Scala analysis: levy-04-malkaus
Ex. 4: Niaz & Faiyaz Ahmed Khan, Mālkãus
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 326.000 cents 326.000000 2: 495.000 cents 495.000000 3: 834.000 cents 834.000000 4: 1006.000 cents 1006.000000 5: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 194.0000 cents 194.0000 1: 326.0000 cents 326.0000 2: 169.0000 cents 169.0000 3: 339.0000 cents 339.0000 4: 172.0000 cents 172.0000 5: 194.0000 cents 194.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 169.00000 cents 1: 1 172.00000 cents 1: 1 194.00000 cents 1: 1 326.00000 cents 1: 1 339.00000 cents 2: 1 366.00000 cents 2: 1 495.00000 cents 2: 1 508.00000 cents 2: 1 511.00000 cents 2: 1 520.00000 cents 3: 1 680.00000 cents 3: 1 689.00000 cents 3: 1 692.00000 cents 3: 1 705.00000 cents 3: 1 834.00000 cents 4: 1 861.00000 cents 4: 1 874.00000 cents 4: 1 1006.00000 cents 4: 1 1028.00000 cents 4: 1 1031.00000 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 : 326.0 495.0 834.0 1006.0 1200.0 326.0 : 169.0 508.0 680.0 874.0 1200.0 495.0 : 339.0 511.0 705.0 1031.0 1200.0 834.0 : 172.0 366.0 692.0 861.0 1200.0 1006.0: 194.0 520.0 689.0 1028.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 169.0000 .. 339.0000 cents 170.00000 cents 169.00000 cents 2: 366.0000 .. 520.0000 cents 154.00000 cents 27.00000 cents 3: 680.0000 .. 834.0000 cents 154.00000 cents 160.00000 cents 4: 861.0000 .. 1031.0000 cents 170.00000 cents 27.00000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 169.00000 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 339.00000 cents Average / Smallest step : 1.420118 Largest / Average step : 1.412500 Largest / Smallest step : 2.005917 Median interval of one step : 194.00000 cents, amount: 1 Least squares average step : 251.67273 cents, oct.: 1258.36364 cents Scale is strictly proper Scale is a mode of a 1200-tone equal temperament with octave 1200.000 cents degrees: 326 495 834 1006 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: 163 = 158 more = 3260.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDE Step pattern size order : DAEBC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 27.00000 cents Scale diversity : 1.388348 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.460000 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 : 3.00000 cents Number of recognisable fifths : 3, average 695.3333 cents Best fifths form a closed circle Formal octave complements present : 1 = 20.0000% Limited inverse transpositions with margin 157.0000 cents: 3 -- Rational properties --
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 67.4285 c. M: 114.0000 c. 7: 2 1 2 1 1 P M ME S SD: 18.4454 c. M:-23.1429 c. Thai mode 3 17: 5 2 5 2 3 P T3 SD: 15.5738 c. M:-26.9412 c. 19: 5 3 5 3 3 SP M DE S SD: 8.9186 c. M: 12.9474 c. 26: 7 4 7 4 4 SP M DE S SD: 7.3232 c. M:-12.6923 c. 29: 8 4 8 4 5 SP T3 SD: 6.8587 c. M: 12.8966 c. 32: 9 4 9 5 5 SP T3 S SD: 7.8962 c. M:-11.5000 c. 33: 9 5 9 5 5 SP M DE S SD: 8.4161 c. M:-14.0909 c. 36: 10 5 10 5 6 SP T3 SD: 4.8005 c. M:-7.3333 c. 49: 13 7 14 7 