Scala analysis: smalldi11
Small diesic 11-note block, <10/9, 126/125, 1728/1715> commas
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 7/6 266.870906 septimal minor third 3: 6/5 315.641287 minor third 4: 216/175 364.411668 5: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 6: 10/7 617.487807 Euler's tritone 7: 175/108 835.588332 8: 5/3 884.358713 major sixth, BP sixth 9: 12/7 933.129094 septimal major sixth 10: 35/18 1151.229619 septimal semi-diminished octave 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 245/216 218.1005 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 36/35 48.7704 septimal diesis, 1/4-tone 5: 245/216 218.1005 6: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 7: 245/216 218.1005 8: 36/35 48.7704 septimal diesis, 1/4-tone 9: 36/35 48.7704 septimal diesis, 1/4-tone 10: 245/216 218.1005 11: 36/35 48.7704 septimal diesis, 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 6 36/35 48.770 cents septimal diesis, 1/4-tone 1: 4 245/216 218.101 cents 2: 3 1296/1225 97.541 cents two (septimal diesis, 1/4-tone) 2: 2 125/108 253.076 cents semi-augmented whole tone 2: 6 7/6 266.871 cents septimal minor third 3: 2 25/21 301.847 cents BP second, quasi-equal minor third 3: 8 6/5 315.641 cents minor third 3: 1 30625/23328 471.177 cents 4: 2 60/49 350.617 cents smaller approximation to neutral third 4: 4 216/175 364.412 cents 4: 2 875/648 519.947 cents 4: 3 49/36 533.742 cents Arabic lute acute fourth 5: 2 7776/6125 413.182 cents 5: 5 25/18 568.717 cents classic augmented fourth 5: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 4 10/7 617.488 cents Euler's tritone 6: 5 36/25 631.283 cents classic diminished fifth 6: 2 6125/3888 786.818 cents 7: 3 72/49 666.258 cents Arabic lute grave fifth 7: 2 1296/875 680.053 cents 7: 4 175/108 835.588 cents 7: 2 49/30 849.383 cents larger approximation to neutral sixth 8: 1 46656/30625 728.823 cents 8: 8 5/3 884.359 cents major sixth, BP sixth 8: 2 42/25 898.153 cents quasi-equal major sixth 9: 6 12/7 933.129 cents septimal major sixth 9: 2 216/125 946.924 cents semi-augmented sixth 9: 3 1225/648 1102.459 cents 10: 4 432/245 981.899 cents 10: 6 35/18 1151.230 cents septimal semi-diminished octave 10: 1 49/25 1165.024 cents BP eighth Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.20000 = 16/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 48.8 266.9 315.6 364.4 582.5 617.5 835.6 884.4 933.1 1151.2 1200.0 48.8 : 218.1 266.9 315.6 533.7 568.7 786.8 835.6 884.4 1102.5 1151.2 1200.0 266.9 : 48.8 97.5 315.6 350.6 568.7 617.5 666.3 884.4 933.1 981.9 1200.0 315.6 : 48.8 266.9 301.8 519.9 568.7 617.5 835.6 884.4 933.1 1151.2 1200.0 364.4 : 218.1 253.1 471.2 519.9 568.7 786.8 835.6 884.4 1102.5 1151.2 1200.0 582.5 : 35.0 253.1 301.8 350.6 568.7 617.5 666.3 884.4 933.1 981.9 1200.0 617.5 : 218.1 266.9 315.6 533.7 582.5 631.3 849.4 898.2 946.9 1165.0 1200.0 835.6 : 48.8 97.5 315.6 364.4 413.2 631.3 680.1 728.8 946.9 981.9 1200.0 884.4 : 48.8 266.9 315.6 364.4 582.5 631.3 680.1 898.2 933.1 1151.2 1200.0 933.1 : 218.1 266.9 315.6 533.7 582.5 631.3 849.4 884.4 1102.5 1151.2 1200.0 1151.2: 48.8 97.5 315.6 364.4 413.2 631.3 666.3 884.4 933.1 981.