Scala analysis: Greece_Fourth
Fourth (Voice), Greece
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 139.000 cents 139.000000 2: 339.000 cents 339.000000 3: 528.000 cents 528.000000 4: 661.000 cents 661.000000 5: 845.000 cents 845.000000 6: 1073.000 cents 1073.000000 7: 1201.000 cents 1201.000000
SHOW/INTERVAL
0: 128.0000 cents 128.0000 1: 139.0000 cents 139.0000 2: 200.0000 cents 200.0000 3: 189.0000 cents 189.0000 4: 133.0000 cents 133.0000 5: 184.0000 cents 184.0000 6: 228.0000 cents 228.0000 7: 128.0000 cents 128.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 128.00000 cents 1: 1 133.00000 cents 1: 1 139.00000 cents 1: 1 184.00000 cents 1: 1 189.00000 cents 1: 1 200.00000 cents 1: 1 228.00000 cents 2: 1 267.00000 cents 2: 1 317.00000 cents 2: 1 322.00000 cents 2: 1 339.00000 cents 2: 1 356.00000 cents 2: 1 389.00000 cents 2: 1 412.00000 cents 3: 1 467.00000 cents 3: 1 495.00000 cents 3: 1 506.00000 cents 3: 1 522.00000 cents 3: 1 528.00000 cents 3: 1 540.00000 cents 3: 1 545.00000 cents 4: 1 656.00000 cents 4: 1 661.00000 cents 4: 1 673.00000 cents 4: 1 679.00000 cents 4: 1 695.00000 cents 4: 1 706.00000 cents 4: 1 734.00000 cents 5: 1 789.00000 cents 5: 1 812.00000 cents 5: 1 845.00000 cents 5: 1 862.00000 cents 5: 1 879.00000 cents 5: 1 884.00000 cents 5: 1 934.00000 cents 6: 1 973.00000 cents 6: 1 1001.00000 cents 6: 1 1012.00000 cents 6: 1 1017.00000 cents 6: 1 1062.00000 cents 6: 1 1068.00000 cents 6: 1 1073.00000 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 : 139.0 339.0 528.0 661.0 845.0 1073.0 1201.0 139.0 : 200.0 389.0 522.0 706.0 934.0 1062.0 1201.0 339.0 : 189.0 322.0 506.0 734.0 862.0 1001.0 1201.0 528.0 : 133.0 317.0 545.0 673.0 812.0 1012.0 1201.0 661.0 : 184.0 412.0 540.0 679.0 879.0 1068.0 1201.0 845.0 : 228.0 356.0 495.0 695.0 884.0 1017.0 1201.0 1073.0: 128.0 267.0 467.0 656.0 789.0 973.0 1201.0 1201.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 128.0000 .. 228.0000 cents 100.00000 cents 128.00000 cents 2: 267.0000 .. 412.0000 cents 145.00000 cents 39.00000 cents 3: 467.0000 .. 545.0000 cents 78.00000 cents 55.00000 cents 4: 656.0000 .. 734.0000 cents 78.00000 cents 111.00000 cents 5: 789.0000 .. 934.0000 cents 145.00000 cents 55.00000 cents 6: 973.0000 .. 1073.0000 cents 100.00000 cents 39.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 128.00000 cents, class 1 Average step (divided formal octave): 171.5714 cents Largest one step interval : 228.00000 cents Average / Smallest step : 1.340402 Largest / Average step : 1.328893 Largest / Smallest step : 1.781250 Median interval of one step : 184.00000 cents, amount: 1 Least squares average step : 172.25000 cents, oct.: 1205.75000 cents Scale is strictly proper Scale is a mode of a 1201-tone equal temperament with octave 1201.000 cents degrees: 139 339 528 661 845 1073 1201 Least number of segments generator : 601 of 601.