Scala analysis: CD13_08_Iraq
Taqsîm, 'ûd - Ensemble de Muhammad Al-Qubbbânjî (hakimi/huzam, Iraq)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 176.853 cents 176.852506 2: 370.704 cents 370.704365 3: 580.219 cents 580.218797 4: 722.456 cents 722.456159 5: 866.608 cents 866.607503 6: 1074.837 cents 1074.837259 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 125.1627 cents 125.1627 1: 176.8525 cents 176.8525 2: 193.8519 cents 193.8519 3: 209.5144 cents 209.5144 4: 142.2374 cents 142.2374 5: 144.1513 cents 144.1513 6: 208.2298 cents 208.2298 7: 125.1627 cents 125.1627
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 125.16274 cents 1: 1 142.23736 cents 1: 1 144.15134 cents 1: 1 176.85251 cents 1: 1 193.85186 cents 1: 1 208.22976 cents 1: 1 209.51443 cents 2: 1 286.38871 cents 2: 1 302.01525 cents 2: 1 333.39250 cents 2: 1 351.75179 cents 2: 1 352.38110 cents 2: 1 370.70437 cents 2: 1 403.36629 cents 3: 1 477.54384 cents 3: 1 494.61846 cents 3: 1 495.86711 cents 3: 1 495.90314 cents 3: 1 510.24500 cents 3: 1 545.60365 cents 3: 1 580.21880 cents 4: 1 619.78120 cents 4: 1 654.39635 cents 4: 1 689.75500 cents 4: 1 704.09686 cents 4: 1 704.13289 cents 4: 1 705.38154 cents 4: 1 722.45616 cents 5: 1 796.63371 cents 5: 1 829.29563 cents 5: 1 847.61890 cents 5: 1 848.24821 cents 5: 1 866.60750 cents 5: 1 897.98475 cents 5: 1 913.61129 cents 6: 1 990.48557 cents 6: 1 991.77024 cents 6: 1 1006.14814 cents 6: 1 1023.14749 cents 6: 1 1055.84866 cents 6: 1 1057.76264 cents 6: 1 1074.83726 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 : 176.9 370.7 580.2 722.5 866.6 1074.8 1200.0 176.9 : 193.9 403.4 545.6 689.8 898.0 1023.1 1200.0 370.7 : 209.5 351.8 495.9 704.1 829.3 1006.1 1200.0 580.2 : 142.2 286.4 494.6 619.8 796.6 990.5 1200.0 722.5 : 144.2 352.4 477.5 654.4 848.2 1057.8 1200.0 866.6 : 208.2 333.4 510.2 704.1 913.6 1055.8 1200.0 1074.8: 125.2 302.0 495.9 705.4 847.6 991.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 125.1627 .. 209.5144 cents 84.35169 cents 125.16274 cents 2: 286.3887 .. 403.3663 cents 116.97758 cents 76.87427 cents 3: 477.5438 .. 580.2188 cents 102.67496 cents 74.17755 cents 4: 619.7812 .. 722.4562 cents 102.67496 cents 39.56241 cents 5: 796.6337 .. 913.6113 cents 116.97758 cents 74.17755 cents 6: 990.4856 .. 