Scala analysis: xen18-darreg-djami-hidjaz
Maqam Hidjaz
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: 294.000 cents 294.000000 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: 114.0000 cents 114.0000 3: 204.0000 cents 204.0000 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 : 180.0 294.0 498.0 678.0 882.0 996.0 1200.0 180.0 : 114.0 318.0 498.0 702.0 816.0 1020.0 1200.0 294.0 : 204.0 384.0 588.0 702.0 906.0 1086.0 1200.0 498.0 : 180.0 384.0 498.0 702.0 882.0 996.0 1200.0 678.0 : 204.0 318.0 522.0 702.0 816.0 1020.0 1200.0 882.0 : 114.0 318.0 498.0 612.0 816.0 996.0 1200.0 996.0 : 204.0 384.0 498.0 702.0 882.0 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 : 169.71429 cents, oct.: 1188.00000 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 49 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 Scale is fully connected major-minor triadic in 200-tone equal temperament Step pattern alph. order: ABCACBC Step pattern size order : MSLMLSL 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 sum-free (all different intervals) 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 0.0 384.000 702.000 cents Most common triad is 0.0 498.000 702.000 cents, amount: 3 Number of recognisable fifths : 5, average 702.0000 cents 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: 25.2530 c. M:-48.8571 c. Lebeng 11: 2 1 2 1 2 1 2 P M ME I SD: 28.4205 c. M:-47.4545 c. Superkleismic-7 12: 2 1 2 2 2 1 2 P M ME I SD: 13.4377 c. M:-22.0000 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 19: 3 2 3 3 3 2 3 SP M ME I SD: 12.6113 c. M:-21.7895 c. Nineteen-tone Dorian 25: 4 2 4 4 4 3 4 SP T3 SD: 12.0000 c. M: 18.0000 c. 28: 4 3 5 4 5 2 5 P SD: 11.1098 c. M:-18.0000 c. 29: 4 3 5 4 5 3 5 SP T3 SD: 9.7307 c. M: 15.9310 c. 33: 5 3 6 5 5 3 6 SP SD: 9.1778 c. M: 14.1818 c. 34: 5 3 6 5 6 3 6 P T3 SD: 6.3080 c. M: 11.6471 c. 41: 6 4 7 6 7 4 7 SP T3 SD: 2.9497 c. M: 4.8293 c. 53: 8 5 9 8 9 5 9 SP T3 SD: 0.7606 c. M:-1.2453 c. 147: 22 14 25 22 25 14 25 SP T3 SD: 0.2742 c. M: 0.4490 c. 200: 30 19 34 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: 24.7918 cents 5 x 6:7 x 8:9:10 S SD: 22.5777 cents 6 x 7:8:9:10:11:12 S SD: 10.7536 cents 7:8 x 9:10:12 x 14 S SD: 22.6743 cents 8:9 x 11:12:13:14:16 SD: 13.3819 cents 9:10:11:12:13:15:16:18 SD: 9.6640 cents 12:13:14:16:18:20:21:24 S SD: 8.7715 cents 15:17:18:20:22:25:27:30 SD: 7.1568 cents 17:19:20:23:25:28:30:34 SD: 5.6331 cents 18:20:21:24:27:30:32:36 S SD: 5.1926 cents 21:23:25:28:31:35:37:42 SD: 4.1058 cents 27:30:32:36:40:45:48:54 S SD: 0.5953 cents 156:173:185:208:231:260:277:312 SD: 0.5419 cents 173:192:205:231:256:288:308:346 SD: 0.5288 cents 183:203:217:244:271:305:325:366 SD: 0.5084 cents 184:204:218:245:272:306:327:368 SD: 0.4817 cents 194:215:230:259:287:323:345:388 SD: 0.4664 cents 211:234:250:281:312:351:375:422 SD: 0.3694 cents 238:264:282:317:352:396:423:476 SD: 0.2915 cents 265:294:314:353:392:441:471:530 SD: 0.2407 cents 292:324:346:389:432:486:519:584 SD: 0.2123 cents 319:354:378:425:472:531:567:638 SD: 0.2016 cents 357:396:423:476:528:594:635:714 SD: 0.1960 cents 384:426:455:512:568:639:683:768 SD: 0.1591 cents 411:456:487:548:608:684:731:822 SD: 0.1351 cents 438:486:519:584:648:729:779:876 SD: 0.1241 cents 486:539:576:648:719:809:864:972 SD: 0.1218 cents 513:569:608:684:759:854:912:1026 SD: 0.1081 cents 540:599:640:720:799:899:960:1080 SD: 0.1041 cents