Scala analysis: CD03_08_rast_Egypt

Suite - Aziz 'Uthmân (rast, Egypt)

Generated by Scala: https://www.huygens-fokker.org/scala/

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:        207.890 cents     207.889832
  2:        354.940 cents     354.940070
  3:        502.193 cents     502.192678
  4:        697.875 cents     697.875174
  5:        838.296 cents     838.295610
  6:        995.718 cents     995.718438
  7:       1200.000 cents    1200.000000
SHOW/INTERVAL
  0:        204.2816 cents    204.2816
  1:        207.8898 cents    207.8898
  2:        147.0502 cents    147.0502
  3:        147.2526 cents    147.2526
  4:        195.6825 cents    195.6825
  5:        140.4204 cents    140.4204
  6:        157.4228 cents    157.4228
  7:        204.2816 cents    204.2816
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 140.42044 cents
  1:   1 147.05024 cents
  1:   1 147.25261 cents
  1:   1 157.42283 cents
  1:   1 195.68250 cents
  1:   1 204.28156 cents
  1:   1 207.88983 cents
  2:   1 294.30285 cents
  2:   1 297.84326 cents
  2:   1 336.10293 cents
  2:   1 342.93510 cents
  2:   1 354.94007 cents
  2:   1 361.70439 cents
  2:   1 412.17139 cents
  3:   1 483.35554 cents
  3:   1 489.98534 cents
  3:   1 493.52576 cents
  3:   1 502.12483 cents
  3:   1 502.19268 cents
  3:   1 559.22163 cents
  3:   1 569.59422 cents
  4:   1 630.40578 cents
  4:   1 640.77837 cents
  4:   1 697.80732 cents
  4:   1 697.87517 cents
  4:   1 706.47424 cents
  4:   1 710.01466 cents
  4:   1 716.64446 cents
  5:   1 787.82861 cents
  5:   1 838.29561 cents
  5:   1 845.05993 cents
  5:   1 857.06490 cents
  5:   1 863.89707 cents
  5:   1 902.15674 cents
  5:   1 905.69715 cents
  6:   1 992.11017 cents
  6:   1 995.71844 cents
  6:   1 1004.31750 cents
  6:   1 1042.57717 cents
  6:   1 1052.74739 cents
  6:   1 1052.94976 cents
  6:   1 1059.57956 cents
Highest number of different intervals for one interval class: 7
Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
         1     2     3     4     5     6      7     
 0.0   : 207.9 354.9 502.2 697.9 838.3 995.7  1200.0
 207.9 : 147.1 294.3 490.0 630.4 787.8 992.1  1200.0
 354.9 : 147.3 342.9 483.4 640.8 845.1 1052.9 1200.0
 502.2 : 195.7 336.1 493.5 697.8 905.7 1052.7 1200.0
 697.9 : 140.4 297.8 502.1 710.0 857.1 1004.3 1200.0
 838.3 : 157.4 361.7 569.6 716.6 863.9 1059.6 1200.0
 995.7 : 204.3 412.2 559.2 706.5 902.2 1042.6 1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  140.4204  .. 207.8898 cents      67.46940 cents                     140.42044 cents
  2:  294.3028  .. 412.1714 cents      117.86855 cents                    86.41301 cents
  3:  483.3555  .. 569.5942 cents      86.23868 cents                     71.18415 cents
  4:  630.4058  .. 716.6445 cents      86.23868 cents                     60.81156 cents
  5:  787.8286  .. 905.6972 cents      117.86855 cents                    71.18415 cents
  6:  992.1102  .. 1059.5796 cents     67.46940 cents                     86.41301 cents
SHOW DATA
Number of notes                     : 7
-- Interval properties --
Smallest interval                   : 140.42044 cents, class 1
Average step (divided formal octave): 171.4286 cents
Largest one step interval           : 207.88983 cents
Average / Smallest step             : 1.220824
Largest / Average step              : 1.212691
Largest / Smallest step             : 1.480481
Median interval of one step         : 157.42283 cents, amount: 1
Least squares average step          : 169.86884 cents, oct.:  1189.08187 cents
Scale is strictly proper
Step pattern alph. order: ABCDEFG
Step pattern size order : GBCEADF
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 60.81156 cents
Scale diversity                     : 1.441665
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.547372
Rothenberg efficiency               : 0.285714   redundancy: 0.714286
Efficiency x scale size             : 2.000000
Number of different interval sizes  : 42 = 7.00000 / class
Number of one step interval sizes   : 7
Highest interval variety            : 7
Mean interval variety               : 7.00000 = 7
Median interval variety             : 7
Lowest interval variety             : 7
Smallest interval difference        : 0.06785 cents
Number of recognisable fifths       : 5, average 705.7632 cents
Number of appreciable fifths        : 4, average 703.0428 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: 21.3945 c. M: 36.4613 c.  Lebeng
 10:  2 1 1 2 1 1 2   P   D3 I SD: 21.7696 c. M: 35.7184 c. 
