75:84 SD: 1.4837 cents 66:74:80:88:99:108:118:132 SD: 1.3143 cents 82:92:100:109:123:134:147:164 SD: 0.7500 cents 100:112:122:133:150:164:179:200 SD: 0.7410 cents 115:129:140:153:173:188:206:230 SD: 0.7054 cents 124:139:151:165:186:203:222:248 SD: 0.2238 cents 317:355:386:422:476:519:568:634 SD: 0.2223 cents 363:407:442:483:545:594:650:726 SD: 0.2069 cents 399:447:486:531:599:653:715:798 SD: 0.1646 cents 441:494:537:587:662:722:790:882 SD: 0.1152 cents 523:586:637:696:785:856:937:1046 SD: 0.0974 cents 565:633:688:752:848:925:1012:1130 SD: 0.0737 cents