Scala analysis: terrain
JI version of generated scale for 63/50 and 10/9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 50/49 34.975615 Erlich's decatonic comma, tritonic diesis 2: 10/9 182.403712 minor whole tone 3: 500/441 217.379327 4: 63/50 400.108480 quasi-equal major third 5: 9/7 435.084095 septimal major third, BP third 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 10/7 617.487807 Euler's tritone 8: 100/63 799.891520 quasi-equal minor sixth 9: 81/50 835.192576 acute minor sixth 10: 441/250 982.620673 11: 9/5 1017.596288 just minor seventh, BP seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 2: 49/45 147.4281 BP minor semitone 3: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 4: 27783/25000 182.7292 5: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 6: 49/45 147.4281 BP minor semitone 7: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 8: 10/9 182.4037 minor whole tone 9: 5103/5000 35.3011 10: 49/45 147.4281 BP minor semitone 11: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 12: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 1 5103/5000 35.301 cents 1: 3 49/45 147.428 cents BP minor semitone 1: 2 10/9 182.404 cents minor whole tone 1: 1 27783/25000 182.729 cents 2: 5 10/9 182.404 cents minor whole tone 2: 1 27783/25000 182.729 cents 2: 3 500/441 217.379 cents 2: 3 567/500 217.705 cents 3: 2 500/441 217.379 cents 3: 1 567/500 217.705 cents 3: 1 25000/21609 252.355 cents 3: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 3: 3 100/81 364.807 cents grave major third 3: 3 3087/2500 365.133 cents 4: 4 5000/3969 399.783 cents 4: 8 63/50 400.108 cents quasi-equal major third 5: 1 250000/194481 434.759 cents 5: 5 9/7 435.084 cents septimal major third, BP third 5: 1 1000/729 547.211 cents 5: 2 343/250 547.537 cents 5: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 1 50000/35721 582.187 cents 6: 5 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 5 10/7 617.488 cents Euler's tritone 6: 1 35721/25000 617.813 cents 7: 3 10/7 617.488 cents Euler's tritone 7: 2 500/343 652.463 cents 7: 1 729/500 652.789 cents 7: 5 14/9 764.916 cents septimal minor sixth 7: 1 194481/125000 765.241 cents 8: 8 100/63 799.892 cents quasi-equal minor sixth 8: 4 3969/2500 800.217 cents two (quasi-equal major third) 9: 3 5000/3087 834.867 cents 9: 3 81/50 835.193 cents acute minor sixth 9: 2 140/81 947.320 cents 9: 1 21609/12500 947.645 cents 9: 1 1000/567 982.295 cents 9: 2 441/250 982.621 cents 10: 3 1000/567 982.295 cents 10: 3 441/250 982.621 cents 10: 1 50000/27783 1017.271 cents 10: 5 9/5 1017.596 cents just minor seventh, BP seventh 11: 1 50000/27783 1017.271 cents 11: 2 9/5 1017.596 cents just minor seventh, BP seventh 11: 3 90/49 1052.572 cents 11: 1 10000/5103 1164.699 cents 11: 5 49/25 1165.024 cents BP eighth Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.36364 = 48/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 35.0 182.4 217.4 400.1 435.1 