Scala analysis: CD10_11_Egypt

Fin de la messe - Mîkhâ'îl Jirjis al-Batânûnî (unknown maqam, Egypt)

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:        196.601 cents     196.601293
  2:        504.485 cents     504.485119
  3:        716.962 cents     716.962266
  4:        952.983 cents     952.983261
  5:       1200.000 cents    1200.000000
SHOW/INTERVAL
  0:        247.0167 cents    247.0167
  1:        196.6013 cents    196.6013
  2:        307.8838 cents    307.8838
  3:        212.4771 cents    212.4771
  4:        236.0210 cents    236.0210
  5:        247.0167 cents    247.0167
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 196.60129 cents
  1:   1 212.47715 cents
  1:   1 236.02099 cents
  1:   1 247.01674 cents
  1:   1 307.88383 cents
  2:   1 443.61803 cents
  2:   1 448.49814 cents
  2:   1 483.03773 cents
  2:   1 504.48512 cents
  2:   1 520.36097 cents
  3:   1 679.63903 cents
  3:   1 695.51488 cents
  3:   1 716.96227 cents
  3:   1 751.50186 cents
  3:   1 756.38197 cents
  4:   1 892.11617 cents
  4:   1 952.98326 cents
  4:   1 963.97901 cents
  4:   1 987.52285 cents
  4:   1 1003.39871 cents
Highest number of different intervals for one interval class: 5
Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
         1     2     3     4      5     
 0.0   : 196.6 504.5 717.0 953.0  1200.0
 196.6 : 307.9 520.4 756.4 1003.4 1200.0
 504.5 : 212.5 448.5 695.5 892.1  1200.0
 717.0 : 236.0 483.0 679.6 987.5  1200.0
 953.0 : 247.0 443.6 751.5 964.0  1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  196.6013  .. 307.8838 cents      111.28253 cents                    196.60129 cents
  2:  443.6180  .. 520.3610 cents      76.74294 cents                     135.73421 cents
  3:  679.6390  .. 756.3820 cents      76.74294 cents                     159.27805 cents
  4:  892.1162  .. 1003.3987 cents     111.28253 cents                    135.73421 cents
SHOW DATA
Number of notes                     : 5
-- Interval properties --
Smallest interval                   : 196.60129 cents, class 1
Average step (divided formal octave): 240.0000 cents
Largest one step interval           : 307.88383 cents
Average / Smallest step             : 1.220745
Largest / Average step              : 1.282849
Largest / Smallest step             : 1.566032
Median interval of one step         : 236.02099 cents, amount: 1
Least squares average step          : 239.42530 cents, oct.:  1197.12649 cents
Scale is strictly proper
Step pattern alph. order: ABCDE
Step pattern size order : AEBCD
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 135.73421 cents
Scale diversity                     : 1.394460
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.686624
Rothenberg efficiency               : 0.400000   redundancy: 0.600000
Efficiency x scale size             : 2.000000
Number of different interval sizes  : 20 = 5.00000 / class
Number of one step interval sizes   : 5
Highest interval variety            : 5
Mean interval variety               : 5.00000 = 5
Median interval variety             : 5
Lowest interval variety             : 5
Smallest interval difference        : 4.88011 cents
Number of recognisable fifths       : 2, average 706.2386 cents
Number of appreciable fifths        : 1, average 695.5149 cents
Best fifths form a closed circle
Best minor thirds form a closed circle
Formal octave complements present   : 1 = 20.0000%
Limited transpositions with margin 111.2825 cents:
 3
Limited inverse transpositions with margin 111.2825 cents:
 3
-- Rational properties --
FIT/MODE
  5:  1 1 1 1 1  SP B ME I SD: 22.5452 c. M:-43.3987 c. 
 12:  2 3 2 3 2  SP M ME I SD: 22.4943 c. M:-47.0167 c.  Suspended Pentatonic, Raga Madhyamavati, Madhmat Sarang, Megh, Egyptian, Shang, Rui Bin, Jin Yu, Qing Yu: China, Yo: Japan, Ngu Cung Dao: Vietnam, Yematebela wofe: Ethiopia
 13:  2 3 3 2 3  SP M ME S SD: 25.8638 c. M: 42.9467 c. 
 14:  2 4 2 3 3  SP   D3 S SD: 19.0194 c. M: 31.2480 c. 
 17:  3 4 3 4 3  SP M ME I SD: 18.4547 c. M:-35.2520 c.  Seventeen-tone Suspended Pentatonic
 18:  3 5 3 3 4  SP   T3   SD: 17.3084 c. M:-28.8482 c. 
 19:  3 5 3 4 4  SP   D3 S SD: 10.7415 c. M: 22.2254 c. 
 23:  4 6 4 4 5  SP   T3   SD: 12.7858 c. M:-17.2540 c. 
 24:  4 6 4 5 5  SP   D3 S SD: 8.1029 c. M: 16.9623 c. 
 29:  5 7 5 6 6  SP   D3 S SD: 8.4041 c. M: 13.5140 c. 
 30:  5 8 5 6 6  SP   T3 S SD: 7.8832 c. M:-15.5149 c. 
 35:  6 9 6 7 7  SP   T3 S SD: 6.8929 c. M:-9.8006 c. 