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1062 of 1062.000 cents and inv. generated superset size: 144 = 137 more = 2057.143% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFG Step pattern size order : CFEBDGA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 39.00000 cents Scale diversity : 1.535780 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.462115 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 : 5.00000 cents Number of recognisable fifths : 2, average 700.5000 cents Number of recognisable fourths : 2, average 500.5000 cents Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 23.7779 c. M: 43.5714 c. Lebeng 11: 1 2 2 1 2 2 1 P D3 I SD: 19.0479 c. M: 29.8182 c. 16: 2 3 2 2 2 3 2 SP M ME I SD: 18.9868 c. M:-36.3125 c. Armodue-7, Antidorian 17: 2 3 2 2 3 3 2 SP D3 S SD: 17.5109 c. M: 33.4706 c. Dastgah-e Sehgah 18: 2 3 3 2 3 3 2 SP D3 I SD: 9.7314 c. M:-22.3889 c. 20: 2 4 3 2 3 4 2 P I SD: 12.2300 c. M:-21.3000 c. 25: 3 4 4 3 4 4 3 SP D3 I SD: 10.7980 c. M:-19.7200 c. 26: 3 4 4 3 4 5 3 SP SD: 12.7643 c. M: 19.8846 c. 27: 3 5 4 3 4 5 3 SP I SD: 7.7147 c. M:-16.8519 c. 29: 3 5 5 3 4 6 3 P SD: 9.8643 c. M: 16.7241 c. 31: 4 5 5 3 5 6 3 SP SD: 10.3755 c. M:-15.9677 c. 34: 4 6 5 4 5 6 4 SP I SD: 8.4404 c. M:-14.2353 c. 36: 4 6 6 4 5 7 4 SP SD: 6.3475 c. M: 10.9722 c. 44: 5 7 7 5 7 8 5 SP SD: 6.9055 c. M: 11.4545 c. 45: 5 8 7 5 7 8 5 SP I SD: 6.2985 c. M:-9.0444 c. 46: 5 8 7 5 7 9 5 SP SD: 6.2262 c. M: 9.5217 c. 47: 5 8 8 5 7 9 5 SP SD: 6.1104 c. M: 11.2340 c. 50: 6 8 8 6 7 10 5 SP SD: 5.9563 c. M:-11.5600 c. 53: 6 9 8 6 8 10 6 SP SD: 5.0394 c. M: 7.9623 c. 54: 6 9 9 6 8 10 6 SP SD: 4.8058 c. M:-6.2222 c. 57: 7 9 9 6 9 11 6 SP SD: 4.5623 c. M:-8.4912 c. 60: 7 10 9 7 9 12 6 SP SD: 4.4921 c. M:-7.9000 c. 64: 7 11 10 7 10 12 7 SP SD: 3.6971 c. M: 7.6406 c. 71: 8 12 11 8 11 13 8 SP SD: 3.4437 c. M: 7.3239 c. 75: 9 12 12 8 12 14 8 SP SD: 3.1027 c. M:-5.1200 c. 78: 9 13 12 9 12 15 8 SP SD: 2.6257 c. M:-4.8205 c. 84: 10 14 13 9 13 16 9 SP SD: 2.6045 c. M:-4.1429 c. 95: 11 16 15 10 15 18 10 SP SD: 2.2003 c. M: 3.6105 c. 102: 12 17 16 11 16 19 11 SP SD: 1.9768 c. M:-2.7647 c. 111: 13 18 18 12 17 21 12 SP SD: 1.9194 c. M: 3.5856 c. 114: 13 19 18 13 17 22 12 SP SD: 1.8479 c. M:-2.7105 c. 131: 15 22 21 14 20 25 14 SP SD: 1.6725 c. M:-3.7405 c. 138: 16 23 22 15 21 26 15 SP SD: 1.5035 c. M:-2.8768 c. 162: 19 27 25 18 25 31 17 SP SD: 1.4903 c. M:-2.0247 c. 171: 20 28 27 19 26 33 18 SP SD: 1.4723 c. M: 2.1930 c. 180: 21 30 28 20 28 34 19 SP SD: 1.2553 c. M:-2.3722 c. 189: 22 31 30 21 29 36 20 SP SD: 0.9805 c. M: 2.2116 c. 196: 23 32 31 22 30 37 21 SP SD: 1.2050 c. M: 1.9847 c. 198: 23 33 31 22 30 38 21 SP SD: 0.8214 c. M: 1.8737 c. 205: 24 34 32 23 31 39 22 SP SD: 1.0309 c. M:-1.6049 c. 209: 24 35 33 23 32 40 22 SP SD: 0.7770 c. M:-1.5789 c. 216: 25 36 34 24 33 41 23 SP SD: 0.2804 c. M:-0.6620 c. 534: 62 89 84 59 82 101 57 SP SD: 0.4401 c. M:-0.6479 c. 536: 62 89 85 59 82 102 57 SP SD: 0.4188 c. M:-0.7985 c. 543: 63 90 86 60 83 103 58 SP SD: 0.3871 c. M:-0.6169 c. 553: 64 92 87 61 85 105 59 SP SD: 0.3286 c. M: 