Scala analysis: DimensionECF
Dimension ECF (Dimension Tuning Optimized for Fifths)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 119.558 cents 119.558220 2: 28/25 196.198479 middle second 3: 6/5 315.641287 minor third 4: 613/500 352.750775 5: 505.775 cents 505.774990 6: 621.759 cents 621.758680 7: 3/2 701.955001 perfect fifth 8: 201/125 822.320888 9: 837/500 891.959433 10: 1011.526 cents 1011.526340 11: 1831/1000 1047.158149
SHOW/INTERVAL
0: 35.6318 cents 35.6318 1: 119.5582 cents 119.5582 2: 76.6403 cents 76.6403 3: 15/14 119.4428 major diatonic semitone 4: 613/600 37.1095 5: 153.0242 cents 153.0242 6: 115.9837 cents 115.9837 7: 80.1963 cents 80.1963 8: 134/125 120.3659 9: 279/268 69.6385 10: 119.5669 cents 119.5669 11: 35.6318 cents 35.6318
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 35.63181 cents 1: 1 613/600 37.109 cents 1: 1 279/268 69.639 cents 1: 1 76.64026 cents 1: 1 80.19632 cents 1: 1 115.98369 cents 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 119.55822 cents 1: 1 119.56691 cents 1: 1 134/125 120.366 cents 1: 1 153.02422 cents 2: 1 155.19003 cents 2: 1 1831/1674 155.199 cents 2: 1 613/560 156.552 cents 2: 1 189.20545 cents 2: 1 279/250 190.004 cents 2: 1 190.13370 cents 2: 1 196.08307 cents 2: 1 196.18001 cents 2: 1 28/25 196.198 cents middle second 2: 1 200.56221 cents 2: 1 269.00791 cents 3: 1 1831/1608 224.837 cents 3: 1 231.83029 cents 3: 1 233.19255 cents 3: 1 270.20075 cents 3: 1 274.75694 cents 3: 1 306.11739 cents 3: 1 309.57134 cents 3: 1 309.57651 cents 3: 1 6/5 315.641 cents minor third 3: 1 316.54590 cents 3: 1 750/613 349.204 cents 4: 1 344.39548 cents 4: 1 1831/1500 345.203 cents 4: 1 351.27310 cents 4: 1 25634/20925 351.397 cents 4: 1 613/500 352.751 cents 4: 1 386.18444 cents 4: 1 386.21677 cents 4: 1 5/4 386.314 cents major third 4: 1 389.76766 cents 4: 1 425.56020 cents 4: 1 804/613 469.570 cents 5: 1 388.38258 cents 5: 1 12817/10050 421.036 cents 5: 1 425.39947 cents 5: 1 464.76137 cents 5: 1 1831/1395 470.840 cents 5: 1 502.20046 cents 5: 1 505.75135 cents 5: 1 75/56 505.757 cents marvelous fourth 5: 1 505.77499 cents 5: 1 67/50 506.680 cents 5: 1 837/613 539.209 cents 6: 1 1122403/837000 507.949 cents 6: 1 1831/1340 540.479 cents 6: 1 541.38316 cents 6: 1 12817/9375 541.402 cents 6: 1 541.40680 cents 6: 1 544.95769 cents 6: 1 279/200 576.318 cents 6: 1 582.39678 cents 6: 1 621.75868 cents 6: 1 201/140 626.122 cents 6: 1 658.77557 cents 7: 1 1122403/804000 577.588 cents 7: 1 621.59795 cents 7: 1 657.39049 cents 7: 1 1831/1250 660.844 cents 7: 1 660.94138 cents 7: 1 660.97371 cents 7: 1 1831/1226 694.407 cents 7: 1 837/560 695.761 cents 7: 1 695.88505 cents 7: 1 3/2 701.955 cents perfect fifth 7: 1 702.76267 cents 8: 1 1122403/750000 697.954 