Scala analysis: Greece_Fourth_Plagal

Fourth Plagal (Voice), Greece

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:        222.000 cents     222.000000
  2:        378.000 cents     378.000000
  3:        517.000 cents     517.000000
  4:        718.000 cents     718.000000
  5:        917.000 cents     917.000000
  6:       1089.000 cents    1089.000000
  7:       1200.000 cents    1200.000000
SHOW/INTERVAL
  0:        111.0000 cents    111.0000
  1:        222.0000 cents    222.0000
  2:        156.0000 cents    156.0000
  3:        139.0000 cents    139.0000
  4:        201.0000 cents    201.0000
  5:        199.0000 cents    199.0000
  6:        172.0000 cents    172.0000
  7:        111.0000 cents    111.0000
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 111.00000 cents
  1:   1 139.00000 cents
  1:   1 156.00000 cents
  1:   1 172.00000 cents
  1:   1 199.00000 cents
  1:   1 201.00000 cents
  1:   1 222.00000 cents
  2:   1 283.00000 cents
  2:   1 295.00000 cents
  2:   1 333.00000 cents
  2:   1 340.00000 cents
  2:   1 371.00000 cents
  2:   1 378.00000 cents
  2:   1 400.00000 cents
  3:   1 482.00000 cents
  3:   1 489.00000 cents
  3:   1 496.00000 cents
  3:   1 505.00000 cents
  3:   1 517.00000 cents
  3:   1 539.00000 cents
  3:   1 572.00000 cents
  4:   1 628.00000 cents
  4:   1 661.00000 cents
  4:   1 683.00000 cents
  4:   1 695.00000 cents
  4:   1 704.00000 cents
  4:   1 711.00000 cents
  4:   1 718.00000 cents
  5:   1 800.00000 cents
  5:   1 822.00000 cents
  5:   1 829.00000 cents
  5:   1 860.00000 cents
  5:   1 867.00000 cents
  5:   1 905.00000 cents
  5:   1 917.00000 cents
  6:   1 978.00000 cents
  6:   1 999.00000 cents
  6:   1 1001.00000 cents
  6:   1 1028.00000 cents
  6:   1 1044.00000 cents
  6:   1 1061.00000 cents
  6:   1 1089.00000 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   : 222.0 378.0 517.0 718.0 917.0 1089.0 1200.0
 222.0 : 156.0 295.0 496.0 695.0 867.0 978.0  1200.0
 378.0 : 139.0 340.0 539.0 711.0 822.0 1044.0 1200.0
 517.0 : 201.0 400.0 572.0 683.0 905.0 1061.0 1200.0
 718.0 : 199.0 371.0 482.0 704.0 860.0 999.0  1200.0
 917.0 : 172.0 283.0 505.0 661.0 800.0 1001.0 1200.0
 1089.0: 111.0 333.0 489.0 628.0 829.0 1028.0 1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  111.0000  .. 222.0000 cents      111.00000 cents                    111.00000 cents
  2:  283.0000  .. 400.0000 cents      117.00000 cents                    61.00000 cents
  3:  482.0000  .. 572.0000 cents      90.00000 cents                     82.00000 cents
  4:  628.0000  .. 718.0000 cents      90.00000 cents                     56.00000 cents
  5:  800.0000  .. 917.0000 cents      117.00000 cents                    82.00000 cents
  6:  978.0000  .. 1089.0000 cents     111.00000 cents                    61.00000 cents
SHOW DATA
Number of notes                     : 7
-- Interval properties --
Smallest interval                   : 111.00000 cents, class 1
Average step (divided formal octave): 171.4286 cents
Largest one step interval           : 222.00000 cents
Average / Smallest step             : 1.544402
Largest / Average step              : 1.295000
Largest / Smallest step             : 2.000000
Median interval of one step         : 172.00000 cents, amount: 1
Least squares average step          : 178.00000 cents, oct.:  1246.00000 cents
Scale is strictly proper
Scale is a mode of a 1200-tone equal temperament with octave  1200.000 cents
  degrees: 222 378 517 718 917 1089 1200
Least number of segments generator  : 601 of 601.000 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 857 of 857.000 cents and inv.
  generated superset size: 424 = 417 more = 6057.143%
Number of contiguous 1-step segments: 0
Step pattern alph. order: ABCDEFG
Step pattern size order : GCBFEDA
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 56.00000 cents
Scale diversity                     : 1.602219
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.470000
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        : 2.00000 cents
Number of recognisable fifths       : 4, average 707.0000 cents
Number of appreciable fifths        : 3, average 703.3333 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: 41.5361 c. M: 60.4286 c.  Lebeng
  9:  2 1 1 1 2 1 1   P M ME S SD: 29.6324 c. M: 51.3333 c. 
