Scala analysis: m2scra
Rational approximation to 2/7-comma meantone (1/1 = 262.9333Hz)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 19825/17748 191.597289 3: 11811/9860 312.565880 4: 19685/15776 383.238307 5: 1979/1479 504.179472 6: 49475/35496 574.851899 7: 5895/3944 695.798714 8: 49125/31552 766.471141 9: 6585/3944 887.428667 10: 35307/19720 1008.353628 11: 58845/31552 1079.026055 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 63104/58845 120.9739 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 1586/1479 120.9249 3: 106299/99125 120.9686 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 63328/59055 120.9412 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 10611/9895 120.9468 8: 25/24 70.6724 classic chromatic semitone, minor chroma 9: 3512/3275 120.9575 10: 11769/10975 120.9250 11: 25/24 70.6724 classic chromatic semitone, minor chroma 12: 63104/58845 120.9739
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 1586/1479 120.925 cents 1: 1 11769/10975 120.925 cents 1: 1 63328/59055 120.941 cents 1: 1 10611/9895 120.947 cents 1: 1 3512/3275 120.958 cents 1: 1 106299/99125 120.969 cents 1: 1 63104/58845 120.974 cents 2: 1 19825/17748 191.597 cents 2: 1 3923/3512 191.597 cents 2: 2 39580/35433 191.614 cents 2: 2 17685/15832 191.619 cents 2: 1 439/393 191.630 cents 2: 1 35433/31720 191.641 cents 2: 2 39440/35307 191.646 cents 2: 1 94152/81875 241.882 cents 2: 1 70866/61625 241.893 cents 3: 1 247375/212598 262.286 cents 3: 1 147375/126656 262.292 cents 3: 1 123250/105921 262.319 cents 3: 2 3923/3275 312.555 cents 3: 1 4716/3937 312.560 cents 3: 2 11811/9860 312.566 cents 3: 1 126880/105921 312.571 cents 3: 1 7888/6585 312.571 cents 3: 1 11853/9895 312.577 cents 3: 1 23748/19825 312.582 cents 4: 1 3923/3144 383.227 cents 4: 2 9825/7874 383.233 cents 4: 1 19685/15776 383.238 cents 4: 1 396500/317763 383.244 cents 4: 1 4930/3951 383.244 cents 4: 1 19755/15832 383.249 cents 4: 1 1979/1586 383.255 cents 4: 1 317763/247375 433.502 cents 4: 1 15832/12325 433.507 cents 4: 1 63104/49125 433.529 cents 4: 1 125984/98075 433.540 cents 5: 1 81875/62992 453.905 cents 5: 1 15860/11853 504.169 cents 5: 2 105921/79160 504.174 cents 5: 2 1979/1479 504.179 cents 5: 1 5268/3937 504.190 cents 5: 2 7888/5895 504.201 cents 5: 1 10611/7930 504.201 cents 5: 2 15748/11769 504.212 cents 6: 1 176535/126656 574.847 cents 6: 1 49475/35496 574.852 cents 6: 1 10975/7874 574.863 cents 6: 1 4930/3537 574.874 cents 6: 1 17685/12688 574.874 cents 6: 1 98425/70614 574.885 cents 6: 1 141228/98425 625.115 cents 6: 1 25376/17685 625.126 cents 6: 1 3537/2465 625.126 cents 6: 1 15748/10975 625.137 cents 6: 1 70992/49475 625.148 cents 6: 1 253312/176535 625.153 cents 7: 2 11769/7874 695.788 cents 7: 1 15860/10611 695.799 cents 7: 2 5895/3944 695.799 cents 7: 1 3937/2634 695.810 cents 7: 2 2958/1979 695.821 cents 7: 2 158320/105921 695.826 cents 7: 1 11853/7930 695.831 cents 7: 1 125984/81875 746.095 cents 8: 1 98075/62992 766.460 cents 8: 1 49125/31552 766.471 cents 8: 1 12325/7916 766.493 cents 8: 1 494750/317763 766.498 cents 8: 1 3172/1979 816.745 cents 8: 1 31664/19755 816.751 cents 8: 1 3951/2465 816.756 cents 8: 1 317763/198250 816.756 cents 8: 1 31552/19685 816.762 cents 8: 2 