Scala analysis: Turkey_A-I
A-I (Ney), Turkey
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 210.000 cents 210.000000 2: 397.000 cents 397.000000 3: 510.000 cents 510.000000 4: 706.000 cents 706.000000 5: 925.000 cents 925.000000 6: 1090.000 cents 1090.000000 7: 1219.000 cents 1219.000000
SHOW/INTERVAL
0: 129.0000 cents 129.0000 1: 210.0000 cents 210.0000 2: 187.0000 cents 187.0000 3: 113.0000 cents 113.0000 4: 196.0000 cents 196.0000 5: 219.0000 cents 219.0000 6: 165.0000 cents 165.0000 7: 129.0000 cents 129.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 113.00000 cents 1: 1 129.00000 cents 1: 1 165.00000 cents 1: 1 187.00000 cents 1: 1 196.00000 cents 1: 1 210.00000 cents 1: 1 219.00000 cents 2: 1 294.00000 cents 2: 1 300.00000 cents 2: 1 309.00000 cents 2: 1 339.00000 cents 2: 1 384.00000 cents 2: 1 397.00000 cents 2: 1 415.00000 cents 3: 1 496.00000 cents 3: 1 504.00000 cents 3: 1 510.00000 cents 3: 1 513.00000 cents 3: 1 526.00000 cents 3: 1 528.00000 cents 3: 1 580.00000 cents 4: 1 639.00000 cents 4: 1 691.00000 cents 4: 1 693.00000 cents 4: 1 706.00000 cents 4: 1 709.00000 cents 4: 1 715.00000 cents 4: 1 723.00000 cents 5: 1 804.00000 cents 5: 1 822.00000 cents 5: 1 835.00000 cents 5: 1 880.00000 cents 5: 1 910.00000 cents 5: 1 919.00000 cents 5: 1 925.00000 cents 6: 1 1000.00000 cents 6: 1 1009.00000 cents 6: 1 1023.00000 cents 6: 1 1032.00000 cents 6: 1 1054.00000 cents 6: 1 1090.00000 cents 6: 1 1106.00000 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 : 210.0 397.0 510.0 706.0 925.0 1090.0 1219.0 210.0 : 187.0 300.0 496.0 715.0 880.0 1009.0 1219.0 397.0 : 113.0 309.0 528.0 693.0 822.0 1032.0 1219.0 510.0 : 196.0 415.0 580.0 709.0 919.0 1106.0 1219.0 706.0 : 219.0 384.0 513.0 723.0 910.0 1023.0 1219.0 925.0 : 165.0 294.0 504.0 691.0 804.0 1000.0 1219.0 1090.0: 129.0 339.0 526.0 639.0 835.0 1054.0 1219.0 1219.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 113.0000 .. 219.0000 cents 106.00000 cents 113.00000 cents 2: 294.0000 .. 415.0000 cents 121.00000 cents 75.00000 cents 3: 496.0000 .. 580.0000 cents 84.00000 cents 81.00000 cents 4: 639.0000 .. 723.0000 cents 84.00000 cents 59.00000 cents 5: 804.0000 .. 925.0000 cents 121.00000 cents 81.00000 cents 6: 1000.0000 .. 1106.0000 cents 106.00000 cents 75.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 113.00000 cents, class 1 Average step (divided formal octave): 174.1429 cents Largest one step interval : 219.00000 cents Average / Smallest step : 1.541087 Largest / Average step : 1.257588 Largest / Smallest step : 1.938053 Median interval of one step : 187.00000 cents, amount: 1 Least squares average step : 178.97143 cents, oct.: 1252.80000 cents Scale is strictly proper Scale is a mode of a 1219-tone equal temperament with octave 1219.000 cents degrees: 210 397 510 706 925 1090 1219 Least number of segments generator : 610 of 610.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 760 of 760.000 cents and inv. generated superset size: 294 = 287 more = 4200.