8 SP SD: 4.2623 c. M: 7.6327 c. 55: 15 8 15 8 9 SP T3 SD: 3.9444 c. M:-6.8182 c. 56: 15 8 16 8 9 SP SD: 2.4386 c. M: 4.5714 c. 63: 17 9 18 9 10 SP SD: 2.6093 c. M:-4.0952 c. 82: 22 12 23 12 13 SP SD: 2.7233 c. M: 4.0488 c. 85: 23 12 24 12 14 SP SD: 1.8371 c. M: 3.6471 c. 92: 25 13 26 13 15 SP SD: 0.8689 c. M: 1.6522 c. 187: 51 26 53 27 30 SP SD: 0.9653 c. M:-1.4866 c. 203: 55 29 57 29 33 SP SD: 0.9573 c. M:-1.5517 c. 206: 56 29 58 30 33 SP SD: 0.9132 c. M:-1.7670 c. 209: 57 29 59 30 34 SP SD: 1.1601 c. M: 1.4641 c. 210: 57 30 59 30 34 SP SD: 0.9835 c. M:-2.1429 c. 216: 59 30 61 31 35 SP SD: 0.9068 c. M:-1.7778 c. 223: 61 31 63 32 36 SP SD: 1.0155 c. M:-2.2511 c. 233: 63 33 66 33 38 SP SD: 1.0702 c. M: 1.7082 c. 235: 64 33 66 34 38 SP SD: 0.8380 c. M: 1.6596 c. 240: 65 34 68 34 39 SP SD: 0.7746 c. M: 1.0000 c. 265: 72 37 75 38 43 SP SD: 0.7932 c. M: 1.4151 c. 272: 74 38 77 39 44 SP SD: 0.4572 c. M: 0.8824 c. 279: 76 39 79 40 45 SP SD: 0.5079 c. M:-0.8817 c. 291: 79 41 82 42 47 SP SD: 0.4755 c. M: 1.0103 c. 298: 81 42 84 43 48 SP SD: 0.4059 c. M:-0.7114 c. 335: 91 47 95 48 54 SP SD: 0.4830 c. M: 0.6716 c. 354: 96 50 100 51 57 SP SD: 0.4376 c. M:-0.7797 c. 364: 99 51 103 52 59 SP SD: 0.3589 c. M: 0.5055 c. 371: 101 52 105 53 60 SP SD: 0.3846 c. M:-0.6846 c. 383: 104 54 108 55 62 SP SD: 0.2919 c. M: 0.5796 c. 390: 106 55 110 56 63 SP SD: 0.2093 c. M:-0.3846 c. 538: 146 76 152 77 87 SP SD: 0.1965 c. M: 0.3494 c. 570: 155 80 161 82 92 SP SD: 0.2714 c. M:-0.3158 c. 630: 171 89 178 90 102 SP SD: 0.2456 c. M: 0.2857 c. 662: 180 93 187 95 107 SP SD: 0.1597 c. M:-0.2840 c. 718: 195 101 203 103 116 SP SD: 0.1491 c. M: 0.2925 c. 754: 205 106 213 108 122 SP SD: 0.1403 c. M:-0.2599 c. 810: 220 114 229 116 131 SP SD: 0.1008 c. M: 0.1852 c. 1108: 301 156 313 159 179 SP SD: 0.0721 c. M:-0.1372 c. 1193: 324 168 337 171 193 SP SD: 0.1082 c. M: 0.1358 c. 1200: 326 169 339 172 194 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x 2 S SD: 0.0000 cents 2 x x 3 x 4 S SD: 66.0225 cents 3 x 4:5 x 6 S SD: 16.8169 cents 4:5 x 6:7:8 S SD: 37.4629 cents 5:6:7:8:9:10 H SD: 18.2349 cents 6:7:8:10:11:12 S SD: 17.8010 cents 9:11:12:15:16:18 SD: 11.1387 cents 10:12:13:16:18:20 SD: 9.6290 cents 14:17:19:23:25:28 SD: 8.6946 cents 15:18:20:24:27:30 S SD: 5.1525 cents 18:22:24:29:32:36 SD: 5.0407 cents 19:23:25:31:34:38 SD: 4.9114 cents 24:29:32:39:43:48 SD: 1.6396 cents 57:69:76:92:102:114 SD: 1.5620 cents 58:70:77:94:104:116 SD: 1.3867 cents 63:76:84:102:113:126 SD: 1.2777 cents 76:92:101:123:136:152 SD: 1.1326 cents 81:98:108:131:145:162 SD: 1.1167 cents 97:117:129:157:173:194 SD: 0.9617 cents 100:121:133:162:179:200 SD: 0.9583 cents 112:135:149:181:200:224 SD: 0.9292 cents 115:139:153:186:206:230 SD: 0.8480 cents 121:146:161:196:216:242 SD: 0.6233 cents 136:164:181:220:243:272 SD: 0.5196 cents 160:193:213:259:286:320 SD: 0.2979 cents 184:222:245:298:329:368 SD: 0.2802 cents 236:285:314:382:422:472 SD: 0.1847 cents 372:449:495:602:665:744 SD: 0.1819 cents 396:478:527:641:708:792 SD: 0.0765 cents 420:507:559:680:751:840 SD: 0.0455 cents