Scala analysis: Turkey_A-IV
A-IV (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: 391.000 cents 391.000000 3: 511.000 cents 511.000000 4: 714.000 cents 714.000000 5: 949.000 cents 949.000000 6: 1121.000 cents 1121.000000 7: 1250.000 cents 1250.000000
SHOW/INTERVAL
0: 129.0000 cents 129.0000 1: 210.0000 cents 210.0000 2: 181.0000 cents 181.0000 3: 120.0000 cents 120.0000 4: 203.0000 cents 203.0000 5: 235.0000 cents 235.0000 6: 172.0000 cents 172.0000 7: 129.0000 cents 129.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 120.00000 cents 1: 1 129.00000 cents 1: 1 172.00000 cents 1: 1 181.00000 cents 1: 1 203.00000 cents 1: 1 210.00000 cents 1: 1 235.00000 cents 2: 2 301.00000 cents 2: 1 323.00000 cents 2: 1 339.00000 cents 2: 1 391.00000 cents 2: 1 407.00000 cents 2: 1 438.00000 cents 3: 1 504.00000 cents 3: 2 511.00000 cents 3: 1 520.00000 cents 3: 1 536.00000 cents 3: 1 558.00000 cents 3: 1 610.00000 cents 4: 1 640.00000 cents 4: 1 692.00000 cents 4: 1 714.00000 cents 4: 1 730.00000 cents 4: 2 739.00000 cents 4: 1 746.00000 cents 5: 1 812.00000 cents 5: 1 843.00000 cents 5: 1 859.00000 cents 5: 1 911.00000 cents 5: 1 927.00000 cents 5: 2 949.00000 cents 6: 1 1015.00000 cents 6: 1 1040.00000 cents 6: 1 1047.00000 cents 6: 1 1069.00000 cents 6: 1 1078.00000 cents 6: 1 1121.00000 cents 6: 1 1130.00000 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.33333 = 19/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 210.0 391.0 511.0 714.0 949.0 1121.0 1250.0 210.0 : 181.0 301.0 504.0 739.0 911.0 1040.0 1250.0 391.0 : 120.0 323.0 558.0 730.0 859.0 1069.0 1250.0 511.0 : 203.0 438.0 610.0 739.0 949.0 1130.0 1250.0 714.0 : 235.0 407.0 536.0 746.0 927.0 1047.0 1250.0 949.0 : 172.0 301.0 511.0 692.0 812.0 1015.0 1250.0 1121.0: 129.0 339.0 520.0 640.0 843.0 1078.0 1250.0 1250.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 120.0000 .. 235.0000 cents 115.00000 cents 120.00000 cents 2: 301.0000 .. 438.0000 cents 137.00000 cents 66.00000 cents 3: 504.0000 .. 610.0000 cents 106.00000 cents 66.00000 cents 4: 640.0000 .. 746.0000 cents 106.00000 cents 30.00000 cents 5: 812.0000 .. 949.0000 cents 137.00000 cents 66.00000 cents 6: 1015.0000 .. 1130.0000 cents 115.00000 cents 66.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 120.00000 cents, class 1 Average step (divided formal octave): 178.5714 cents Largest one step interval : 235.00000 cents Average / Smallest step : 1.488095 Largest / Average step : 1.316000 Largest / Smallest step : 1.958333 Median interval of one step : 181.00000 cents, amount: 1 Least squares average step : 182.87143 cents, oct.: 1280.10000 cents Scale is strictly proper Scale is a mode of a 1250-tone equal temperament with octave 1250.000 cents degrees: 210 391 511 714 949 1121 1250 Least number of segments generator : 627 of 627.