 10:  2 1 1 2 2 1 1   P   D3 S SD: 23.7577 c. M:-43.0000 c.  Pseudo Rast
 12:  2 2 1 2 2 2 1   P M ME S SD: 16.8650 c. M: 22.0000 c.  G.Lydian, M.Ionian, M.Hypolydian, Major, Bilaval That, Mela Shankarabharanam, Raga Atana, Ghana Heptatonic, Peruvian Major, Matzore, Rast ascending: Greece, 4th plagal Byzantine, Ararai: Ethiopia, Makam Cargah, Ajam Ashiran, Dastgah-e Mahur, Dastgah-e Rast Panjgah, Xin: China, DS2, Heptatonia prima
 17:  3 2 2 3 3 2 2  SP   D3 S SD: 18.1823 c. M: 30.1765 c.  Pseudo Rast
 18:  3 3 2 3 3 2 2  SP   D3 S SD: 17.8703 c. M: 22.3333 c. 
 20:  4 2 3 3 3 3 2  SP   D3 S SD: 14.8853 c. M:-23.0000 c. 
 21:  4 3 2 4 3 3 2  SP   T3   SD: 12.9316 c. M:-24.8571 c. 
 22:  4 3 2 4 4 3 2   P        SD: 11.3291 c. M: 26.0909 c.  Shadja Grama, Murchhana Uttaramandra, Shuddha Swara Saptaka
 25:  5 3 3 4 4 4 2  SP        SD: 10.2470 c. M:-18.0000 c. 
 28:  5 4 3 5 4 4 3  SP   T3   SD: 10.9277 c. M: 17.5714 c. 
 29:  5 4 3 5 5 4 3  SP        SD: 12.5704 c. M: 20.4483 c. 
 30:  6 3 4 5 5 4 3  SP      S SD: 10.3579 c. M: 18.0000 c. 
 32:  6 4 4 5 5 5 3  SP        SD: 7.5923 c. M: 17.0000 c. 
 33:  6 4 4 6 5 5 3  SP        SD: 7.8888 c. M: 14.3636 c. 
 34:  6 5 4 5 6 5 3  SP        SD: 8.7588 c. M:-12.4118 c. 
 35:  6 5 4 6 6 5 3  SP        SD: 7.7420 c. M: 16.2857 c. 
 39:  7 5 5 6 7 5 4  SP        SD: 7.9877 c. M: 12.0769 c. 
 42:  8 5 5 7 7 6 4  SP        SD: 4.2375 c. M: 6.5714 c. 
 54:  10 7 6 9 9 8 5  SP        SD: 4.0870 c. M: 6.8889 c. 
 60:  11 8 7 10 10 8 6  SP        SD: 3.9821 c. M: 9.0000 c. 
 63:  12 8 7 11 10 9 6  SP        SD: 3.9854 c. M:-6.5714 c. 
 67:  12 9 8 11 11 10 6  SP        SD: 3.5275 c. M: 7.0746 c. 
 72:  13 10 8 12 12 10 7  SP        SD: 3.6056 c. M: 5.6667 c. 
 76:  14 10 9 12 13 11 7  SP        SD: 3.2899 c. M: 7.4737 c. 
 77:  14 10 9 13 13 11 7  SP        SD: 2.6399 c. M: 3.9740 c. 
 85:  16 11 10 14 14 12 8  SP        SD: 2.9762 c. M:-5.3529 c. 
 86:  16 11 10 14 15 12 8  SP        SD: 2.9306 c. M: 6.3721 c. 
 97:  18 13 11 16 16 14 9  SP        SD: 2.3954 c. M:-5.5052 c. 
 98:  18 13 11 17 16 14 9  SP        SD: 2.2275 c. M:-4.4490 c. 
 102: 19 13 12 17 17 15 9  SP        SD: 2.1324 c. M:-5.1176 c. 
 107: 20 14 12 18 18 15 10  SP        SD: 1.9178 c. M:-3.3084 c. 
 109: 20 14 13 18 18 16 10  SP        SD: 2.2097 c. M: 3.6881 c. 
 114: 21 15 13 19 19 16 11  SP        SD: 2.1564 c. M: 4.7895 c. 
 118: 22 15 14 20 19 17 11  SP        SD: 2.0265 c. M:-4.0339 c. 
 120: 22 16 14 20 20 17 11  SP        SD: 2.1044 c. M:-3.0000 c. 
 123: 23 16 14 21 20 18 11  SP        SD: 2.4228 c. M:-3.9512 c. 
 127: 23 17 15 21 21 18 12  SP        SD: 2.2363 c. M: 4.6772 c. 
 130: 24 17 15 22 21 19 12  SP        SD: 1.4359 c. M: 3.1538 c. 
 139: 26 18 16 23 23 20 13  SP        SD: 1.5891 c. M:-2.4604 c. 
 140: 26 18 16 24 23 20 13  SP        SD: 1.3649 c. M: 2.7143 c. 
 162: 30 21 19 27 27 23 15  SP        SD: 0.8445 c. M:-1.5185 c. 