15748/9825 816.767 cents 8: 1 6288/3923 816.773 cents 9: 1 19825/11874 887.418 cents 9: 1 19790/11853 887.423 cents 9: 1 6585/3944 887.429 cents 9: 1 105921/63440 887.429 cents 9: 2 19720/11811 887.434 cents 9: 1 3937/2358 887.440 cents 9: 2 6550/3923 887.445 cents 9: 1 105921/61625 937.681 cents 9: 1 253312/147375 937.708 cents 9: 1 425196/247375 937.714 cents 10: 1 61625/35433 958.107 cents 10: 1 81875/47076 958.118 cents 10: 2 35307/19720 1008.354 cents 10: 1 63440/35433 1008.359 cents 10: 1 786/439 1008.370 cents 10: 2 31664/17685 1008.381 cents 10: 2 35433/19790 1008.386 cents 10: 1 7024/3923 1008.403 cents 10: 1 35496/19825 1008.403 cents 11: 1 58845/31552 1079.026 cents 11: 1 198250/106299 1079.031 cents 11: 1 3275/1756 1079.042 cents 11: 1 19790/10611 1079.053 cents 11: 1 59055/31664 1079.059 cents 11: 1 21950/11769 1079.075 cents 11: 1 1479/793 1079.075 cents 11: 5 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 12 Average number of different intervals per interval class: 9.45455 = 104/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 70.7 191.6 312.6 383.2 504.2 574.9 695.8 766.5 887.4 1008.4 1079.0 1200.0 70.7 : 120.9 241.9 312.6 433.5 504.2 625.1 695.8 816.8 937.7 1008.4 1129.3 1200.0 191.6 : 121.0 191.6 312.6 383.3 504.2 574.9 695.8 816.8 887.4 1008.4 1079.1 1200.0 312.6 : 70.7 191.6 262.3 383.2 453.9 574.9 695.8 766.5 887.4 958.1 1079.0 1200.0 383.2 : 120.9 191.6 312.6 383.2 504.2 625.1 695.8 816.8 887.4 1008.4 1129.3 1200.0 504.2 : 70.7 191.6 262.3 383.2 504.2 574.8 695.8 766.5 887.4 1008.4 1079.1 1200.0 574.9 : 120.9 191.6 312.6 433.5 504.2 625.1 695.8 816.7 937.7 1008.4 1129.3 1200.0 695.8 : 70.7 191.6 312.6 383.2 504.2 574.9 695.8 816.8 887.4 1008.4 1079.1 1200.0 766.5 : 121.0 241.9 312.6 433.5 504.2 625.1 746.1 816.8 937.7 1008.4 1129.3 1200.0 887.4 : 120.9 191.6 312.6 383.2 504.2 625.1 695.8 816.8 887.4 1008.4 1079.0 1200.0 1008.4: 70.7 191.6 262.3 383.2 504.2 574.9 695.8 766.5 887.4 958.1 1079.1 1200.0 1079.0: 121.0 191.6 312.6 433.5 504.2 625.2 695.8 816.8 887.4 1008.4 1129.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 120.9739 cents 504832/490375, 50.3015 cents 25/24, 70.6724 cents 2: 191.5973 .. 241.8935 cents 2551176/2478125, 50.2962 cents 388867375/373323264, 70.6233 cents 3: 262.2860 .. 312.5822 cents 2551176/2478125, 50.2962 cents 20.39257 cents 4: 383.2273 .. 433.5398 cents 396093696/384748225, 50.3125 cents 77773475/74663712, 70.6452 cents 5: 453.9053 .. 504.2123 cents 991998016/963586875, 50.3070 cents 20.36544 cents 6: 574.8466 .. 625.1534 cents 50.30683 cents 2077640415/1994578688, 70.6343 cents 7: 695.7877 .. 746.0947 cents 991998016/963586875, 50.3070 cents 2077640415/1994578688, 70.6343 cents 8: 766.4602 .. 816.7727 cents 396093696/384748225, 50.3125 cents 20.36544 cents 9: 887.4178 .. 937.7140 cents 2551176/2478125, 50.2962 cents 77773475/74663712, 70.6452 cents 10: 958.1065 .. 1008.4027 cents 2551176/2478125, 50.2962 cents 20.39257 cents 11: 1079.0261 .. 