1074.8373 cents 84.35169 cents 76.87427 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 125.16274 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 209.51443 cents Average / Smallest step : 1.369645 Largest / Average step : 1.222168 Largest / Smallest step : 1.673936 Median interval of one step : 176.85251 cents, amount: 1 Least squares average step : 176.64860 cents, oct.: 1236.54017 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : DEGBCFA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 39.56241 cents Scale diversity : 1.544693 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.493326 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 : 0.03603 cents Number of recognisable fifths : 4, average 700.8416 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: 35.3192 c. M: 65.9331 c. Lebeng 8: 1 1 2 1 1 1 1 P M ME S SD: 35.0552 c. M: 70.7044 c. 10: 1 2 2 1 1 2 1 P D3 S SD: 25.2946 c. M: 56.8525 c. 11: 2 1 2 2 1 2 1 P M ME S SD: 31.1552 c. M: 43.4316 c. 12: 2 2 2 1 2 2 1 P M ME S SD: 24.0174 c. M:-33.3925 c. G.Hypolydian, M.Lydian, G.M.Hypolocrian, Rut biscale ascending, Kalyan That (Yaman), Mela Mecakalyani, Raga Chandrakant, Malarani, Shuddh Kalyan, Ping, Kung, Gu: China 13: 2 2 2 2 1 3 1 P D3 S SD: 21.9674 c. M: 35.8383 c. 15: 2 3 2 2 2 2 2 SP M ME S SD: 20.5290 c. M: 34.8373 c. Miller's Porcupine-7 Major 17: 2 3 3 2 2 3 2 SP D3 S SD: 19.7926 c. M: 35.6760 c. 18: 3 3 3 2 2 3 2 P D3 SD: 16.7776 c. M:-29.2956 c. 19: 3 3 3 2 3 3 2 SP M ME S SD: 14.3725 c. M: 27.7193 c. Nineteen-tone Lydian 20: 3 3 4 2 2 4 2 P SD: 13.3974 c. M: 26.6075 c. 22: 3 4 4 2 3 4 2 P SD: 12.8944 c. M:-19.7812 c. 25: 4 4 4 3 3 4 3 SP D3 SD: 10.6348 c. M: 18.8373 c. 27: 4 4 5 3 3 5 3 SP SD: 11.4827 c. M: 22.1631 c. 28: 4 5 5 3 3 5 3 P SD: 10.5871 c. M:-19.7812 c. 29: 4 5 5 3 4 5 3 SP SD: 8.4528 c. M: 19.0079 c. 32: 5 5 5 4 4 6 3 SP SD: 10.1568 c. M: 17.7188 c. 33: 5 5 6 4 4 6 3 SP SD: 7.5226 c. M:-16.0718 c. 35: 5 6 6 4 4 6 4 SP SD: 6.7291 c. M: 11.9801 c. 40: 6 6 7 5 5 7 4 SP SD: 6.2463 c. M: 10.7044 c. 46: 7 7 8 6 5 8 5 SP SD: 5.6994 c. M:-7.9786 c. 48: 7 8 8 6 6 8 5 SP SD: 4.2435 c. M:-8.3925 c. 58: 9 9 10 7 7 10 6 SP SD: 3.7927 c. M:-9.3544 c. 66: 10 10 12 8 8 11 7 SP SD: 4.5083 c. M: 7.0680 c. 68: 10 11 12 8 8 12 7 SP SD: 1.3174 c. M:-2.1341 c. 116: 17 19 20 14 14 20 12 SP SD: 1.4226 c. M:-2.3580 c. 143: 21 23 25 17 17 25 15 SP SD: 1.2115 c. M: 2.2718 c. 161: 24 26 28 19 19 28 17 SP SD: 1.5124 c. M:-2.0295 c. 163: 24 26 29 19 20 28 17 SP SD: 1.4197 c. M: 2.6062 c. 176: 26 28 31 21 21 31 18 SP SD: 1.3880 c. M: 2.5225 c. 184: 27 30 32 22 22 32 19 SP SD: 0.9260 c. M:-1.4569 c. 223: 33 36 39 26 27 39 23 SP SD: 0.9016 c. M:-1.3959 c. 252: 37 41 44 30 30 44 26 SP SD: 0.8592 c. M:-1.3534 c. 259: 38 42 45 31 31 45 27 SP SD: 0.5233 c. M: 1.0682 c. 314: 46 51 55 37 38 54 33 SP SD: 0.6894 c. M: 1.0563 c. 317: 47 51 55 38 38 55 33 SP SD: 0.6266 c. M:-1.0655 c. 327: 48 53 57 39 