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.9756 .. 218.1005 cents 2401/2160, 183.1249 cents 50/49, 34.9756 cents 2: 97.5408 .. 266.8709 cents 8575/7776, 169.3301 cents 279936/300125,-120.5598 cents 3: 301.8465 .. 471.1767 cents 8575/7776, 169.3301 cents 50/49, 34.9756 cents 4: 350.6169 .. 533.7418 cents 2401/2160, 183.1249 cents 279936/300125,-120.5598 cents 5: 413.1820 .. 582.5122 cents 8575/7776, 169.3301 cents 279936/300125,-120.5598 cents 6: 617.4878 .. 786.8180 cents 8575/7776, 169.3301 cents 50/49, 34.9756 cents 7: 666.2582 .. 849.3831 cents 2401/2160, 183.1249 cents 279936/300125,-120.5598 cents 8: 728.8233 .. 898.1535 cents 8575/7776, 169.3301 cents 279936/300125,-120.5598 cents 9: 933.1291 .. 1102.4592 cents 8575/7776, 169.3301 cents 50/49, 34.9756 cents 10: 981.8995 .. 1165.0244 cents 2401/2160, 183.1249 cents 279936/300125,-120.5598 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 50/49, 34.9756 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 245/216, 218.1005 cents Average / Smallest step : 3.119056 Largest / Average step : 1.999255 Largest / Smallest step : 6.235788 Median interval of one step : 36/35, 48.7704 cents, amount: 6 Most common interval of one step : 36/35, 48.7704 cents, amount: 6 Least squares average step : 109.95853 cents, oct.: 1209.54384 cents Scale is not proper Scale is a mode of a 1304-tone equal temperament with octave 2/1 degrees: 53 290 343 396 633 671 908 961 1014 1251 1304 Least number of segments generator : 653 of 600.920 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1077 of 991.104 cents and inv. generated superset size: 87 = 76 more = 790.909% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABCBAABA Step pattern size order : MLMMLSLMMLM Scale is a Constant Structure, by a margin of 34.97561 cents Scale diversity : 1.286824 Lumma stability : 0.145732 Lumma impropriety factor : 0.506141 Rothenberg efficiency : 0.428099 redundancy: 0.571901 Efficiency x scale size : 4.709091 Number of different interval sizes : 32 = 3.20000 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.20000 = 16/5 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 126/125, 13.7948 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 8 Most common triad is 0.0 315.641 884.359 cents, amount: 5 Number of recognisable fifths : 0 Scale contains a complete diamond : 3 5 7 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 11 = 100.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 5-6 -- Rational properties -- Prime limit : 7 Odd number limit : 30625 (O: 30625 U: 30625) Highest odd numerator or denominator: 175 Scale harmonicity : 0.014887 Average absolute harmonicity : 0.146299 Specific harmonicity : 0.086920 Fundamental : 1/18900, -14.2061 octaves, 0.0138 Hz. Guide tone : 37800, 15.2061 octaves, 9889446.368 Hz. Exponens Consonantiae : 7.144200E+08, 29.41220 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 440.5, average 40.04545 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.35254, average 1.12296 Sum of Tenney's harmonic distance : 24.64460, average 2.24042 Vogel's harmonic complexity : 28.54545 Wille's k value : 15312 Wilson's harmonic complexity : 52 Rectangular lattice diameter : 12 Triangular lattice diameter : 6 Lattice compactness : 215.68624, average 3.26797 Lattice compactness (without 2's) : 179.39982, average 2.71818 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.54545 14 1 3: -3 .. 