1129.3276 cents 504832/490375, 50.3015 cents 388867375/373323264, 70.6233 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 63104/58845, 120.9739 cents Average / Smallest step : 1.414979 Largest / Average step : 1.209739 Largest / Smallest step : 1.711756 Median interval of one step : 120.92491 cents, amount: 0 Most common interval of one step : 25/24, 70.6724 cents, amount: 5 Least squares average step : 98.82549 cents, oct.: 1185.90586 cents Scale is strictly proper Step pattern alph. order: ABCADAEAFGAH Step pattern size order : ABFACADAEBAG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 20.36544 cents Scale diversity : 1.220625 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.538889 Rothenberg efficiency : 0.217803 redundancy: 0.782197 Efficiency x scale size : 2.613636 Number of different interval sizes : 104 = 9.45455 / class Number of one step interval sizes : 8 Highest interval variety : 12 Mean interval variety : 9.45455 = 104/11 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 17406351/17406350, 0.0001 cents Most common intervals : 25/24, 70.6724 cents & inv., amount: 5 Number of recognisable fifths : 11, average 695.8096 cents Best fifths form a closed circle Length of longest harmonic part : 1 at degree 0 Formal octave complements present : 1 = 8.3333% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 3923 Odd number limit : 317763 (O: 317763 U: 317763) Highest odd numerator or denominator: 58845 Harmonicity values : limit above prime count Fundamental : 1/1419840, -20.4373 octaves, 0.0002 Hz. Guide tone : too high to compute Sum of Mann's harmonic distance : 214827.5, average 17902.29167 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 43.65032, average 3.63753 Sum of Tenney's harmonic distance : 85.97757, average 7.16480 Vogel's harmonic complexity : 1101.41667 Wille's k value : 1324012 Lattice compactness : 300.42504, average 3.85160 Lattice compactness (without 2's) : 198.09196, average 2.53964 Number of different primes : 13 Prime exponents' range, average, count, tones@limit: 2: -6 .. 1 -2.91667 37 1 3: -2 .. 2 0.16667 14 5: -1 .. 3 0.91667 15 1 13: 0 .. 1 0.08333 1 17: -1 .. 0 -0.83333 10 29: -1 .. 0 -0.83333 10 31: 0 .. 1 0.16667 2 61: 0 .. 1 0.08333 1 1 127: 0 .. 1 0.16667 2 2 131: 0 .. 1 0.16667 2 2 439: 0 .. 1 0.08333 1 1 1979: 0 .. 1 0.16667 2 2 3923: 0 .. 1 0.16667 2 2 Average exponent except 2's : 6 / 12 = 0.50000 Average absolute exponent except 2's: 62 / 12 = 5.16667
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 17.8630 c. M:-33.5289 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 4.5699 c. M: 8.5764 c. Meantone Chromatic (1/3-comma) 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 4.1138 c. M:-7.7224 c. Meantone Chromatic (53/220-comma) 50: 3 5 5 3 5 3 5 3 5 5 3 5 SP M DE SD: 0.8141 c. M:-1.5289 c. Meantone Chromatic (5/18-comma), Eair-12 69: 4 7 7 4 7 4 7 4 7 7 4 7 SP M DE SD: 0.6686 c. M: 1.2537 c. Meantone Chromatic (5/17-comma), Synch-Meantone-12 119: 7 12 12 7 12 7 12 7 12 12 7 12 SP M DE SD: 0.0474 c. M: 0.0846 c. Meantone Chromatic (2/7-comma), Zarlino 526: 31 53 53 31 53 31 53 31 53 53 31 53 SP M DE SD: 0.0383 c. M:-0.0688 c. 645: 38 65 65 38 65 38 65 38 65 65 38 65 SP M DE SD: 0.0247 c. M:-0.0437 c. 764: 45 77 77 45 77 45 77 45 77 77 45 77 SP M DE SD: 0.0167 c. M:-0.0315 c. 883: 52 89 89 52 89 52 89 52 89 89 52 89 SP M DE SD: 0.0132 c. M:-0.0269 c. 1002: 59 101 101 59 101 59 101 59 101 101 59 101 SP M DE SD: 0.0131 c. M:-0.0296 c. 1647: 97 166 166 97 