 16:  3 2 2 2 2 2 3   P   D3 I SD: 18.3016 c. M: 22.8752 c. 
 17:  3 2 2 3 2 2 3  SP   D3 I SD: 6.3372 c. M:-8.7632 c.  Safi al-Din's maqam Rast
 24:  4 3 3 4 3 3 4  SP   D3 I SD: 5.9917 c. M:-11.7044 c.  Miha'il Musaqa's mode: Egypt, Neutral Diatonic Hypodorian, Dastgah-e Sehgah, Maqam Nairuz
 40:  7 5 5 6 5 5 7  SP      I SD: 5.1911 c. M: 7.8752 c. 
 41:  7 5 5 7 5 5 7  SP   D3 I SD: 5.0069 c. M:-10.4849 c. 
 50:  9 6 6 8 6 7 8  SP        SD: 5.9988 c. M:-12.2816 c. 
 52:  9 6 7 8 6 7 9  SP        SD: 5.4348 c. M: 8.7862 c. 
 53:  9 7 6 9 6 7 9  SP      I SD: 3.8525 c. M:-7.3241 c. 
 57:  10 7 7 9 7 7 10  SP      I SD: 3.5550 c. M: 6.2448 c. 
 64:  11 8 8 10 8 8 11  SP      I SD: 3.1962 c. M:-5.4544 c. 
 70:  12 9 8 12 8 9 12  SP      I SD: 3.4972 c. M:-5.0599 c. 
 74:  13 9 9 12 9 9 13  SP      I SD: 3.3708 c. M: 6.5292 c. 
 77:  13 10 9 13 9 10 13  SP      I SD: 3.3309 c. M: 5.2924 c. 
 81:  14 10 10 13 10 10 14  SP      I SD: 2.7508 c. M:-6.1488 c. 
 82:  14 10 10 14 9 11 14  SP        SD: 3.4386 c. M: 4.6317 c. 
 84:  15 10 10 14 10 11 14  SP        SD: 3.6688 c. M:-6.3959 c. 
 86:  15 10 11 14 10 11 15  SP        SD: 3.0633 c. M: 6.1029 c. 
 88:  15 11 11 14 10 12 15  SP        SD: 3.0417 c. M: 6.4774 c. 
 93:  16 12 11 15 11 12 16  SP      I SD: 2.6607 c. M:-6.3503 c. 
 94:  16 12 11 16 11 12 16  SP      I SD: 3.2595 c. M: 4.3203 c. 
 96:  17 11 12 16 11 13 16  SP        SD: 3.2502 c. M: 4.9401 c. 
 98:  17 12 12 16 11 13 17  SP        SD: 2.5922 c. M: 5.6425 c. 
 105: 18 13 13 17 12 14 18  SP        SD: 1.8621 c. M: 4.0099 c. 
 119: 21 14 15 19 14 16 20  SP        SD: 2.2637 c. M:-3.8749 c. 
 122: 21 15 15 20 14 16 21  SP        SD: 1.3721 c. M: 2.2758 c. 
 146: 25 18 18 24 17 19 25  SP        SD: 1.2417 c. M: 2.4104 c. 
 163: 28 20 20 27 19 21 28  SP        SD: 1.4482 c. M: 1.8534 c. 
 169: 29 21 21 27 20 22 29  SP        SD: 1.4454 c. M: 2.0172 c. 
 172: 30 21 21 28 20 23 29  SP        SD: 1.0571 c. M:-1.9560 c. 
 189: 33 23 23 31 22 25 32  SP        SD: 0.8426 c. M:-1.6340 c. 