3 0.00000 14 5: -2 .. 2 0.00000 10 2 7: -1 .. 1 0.00000 8 8 Average exponent except 2's : 0 / 11 = 0.00000 Average absolute exponent except 2's: 32 / 11 = 2.90909 Scale is weakly epimorphic with val: <11 15 24 31| Scale is weakly epimorphic with val: <11 15 24 34| Scale is weakly epimorphic with val: <11 15 25 30| Scale is weakly epimorphic with val: <11 15 25 34| Scale is weakly epimorphic with val: <11 15 27 29| Scale is weakly epimorphic with val: <11 15 27 33| Scale is weakly epimorphic with val: <11 15 28 29| Scale is weakly epimorphic with val: <11 15 28 32| Scale is weakly epimorphic with val: <11 16 24 28| Scale is JI-epimorphic with val: <11 16 24 29| Scale is weakly epimorphic with val: <11 16 25 32| Scale is weakly epimorphic with val: <11 16 26 31| Scale is weakly epimorphic with val: <11 16 28 30| Scale is weakly epimorphic with val: <11 16 28 34| Scale is weakly epimorphic with val: <11 16 29 30| Scale is weakly epimorphic with val: <11 16 29 33| Scale is weakly epimorphic with val: <11 17 24 33| Scale is weakly epimorphic with val: <11 17 25 29| Scale is JI-epimorphic with val: <11 17 25 30| Scale is weakly epimorphic with val: <11 17 26 33| Scale is weakly epimorphic with val: <11 17 27 32| Scale is weakly epimorphic with val: <11 17 29 31| Scale is weakly epimorphic with val: <11 18 25 28| Scale is weakly epimorphic with val: <11 18 25 34| Scale is weakly epimorphic with val: <11 18 26 30| Scale is JI-epimorphic with val: <11 18 26 31| Scale is weakly epimorphic with val: <11 18 27 34| Scale is weakly epimorphic with val: <11 18 28 33| Scale is weakly epimorphic with val: <11 19 24 32| Scale is weakly epimorphic with val: <11 19 24 34| Scale is weakly epimorphic with val: <11 19 25 28| Scale is weakly epimorphic with val: <11 19 26 29| Scale is weakly epimorphic with val: <11 19 27 31| Scale is JI-epimorphic with val: <11 19 27 32| Scale is weakly epimorphic with val: <11 19 29 34|
FIT/MODE
11: 0 2 0 1 2 0 2 1 0 2 1 N T3 SD: 56.2367 c. M: 97.4595 c. 12: 0 2 1 0 2 1 2 0 1 2 1 N T3 SD: 52.6246 c. M: 84.3587 c. 13: 1 2 0 1 2 1 2 1 0 2 1 N T3 I SD: 28.0927 c. M:-43.5373 c. 14: 1 2 1 0 3 0 3 0 1 2 1 N I SD: 23.2403 c. M:-36.9439 c. 18: 1 3 1 0 4 0 4 0 1 3 1 N I SD: 18.6109 c. M:-31.0783 c. 19: 1 3 1 1 3 1 3 1 1 3 1 N M DE I SD: 12.2075 c. M: 14.5357 c. 22: 1 4 1 1 4 0 4 1 1 4 1 N I SD: 12.1487 c. M:-17.4878 c. 23: 1 4 1 1 4 1 4 1 1 4 1 N M DE I SD: 4.8419 c. M:-8.5991 c. 49: 2 9 2 2 9 1 9 2 2 9 2 N I SD: 3.0125 c. M:-5.2429 c. 72: 3 13 3 3 13 2 13 3 3 13 3 N I SD: 1.2332 c. M:-2.2550 c. 76: 3 14 3 3 14 2 14 3 3 14 3 N I SD: 1.2683 c. M:-1.6983 c. 99: 4 18 4 4 18 3 18 4 4 18 4 N I SD: 0.5127 c. M:-0.7753 c. 171: 7 31 7 7 31 5 31 7 7 31 7 N I SD: 0.2834 c. M:-0.5006 c. 247: 10 45 10 10 45 7 45 10 10 45 10 N I SD: 0.2714 c. M:-0.4838 