Scala analysis: diaopt5
5-limit optimized diatonic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 192.103 cents 192.103000 2: 384.205 cents 384.205000 3: 502.262 cents 502.262000 4: 696.895 cents 696.895000 5: 887.311 cents 887.311000 6: 1081.943 cents 1081.943000 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 118.0570 cents 118.0570 1: 192.1030 cents 192.1030 2: 192.1020 cents 192.1020 3: 118.0570 cents 118.0570 4: 194.6330 cents 194.6330 5: 190.4160 cents 190.4160 6: 194.6320 cents 194.6320 7: 118.0570 cents 118.0570
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 118.05700 cents 1: 1 190.41600 cents 1: 1 192.10200 cents 1: 1 192.10300 cents 1: 1 194.63200 cents 1: 1 194.63300 cents 2: 1 310.15900 cents 2: 1 310.16000 cents 2: 1 312.68900 cents 2: 1 312.69000 cents 2: 1 384.20500 cents 2: 1 385.04800 cents 2: 1 385.04900 cents 3: 2 502.26200 cents 3: 1 503.10500 cents 3: 1 503.10600 cents 3: 2 504.79200 cents 3: 1 579.68100 cents 4: 1 620.31900 cents 4: 2 695.20800 cents 4: 1 696.89400 cents 4: 1 696.89500 cents 4: 2 697.73800 cents 5: 1 814.95100 cents 5: 1 814.95200 cents 5: 1 815.79500 cents 5: 1 887.31000 cents 5: 1 887.31100 cents 5: 1 889.84000 cents 5: 1 889.84100 cents 6: 1 1005.36700 cents 6: 1 1005.36800 cents 6: 1 1007.89700 cents 6: 1 1007.89800 cents 6: 1 1009.58400 cents 6: 2 1081.94300 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 192.1 384.2 502.3 696.9 887.3 1081.9 1200.0 192.1 : 192.1 310.2 504.8 695.2 889.8 1007.9 1200.0 384.2 : 118.1 312.7 503.1 697.7 815.8 1007.9 1200.0 502.3 : 194.6 385.0 579.7 697.7 889.8 1081.9 1200.0 696.9 : 190.4 385.0 503.1 695.2 887.3 1005.4 1200.0 887.3 : 194.6 312.7 504.8 696.9 815.0 1009.6 1200.0 1081.9: 118.1 310.2 502.3 620.3 815.0 1005.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 118.0570 .. 194.6330 cents 76.57600 cents 118.05700 cents 2: 310.1590 .. 385.0490 cents 74.89000 cents 115.52600 cents 3: 502.2620 .. 579.6810 cents 77.41900 cents 117.21300 cents 4: 620.3190 .. 697.7380 cents 77.41900 cents 40.63800 cents 5: 814.9510 .. 889.8410 cents 74.89000 cents 117.21300 cents 6: 1005.3670 .. 1081.9430 cents 76.57600 cents 115.52600 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 118.05700 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 194.63300 cents Average / Smallest step : 1.452083 Largest / Average step : 1.135359 Largest / Smallest step : 1.648636 Median interval of one step : 192.10200 cents, amount: 1 Most common interval of one step : 118.05700 cents, amount: 2 Least squares average step : 175.59351 cents, oct.: 1229.15460 cents Scale is strictly proper Step pattern alph. order: ABCDEFC Step pattern size order : DCAFBEA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 