39 57 34 SP SD: 0.4396 c. M: 0.7057 c. 414: 61 67 72 49 50 72 43 SP SD: 0.4053 c. M: 0.7170 c. 440: 65 71 77 52 53 76 46 SP SD: 0.4303 c. M:-0.6903 c. 482: 71 78 84 57 58 84 50 SP SD: 0.3415 c. M:-0.6814 c. 508: 75 82 89 60 61 88 53 SP SD: 0.4058 c. M:-0.8836 c. 515: 76 83 90 61 62 89 54 SP SD: 0.2913 c. M: 0.6625 c. 530: 78 86 92 63 64 92 55 SP SD: 0.4710 c. M:-0.6344 c. 537: 79 87 94 63 65 93 56 SP SD: 0.4493 c. M:-0.7868 c. 548: 81 88 96 65 66 95 57 SP SD: 0.4001 c. M: 0.6314 c. 550: 81 89 96 65 66 96 57 SP SD: 0.3729 c. M:-0.7991 c. 583: 86 94 102 69 70 101 61 SP SD: 0.2000 c. M: 0.3947 c. 699: 103 113 122 83 84 121 73 SP SD: 0.1866 c. M:-0.3453 c. 767: 113 124 134 91 92 133 80 SP SD: 0.1745 c. M:-0.3600 c. 842: 124 136 147 100 101 146 88 SP SD: 0.1498 c. M: 0.2529 c. 910: 134 147 159 108 109 158 95 SP SD: 0.1446 c. M: 0.2339 c. 997: 147 161 174 118 120 173 104 SP SD: 0.1174 c. M: 0.2897 c. 1065: 157 172 186 126 128 185 111 SP SD: 0.1018 c. M: 0.2026 c. 1181: 174 191 206 140 142 205 123 SP SD: 0.1066 c. M:-0.1839 c. 1324: 195 214 231 157 159 230 138 SP SD: 0.1044 c. M: 0.1584 c. 1580: 233 255 276 187 190 274 165 SP SD: 0.1029 c. M: 0.1777 c. 1648: 243 266 288 195 198 286 172 SP SD: 0.0932 c. M: 0.1261 c. 1696: 250 274 296 201 204 294 177 SP SD: 0.0671 c. M:-0.1378 c. 1764: 260 285 308 209 212 306 184 SP SD: 0.0353 c. M:-0.0592 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: 10.2506 cents 3 x x 4 x 5 x 6 S SD: 28.0231 cents 4 x 5 x 6:7 x 8 S SD: 26.3540 cents 5 x 6:7 x 8:9:10 S SD: 19.0939 cents 6:7 x 8:9:10:11:12 S SD: 21.2395 cents 7:8:9:10:11:12:13:14 H SD: 18.3636 cents 8:9:10:11:12:13:15:16 SD: 7.9435 cents 17:19:21:24:26:28:32:34 SD: 4.8232 cents 20:22:25:28:30:33:37:40 SD: 4.2997 cents 25:28:31:35:38:41:47:50 SD: 4.0841 cents 28:31:35:39:43:46:52:56 SD: 3.9323 cents 29:32:36:41:44:48:54:58 SD: 3.0693 cents 35:39:43:49:53:58:65:70 SD: 2.8871 cents 37:41:46:52:56:61:69:74 SD: 1.8191 cents 58:64:72:81:88:96:108:116 SD: 1.3874 cents 63:70:78:88:96:104:117:126 SD: 1.3656 cents 66:73:82:92:100:109:123:132 SD: 1.2807 cents 75:83:93:105:114:124:140:150 SD: 1.1384 cents 83:92:103:116:126:137:154:166 SD: 0.8470 cents 100:111:124:140:152:165:186:200 SD: 0.7693 cents 121:134:150:169:184:200:225:242 SD: 0.7460 cents 129:143:160:180:196:213:240:258 SD: 0.7048 cents 131:145:162:183:199:216:244:262 SD: 0.6180 cents 151:167:187:211:229:249:281:302 SD: 0.4590 cents 168:186:208:235:255:277:313:336 SD: 0.4187 cents 206:228:255:288:313:340:383:412 SD: 0.4128 cents 214:237:265:299:325:353:398:428 SD: 0.2531 cents 251:278:311:351:381:414:467:502 SD: 0.0811 cents