cents 8: 1 730.61225 cents 8: 1 1831/1200 731.517 cents 8: 1 737.58164 cents 8: 1 737.58681 cents 8: 1 741.04076 cents 8: 1 772.40121 cents 8: 1 776.95740 cents 8: 1 813.96559 cents 8: 1 815.32786 cents 8: 1 201/125 822.321 cents 9: 1 778.15024 cents 9: 1 846.59594 cents 9: 1 1831/1120 850.960 cents 9: 1 850.97814 cents 9: 1 851.07508 cents 9: 1 857.02445 cents 9: 1 1831/1116 857.154 cents 9: 1 857.95270 cents 9: 1 25634/15325 890.606 cents 9: 1 837/500 891.959 cents 9: 1 891.96812 cents 10: 1 894.13393 cents 10: 1 1831/1072 926.792 cents 10: 1 927.59124 cents 10: 1 927.59993 cents 10: 1 12817/7500 927.715 cents 10: 1 931.17446 cents 10: 1 966.96183 cents 10: 1 970.51789 cents 10: 1 122677/69750 977.520 cents 10: 1 5493/3065 1010.049 cents 10: 1 1011.52634 cents Highest number of different intervals for one interval class: 11 Average number of different intervals per interval class: 11.00000 = 11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 119.6 196.2 315.6 352.8 505.8 621.8 702.0 822.3 892.0 1011.5 1047.2 119.6 : 76.6 196.1 233.2 386.2 502.2 582.4 702.8 772.4 892.0 927.6 1047.2 196.2 : 119.4 156.6 309.6 425.6 505.8 626.1 695.8 815.3 851.0 970.5 1047.2 315.6 : 37.1 190.1 306.1 386.3 506.7 576.3 695.9 731.5 851.1 927.7 1047.2 352.8 : 153.0 269.0 349.2 469.6 539.2 658.8 694.4 814.0 890.6 1010.0 1047.2 505.8 : 116.0 196.2 316.5 386.2 505.8 541.4 660.9 737.6 857.0 894.1 1047.2 621.8 : 80.2 200.6 270.2 389.8 425.4 545.0 621.6 741.0 778.2 931.2 1047.2 702.0 : 120.4 190.0 309.6 345.2 464.8 541.4 660.8 698.0 851.0 967.0 1047.2 822.3 : 69.6 189.2 224.8 344.4 421.0 540.5 577.6 730.6 846.6 926.8 1047.2 892.0 : 119.6 155.2 274.8 351.4 470.8 507.9 661.0 777.0 857.2 977.5 1047.2 1011.5: 35.6 155.2 231.8 351.3 388.4 541.4 657.4 737.6 858.0 927.6 1047.2 1047.2
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6318 .. 153.0242 cents 117.39241 cents 35.63181 cents 2: 155.1900 .. 269.0079 cents 113.81788 cents 2.16581 cents 3: 224.8373 .. 349.2042 cents 1206000/1122403, 124.3670 cents -44.17064 cents 4: 344.3955 .. 469.5701 cents 125.17463 cents -4.80874 cents 5: 388.3826 .. 539.2087 cents 150.82607 cents -81.18753 cents 6: 507.9495 .. 658.7756 cents 150.82607 cents 688033039/700569000,-31.2592 cents 7: 577.5880 .. 702.7627 cents 125.17463 cents -81.18753 cents 8: 697.9539 .. 822.3209 cents 1206000/1122403, 124.3670 cents -4.80874 cents 9: 778.1502 .. 891.9681 cents 113.81788 cents -44.17064 cents 10: 894.1339 .. 