166 97 166 97 166 166 97 166 SP M DE SD: 0.0145 c. M:-0.0268 c. 1885: 111 190 190 111 190 111 190 111 190 190 111 190 SP M DE SD: 0.0129 c. M:-0.0283 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 3.0781 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.2866 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 10.0306 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 9.7629 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.2088 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 13.1483 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.4783 cents 9 x 10:11 x 12 x 13:14:15:16:17:18 S SD: 8.2294 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.7372 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.2053 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 8.6602 cents 13:14:15 x 16:17:18:19:20:22:23:24:26 S SD: 9.9436 cents 14:15:16:17 x 19:20:21:22:23:25:26:28 SD: 8.1669 cents 15:16:17:18:19:20:21:22:23:25:27:28:30 SD: 5.8734 cents 16:17:18:19:20:21:22:24:25:27:29:30:32 SD: 5.3902 cents 18:19:20:22 x 24:25:27:28:30:32:34:36 SD: 4.6217 cents 20:21:22:24:25:27:28:30:31:33:36:37:40 SD: 3.7357 cents 24:25:27:29:30:32:33:36:37:40:43:45:48 SD: 3.1239 cents 33:34:37:40:41:44:46:49:51:55:59:62:66 SD: 3.1043 cents 36:38:40:43:45:48:50:54:56:60:64:67:72 SD: 2.5454 cents 41:43:46:49:51:55:57:61:64:68:73:76:82 SD: 2.2078 cents 44:46:49:53:55:59:61:66:69:73:79:82:88 SD: 2.0530 cents 45:47:50:54:56:60:63:67:70:75:81:84:90 SD: 1.6197 cents 51:53:57:61:64:68:71:76:79:85:91:95:102 SD: 1.4843 cents 61:64:68:73:76:82:85:91:95:102:109:114:122 SD: 1.4029 cents 66:69:74:79:82:88:92:99:103:110:118:123:132 SD: 1.3115 cents 69:72:77:83:86:92:96:103:107:115:124:129:138 SD: 1.2847 cents 75:78:84:90:94:100:105:112:117:125:134:140:150 SD: 1.2707 cents 76:79:85:91:95:102:106:114:118:127:136:142:152 SD: 0.9521 cents 95:99:106:114:119:127:132:142:148:159:170:177:190 SD: 0.8862 cents 97:101:108:116:121:130:135:145:151:162:174:181:194 SD: 0.6818 cents 101:105:113:121:126:135:141:151:157:169:181:188:202 SD: 0.6808 cents 121:126:135:145:151:162:169:181:188:202:217:226:242 SD: 0.5802 cents 142:148:159:170:177:190:198:212:221:237:254:265:284 SD: 0.4693 cents 162:169:181:194:202:217:226:242:252:270:290:302:324 SD: 0.4389 cents 172:179:192:206:215:230:240:257:268:287:308:321:344 SD: 0.3991 cents 213:222:238:255:266:285:297:318:332:356:381:397:426 SD: 0.3682 cents 214:223:239:256:267:286:298:320:333:357:383:399:428 SD: 0.3463 cents 221:230:247:265:276:296:308:330:344:369:396:412:442 SD: 0.3451 cents 237:247:265:284:296:317:330:354:369:396:424:442:474 SD: 0.3245 cents 239:249:267:286:298:320:333:357:372:399:428:446:478 SD: 0.2519 cents 267:278:298:320:333:357:372:399:416:446:478:498:534 SD: 0.2442 cents 287:299:321:344:358:384:400:429:447:479:514:535:574 SD: 0.2394 cents 334:348:373:400:417:447:466:499:520:558:598:623:668 SD: 0.2104 cents 343:357:383:411:428:459:478:513:534:573:614:640:686 SD: 0.1994 cents 358:373:400:429:447:479:499:535:557:598:641:668:716 SD: 0.1862 cents 384:400:429:460:479:514:535:574:598:641:688:716:768 SD: 0.1487 cents 429:447:479:514:535:574:598:641:668:716:768:800:858 SD: 0.1385 cents 505:526:564:605:630:676:704:755:786:843:904:942:1010 SD: 0.1084 cents