Scala analysis: United_Kingdom_Bagpipe_03
Bagpipe 3 (Bagpipes), United Kingdom
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 204.000 cents 204.000000 2: 386.000 cents 386.000000 3: 551.000 cents 551.000000 4: 702.000 cents 702.000000 5: 908.000 cents 908.000000 6: 1049.000 cents 1049.000000 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 151.0000 cents 151.0000 1: 204.0000 cents 204.0000 2: 182.0000 cents 182.0000 3: 165.0000 cents 165.0000 4: 151.0000 cents 151.0000 5: 206.0000 cents 206.0000 6: 141.0000 cents 141.0000 7: 151.0000 cents 151.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 141.00000 cents 1: 2 151.00000 cents 1: 1 165.00000 cents 1: 1 182.00000 cents 1: 1 204.00000 cents 1: 1 206.00000 cents 2: 1 292.00000 cents 2: 1 316.00000 cents 2: 2 347.00000 cents 2: 1 355.00000 cents 2: 1 357.00000 cents 2: 1 386.00000 cents 3: 1 496.00000 cents 3: 3 498.00000 cents 3: 1 522.00000 cents 3: 1 537.00000 cents 3: 1 551.00000 cents 4: 1 649.00000 cents 4: 1 663.00000 cents 4: 1 678.00000 cents 4: 3 702.00000 cents 4: 1 704.00000 cents 5: 1 814.00000 cents 5: 1 843.00000 cents 5: 1 845.00000 cents 5: 2 853.00000 cents 5: 1 884.00000 cents 5: 1 908.00000 cents 6: 1 994.00000 cents 6: 1 996.00000 cents 6: 1 1018.00000 cents 6: 1 1035.00000 cents 6: 2 1049.00000 cents 6: 1 1059.00000 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.66667 = 17/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 204.0 386.0 551.0 702.0 908.0 1049.0 1200.0 204.0 : 182.0 347.0 498.0 704.0 845.0 996.0 1200.0 386.0 : 165.0 316.0 522.0 663.0 814.0 1018.0 1200.0 551.0 : 151.0 357.0 498.0 649.0 853.0 1035.0 1200.0 702.0 : 206.0 347.0 498.0 702.0 884.0 1049.0 1200.0 908.0 : 141.0 292.0 496.0 678.0 843.0 994.0 1200.0 1049.0: 151.0 355.0 537.0 702.0 853.0 1059.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 141.0000 .. 206.0000 cents 65.00000 cents 141.00000 cents 2: 292.0000 .. 386.0000 cents 94.00000 cents 86.00000 cents 3: 496.0000 .. 551.0000 cents 55.00000 cents 110.00000 cents 4: 649.0000 .. 704.0000 cents 55.00000 cents 98.00000 cents 5: 814.0000 .. 908.0000 cents 94.00000 cents 110.00000 cents 6: 994.0000 .. 1059.0000 cents 65.00000 cents 86.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 141.00000 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 206.00000 cents Average / Smallest step : 1.215805 Largest / Average step : 1.201667 Largest / Smallest step : 1.460993 Median interval of one step : 165.00000 cents, amount: 1 Most common interval of one step : 151.00000 cents, amount: 2 Least squares average step : 176.22143 cents, oct.: 1233.55000 cents Scale is strictly proper Scale is a mode of a 1200-tone equal temperament with octave 1200.000 cents degrees: 204 386 551 702 908 1049 1200 Least number of segments generator : 601 of 601.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 917 of 917.000 cents and inv. generated superset size: 328 = 321 more = 4685.714% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFD Step pattern size order : EDCBFAB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 86.00000 cents Scale diversity : 1.384233 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.643333 Rothenberg efficiency : 0.341497 redundancy: 0.658503 Efficiency x scale size : 2.390476 Number of different interval sizes : 34 = 5.66667 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 5.66667 = 17/3 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 2.00000 cents Most common intervals : 498.00000 cents & inv., amount: 3 Number of recognisable fifths : 4, average 702.5000 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% Limited inverse transpositions with margin 