1011.5263 cents 117.39241 cents 2.16581 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 35.63181 cents, class 1 Average step (divided formal octave): 95.1962 cents Largest one step interval : 153.02422 cents Average / Smallest step : 2.671663 Largest / Average step : 1.607461 Largest / Smallest step : 4.294596 Median interval of one step : 115.98369 cents, amount: 1 Least squares average step : 99.37391 cents, oct.: 1093.11303 cents Scale is not proper Step pattern alph. order: ABCDEFGHIJK Step pattern size order : HDGBKFEJCIA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.16073 cents Scale diversity : 1.402923 Lumma stability : 0.072191 Lumma impropriety factor : 0.278461 Rothenberg efficiency : 0.181818 redundancy: 0.818182 Efficiency x scale size : 2.000000 Number of different interval sizes : 110 = 11.00000 / class Number of one step interval sizes : 11 Highest interval variety : 11 Mean interval variety : 11.00000 = 11 Median interval variety : 11 Lowest interval variety : 11 Smallest interval difference : 0.00517 cents Number of recognisable fifths : 6, average 698.1208 cents Number of recognisable fourths : 6, average 505.6854 cents Formal octave complements present : 1 = 9.0909% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 1831 (not all pitches rational)
FIT/MODE
11: 1 1 1 1 1 2 0 2 0 2 0 N T3 SD: 30.3842 c. M:-44.6147 c. 12: 1 1 1 1 2 1 1 1 1 1 1 P M ME S SD: 29.0488 c. M: 53.8517 c. 13: 1 1 2 0 2 2 1 1 1 1 1 N T3 SD: 26.3055 c. M: 44.9188 c. 15: 2 1 2 0 2 2 1 2 1 2 0 N SD: 18.6041 c. M:-35.6318 c. 17: 2 1 2 0 3 2 1 2 1 2 1 N SD: 21.3562 c. M: 44.7631 c. 20: 2 2 2 1 3 2 1 3 1 2 1 N SD: 13.2148 c. M: 21.3022 c. 21: 2 2 2 1 3 2 2 2 2 2 1 N SD: 13.9288 c. M: 24.4861 c. 23: 3 1 3 1 3 3 1 3 2 2 1 N SD: 12.4788 c. M: 19.0258 c. 25: 3 2 3 0 4 3 2 3 1 3 1 N SD: 11.6237 c. M:-19.4493 c. 27: 3 2 3 1 4 3 2 3 2 3 1 N SD: 3.6760 c. M: 7.8645 c. 60: 7 4 7 2 9 7 4 7 4 7 2 N SD: 3.1104 c. M:-6.5362 c. 69: 8 5 8 2 10 8 5 8 5 8 2 N SD: 3.2312 c. M:-5.2794 c. 79: 9 6 9 3 11 9 6 9 5 9 3 N SD: 2.6626 c. M:-5.1387 c. 89: 10 7 10 3 13 10 7 10 6 10 3 N SD: 2.1004 c. M:-3.9943 c. 106: 12 8 12 4 15 12 8 12 7 12 4 N SD: 2.0208 c. M: 3.8836 c. 113: 13 8 13 4 17 12 9 13 7 13 4 N SD: 1.8814 c. M:-3.9038 c. 116: 13 9 13 4 17 13 9 13 8 13 4 N SD: 1.3871 c. M:-2.4005 c. 143: 16 11 16 5 21 16 11 16 10 16 5 N SD: 1.3367 c. M: 2.3937 c. 149: 17 11 17 5 22 16 12 17 10 17 5 N SD: 1.1604 c. M: 3.3029 c. 155: 18 11 18 5 23 17 12 18 10 18 5 N SD: 1.2890 c. M:-2.0472 c. 176: 20 13 20 6 26 19 14 20 12 20 6 N SD: 1.1329 c. M: 2.9834 c. 182: 21 13 21 6 27 20 14 21 12 21 6 N SD: 0.8336 c. M: 1.7802 c. 209: 24 15 24 7 31 23 16 24 14 24 7 N SD: 0.7689 c. M: 2.0279 c. 228: 26 17 26 8 33 25 18 26 15 26 8 N SD: 0.9603 c. M: 1.7308 c. 236: 27 17 27 8 35 26 18 27 16 27 8 N SD: 0.9315 c. M: 2.2190 c. 246: 28 18 28 9 36 27 19 28 17 28 8 N SD: 0.8927 c. M:-1.9561 c. 255: 29 19 29 9 37 28 20 29 17 29 9 N SD: 0.8733 c. M: 1.6768 c. 256: 29 19 29 9 38 28 20 29 17 29 9 N SD: 0.8750 c. M:-1.6044 c. 261: 30 19 30 