 38:  6 10 7 7 8  SP        SD: 5.8382 c. M:-9.3535 c. 
 43:  7 11 8 8 9  SP        SD: 4.4207 c. M:-8.6191 c. 
 47:  8 12 8 9 10  SP        SD: 5.8250 c. M: 8.3024 c. 
 48:  8 12 9 9 10  SP        SD: 4.5863 c. M:-8.0377 c. 
 50:  8 13 9 10 10  SP        SD: 3.9967 c. M:-7.0167 c. 
 54:  9 14 9 11 11  SP   T3 S SD: 4.3888 c. M:-6.6260 c. 
 55:  9 14 10 11 11  SP        SD: 3.6230 c. M:-7.0167 c. 
 57:  9 15 10 11 12  SP        SD: 4.1063 c. M: 7.1276 c. 
 62:  10 16 11 12 13  SP        SD: 2.5583 c. M: 4.5962 c. 
 67:  11 17 12 13 14  SP        SD: 2.1602 c. M: 3.7295 c. 
 92:  15 24 16 18 19  SP        SD: 1.9732 c. M:-4.2105 c. 
 97:  16 25 17 19 20  SP        SD: 1.3950 c. M:-2.7314 c. 
 117: 19 30 21 23 24  SP        SD: 1.2961 c. M: 1.9210 c. 
 141: 23 36 25 28 29  SP        SD: 1.4570 c. M: 2.3575 c. 
 147: 24 38 26 29 30  SP        SD: 1.3864 c. M:-2.1188 c. 
 152: 25 39 27 30 31  SP        SD: 1.3054 c. M:-2.2799 c. 
 159: 26 41 28 31 33  SP        SD: 1.0661 c. M: 2.0399 c. 
 164: 27 42 29 32 34  SP        SD: 0.9164 c. M: 1.7637 c. 
 166: 27 43 29 33 34  SP        SD: 1.2327 c. M:-1.5390 c. 
 169: 28 43 30 33 35  SP        SD: 1.2105 c. M:-2.2153 c. 
 171: 28 44 30 34 35  SP        SD: 0.8900 c. M:-1.4027 c. 
 209: 34 54 37 41 43  SP        SD: 0.7863 c. M: 1.3860 c. 
 214: 35 55 38 42 44  SP        SD: 0.4159 c. M:-0.7947 c. 
 281: 46 72 50 55 58  SP        SD: 0.4530 c. M: 0.6701 c. 
 335: 55 86 59 66 69  SP        SD: 0.4091 c. M:-0.5895 c. 
 378: 62 97 67 74 78  SP        SD: 0.3841 c. M: 0.6023 c. 
 390: 64 100 69 77 80  SP        SD: 0.4163 c. M:-0.8629 c. 
 433: 71 111 77 85 89  SP        SD: 0.4108 c. M:-0.8206 c. 
 447: 73 115 79 88 92  SP        SD: 0.3082 c. M: 0.6281 c. 
 452: 74 116 80 89 93  SP        SD: 0.1082 c. M: 0.1481 c. 
 1001: 164 257 177 197 206  SP        SD: 0.1044 c. M:-0.2102 c. 
 1068: 175 274 189 210 220  SP        SD: 0.0927 c. M: 0.1743 c. 
 1185: 194 304 210 233 244  SP        SD: 0.1088 c. M: 0.1813 c. 
 1220: 200 313 216 240 251  SP        SD: 0.1003 c. M:-0.1315 c. 
 1282: 210 329 227 252 264  SP        SD: 0.0527 c. M: 0.0971 c. 
 1734: 284 445 307 341 357  SP        SD: 0.0340 c. M: 0.0615 c. 
 2191: 359 562 388 431 451  SP        SD: 0.0307 c. M: 0.0579 c. 
FIT/HARMONIC
 1 x x x x 2  S SD: 0.0000 cents
 2 x x 3 x 4  S SD: 7.5036 cents
 3 x 4 x 5:6  S SD: 22.9754 cents
 4 x 5:6:7:8  S SD: 30.0424 cents
 6:7:8:9:10:12  S SD: 19.9137 cents
 8:9:11:12:14:16    SD: 10.4364 cents
 14:16:19:21:24:28    SD: 9.7988 cents
 15:17:20:23:26:30    SD: 6.2495 cents
 18:20:24:27:31:36    SD: 4.9351 cents
 23:26:31:35:40:46    SD: 4.5577 cents
 26:29:35:39:45:52    SD: 3.9780 cents
 27:30:36:41:47:54    SD: 3.6125 cents
 33:37:44:50:57:66    SD: 1.9538 cents
 41:46:55:62:71:82    SD: 1.0953 cents
 68:76:91:103:118:136    SD: 0.9257 cents
 101:113:135:153:175:202    SD: 0.7950 cents
 109:122:146:165:189:218    SD: 0.4570 cents
 142:159:190:215:246:284    SD: 0.4457 cents
 166:186:222:251:288:332    SD: 0.3873 cents
 207:232:277:313:359:414    SD: 0.2814 cents
 275:308:368:416:477:550    SD: 0.1506 cents
 316:354:423:478:548:632    SD: 0.1234 cents
 458:513:613:693:794:916    SD: 0.1074 cents