 174: 32 23 20 29 29 25 16  SP        SD: 0.8067 c. M: 1.3103 c. 
 216: 40 28 25 36 36 31 20  SP        SD: 0.5492 c. M: 1.3333 c. 
 292: 54 38 34 49 48 42 27  SP        SD: 0.5821 c. M:-1.1781 c. 
 314: 58 41 36 53 52 45 29  SP        SD: 0.4908 c. M: 1.0764 c. 
 323: 60 42 37 54 54 46 30  SP        SD: 0.7218 c. M: 0.9721 c. 
 334: 62 43 39 56 55 48 31  SP        SD: 0.5884 c. M: 0.8323 c. 
 336: 62 44 39 56 56 48 31  SP        SD: 0.5637 c. M:-0.8571 c. 
 346: 64 45 40 58 57 50 32  SP        SD: 0.5353 c. M: 1.3931 c. 
 378: 70 49 44 63 63 54 35  SP        SD: 0.3435 c. M: 0.5397 c. 
 476: 88 62 55 80 79 68 44  SP        SD: 0.3263 c. M:-0.6471 c. 
 508: 94 66 59 85 84 73 47  SP        SD: 0.2195 c. M: 0.4646 c. 
 518: 96 67 60 87 86 74 48  SP        SD: 0.3091 c. M: 0.3977 c. 
 585: 108 76 68 98 97 84 54  SP        SD: 0.2925 c. M: 0.5641 c. 
 615: 114 80 71 103 102 88 57  SP        SD: 0.2782 c. M:-0.5366 c. 
 670: 124 87 78 112 111 96 62  SP        SD: 0.2497 c. M:-0.6119 c. 
 682: 126 89 79 114 113 98 63  SP        SD: 0.2348 c. M:-0.3021 c. 
 692: 128 90 80 116 115 99 64  SP        SD: 0.1611 c. M:-0.3410 c. 
 822: 152 107 95 138 136 118 76  SP        SD: 0.1580 c. M:-0.2482 c. 
 984: 182 128 114 165 163 141 91  SP        SD: 0.1205 c. M:-0.2927 c. 
 1026: 190 133 119 172 170 147 95  SP        SD: 0.1368 c. M: 0.2222 c. 
 1038: 192 135 120 174 172 149 96  SP        SD: 0.1318 c. M: 0.2370 c. 
 1188: 220 154 138 199 197 170 110  SP        SD: 0.1704 c. M: 0.2222 c. 
 1200: 222 156 139 201 199 172 111  SP        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: 8.0225 cents
 3 x x 4 x 5 x 6  S SD: 12.5819 cents
 4 x 5 x 6:7 x 8  S SD: 13.7215 cents
 5 x 6:7:8 x 9:10  S SD: 29.9565 cents
 6:7 x 8:9:10:11:12  S SD: 12.0953 cents
 7:8:9 x 11:12:13:14    SD: 14.9642 cents
 8:9:10:11:12:14:15:16  S SD: 9.6023 cents
 14:16:17:19:21:24:26:28    SD: 7.5467 cents
 16:18:20:22:24:27:30:32  S SD: 6.3182 cents
 17:19:21:23:26:29:32:34    SD: 5.4556 cents
 20:23:25:27:30:34:38:40    SD: 5.0041 cents
 21:24:26:28:32:36:39:42  S SD: 4.9421 cents
 23:26:29:31:35:39:43:46    SD: 3.9321 cents
 29:33:36:39:44:49:54:58    SD: 2.4258 cents
 37:42:46:50:56:63:69:74    SD: 1.7375 cents
 49:56:61:66:74:83:92:98    SD: 1.6287 cents
 57:65:71:77:86:97:107:114    SD: 1.4010 cents
 66:75:82:89:100:112:124:132    SD: 0.5941 cents
 103:117:128:139:156:175:193:206    SD: 0.5179 cents
 152:173:189:205:230:258:285:304    SD: 0.4055 cents
 169:192:210:228:256:287:317:338    SD: 0.4034 cents
 212:241:264:286:321:360:398:424    SD: 0.3817 cents
 218:248:271:294:330:370:409:436    SD: 0.3242 cents
 233:265:290:314:353:396:437:466    SD: 0.3055 cents
 241:274:300:325:365:409:452:482    SD: 0.2841 cents
 299:340:372:403:453:508:561:598    SD: 0.2218 cents
 385:438:479:519:583:654:722:770    SD: 0.2080 cents
 402:457:500:542:609:683:754:804    SD: 0.1929 cents
 451:513:561:608:683:766:846:902    SD: 0.1629 cents
 475:540:591:640:719:807:891:950    SD: 0.1558 cents
 483:549:601:651:731:820:906:966    SD: 0.1494 cents
 541:615:673:729:819:919:1015:1082    SD: 0.1160 cents
 578:657:719:779:875:982:1084:1156    SD: 0.1141 cents