9 38 29 20 30 17 30 9 N SD: 0.6472 c. M:-1.3146 c. 271: 31 20 31 9 40 30 21 31 18 31 9 N SD: 0.8081 c. M:-1.3025 c. 288: 33 21 33 10 42 32 22 33 19 33 10 N SD: 0.5280 c. M: 1.1478 c. 315: 36 23 36 11 46 35 24 36 21 36 11 N SD: 0.6141 c. M: 1.2159 c. 325: 37 24 37 11 48 36 25 37 22 37 11 N SD: 0.5795 c. M: 1.5500 c. 362: 41 27 41 13 53 40 28 41 24 42 12 N SD: 0.6725 c. M: 1.0072 c. 377: 43 28 43 13 55 42 29 43 25 43 13 N SD: 0.5454 c. M:-1.0117 c. 385: 44 28 44 14 56 43 29 44 26 44 13 N SD: 0.5281 c. M:-1.0964 c. 391: 45 28 45 14 57 43 30 45 26 45 13 N SD: 0.5434 c. M:-0.9587 c. 404: 46 30 46 14 59 45 31 46 27 46 14 N SD: 0.4804 c. M:-0.7917 c. 464: 53 34 53 16 68 51 36 53 31 53 16 N SD: 0.5367 c. M: 1.1369 c. 465: 53 34 53 17 68 51 36 53 31 53 16 N SD: 0.4805 c. M:-0.9144 c. 470: 54 34 54 16 69 52 36 54 31 54 16 N SD: 0.4583 c. M: 0.7610 c. 480: 55 35 55 17 70 53 37 55 32 55 16 N SD: 0.4418 c. M:-0.7265 c. 507: 58 37 58 18 74 56 39 58 34 58 17 N SD: 0.2960 c. M:-0.5200 c. 534: 61 39 61 19 78 59 41 61 36 61 18 N SD: 0.2633 c. M: 0.6743 c. 588: 67 43 67 21 86 65 45 68 39 67 20 N SD: 0.2614 c. M:-0.4462 c. 795: 91 58 91 28 116 88 61 91 53 91 27 N SD: 0.2382 c. M:-0.4819 c. 822: 94 60 94 29 120 91 63 95 54 94 28 N SD: 0.2314 c. M:-0.6282 c. 843: 96 62 96 30 123 93 65 97 56 96 29 N SD: 0.2664 c. M: 0.6684 c. 849: 97 62 97 30 124 94 65 98 56 97 29 N SD: 0.1542 c. M:-0.3581 c. 876: 100 64 100 31 128 97 67 101 58 100 30 N SD: 0.1523 c. M: 0.2634 c. 965: 110 71 110 34 141 107 74 111 64 110 33 N SD: 0.1388 c. M:-0.2137 c. 1174: 134 86 134 41 172 130 90 135 78 134 40 N SD: 0.1380 c. M: 0.4275 c. 1201: 137 88 137 43 175 133 92 138 80 137 41 N SD: 0.1329 c. M:-0.3708 c. 1350: 154 99 154 48 197 150 103 155 90 154 46 N SD: 0.1275 c. M:-0.3308 c. 1356: 155 99 155 48 198 150 104 156 90 155 46 N SD: 0.1083 c. M:-0.2051 c. 1383: 158 101 158 49 202 153 106 159 92 158 47 N SD: 0.0709 c. M: 0.1268 c. 1499: 171 110 171 53 219 166 115 172 100 171 51 N SD: 0.0803 c. M:-0.1159 c. 2087: 238 153 238 74 305 231 160 240 139 238 71 N SD: 0.0720 c. M:-0.1571 c. 2120: 242 155 242 75 310 235 162 244 141 242 72 N SD: 0.0728 c. M:-0.1150 c. 2226: 254 163 254 79 325 247 170 256 148 254 76 N SD: 0.0732 c. M:-0.1385 c. 2259: 258 165 258 80 330 250 173 260 150 258 77 N SD: 0.0796 c. M: 0.1412 c. 2321: 265 170 265 82 339 257 178 267 154 265 79 N SD: 0.0793 c. M:-0.1755 c. 2348: 268 172 268 83 343 260 180 270 156 268 80 N SD: 0.0495 c. M:-0.1117 c. 2375: 271 174 271 84 347 263 182 273 158 271 81 N SD: 0.0478 c. M: 0.0818 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 152.8419 cents 2 x x x x x x 3 x x x 4 S SD: 76.4209 cents 3 x x x x 4 x x x 5 x x S SD: 5.4204 cents 4 x x x 5 x x 6 x x 7 x S SD: 18.1040 cents 5 x x 6 x x 7 x 8 