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1033 of 1033.000 cents and inv. generated superset size: 287 = 280 more = 4100.000% 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 30.00000 cents Scale diversity : 1.495285 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.427200 Rothenberg efficiency : 0.312925 redundancy: 0.687075 Efficiency x scale size : 2.190476 Number of different interval sizes : 38 = 6.33333 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 6.33333 = 19/3 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 7.00000 cents Number of recognisable fifths : 2, average 703.0000 cents Number of recognisable fourths : 3, average 508.6667 cents Best fifths form a closed circle Best major 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 137.0000 cents: 2 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 34.5466 c. M: 56.1429 c. Lebeng 9: 2 1 1 1 2 1 1 P M ME S SD: 34.3455 c. M:-67.7778 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 29.0074 c. M:-51.0000 c. Pseudo Rast 12: 2 2 1 2 2 2 1 P M ME S SD: 15.7536 c. M:-25.6667 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: 14.6294 c. M: 23.3529 c. Pseudo Rast 19: 3 3 2 3 3 3 2 SP M ME S SD: 13.5730 c. M: 27.9474 c. Nineteen-tone Major, Ionian 20: 3 3 2 3 4 3 2 P T3 S SD: 15.7378 c. M: 26.5000 c. 22: 4 3 2 4 4 3 2 P SD: 14.5044 c. M:-24.6364 c. Shadja Grama, Murchhana Uttaramandra, Shuddha Swara Saptaka 25: 4 4 2 4 5 3 3 SP SD: 11.5882 c. M: 21.0000 c. 26: 4 4 3 4 5 3 3 SP SD: 12.6074 c. M:-17.8462 c. 28: 5 4 2 5 5 4 3 P SD: 10.9852 c. M: 19.9286 c. 29: 5 4 3 5 5 4 3 SP SD: 7.8497 c. M:-18.7586 c. 30: 5 4 3 5 6 4 3 P SD: 8.5774 c. M: 16.0000 c. 32: 5 5 3 5 6 5 3 P T3 S SD: 9.3814 c. M: 14.6875 c. 35: 6 5 3 6 7 4 4 SP SD: 9.0125 c. M:-15.2857 c. 37: 6 5 4 6 7 5 4 SP SD: 8.5721 c. M: 19.3784 c. 39: 7 5 4 6 8 5 4 SP SD: 8.3393 c. M:-14.3590 c. 41: 7 6 4 6 8 6 4 SP SD: 6.7764 c. M: 12.7805 c. 42: 7 6 4 7 8 6 4 P SD: 4.7146 c. M:-9.9524 c. 47: 8 7 4 8 9 6 5 SP SD: 5.4350 c. M:-8.4468 c. 49: 8 7 5 8 9 7 5 SP SD: 4.3712 c. M: 8.3469 c. 54: 9 8 5 9 10 7 6 SP SD: 4.1893 c. M: 9.8889 c. 58: 10 8 6 9 11 8 6 SP SD: 3.5302 c. M:-6.2414 c. 67: 11 10 6 11 13 9 7 SP SD: 3.9728 c. M: 7.2687 c. 70: 12 10 7 11 13 10 7 SP SD: 3.6160 c. M:-6.8571 c. 79: 13 12 7 13 15 11 8 SP SD: 3.1870 c. M: 4.6709 c. 95: 16 14 9 15 18 13 10 SP SD: 2.3987 c. M:-3.7368 c. 96: 16 14 9 16 18 13 10 SP SD: 1.7508 c. M: 3.1875 c. 124: 21 18 12 20 23 17 13 SP SD: 1.9401 c. M:-3.1129 c. 125: 21 18 12 20 24 17 13 SP SD: 1.6903 c. M: 4.0000 c. 137: 23 20 13 22 26 19 14 SP SD: 1.1212 c. M: 2.3212 c. 154: 26 22 15 25 29 21 16 SP SD: 0.7962 c. M: 1.3896 c. 166: 28 24 16 27 31 23 17 SP SD: 0.8453 c. M:-1.3614 c. 233: 39 34 22 38 44 32 24 SP