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