70.0000 cents: 2 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 32.8180 c. M: 50.8571 c. Lebeng 9: 2 1 1 1 2 1 1 P M ME S SD: 30.7932 c. M:-62.6667 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 27.4695 c. M: 51.0000 c. G.Hypophrygian, G.Ionian (Iastian), M.Mixolydian, G.M.Hypoionian, Hypermixolydian, Mischung 3, Khamaj That, Mela Harikambhoji, Raga Balahamsa, Bhim, Devamanohari, Harini, Janjhuti, Kaamaai, Khambhavati, Surati, Gregorian nr.7, Enharmonic Byzantine Liturgical, Rast descending: Greece, Ching, Shang: China 13: 2 2 2 2 2 1 2 SP M ME S SD: 21.8822 c. M:-36.4615 c. Karakalian 15: 3 2 2 2 2 2 2 SP M ME S SD: 19.8638 c. M:-36.0000 c. Porky-7 16: 3 2 2 2 3 2 2 SP M ME S SD: 17.0378 c. M: 27.0000 c. Antiphrygian 17: 3 2 3 2 3 2 2 SP M ME S SD: 14.8597 c. M: 33.0588 c. Neutral Hypolydian, Mohajira-7 19: 3 3 3 2 3 3 2 SP M ME S SD: 16.0011 c. M:-24.6842 c. Nineteen-tone Lydian 22: 4 3 3 3 4 2 3 SP D3 SD: 10.8940 c. M:-19.2727 c. 24: 4 4 3 3 4 3 3 SP D3 S SD: 6.3471 c. M:-14.0000 c. Neutral Diatonic Hypophrygian 34: 6 5 5 4 6 4 4 SP SD: 8.0868 c. M:-13.7059 c. 37: 6 6 5 5 6 4 5 SP SD: 7.1306 c. M:-11.5135 c. 41: 7 6 6 5 7 5 5 SP SD: 3.3701 c. M: 5.5122 c. 65: 11 10 9 8 11 8 8 SP SD: 2.2177 c. M: 3.3846 c. 87: 15 13 12 11 15 10 11 SP SD: 1.5619 c. M:-2.8966 c. 111: 19 17 15 14 19 13 14 SP SD: 1.3574 c. M:-3.1892 c. 118: 20 18 16 15 20 14 15 SP SD: 1.4614 c. M: 2.9153 c. 128: 22 19 18 16 22 15 16 SP SD: 1.5295 c. M:-2.2500 c. 135: 23 20 19 17 23 16 17 SP SD: 1.5269 c. M: 3.7778 c. 152: 26 23 21 19 26 18 19 SP SD: 0.9544 c. M:-1.6316 c. 181: 31 27 25 23 31 21 23 SP SD: 1.0611 c. M:-1.5249 c. 205: 35 31 28 26 35 24 26 SP SD: 0.7118 c. M: 1.1951 c. 246: 42 37 34 31 42 29 31 SP SD: 0.5249 c. M:-0.8780 c. 342: 58 52 47 43 59 40 43 SP SD: 0.3643 c. M:-0.7719 c. 383: 65 58 53 48 66 45 48 SP SD: 0.4590 c. M: 0.6214 c. 407: 69 62 56 51 70 48 51 SP SD: 0.3750 c. M:-0.6314 c. 436: 74 66 60 55 75 51 55 SP SD: 0.3960 c. M: 0.6789 c. 453: 77 69 62 57 78 53 57 SP SD: 0.3669 c. M:-0.7550 c. 460: 78 70 63 58 79 54 58 SP SD: 0.3360 c. M: 0.5652 c. 494: 84 75 68 62 85 58 62 SP SD: 0.3020 c. M:-0.5020 c. 501: 85 76 69 63 86 59 63 SP SD: 0.2427 c. M: 0.4072 c. 547: 93 83 75 69 94 64 69 SP SD: 0.2173 c. M: 0.3711 c. 588: 100 89 81 74 101 69 74 SP SD: 0.1295 c. M: 0.2857 c. 612: 104 93 84 77 105 72 77 SP SD: 0.1245 c. M:-0.2745 c. 954: 162 145 131 120 164 112 120 SP SD: 0.1354 c. M: 0.2264 c. 1048: 178 159 144 132 180 123 132 SP SD: 0.1384 c. M: 0.2366 c. 1089: 185 165 150 137 187 128 137 SP SD: 0.1384 c. M: 0.3251 c. 1113: 189 169 153 140 191 131 140 SP SD: 0.1221 c. M: 0.2264 c. 1135: 193 172 156 143 195 133 143 SP SD: 0.1270 c. M:-0.1938 c. 1159: 197 176 159 146 199 136 146 SP SD: 0.1192 c. M:-0.1950 c. 1200: 204 182 165 151 206 141 151 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: 0.0225 cents 3 x x 4 x 5 x 6 S SD: 19.3309 cents 4 x 5 x 6:7 x 8 S SD: 15.2067 cents 5 x 6:7 x 8:9:10 S SD: 25.1592 cents 6:7 x 8:9:10:11:12 S SD: 14.2556 cents 8:9:10:11:12:14:15:16 S SD: 10.3431 cents 13:15:16:18:20:22:24:26 SD: 9.9486 cents 14:16:18:19:21:24:26:28 SD: 9.8896 cents 15:17:19:21:23:25:27:30 SD: 9.7769 cents 16:18:20:22:24:27:29:32 SD: 2.7922 cents 24:27:30:33:36:41:44:48 SD: 2.7309 cents 32:36:40:44:48:54:59:64 SD: 1.4862 cents 48:54:60:66:72:81:88:96 SD: 0.3162 cents 120:135:150:165:180:203:220:240 SD: 0.3161 cents 168:189:210:231:252:284:308:336 SD: 0.1552 cents 216:243:270:297:324:365:396:432 SD: 0.0901 cents 264:297:330:363:396:446:484:528 SD: 0.0879 cents 448:504:560:616:672:757:821:896 SD: 0.0844 cents 480:540:600:660:720:811:880:960 SD: 0.0835 cents 496:558:620:682:744:838:909:992 SD: 0.0767 cents