 213: 37 26 26 35 25 28 36  SP        SD: 0.8358 c. M:-1.4647 c. 
 236: 41 29 29 38 28 31 40  SP        SD: 0.8966 c. M: 1.2650 c. 
 253: 44 31 31 41 30 33 43  SP        SD: 0.7209 c. M:-1.2301 c. 
 282: 49 34 35 46 33 37 48  SP        SD: 0.7018 c. M: 1.7486 c. 
 294: 51 36 36 48 34 39 50  SP        SD: 0.6103 c. M: 1.5609 c. 
 301: 52 37 37 49 35 40 51  SP        SD: 0.5989 c. M: 1.0863 c. 
 311: 54 38 38 51 36 41 53  SP        SD: 0.5174 c. M: 0.9966 c. 
 318: 55 39 39 52 37 42 54  SP        SD: 0.3563 c. M: 0.5598 c. 
 375: 65 46 46 61 44 49 64  SP        SD: 0.2613 c. M: 0.5184 c. 
 564: 98 69 69 92 66 74 96  SP        SD: 0.2762 c. M:-0.6208 c. 
 571: 99 70 70 93 67 75 97  SP        SD: 0.2227 c. M:-0.4287 c. 
 676: 117 83 83 110 79 89 115  SP        SD: 0.2193 c. M: 0.4258 c. 
 686: 119 84 84 112 80 90 117  SP        SD: 0.2489 c. M: 0.3947 c. 
 693: 120 85 85 113 81 91 118  SP        SD: 0.0893 c. M: 0.2004 c. 
 1092: 189 134 134 178 128 143 186  SP        SD: 0.1101 c. M: 0.1975 c. 
 1264: 219 155 155 206 148 166 215  SP        SD: 0.0866 c. M:-0.1676 c. 
 1281: 222 157 157 209 150 168 218  SP        SD: 0.0744 c. M:-0.1119 c. 
 1785: 309 219 219 291 209 234 304  SP        SD: 0.0732 c. M: 0.1587 c. 
 1957: 339 240 240 319 229 257 333  SP        SD: 0.0635 c. M:-0.0931 c. 
 1974: 342 242 242 322 231 259 336  SP        SD: 0.0392 c. M:-0.0751 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: 2.0399 cents
 3 x x 4 x 5 x 6  S SD: 15.4165 cents
 4 x 5 x 6 x 7:8  S SD: 10.3807 cents
 5 x 6:7 x 8:9:10  S SD: 19.0577 cents
 6:7 x 8:9:10:11:12  S SD: 15.3769 cents
 7:8 x 9:10:11:12:14  S SD: 22.6932 cents
 8:9:10:11:12:13:14:16  S SD: 9.2121 cents
 14:16:17:19:21:23:25:28    SD: 6.5891 cents
 18:20:22:24:27:29:32:36    SD: 4.2851 cents
 26:29:32:35:39:42:46:52    SD: 3.7105 cents
 30:34:37:40:45:49:53:60    SD: 2.8935 cents
 32:36:39:43:48:52:57:64    SD: 2.4481 cents
 39:44:48:52:58:63:69:78    SD: 2.4036 cents
 40:45:49:53:60:65:71:80    SD: 2.3945 cents
 45:51:55:60:67:73:80:90    SD: 2.1632 cents
 48:54:59:64:72:78:85:96    SD: 1.4348 cents
 62:70:76:83:93:101:110:124    SD: 1.3390 cents
 71:80:87:95:106:115:126:142    SD: 1.0134 cents
 93:105:114:124:139:151:165:186    SD: 0.9381 cents
 101:114:124:135:151:164:180:202    SD: 0.7589 cents
 119:134:146:159:178:193:212:238    SD: 0.7091 cents
 127:143:156:170:190:206:226:254    SD: 0.6349 cents
 149:168:183:199:223:242:265:298    SD: 0.3321 cents
 220:248:270:294:329:357:391:440    SD: 0.1952 cents
 369:416:453:493:552:599:656:738    SD: 0.1585 cents
 493:556:605:659:738:800:876:986    SD: 0.1456 cents
 562:634:690:751:841:912:999:1124    SD: 0.1338 cents
 580:654:712:775:868:941:1031:1160    SD: 0.1009 cents