Scala analysis: xen18-darreg-djami-iraq-1
Maqam Iraq, without bakiye
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 180.000 cents 180.000000 2: 384.000 cents 384.000000 3: 498.000 cents 498.000000 4: 678.000 cents 678.000000 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: 180.0000 cents 180.0000 2: 204.0000 cents 204.0000 3: 114.0000 cents 114.0000 4: 180.0000 cents 180.0000 5: 204.0000 cents 204.0000 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: 1 294.00000 cents 2: 3 318.00000 cents 2: 3 384.00000 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: 3 816.00000 cents 5: 3 882.00000 cents 5: 1 906.00000 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: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 180.0 384.0 498.0 678.0 882.0 996.0 1200.0 180.0 : 204.0 318.0 498.0 702.0 816.0 1020.0 1200.0 384.0 : 114.0 294.0 498.0 612.0 816.0 996.0 1200.0 498.0 : 180.0 384.0 498.0 702.0 882.0 1086.0 1200.0 678.0 : 204.0 318.0 522.0 702.0 906.0 1020.0 1200.0 882.0 : 114.0 318.0 498.0 702.0 816.0 996.0 1200.0 996.0 : 204.0 384.0 588.0 702.0 882.0 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 .. 384.0000 cents 90.00000 cents 90.00000 cents 3: 498.0000 .. 588.0000 cents 90.00000 cents 114.00000 cents 4: 612.0000 .. 702.0000 cents 90.00000 cents 24.00000 cents 5: 816.0000 .. 906.0000 cents 90.00000 cents 114.00000 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 : 171.00000 cents, oct.: 1197.00000 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 200-tone equal temperament with octave 1200.000 cents degrees: 30 64 83 113 147 166 200 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: ABCABCB Step pattern size order : MLSMLSL 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 1 0 0 0 3 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 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 : 1.379224 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.550000 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 24.00000 cents Most common intervals : 498.00000 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 318.000 702.000 cents 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 : 1 = 14.2857% 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: 23.2063 c. M: 41.1429 c. Lebeng 12: 2 2 1 2 2 1 2 P M ME S SD: 14.5602 c. M:-22.0000 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: 9.7399 c. M:-16.7368 c. Nineteen-tone Mixolydian 29: 4 5 3 4 5 3 5 SP T3 SD: 10.5436 c. M: 15.9310 c. 31: 5 5 3 5 5 3 5 SP M DE S SD: 10.3608 c. M:-18.7742 c. Intense Diatonic Hypophrygian, M.Mixolydian 34: 5 6 3 5 6 3 6 P T3 SD: 4.7931 c. M: 7.7647 c. 41: 6 7 4 6 7 4 7 SP T3 SD: 3.1961 c. M: 4.8293 c. 53: 8 9 5 8 9 5 9 SP T3 SD: 0.8242 c. M:-1.2453 c. 147: 22 25 14 22 25 14 25 SP T3 SD: 0.2971 c. M: 0.4490 c. 200: 30 34 19 30 34 19 34 SP T3 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: 11.9775 cents 3 x x 4 x 5 x 6 S SD: 0.7864 cents 4 x 5 x 6 x 7:8 S SD: 9.0748 cents 5 x 6:7 x 8:9:10 S SD: 26.0372 cents 6:7 x 8:9:10:11:12 S SD: 17.4591 cents 7:8:9 x 10:12 x 14 S SD: 21.4516 cents 8:9:10:11:12:13:14:16 S SD: 11.4750 cents 9:10:11:12:13:15:16:18 SD: 7.9061 cents 12:13:15:16:18:20:21:24 SD: 7.8758 cents 15:17:19:20:22:25:27:30 SD: 7.3937 cents 17:19:21:23:25:28:30:34 SD: 5.9339 cents 19:21:24:25:28:32:34:38 SD: 5.6826 cents 21:23:26:28:31:35:37:42 SD: 4.4437 cents 27:30:34:36:40:45:48:54 SD: 2.2364 cents 36:40:45:48:53:60:64:72 SD: 1.3352 cents 63:70:79:84:93:105:112:126 SD: 1.3266 cents 72:80:90:96:107:120:128:144 SD: 1.2644 cents 81:90:101:108:120:135:144:162 SD: 0.6580 cents 117:130:146:156:173:195:208:234 SD: 0.5061 cents 165:183:206:220:244:275:293:330 SD: 0.4560 cents 202:224:252:269:299:336:359:404 SD: 0.4276 cents 217:241:271:289:321:361:386:434 SD: 0.4238 cents 221:245:276:295:327:368:393:442 SD: 0.4020 cents 229:254:286:305:339:381:407:458 SD: 0.3585 cents 238:264:297:317:352:396:423:476 SD: 0.3003 cents 265:294:331:353:392:441:471:530 SD: 0.2777 cents 319:354:398:425:472:531:567:638 SD: 0.2409 cents 346:384:432:461:512:576:615:692 SD: 0.2064 cents 375:416:468:500:555:624:667:750 SD: 0.1992 cents 402:446:502:536:595:669:715:804 SD: 0.1987 cents 411:456:513:548:608:684:731:822 SD: 0.1335 cents 540:599:674:720:799:899:960:1080 SD: 0.1085 cents 576:639:719:768:852:959:1024:1152 SD: 0.0995 cents