40.63800 cents Scale diversity : 1.295948 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.618525 Rothenberg efficiency : 0.326531 redundancy: 0.673469 Efficiency x scale size : 2.285714 Number of different interval sizes : 36 = 6.00000 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 6.00000 = 6 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 0.00100 cents Number of recognisable fifths : 6, average 696.6135 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% Limited inverse transpositions : 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 4-5 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 29.6775 c. M: 53.3716 c. Lebeng 10: 2 1 1 2 1 2 1 P M ME S SD: 29.6444 c. M:-47.8970 c. Sethares Neutral, Beatles-7, Dichotic-7 12: 2 2 1 2 2 2 1 P M ME S SD: 10.7814 c. M:-18.0570 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 19: 3 3 2 3 3 3 2 SP M ME S SD: 4.2433 c. M: 8.2588 c. Nineteen-tone Major, Ionian 31: 5 5 3 5 5 5 3 SP M DE S SD: 1.8586 c. M:-3.0116 c. Thirty-one tone Major, Intense Diatonic Lydian, M.Ionian 50: 8 8 5 8 8 8 5 SP M DE S SD: 1.0773 c. M: 1.9430 c. Fifty tone Major 81: 13 13 8 13 13 13 8 SP M DE S SD: 0.9517 c. M:-1.5779 c. 131: 21 21 13 21 21 21 13 SP M DE S SD: 0.9150 c. M:-1.5548 c. 193: 31 31 19 31 31 31 19 SP M DE S SD: 1.0338 c. M:-1.8082 c. 212: 34 34 21 34 34 34 21 SP M DE S SD: 0.9161 c. M:-1.5116 c. 256: 41 41 25 42 40 42 25 SP S SD: 0.8902 c. M:-1.5425 c. 265: 42 43 26 43 42 43 26 SP T3 SD: 0.8171 c. M: 1.9143 c. 275: 44 44 27 45 43 45 27 SP S SD: 0.7738 c. M: 1.4928 c. 277: 44 45 27 45 44 45 27 SP T3 SD: 0.9446 c. M: 1.4893 c. 284: 45 46 28 46 45 46 28 SP T3 SD: 0.7925 c. M: 1.9622 c. 287: 46 46 28 47 45 47 28 SP S SD: 0.7722 c. M:-1.3628 c. 294: 47 47 29 48 46 48 29 SP S SD: 0.7728 c. M: 1.5967 c. 296: 47 48 29 48 47 48 29 SP T3 SD: 0.7727 c. M: 1.5625 c. 306: 49 49 30 50 48 50 30 SP S SD: 0.6161 c. M:-1.1442 c. 325: 52 52 32 53 51 53 32 SP S SD: 0.5754 c. M: 1.1572 c. 337: 54 54 33 55 53 55 33 SP S SD: 0.5345 c. M:-1.0278 c. 356: 57 57 35 58 56 58 35 SP S SD: 0.4437 c. M:-0.8578 c. 368: 59 59 36 60 58 60 36 SP S SD: 0.5155 c. M:-0.9311 c. 375: 60 60 37 61 59 61 37 SP S SD: 0.4654 c. M: 0.9110 c. 387: 62 62 38 63 61 63 38 SP S SD: 0.3796 c. M:-0.7794 c. 406: 65 65 40 66 64 66 40 SP S SD: 0.3498 c. M:-0.6419 c. 418: 67 67 41 68 66 68 41 SP S SD: 0.3771 c. M:-0.7127 c. 437: 70 70 43 71 69 71 43 SP S SD: 0.2941 c. M:-0.5878 c. 456: 73 73 45 74 72 74 45 SP S SD: 0.3192 c. M:-0.4734 c. 468: 75 75 46 76 74 76 46 SP S SD: 0.2984 c. M:-0.5409 c. 487: 78 78 48 79 77 79 48 SP S SD: 0.2697 c. M:-0.4356 c. 549: 88 88 54 89 87 89 54 SP S SD: 0.3118 c. M:-0.4945 c. 568: 91 91 56 92 90 92 56 SP S SD: 0.2851 c. M:-0.5549 c. 775: 124 124 