582.5 617.5 799.9 835.2 982.6 1017.6 1200.0 35.0 : 147.4 182.4 365.1 400.1 547.5 582.5 764.9 800.2 947.6 982.6 1165.0 1200.0 182.4 : 35.0 217.7 252.7 400.1 435.1 617.5 652.8 800.2 835.2 1017.6 1052.6 1200.0 217.4 : 182.7 217.7 365.1 400.1 582.5 617.8 765.2 800.2 982.6 1017.6 1165.0 1200.0 400.1 : 35.0 182.4 217.4 399.8 435.1 582.5 617.5 799.9 834.9 982.3 1017.3 1200.0 435.1 : 147.4 182.4 364.8 400.1 547.5 582.5 764.9 799.9 947.3 982.3 1165.0 1200.0 582.5 : 35.0 217.4 252.7 400.1 435.1 617.5 652.5 799.9 834.9 1017.6 1052.6 1200.0 617.5 : 182.4 217.7 365.1 400.1 582.5 617.5 764.9 799.9 982.6 1017.6 1165.0 1200.0 799.9 : 35.3 182.7 217.7 400.1 435.1 582.5 617.5 800.2 835.2 982.6 1017.6 1200.0 835.2 : 147.4 182.4 364.8 399.8 547.2 582.2 764.9 799.9 947.3 982.3 1164.7 1200.0 982.6 : 35.0 217.4 252.4 399.8 434.8 617.5 652.5 799.9 834.9 1017.3 1052.6 1200.0 1017.6: 182.4 217.4 364.8 399.8 582.5 617.5 764.9 799.9 982.3 1017.6 1165.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.9756 .. 182.7292 cents 1361367/1250000, 147.7535 cents 50/49, 34.9756 cents 2: 182.4037 .. 217.7048 cents 5103/5000, 35.3011 cents 250000/250047,-0.3254 cents 3: 217.3793 .. 365.1329 cents 1361367/1250000, 147.7535 cents 250000/250047,-0.3254 cents 4: 399.7830 .. 400.1085 cents 250047/250000, 0.3254 cents 12500000/12252303, 34.6502 cents 5: 434.7587 .. 582.5122 cents 1361367/1250000, 147.7535 cents 12500000/12252303, 34.6502 cents 6: 582.1868 .. 617.8132 cents 1275989841/1250000000, 35.6265 cen 250000/250047,-0.3254 cents 7: 617.4878 .. 765.2413 cents 1361367/1250000, 147.7535 cents 250000/250047,-0.3254 cents 8: 799.8915 .. 800.2170 cents 250047/250000, 0.3254 cents 12500000/12252303, 34.6502 cents 9: 834.8671 .. 982.6207 cents 1361367/1250000, 147.7535 cents 12500000/12252303, 34.6502 cents 10: 982.2952 .. 1017.5963 cents 5103/5000, 35.3011 cents 250000/250047,-0.3254 cents 11: 1017.2708 .. 1165.0244 cents 1361367/1250000, 147.7535 cents 250000/250047,-0.3254 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 50/49, 34.9756 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 27783/25000, 182.7292 cents Average / Smallest step : 2.859135 Largest / Average step : 1.827292 Largest / Smallest step : 5.224473 Median interval of one step : 91.36458 cents, amount: 0 Most common interval of one step : 50/49, 34.9756 cents, amount: 5 Least squares average step : 95.35522 cents, oct.: 1144.26267 cents Scale is not proper Step pattern alph. order: ABACABADEBAD Step pattern size order : ACAEACADBCAD Scale is not a Constant Structure Scale diversity : 1.100162 Lumma stability : 0.173793 Lumma impropriety factor : 0.001627 Rothenberg efficiency : 0.387296 redundancy: 0.612704 Efficiency x scale size : 4.647547 Number of different interval sizes : 38 = 3.45455 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 4.36364 = 48/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 250047/250000, 0.3254 cents Number of recognisable