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFG Step pattern size order : FDAEGCB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 59.00000 cents Scale diversity : 1.528164 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.489746 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 : 5, average 702.8000 cents Number of appreciable fifths : 4, average 699.7500 cents Number of recognisable fourths : 4, average 505.7500 cents Number of appreciable fourths : 3, average 503.3333 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% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 121.0000 cents: 2 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 35.6310 c. M: 54.2857 c. Lebeng 9: 2 1 1 1 2 1 1 P M ME S SD: 29.7807 c. M:-60.8889 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 28.8828 c. M:-50.2000 c. Pseudo Rast 12: 2 2 1 2 2 2 1 P M ME S SD: 12.1374 c. M:-27.4167 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 16: 3 2 2 2 3 2 2 SP M ME S SD: 17.8109 c. M: 23.3750 c. Antiphrygian 17: 3 3 1 3 3 2 2 SP D3 S SD: 15.0106 c. M:-33.2353 c. Naghmeh Bayat-e Tork, Naghmeh Dashti 19: 3 3 2 3 3 3 2 SP M ME S SD: 12.9907 c. M: 26.7895 c. Nineteen-tone Major, Ionian 21: 4 3 2 3 4 3 2 SP T3 SD: 11.9737 c. M:-22.1905 c. 22: 4 3 2 4 4 3 2 P SD: 12.9285 c. M:-18.1818 c. Shadja Grama, Murchhana Uttaramandra, Shuddha Swara Saptaka 24: 4 4 2 4 4 3 3 SP D3 S SD: 10.8624 c. M: 23.3750 c. Maqam Jahargah (Jiharkah), Naghmeh Bayat-e Tork, Naghmeh Dashti 28: 5 4 3 4 5 4 3 SP T3 SD: 7.9937 c. M:-12.4286 c. 29: 5 4 3 5 5 4 3 SP SD: 8.1303 c. M: 18.6897 c. 36: 6 6 3 6 6 5 4 SP SD: 6.7726 c. M: 10.7500 c. 40: 7 6 4 6 7 6 4 SP T3 SD: 6.1953 c. M: 10.7500 c. 41: 7 6 4 7 7 6 4 SP SD: 6.5896 c. M: 10.4878 c. 45: 8 7 4 7 8 6 5 SP SD: 5.5336 c. M:-9.3333 c. 46: 8 7 4 8 8 6 5 SP SD: 4.7094 c. M:-9.5000 c. 47: 8 7 5 7 9 6 5 SP SD: 6.0317 c. M:-8.7234 c. 50: 9 7 5 8 9 7 5 SP SD: 5.2653 c. M:-9.4200 c. 55: 9 9 5 9 10 7 6 SP SD: 5.0069 c. M: 10.5273 c. 57: 10 9 5 9 10 8 6 SP SD: 4.5102 c. M:-9.3333 c. 58: 10 9 5 10 10 8 6 SP SD: 4.1201 c. M:-8.5862 c. 59: 10 9 6 9 11 8 6 SP SD: 4.3766 c. M:-6.5254 c. 62: 11 9 6 10 11 8 7 SP SD: 4.3688 c. M: 8.6290 c. 64: 11 10 6 10 12 8 7 SP SD: 4.0797 c. M:-8.2969 c. 67: 12 10 6 11 12 9 7 SP SD: 3.8577 c. M:-8.3284 c. 74: 13 11 7 12 13 10 8 SP SD: 2.3875 c. M:-4.1486 c. 76: 13 12 7 12 14 10 8 SP SD: 2.8603 c. M:-5.2895 c. 83: 14 13 8 13 15 11 9 SP SD: 2.5910 c. M: 4.3855 c. 86: 15 13 8 14 15 12 9 SP SD: 2.0633 c. M: 3.6628 c. 105: 18 16 10 17 19 14 11 SP SD: 1.9819 c. M:-3.7619 c. 129: 22 20 12 21 23 17 14 SP SD: 1.8487 c. M: 3.2946 c. 133: 23 20 13 21 24 18 14 SP SD: 1.7183 c. M:-3.2632 c. 141: 24 22 13 23 25 19 15 SP SD: 1.5018 c. M:-2.9220 c. 145: 25 22 14 23 26 20 15 SP SD: 1.6897 c. M:-2.8966 c. 150: 26 23 14 24 27 20 16 SP SD: 1.2659 c. M:-1.9800 c. 162: 28 25 15 26 29 22 17 SP SD: 1.1813 c. M:-1.8086 c. 169: 29 26 16 27 30 23 18 SP SD: 1.1795 c. M:-2.1243 c. 199: 34 31 18 32 36 27 21 SP SD: 1.1566 c. M: 1.7286 c. 225: 39 34 21 36 41 30 24 SP SD: 1.2213 c. M: 1.6889 c. 227: 39 35 21 36 41 31 24 SP SD: 1.1154 c. M: 2.5242 c. 236: 41 36 22 38 42 32 25 SP SD: 1.0961 c. M:-1.7754 c. 237: 41 36 22 38 43 32 25 SP SD: 0.8437 c. M: 1.3460 c. 254: 44 39 23 41 46 34 27 SP SD: 0.9961 c. M:-1.3346 c. 256: 44 39 24 41 46 35 27 SP SD: 0.9953 c. M: 1.7773 c. 261: 45 40 24 42 47 35 28 SP SD: 0.8144 c. M: 1.7739 c. 