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