fifths : 0 Best fifths form a closed circle Scale contains a complete diamond : 5 7 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 9 = 75.0000% Limited transpositions with margin 147.7535 cents: 4 8 Limited inverse transpositions with margin 147.7535 cents: 3 7 11 Inversional symmetry on intervals : 1-2 3-4 5-6 7-8 9-10 11-12 -- Rational properties -- Prime limit : 7 Odd number limit : 194481 (O: 194481 U: 194481) Highest odd numerator or denominator: 441 Scale harmonicity : 0.010148 Average absolute harmonicity : 0.127000 Specific harmonicity : 0.063758 Fundamental : 1/110250, -16.7504 octaves, 0.0024 Hz. Guide tone : 1984500, 20.9203 octaves, 519195934.340 Hz. Exponens Consonantiae : 2.187911E+11, 37.67076 octaves Euler's gradus suavitatis : 64 Sum of Mann's harmonic distance : 1109.5, average 92.45833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 17.03916, average 1.41993 Sum of Tenney's harmonic distance : 33.77705, average 2.81475 Vogel's harmonic complexity : 36.16667 Wille's k value : 97240 Wilson's harmonic complexity : 76 Rectangular lattice diameter : 16 Triangular lattice diameter : 8 Lattice compactness : 298.10803, average 3.82190 Lattice compactness (without 2's) : 279.07326, average 3.57786 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.41667 11 1 3: -2 .. 4 0.50000 18 5: -3 .. 3 0.00000 18 3 7: -2 .. 2 -0.25000 11 8 Average exponent except 2's : 3 / 12 = 0.25000 Average absolute exponent except 2's: 47 / 12 = 3.91667 Scale is weakly epimorphic with val: <12 17 25 32| Scale is weakly epimorphic with val: <12 17 25 36| Scale is weakly epimorphic with val: <12 17 27 36| Scale is weakly epimorphic with val: <12 17 29 32| Scale is weakly epimorphic with val: <12 17 31 32| Scale is weakly epimorphic with val: <12 17 31 36| Scale is weakly epimorphic with val: <12 18 25 34| Scale is weakly epimorphic with val: <12 18 27 34| Scale is weakly epimorphic with val: <12 18 31 34| Scale is weakly epimorphic with val: <12 19 25 32| Scale is weakly epimorphic with val: <12 19 27 32| Scale is weakly epimorphic with val: <12 19 27 36| Scale is weakly epimorphic with val: <12 19 29 36| Scale is weakly epimorphic with val: <12 19 31 32| Scale is weakly epimorphic with val: <12 20 27 34| Scale is weakly epimorphic with val: <12 20 29 34| Scale is weakly epimorphic with val: <12 21 25 36| Scale is weakly epimorphic with val: <12 21 27 32| Scale is weakly epimorphic with val: <12 21 29 32| Scale is weakly epimorphic with val: <12 21 29 36| Scale is weakly epimorphic with val: <12 21 31 36|
FIT/MODE