273: 47 42 25 44 49 37 29 SP SD: 0.5477 c. M: 0.9670 c. 366: 63 56 34 59 66 49 39 SP SD: 0.5690 c. M:-0.9071 c. 378: 65 58 35 61 68 51 40 SP SD: 0.3452 c. M:-0.5370 c. 406: 70 62 38 65 73 55 43 SP SD: 0.3600 c. M: 0.6749 c. 435: 75 67 40 70 78 59 46 SP SD: 0.3756 c. M:-0.9264 c. 464: 80 71 43 75 83 63 49 SP SD: 0.3499 c. M:-0.7047 c. 528: 91 81 49 85 95 71 56 SP SD: 0.3777 c. M:-0.7936 c. 540: 93 83 50 87 97 73 57 SP SD: 0.3475 c. M:-0.5685 c. 547: 94 84 51 88 98 74 58 SP SD: 0.3316 c. M: 0.5192 c. 568: 98 87 53 91 102 77 60 SP SD: 0.3315 c. M:-0.7782 c. 651: 112 100 60 105 117 88 69 SP SD: 0.2893 c. M: 0.6790 c. 672: 116 103 62 108 121 91 71 SP SD: 0.2699 c. M:-0.4226 c. 679: 117 104 63 109 122 92 72 SP SD: 0.2764 c. M: 0.4521 c. 755: 130 116 70 121 136 102 80 SP SD: 0.2151 c. M: 0.4331 c. 767: 132 118 71 123 138 104 81 SP SD: 0.2304 c. M: 0.3468 c. 784: 135 120 73 126 141 106 83 SP SD: 0.2084 c. M: 0.5140 c. 801: 138 123 74 129 144 108 85 SP SD: 0.2072 c. M: 0.3571 c. 813: 140 125 75 131 146 110 86 SP SD: 0.1798 c. M:-0.3370 c. 841: 145 129 78 135 151 114 89 SP SD: 0.1552 c. M: 0.2414 c. 946: 163 145 88 152 170 128 100 SP SD: 0.1580 c. M:-0.2791 c. 1057: 182 162 98 170 190 143 112 SP SD: 0.1811 c. M: 0.2772 c. 1069: 184 164 99 172 192 145 113 SP SD: 0.1776 c. M: 0.2778 c. 1133: 195 174 105 182 204 153 120 SP SD: 0.1566 c. M:-0.2780 c. 1145: 197 176 106 184 206 155 121 SP SD: 0.1543 c. M: 0.2681 c. 1207: 208 185 112 194 217 163 128 SP SD: 0.1207 c. M: 0.2726 c. 1219: 210 187 113 196 219 165 129 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 19.0000 cents 2 x x x 3 x x 4 S SD: 9.7129 cents 3 x x 4 x 5 x 6 S SD: 15.4763 cents 4 x 5 x 6:7 x 8 S SD: 12.2787 cents 5 x 6:7:8 x 9:10 S SD: 34.1039 cents 6:7 x 8:9:10:11:12 S SD: 14.0017 cents 7:8:9 x 11:12:13:14 SD: 15.3765 cents 8:9:10:11:12:14:15:16 S SD: 9.2135 cents 10:11 x 13:15:17:19:20 SD: 12.9141 cents 12:14:15:16:18:20:23:24 SD: 11.8145 cents 14:16:18:19:21:24:26:28 SD: 7.8587 cents 15:17:19:20:23:26:28:30 SD: 7.4054 cents 16:18:20:21:24:27:30:32 S SD: 7.0507 cents 18:20:23:24:27:31:34:36 SD: 7.0170 cents 20:23:25:27:30:34:38:40 SD: 6.5373 cents 23:26:29:31:35:39:43:47 SD: 4.5157 cents 24:27:30:32:36:41:45:49 SD: 3.4899 cents 30:34:38:40:45:51:56:61 SD: 3.4285 cents 31:35:39:42:47:53:58:63 SD: 3.4258 cents 32:36:40:43:48:55:60:65 SD: 2.8356 cents 38:43:48:51:57:65:71:77 SD: 1.9228 cents 47:53:59:63:71:80:88:95 SD: 1.6002 cents 55:62:69:74:83:94:103:111 SD: 1.5327 cents 62:70:78:83:93:106:116:125 SD: 1.4931 cents 78:88:98:105:117:133:146:158 SD: 1.2372 cents 85:96:107:114:128:145:160:172 SD: 0.9097 cents 117:132:147:157:176:200:220:237 SD: 0.8570 cents 123:139:155:165:185:210:231:249 SD: 0.6815 cents 139:157:175:187:209:237:261:281 SD: 0.6143 cents 147:166:185:197:221:251:276:297 SD: 0.5564 cents 163:184:205:219:245:278:306:330 SD: 0.3805 cents 187:211:235:251:281:319:351:378 SD: 0.3071 cents 225:254:283:302:338:384:422:455 SD: 0.2890 cents 286:323:360:384:430:488:537:578 SD: 0.2729 cents 310:350:390:416:466:529:582:627 SD: 0.1734 cents 365:412:459:490:549:623:685:738 SD: 0.1479 cents 496:560:624:666:746:846:931:1003 SD: 0.1450 cents 528:596:664:709:794:901:991:1068 SD: 0.1167 cents