76 126 123 126 76 SP S SD: 0.2829 c. M: 0.5846 c. 794: 127 127 78 129 126 129 78 SP S SD: 0.2578 c. M: 0.4988 c. 813: 130 130 80 132 129 132 80 SP S SD: 0.2714 c. M: 0.4412 c. 825: 132 132 81 134 131 134 81 SP S SD: 0.2192 c. M: 0.4438 c. 844: 135 135 83 137 134 137 83 SP S SD: 0.2139 c. M: 0.3663 c. 856: 137 137 84 139 136 139 84 SP S SD: 0.2028 c. M: 0.3928 c. 875: 140 140 86 142 139 142 86 SP S SD: 0.1738 c. M: 0.3191 c. 894: 143 143 88 145 142 145 88 SP S SD: 0.1908 c. M: 0.3124 c. 906: 145 145 89 147 144 147 89 SP S SD: 0.1572 c. M: 0.2752 c. 925: 148 148 91 150 147 150 91 SP S SD: 0.1503 c. M: 0.2464 c. 937: 150 150 92 152 149 152 92 SP S SD: 0.1656 c. M: 0.2343 c. 944: 151 151 93 153 150 153 93 SP S SD: 0.1877 c. M: 0.3067 c. 956: 153 153 94 155 152 155 94 SP S SD: 0.1332 c. M: 0.2423 c. 1231: 197 197 121 200 195 200 121 SP S SD: 0.1444 c. M: 0.2311 c. 1262: 202 202 124 205 200 205 124 SP S SD: 0.1178 c. M: 0.2018 c. 1281: 205 205 126 208 203 208 126 SP S SD: 0.1108 c. M: 0.1916 c. 1293: 207 207 127 210 205 210 127 SP S SD: 0.1071 c. M:-0.1916 c. 1312: 210 210 129 213 208 213 129 SP S SD: 0.0775 c. M: 0.1279 c. 1331: 213 213 131 216 211 216 131 SP S SD: 0.0904 c. M: 0.1585 c. 1343: 215 215 132 218 213 218 132 SP S SD: 0.0631 c. M:-0.1121 c. 1362: 218 218 134 221 216 221 134 SP S SD: 0.0487 c. M: 0.0863 c. 1393: 223 223 137 226 221 226 137 SP S SD: 0.0222 c. M:-0.0383 c. 1443: 231 231 142 234 229 234 142 SP S SD: 0.0161 c. M: 0.0303 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: 2.5300 cents 3 x x 4 x 5 x 6 S SD: 1.7159 cents 4 x 5 x 6:7 x 8 S SD: 20.4248 cents 5 x 6:7 x 8:9:10 S SD: 28.7765 cents 6:7 x 8:9:10:11:12 S SD: 13.6461 cents 7:8:9 x 10:12:13:14 S SD: 18.7268 cents 8:9:10:11:12:13:15:16 SD: 9.9022 cents 12:13:15:16:18:20:22:24 SD: 9.0164 cents 15:17:19:20:22:25:28:30 SD: 7.0062 cents 16:18:20:21:24:27:30:32 S SD: 5.6148 cents 24:27:30:32:36:40:45:48 S SD: 2.1945 cents 36:40:45:48:54:60:67:72 SD: 1.9871 cents 51:57:64:68:76:85:95:102 SD: 1.8654 cents 60:67:75:80:90:100:112:120 SD: 1.1029 cents 69:77:86:92:103:115:129:138 SD: 1.0354 cents 85:95:106:114:127:142:159:170 SD: 0.9966 cents 93:104:116:124:139:155:174:186 SD: 0.8952 cents 101:113:126:135:151:169:189:202 SD: 0.7929 cents 113:126:141:151:169:189:211:226 SD: 0.7089 cents 121:135:151:162:181:202:226:242 SD: 0.5694 cents 137:153:171:183:205:229:256:274 SD: 0.3871 cents 145:162:181:194:217:242:271:290 SD: 0.3251 cents 214:239:267:286:320:357:400:428 SD: 0.3110 cents 273:305:341:365:408:456:510:546 SD: 0.2645 cents 282:315:352:377:422:471:527:564 SD: 0.2181 cents 333:372:416:445:498:556:622:666 SD: 0.1751 cents 442:494:552:591:661:738:826:884 SD: 0.1653 cents 478:534:597:639:715:798:893:956 SD: 0.1176 cents