c. 270: 11 49 11 11 49 8 49 11 11 49 11 N I SD: 0.1642 c. M:-0.2900 c. 346: 14 63 14 14 63 10 63 14 14 63 14 N I SD: 0.1729 c. M:-0.2498 c. 418: 17 76 17 17 76 12 76 17 17 76 17 N I SD: 0.1586 c. M:-0.2629 c. 441: 18 80 18 18 80 13 80 18 18 80 18 N I SD: 0.1764 c. M:-0.2142 c. 517: 21 94 21 21 94 15 94 21 21 94 21 N I SD: 0.0441 c. M:-0.0797 c. 787: 32 143 32 32 143 23 143 32 32 143 32 N I SD: 0.0276 c. M:-0.0471 c. 1304: 53 237 53 53 237 38 237 53 53 237 53 N I SD: 0.0032 c. M:-0.0055 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x x 4 S SD: 42.2336 cents 3 x x x x 4 x x 5 x x 6 S SD: 28.1557 cents 4 x x x 5 x 6 x x 7 x 8 S SD: 23.5699 cents 5 x x 6 x 7 x 8 x 9 x 10 S SD: 17.4521 cents 6 x 7 x x 8:9 x 10 x x 12 S SD: 23.8909 cents 7 x 8 x 9 x 10:11 x 12 x 14 S SD: 15.8886 cents 8 x 9 x 10:11 x 13 x 14 x 16 SD: 13.6580 cents 9 x x x 11 x 13 x 15 x x 18 SD: 6.3986 cents 10 x x 12 x 14 x 16 x 17:19:20 SD: 7.9792 cents 11:12:13 x 14:15:16:18 x 19:21:22 SD: 14.9950 cents 12:13:14 x 15 x 17:19:20:21:23:24 SD: 12.2984 cents 13:14:15 x 16:18:19:21 x 22:25:26 SD: 10.8494 cents 14:15:16:17 x x 20:23 x 24:27:28 SD: 10.7959 cents 15:16 x 18:19:21 x 24:25:26:29:30 SD: 9.2417 cents 16:17 x 19:20:22:23:26:27 x 31:32 SD: 8.2998 cents 17:18:20 x 21:24 x x 28:29:33:34 SD: 7.3323 cents 18:19:21 x 22:25:26:29:30:31:35:36 SD: 5.4934 cents 19:20:22:23 x x 27:31:32:33:37:38 SD: 6.1616 cents 20:21:23:24:25:28:29:32:33:34:39:40 SD: 5.7894 cents 21:22 x 25:26:29:30:34:35:36:41:42 SD: 4.2919 cents 22:23:26 x 27:31 x 36:37:38:43:44 SD: 5.3312 cents 23:24:27 x 28:32:33:37:38:39:45:46 SD: 4.8330 cents 24:25:28:29:30 x 34:39:40:41:47:48 SD: 3.9055 cents 25:26:29:30:31:35:36:41:42:43:49:50 SD: 3.5987 cents 27:28 x 32:33:38:39:44:45:46:53:54 SD: 4.3404 cents 28:29:33:34:35:39:40:45:47:48:54:56 SD: 4.0502 cents 29:30:34:35:36:41 x 47:48:50:56:58 SD: 3.2270 cents 30:31:35:36:37:42:43:49:50:51:58:60 SD: 2.2222 cents 35:36:41:42:43:49:50:57:58:60:68:70 SD: 1.5510 cents 60:62:70:72:74:84:86:97:100:103:117:120 SD: 1.0939 cents 77:79:90:92:95:108:110:125:128:132:150:154 SD: 1.0663 cents 90:93:105:108:111:126:129:146:150:154:175:180 SD: 0.9669 cents 95:98:111:114:117:133:136:154:158:163:185:190 SD: 0.8279 cents 102:105:119:122:126:143:146:165:170:175:198:204 SD: 0.7738 cents 108:111:126:130:133:151:154:175:180:185:210:216 SD: 0.7221 cents 115:118:134:138:142:161:164:186:192:197:224:230 SD: 0.7132 cents 132:136:154:158:163:185:189:214:220:226:257:264 SD: 0.6915 cents 137:141:160:164:169:192:196:222:228:235:266:274 SD: 0.6211 cents 140:144:163:168:173:196:200:227:233:240:272:280 SD: 0.4628 cents 145:149:169:174:179:203:207:235:242:249:282:290 SD: 0.4263 cents 175:180:204:210:216:245:250:284:292:300:340:350 SD: 0.3516 cents 180:185:210:216:222:252:257:292:300:309:350:360 SD: 0.3423 cents 210:216:245:252:259:294:300:340:350:360:408:420 SD: 0.2186 cents 350:360:408:420:432:490:500:567:583:600:681:700 SD: 0.1910 cents 385:396:449:462:475:539:550:624:642:660:749:770 SD: 0.1508 cents 490:504:572:588:605:686:700:794:817:840:953:980 SD: 0.1289 cents 595:612:694:714:734:833:850:964:992:1020:1157:1190 SD: 0.1096 cents