12: 0 2 0 2 0 2 0 2 0 2 0 2 P B DE SD: 21.4626 c. M: 35.1926 c. 16: 0 2 1 2 1 2 0 3 0 2 1 2 N SD: 21.6763 c. M: 34.9756 c. 20: 1 2 1 3 0 3 0 3 1 2 1 3 N SD: 16.6203 c. M:-25.0244 c. 21: 1 2 1 3 1 2 1 3 1 2 1 3 P B D3 SD: 13.5306 c. M:-22.1672 c. 22: 1 2 1 3 1 3 0 4 0 3 1 3 N SD: 14.8896 c. M:-19.5698 c. 25: 1 3 1 3 1 3 1 4 0 3 1 4 N SD: 14.0204 c. M:-22.6207 c. 27: 1 3 1 4 1 3 1 4 1 3 1 4 P B D3 SD: 5.7549 c. M:-9.4688 c. 33: 1 4 1 5 1 4 1 5 1 4 1 5 P B D3 SD: 0.8112 c. M:-1.3880 c. 105: 3 13 3 16 3 13 3 16 3 13 3 16 P B D3 SD: 0.4761 c. M: 0.9069 c. 138: 4 17 4 21 4 17 4 21 4 17 4 21 P B D3 SD: 0.1877 c. M: 0.4100 c. 171: 5 21 5 26 5 21 5 26 5 21 5 26 P B D3 SD: 0.0971 c. M: 0.1645 c. 480: 14 59 14 73 14 59 14 73 14 59 14 73 P B D3 SD: 0.0984 c. M: 0.1926 c. 651: 19 80 19 99 19 80 19 99 19 80 19 99 P B D3 SD: 0.0952 c. M: 0.1695 c. 822: 24 101 24 125 24 101 24 125 24 101 24 125 P B D3 SD: 0.0942 c. M: 0.1561 c. 993: 29 122 29 151 29 122 29 151 29 122 29 151 P B D3 SD: 0.0940 c. M: 0.1473 c. 1164: 34 143 34 177 34 143 34 177 34 143 34 177 P B D3 SD: 0.0940 c. M:-0.1464 c. 1815: 53 223 53 276 53 223 53 276 53 223 53 276 P B D3 SD: 0.0940 c. M: 0.1513 c. 1856: 54 228 54 283 54 228 54 282 55 228 54 282 N SD: 0.0929 c. M:-0.1523 c. 1889: 55 232 55 288 55 232 55 287 56 232 55 287 N SD: 0.0916 c. M:-0.1700 c. 1922: 56 236 56 293 56 236 56 292 57 236 56 292 N SD: 0.0925 c. M:-0.1872 c. 1928: 56 237 56 294 56 237 56 293 57 237 56 293 N SD: 0.0921 c. M: 0.1594 c. 1961: 57 241 57 299 57 241 57 298 58 241 57 298 N SD: 0.0850 c. M:-0.1432 c. 1994: 58 245 58 304 58 245 58 303 59 245 58 303 N SD: 0.0800 c. M:-0.1276 c. 2027: 59 249 59 309 59 249 59 308 60 249 59 308 N SD: 0.0773 c. M:-0.1306 c. 2060: 60 253 60 314 60 253 60 313 61 253 60 313 N SD: 0.0769 c. M:-0.1472 c. 2099: 61 258 61 320 61 258 61 319 62 258 61 319 N SD: 0.0767 c. M: 0.1330 c. 2132: 62 262 62 325 62 262 62 324 63 262 62 324 N SD: 0.0704 c. M:-0.1185 c. 2165: 63 266 63 330 63 266 63 329 64 266 63 329 N SD: 0.0661 c. M:-0.1045 c. 2198: 64 270 64 335 64 270 64 334 65 270 64 334 N SD: 0.0643 c. M:-0.1122 c. 2231: 65 274 65 340 65 274 65 339 66 274 65 339 N SD: 0.0647 c. M:-0.1279 c. 2270: 66 279 66 346 66 279 66 345 67 279 66 345 N SD: 0.0637 c. M:-0.1106 c. 2303: 67 283 67 351 67 283 67 350 68 283 67 350 N SD: 0.0579 c. M:-0.0975 c. 2336: 68 287 68 356 68 287 68 355 69 287 68 355 N SD: 0.0544 c. M: 0.0848 c. 2369: 69 291 69 361 69 291 69 360 70 291 69 360 N SD: 0.0532 c. M:-0.0966 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: 42.2336 cents 3 x x x x 4 x x x 5 x x 6 S SD: 26.6279 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 21.6727 cents 5 x x x 6 x 7 x 8 x x 9:10 S SD: 17.1172 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 21.7145 cents 7 x x 8 x 9 x 10:11 x 12:13:14 S SD: 10.9450 cents 8 x x 9:10 x 11 x x 13:14 x 16 SD: 6.5903 cents 9 x 10 x 11:12 x 13:14:15:16 x 18 S SD: 13.0680 cents 10 x 11 x x 13:14 x 16 x x 18:20 SD: 4.8848 cents 11 x 12 x 14 x 15:16:17:18:19:20:22 S SD: 10.2032 cents 12 x 13:14:15 x x 17:19 x 21:22:24 SD: 9.6735 cents 13 x 14:15:16:17:18:19 x 21:23 x 26 SD: 10.1460 cents 14 x x 16 x 18 x 20:22:23 x 25:28 SD: 5.0944 cents 15 x x 17:19 x 21 x 24 x 26:27:30 SD: 4.9406 cents 16:17 x 18:20:21:22:23:25:26:28:29:32 SD: 8.4980 cents 17:18:19 x 21:22:24 x 27:28:30:31:34 SD: 8.3894 cents 