Scala analysis: xen18-darreg-djami-rast
Maqam Rast
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: 384.000 cents 384.000000 3: 498.000 cents 498.000000 4: 702.000 cents 702.000000 5: 882.000 cents 882.000000 6: 996.000 cents 996.000000 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 204.0000 cents 204.0000 1: 204.0000 cents 204.0000 2: 180.0000 cents 180.0000 3: 114.0000 cents 114.0000 4: 204.0000 cents 204.0000 5: 180.0000 cents 180.0000 6: 114.0000 cents 114.0000 7: 204.0000 cents 204.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 114.00000 cents 1: 2 180.00000 cents 1: 3 204.00000 cents 2: 2 294.00000 cents 2: 2 318.00000 cents 2: 2 384.00000 cents 2: 1 408.00000 cents 3: 5 498.00000 cents 3: 1 522.00000 cents 3: 1 588.00000 cents 4: 1 612.00000 cents 4: 1 678.00000 cents 4: 5 702.00000 cents 5: 1 792.00000 cents 5: 2 816.00000 cents 5: 2 882.00000 cents 5: 2 906.00000 cents 6: 3 996.00000 cents 6: 2 1020.00000 cents 6: 2 1086.00000 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 204.0 384.0 498.0 702.0 882.0 996.0 1200.0 204.0 : 180.0 294.0 498.0 678.0 792.0 996.0 1200.0 384.0 : 114.0 318.0 498.0 612.0 816.0 1020.0 1200.0 498.0 : 204.0 384.0 498.0 702.0 906.0 1086.0 1200.0 702.0 : 180.0 294.0 498.0 702.0 882.0 996.0 1200.0 882.0 : 114.0 318.0 522.0 702.0 816.0 1020.0 1200.0 996.0 : 204.0 408.0 588.0 702.0 906.0 1086.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 114.0000 .. 204.0000 cents 90.00000 cents 114.00000 cents 2: 294.0000 .. 408.0000 cents 114.00000 cents 90.00000 cents 3: 498.0000 .. 588.0000 cents 90.00000 cents 90.00000 cents 4: 612.0000 .. 702.0000 cents 90.00000 cents 24.00000 cents 5: 792.0000 .. 906.0000 cents 114.00000 cents 90.00000 cents 6: 996.0000 .. 1086.0000 cents 90.00000 cents 90.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 114.00000 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 204.00000 cents Average / Smallest step : 1.503759 Largest / Average step : 1.190000 Largest / Smallest step : 1.789474 Median interval of one step : 180.00000 cents, amount: 2 Most common interval of one step : 204.00000 cents, amount: 3 Least squares average step : 171.85714 cents, oct.: 1203.00000 cents Scale is strictly proper Scale is a mode of a 200-tone equal temperament with octave 1200.000 cents degrees: 34 64 83 117 147 166 200 Least number of segments generator : 101 of 606.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 117 of 702.000 cents and inv. generated superset size: 12 = 5 more = 171.429% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCABCA Step pattern size order : LMSLMSL Interval vector is [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 ] Scale is a Constant Structure, by a margin of 24.00000 cents Scale diversity : 1.426476 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.510000 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 24.00000 cents Most common intervals : 498.00000 cents & inv., amount: 5 Most common triad is 0.0 498.000 702.000 cents, amount: 3 Number of recognisable fifths : 5, average 702.0000 cents Scale contains two identical conjunct tetrachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 5 = 71.4286% Limited inverse transpositions with margin 90.0000 cents: 1 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 26.6267 c. M: 41.1429 c. Lebeng 12: 2 2 1 2 2 1 2 P M ME S SD: 9.4112 c. M:-18.0000 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 19: 3 3 2 3 3 2 3 SP M ME S SD: 8.9279 c. M: 14.5263 c. Nineteen-tone Mixolydian 22: 4 3 2 4 3 2 4 P SD: 9.2083 c. M:-14.1818 c. Murchhana Suddhasadja, Raga Harikambhoji, Palaiyazh 29: 5 4 3 5 4 3 5 SP SD: 6.8150 c. M: 13.0345 c. 31: 5 5 3 5 5 3 5 SP M DE S SD: 7.0907 c. M: 10.4516 c. Intense Diatonic Hypophrygian, M.Mixolydian 34: 6 5 3 6 5 3 6 P SD: 4.9105 c. M: 7.7647 c. 41: 7 6 4 7 6 4 7 SP SD: 2.0659 c. M: 3.9512 c. 53: 9 8 5 9 8 5 9 SP SD: 0.5327 c. M:-1.0189 c. 147: 25 22 14 25 22 14 25 SP SD: 0.1921 c. M: 0.3673 c. 200: 34 30 19 34 30 19 34 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: 0.7864 cents 4 x 5 x 6 x 7:8 S SD: 6.8181 cents 5 x 6:7 x 8:9:10 S SD: 26.0372 cents 6:7 x 8:9:10:11:12 S SD: 13.7497 cents 7:8:9 x 11:12 x 14 SD: 22.3080 cents 8:9:10:11:12:13:14:16 S SD: 10.4066 cents 12:14:15:16:18:20:21:24 S SD: 9.7960 cents 14:16:17:19:21:23:25:28 SD: 9.6269 cents 15:17:19:20:23:25:27:30 SD: 7.4431 cents 16:18:20:21:24:27:28:32 S SD: 6.4748 cents 18:20:22:24:27:30:32:36 S SD: 6.0793 cents 23:26:29:31:35:38:41:46 SD: 5.5761 cents 24:27:30:32:36:40:43:48 SD: 1.9943 cents 48:54:60:64:72:80:85:96 SD: 1.0655 cents 72:81:90:96:108:120:128:144 S SD: 0.4724 cents 198:223:247:264:297:330:352:396 SD: 0.4610 cents 206:232:257:275:309:343:366:412 SD: 0.4572 cents 226:254:282:301:339:376:402:452 SD: 0.4258 cents 230:259:287:307:345:383:409:460 SD: 0.3975 cents 238:268:297:317:357:396:423:476 SD: 0.3579 cents 262:295:327:349:393:436:466:524 SD: 0.3355 cents 270:304:337:360:405:449:480:540 SD: 0.2887 cents 306:344:382:408:459:509:544:612 SD: 0.2437 cents 342:385:427:456:513:569:608:684 SD: 0.1823 cents 378:425:472:504:567:629:672:756 SD: 0.1821 cents 414:466:517:552:621:689:736:828 SD: 0.1531 cents 432:486:539:576:648:719:768:864 SD: 0.1297 cents 480:540:599:640:720:799:853:960 SD: 0.1215 cents 504:567:629:672:756:839:896:1008 SD: 0.0781 cents