SD: 0.6986 c. M: 1.3433 c. 250: 42 36 24 41 47 34 26 SP SD: 0.8452 c. M:-1.0000 c. 262: 44 38 25 43 49 36 27 SP SD: 0.6807 c. M:-1.6489 c. 291: 49 42 28 47 55 40 30 SP SD: 0.4265 c. M: 0.9416 c. 320: 54 46 31 52 60 44 33 SP SD: 0.5738 c. M:-0.9375 c. 357: 60 52 34 58 67 49 37 SP SD: 0.5054 c. M:-1.1569 c. 387: 65 56 37 63 73 53 40 SP SD: 0.3624 c. M: 0.6641 c. 399: 67 58 38 65 75 55 41 SP SD: 0.3677 c. M:-0.6040 c. 457: 77 66 44 74 86 63 47 SP SD: 0.3498 c. M:-0.6127 c. 531: 89 77 51 86 100 73 55 SP SD: 0.4086 c. M: 0.7232 c. 541: 91 78 52 88 102 74 56 SP SD: 0.3829 c. M:-0.6303 c. 543: 91 79 52 88 102 75 56 SP SD: 0.3490 c. M: 0.5654 c. 553: 93 80 53 90 104 76 57 SP SD: 0.2115 c. M:-0.3671 c. 697: 117 101 67 113 131 96 72 SP SD: 0.1678 c. M: 0.2912 c. 851: 143 123 82 138 160 117 88 SP SD: 0.1724 c. M: 0.2832 c. 863: 145 125 83 140 162 119 89 SP SD: 0.1625 c. M:-0.2978 c. 959: 161 139 92 156 180 132 99 SP SD: 0.1294 c. M:-0.2857 c. 1000: 168 145 96 162 188 138 103 SP SD: 0.2113 c. M:-0.2500 c. 1010: 170 146 97 164 190 139 104 SP SD: 0.2219 c. M:-0.3960 c. 1017: 171 147 98 165 191 140 105 SP SD: 0.1600 c. M:-0.3078 c. 1084: 182 157 104 176 204 149 112 SP SD: 0.1295 c. M: 0.2085 c. 1096: 184 159 105 178 206 151 113 SP SD: 0.1119 c. M:-0.1953 c. 1250: 210 181 120 203 235 172 129 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 50.0000 cents 2 x x x 3 x x 4 S SD: 25.7152 cents 3 x x 4 x 5 x 6 S SD: 27.5808 cents 4 x 5 x 6:7 x 8 S SD: 13.8296 cents 5 x 6:7:8:9 x 10 S SD: 33.4280 cents 6:7 x 8:9:10:11:12 S SD: 20.6543 cents 7:8:9 x 11:12:13:14 SD: 18.4580 cents 8:9:10:11:12:14:15:16 S SD: 10.8741 cents 10:11 x 13:15:17:19:21 SD: 14.5297 cents 11:12:14:15:17:19:21:23 SD: 12.1286 cents 12:14:15:16:18:21:23:25 SD: 9.4953 cents 14:16:18:19:21:24:27:29 SD: 8.4206 cents 15:17:19:20:23:26:29:31 SD: 5.8737 cents 21:24:26:28:32:36:40:43 SD: 5.8328 cents 23:26:29:31:35:40:44:47 SD: 3.3771 cents 31:35:39:42:47:54:59:64 SD: 3.2343 cents 32:36:40:43:48:55:61:66 SD: 2.7154 cents 47:53:59:63:71:81:90:97 SD: 1.4509 cents 55:62:69:74:83:95:105:113 SD: 0.9155 cents 102:115:128:137:154:176:195:210 SD: 0.8123 cents 122:138:153:164:184:211:233:251 SD: 0.6773 cents 123:139:154:165:186:213:235:253 SD: 0.6544 cents 149:168:187:200:225:258:285:307 SD: 0.6359 cents 155:175:194:208:234:268:296:319 SD: 0.5048 cents 170:192:213:228:257:294:325:350 SD: 0.4979 cents 178:201:223:239:269:308:340:366 SD: 0.3742 cents 225:254:282:302:340:389:430:463 SD: 0.3077 cents 233:263:292:313:352:403:445:480 SD: 0.2345 cents 396:447:496:532:598:685:757:815 SD: 0.2269 cents 411:464:515:552:621:711:785:846 SD: 0.1599 cents 474:535:594:637:716:820:906:976 SD: 0.1577 cents 560:632:702:752:846:969:1070:1153 SD: 0.1473 cents 597:674:748:802:902:1033:1141:1229 SD: 0.1312 cents