x 9 x S SD: 10.1602 cents 6 x x 7 x 8 x 9 x 10 x 11 S SD: 10.0019 cents 7 x 8 x x 9:10 x 11:12 x 13 S SD: 16.7684 cents 8 x 9 x 10:11 x 12:13 x 14:15 S SD: 12.0416 cents 9 x 10 x 11:12:13 x 14:15:16 x S SD: 9.1370 cents 10 x 11:12 x 13:14:15:16:17:18 x S SD: 9.6786 cents 11:12 x 13 x 15:16:17:18 x x 20 SD: 12.0345 cents 12:13 x 14:15:16:17:18:19:20 x 22 S SD: 7.9015 cents 13:14:15 x 16:17:19:20:21:22:23:24 SD: 9.4003 cents 14:15:16 x 17:19:20:21 x 23:25:26 SD: 6.8148 cents 15:16:17:18 x 20:21:23:24:25:27 x SD: 6.7569 cents 16:17:18:19:20:21:23:24:26:27 x 29 SD: 6.1877 cents 18:19:20 x 22:24:26:27:29:30:32:33 SD: 3.8538 cents 19:20:21:23 x 25:27:29:31:32:34:35 SD: 6.7816 cents 20:21:22:24:25:27:29:30:32:33:36:37 SD: 6.4533 cents 21:23:24:25:26:28:30:32:34:35:38 x SD: 6.6275 cents 22:24:25:26:27:29:32:33:35:37:39:40 SD: 6.2655 cents 23:25:26 x 28:31:33:35:37:39:41:42 SD: 4.9047 cents 24:26:27:29 x 32:34:36:39:40:43:44 SD: 3.7070 cents 26:28:29:31:32:35:37:39:42:44:47:48 SD: 3.2734 cents 28:30:31 x 34:38:40:42:45:47:50:51 SD: 3.7205 cents 30:32:34:36:37:40:43:45:48:50:54:55 SD: 2.6090 cents 33:35:37:40 x 44:47:50:53:55:59:60 SD: 3.6252 cents 34:36:38:41:42:46:49:51:55:57:61:62 SD: 3.2421 cents 35:38:39:42:43:47:50:53:56:59:63:64 SD: 3.1270 cents 36:39:40:43:44:48:52:54:58:60:65:66 SD: 3.0551 cents 39:42:44:47:48:52:56:59:63:65:70:71 SD: 2.6574 cents 40:43:45:48:49:54:57:60:64:67:72:73 SD: 2.0367 cents 44:47:49:53:54:59:63:66:71:74:79:81 SD: 1.7453 cents 56:60:63:67:69:75:80:84:90:94:100:103 SD: 1.6342 cents 58:62:65:70:71:78:83:87:93:97:104:106 SD: 1.3279 cents 74:79:83:89:91:99:106:111:119:124:133:135 SD: 1.1074 cents 84:90:94:101:103:113:120:126:135:141:151:154 SD: 1.0492 cents 94:101:105:113:115:126:135:141:151:157:169:172 SD: 1.0334 cents 98:105:110:118:120:131:140:147:158:164:176:179 SD: 1.0216 cents 100:107:112:120:123:134:143:150:161:167:179:183 SD: 0.8152 cents 110:118:123:132:135:147:158:165:177:184:197:201 SD: 0.8071 cents 124:133:139:149:152:166:178:186:199:208:222:227 SD: 0.7209 cents 125:134:140:150:153:167:179:188:201:209:224:229 SD: 0.6805 cents 136:146:152:163:167:182:195:204:219:228:244:249 SD: 0.6743 cents 141:151:158:169:173:189:202:212:227:236:253:258 SD: 0.5215 cents 150:161:168:180:184:201:215:225:241:251:269:275 SD: 0.4087 cents 194:208:217:233:238:260:278:291:312:325:348:355 SD: 0.3524 cents 224:240:251:269:275:300:321:336:360:375:402:410 SD: 0.3057 cents 266:285:298:319:326:356:381:399:428:445:477:487 SD: 0.2236 cents 324:347:363:389:397:434:464:486:521:542:581:593 SD: 0.2034 cents 350:375:392:420:429:469:501:525:563:586:628:641 SD: 0.1467 cents 460:493:515:552:564:616:659:690:740:770:825:842 SD: 0.1267 cents 574:615:643:689:704:769:822:861:923:961:1030:1051 SD: 0.1175 cents