18:19:20 x x 23:25:26 x 29:32 x 36 SD: 8.2732 cents 19:20:21:22:24 x x 27:30:31 x 34:38 SD: 7.6564 cents 20:21:22:23:25:26:28:29:32 x 35:36:40 SD: 6.4009 cents 21:22:23:24:26:27:29:30:33:34:37:38:42 SD: 5.7509 cents 22:23:24:25:28 x 31 x 35:36:39:40:44 SD: 6.2523 cents 23:24 x 26:29:30:32:33 x 37 x 41:46 SD: 5.8252 cents 24:25 x 27:30:31 x 34:38:39:42:43:48 SD: 4.7137 cents 25:26:28 x x 32:35:36:40:41:44:45:50 SD: 4.6702 cents 26:27:29 x 33 x 36:37:41:42:46:47:52 SD: 4.2075 cents 27:28:30:31:34:35:38:39:43:44:48:49:54 SD: 4.1089 cents 28:29:31:32:35:36:39:40:44:45:49:50:56 SD: 3.7596 cents 29:30:32:33 x 37:41 x 46:47:51:52:58 SD: 3.5853 cents 30:31:33:34:38:39:42:43:48:49:53:54:60 SD: 3.3944 cents 31:32:34:35:39:40:43:44:49:50:55:56:62 SD: 3.3691 cents 32:33 x 36:40:41:45:46:51:52:56:58:64 SD: 3.3156 cents 33:34:37 x 42 x 46:47:52:53:58:59:66 SD: 3.8361 cents 34:35:38:39:43:44:48:49:54:55:60:61:68 SD: 3.1073 cents 35:36:39:40:44:45:49:50:56:57:62:63:70 SD: 2.2778 cents 38:39:42:43:48:49:53:54:60:62:67:68:76 SD: 2.2116 cents 39:40:43:44:49:50:55:56:62:63:69:70:78 SD: 2.2035 cents 41:42:46 x 52:53:57:59:65:66:72:74:82 SD: 2.9568 cents 42:43:47:48:53:54:59:60:67:68:74:76:84 SD: 2.0069 cents 45:46:50:51:57:58:63:64:71:73:79:81:90 SD: 1.5685 cents 53:54:59:60:67:68:74:76:84:86:93:95:106 SD: 1.4079 cents 60:61:67:68:76:77:84:86:95:97:106:108:120 SD: 1.3963 cents 73:74:81:83:92:94:102:104:116:118:129:131:146 SD: 1.3343 cents 80:82:89:91:101:103:112:114:127:130:141:144:160 SD: 1.0677 cents 84:86:93:95:106:108:118:120:133:136:148:151:168 SD: 1.0575 cents 88:90:98:100:111:113:123:126:140:143:155:158:176 SD: 1.0130 cents 89:91:99:101:112:114:125:127:141:144:157:160:178 SD: 0.9141 cents 90:92:100:102:113:116:126:129:143:146:159:162:180 SD: 0.8907 cents 97:99:108:110:122:125:136:139:154:157:171:175:194 SD: 0.8030 cents 105:107:117:119:132:135:147:150:167:170:185:189:210 SD: 0.6609 cents 135:138:150:153:170:174:189:193:214:219:238:243:270 SD: 0.5455 cents 143:146:159:162:180:184:200:204:227:232:252:257:286 SD: 0.4912 cents 150:153:167:170:189:193:210:214:238:243:265:270:300 SD: 0.4348 cents 189:193:210:214:238:243:265:270:300:306:333:340:378 SD: 0.3833 cents 200:204:222:227:252:257:280:286:317:324:353:360:400 SD: 0.3545 cents 242:247:269:274:305:311:339:346:384:392:427:436:484 SD: 0.3046 cents 245:250:272:278:309:315:343:350:389:397:432:441:490 SD: 0.2312 cents 305:311:339:346:384:392:427:436:484:494:538:549:610 SD: 0.2154 cents 343:350:381:389:432:441:480:490:544:556:605:617:686 SD: 0.2031 cents 350:357:389:397:441:450:490:500:556:567:617:630:700 SD: 0.1764 cents 395:403:439:448:498:508:553:564:627:640:697:711:790 SD: 0.1464 cents 530:541:589:601:668:681:742:757:841:859:935:954:1060 SD: 0.1459 cents 539:550:599:611:679:693:755:770:856:873:951:970:1078 SD: 0.1284 cents 577:589:641:654:727:742:808:824:916:935:1018:1039:1154 SD: 0.1255 cents 584:596:649:662:736:751:818:834:927:946:1030:1051:1168 SD: 0.1118 cents