0.7758 c. 571: 66 95 90 63 88 108 61 SP SD: 0.3502 c. M: 0.5552 c. 580: 67 97 91 64 89 110 62 SP SD: 0.3373 c. M:-0.5931 c. 598: 69 100 94 66 92 113 64 SP SD: 0.3795 c. M: 0.5351 c. 603: 70 100 95 67 92 115 64 SP SD: 0.3763 c. M:-0.5307 c. 621: 72 103 98 69 95 118 66 SP SD: 0.3150 c. M: 0.5539 c. 630: 73 105 99 70 96 120 67 SP SD: 0.3174 c. M:-0.5032 c. 685: 79 114 108 76 105 130 73 SP SD: 0.3152 c. M: 0.6161 c. 694: 80 116 109 77 106 132 74 SP SD: 0.2998 c. M: 0.5562 c. 701: 81 117 110 78 107 133 75 SP SD: 0.3112 c. M: 0.4950 c. 705: 82 117 111 78 108 134 75 SP SD: 0.2788 c. M:-0.6908 c. 743: 86 124 117 82 114 141 79 SP SD: 0.3339 c. M:-0.5693 c. 751: 87 125 118 83 115 143 80 SP SD: 0.3293 c. M: 0.6218 c. 752: 87 125 119 83 115 143 80 SP SD: 0.3141 c. M:-0.6316 c. 759: 88 126 120 84 116 144 81 SP SD: 0.3078 c. M:-0.5033 c. 762: 88 127 120 84 117 145 81 SP SD: 0.3003 c. M: 0.6076 c. 769: 89 128 121 85 118 146 82 SP SD: 0.1575 c. M: 0.3719 c. 883: 102 147 139 98 135 168 94 SP SD: 0.2383 c. M: 0.3556 c. 890: 103 148 140 99 136 169 95 SP SD: 0.2311 c. M: 0.3697 c. 921: 107 153 145 102 141 175 98 SP SD: 0.2268 c. M:-0.5299 c. 967: 112 161 152 107 148 184 103 SP SD: 0.2126 c. M: 0.4498 c. 974: 113 162 153 108 149 185 104 SP SD: 0.2307 c. M: 0.3542 c. 978: 113 163 154 108 150 186 104 SP SD: 0.1950 c. M: 0.3272 c. 985: 114 164 155 109 151 187 105 SP SD: 0.0615 c. M: 0.1452 c. 1201: 139 200 189 133 184 228 128 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 1.0000 cents 2 x x x 3 x x 4 S SD: 20.4836 cents 3 x x 4 x 5 x 6 S SD: 16.4904 cents 4 x 5 x 6 x 7:8 S SD: 30.3821 cents 5 x 6:7 x 8:9:10 S SD: 17.3992 cents 6 x 7:8:9:10:11:12 S SD: 16.5714 cents 7:8 x x 10:11:13:14 SD: 23.9159 cents 8:9:10:11:12:13:15:16 SD: 13.4976 cents 9:10:11:12:13:15:17:18 SD: 10.8637 cents 11:12:13:15:16:18:20:22 SD: 9.4213 cents 13:14:16:18:19:21:24:26 SD: 6.6303 cents 19:21:23:26:28:31:35:38 SD: 6.0906 cents 22:24:27:30:32:36:41:44 SD: 3.7529 cents 28:30:34:38:41:46:52:56 SD: 3.5087 cents 33:36:40:45:48:54:61:66 SD: 3.3490 cents 34:37:41:46:50:55:63:68 SD: 3.2668 cents 36:39:44:49:53:59:67:72 SD: 2.4318 cents 37:40:45:50:54:60:69:74 SD: 2.0414 cents 51:55:62:69:75:83:95:102 SD: 1.7817 cents 56:61:68:76:82:91:104:112 SD: 1.5256 cents 70:76:85:95:103:114:130:140 SD: 1.2930 cents 73:79:89:99:107:119:136:146 SD: 0.9303 cents 84:91:102:114:123:137:156:168 SD: 0.5645 cents 129:140:157:175:189:210:240:258 SD: 0.5428 cents 157:170:191:213:230:256:292:314 SD: 0.3626 cents 213:231:259:289:312:347:396:426 SD: 0.2772 cents 297:322:361:403:435:484:552:594 SD: 0.2728 cents 348:377:423:472:510:567:647:696 SD: 0.2644 cents 359:389:437:487:526:585:667:718 SD: 0.2644 cents 361:391:439:490:529:588:671:722 SD: 0.2519 cents 370:401:450:502:542:603:688:740 SD: 0.2117 cents 443:480:539:601:649:722:823:887 SD: 0.2095 cents 480:520:584:651:703:782:892:961 SD: 0.1755 cents 536:581:652:727:785:873:996:1073 SD: 0.1680 cents 550:596:669:746:806:896:1022:1101 SD: 0.1384 cents