Scala analysis: ennon13
Nonoctave Ennealimmal, [3, 5/3] just tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 2: 7/6 266.870906 septimal minor third 3: 63/50 400.108480 quasi-equal major third 4: 10/7 617.487807 Euler's tritone 5: 54/35 750.725382 septimal semi-augmented fifth 6: 5/3 884.358713 major sixth, BP sixth 7: 9/5 1017.596288 just minor seventh, BP seventh 8: 35/18 1151.229619 septimal semi-diminished octave 9: 21/10 1284.467193 minor semitone +1 octave 10: 50/21 1501.846520 BP second, quasi-equal minor third +1 octave 11: 18/7 1635.084095 septimal major 10th 12: 25/9 1768.717426 classic augmented eleventh, BP twelfth 13: 3/1 1901.955001 perfect 12th
SHOW/INTERVAL
0: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 1: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 2: 175/162 133.6333 3: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 4: 500/441 217.3793 5: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 6: 175/162 133.6333 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 8: 175/162 133.6333 9: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 10: 500/441 217.3793 11: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 12: 175/162 133.6333 13: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 4 175/162 133.633 cents 1: 2 500/441 217.379 cents 2: 1 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 2: 8 7/6 266.871 cents septimal minor third 2: 4 60/49 350.617 cents smaller approximation to neutral third 3: 6 63/50 400.108 cents quasi-equal major third 3: 1 1225/972 400.504 cents 3: 2 324/245 483.854 cents 3: 4 250/189 484.250 cents 4: 2 1701/1250 533.346 cents 4: 3 49/36 533.742 cents Arabic lute acute fourth 4: 8 10/7 617.488 cents Euler's tritone 5: 3 147/100 666.979 cents 5: 6 54/35 750.725 cents septimal semi-augmented fifth 5: 4 125/81 751.121 cents 6: 1 3969/2500 800.217 cents two (quasi-equal major third) 6: 2 1458/875 883.963 cents 6: 10 5/3 884.359 cents major sixth, BP sixth 7: 10 9/5 1017.596 cents just minor seventh, BP seventh 7: 2 875/486 1017.992 cents 7: 1 2500/1323 1101.738 cents 8: 4 243/125 1150.834 cents octave - maximal diesis 8: 6 35/18 1151.230 cents septimal semi-diminished octave 8: 3 100/49 1234.976 cents Erlich's decatonic comma, tritonic diesis +1 octave 9: 8 21/10 1284.467 cents minor semitone +1 octave 9: 3 108/49 1368.213 cents Zalzal's mujannab +1 octave 9: 2 1250/567 1368.609 cents BP great semitone, major BP chroma +1 octave 10: 4 567/250 1417.705 cents 10: 2 245/108 1418.101 cents 10: 1 2916/1225 1501.451 cents 10: 6 50/21 1501.847 cents BP second, quasi-equal minor third +1 octave 11: 4 49/20 1551.338 cents larger approximation to neutral third +1 octave 11: 8 18/7 1635.084 cents septimal major 10th 11: 1 625/243 1635.480 cents 12: 2 1323/500 1684.576 cents 12: 4 486/175 1768.322 cents 12: 7 25/9 1768.717 cents classic augmented eleventh, BP twelfth Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.16667 = 19/6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 0.0 : 133.2 266.9 400.1 617.5 750.7 884.4 1017.6 1151.2 1284.5 1501.8 1635.1 1768.7 1902.0 133.2 : 133.6 266.9 484.3 617.5 751.1 884.4 1018.0 1151.2 1368.6 1501.8 1635.5 1768.7 1902.0 266.9 : 133.2 350.6 483.9 617.5 750.7 884.4 1017.6 1235.0 1368.2 1501.8 1635.1 1768.3 1902.0 400.1 : 217.4 350.6 484.3 617.5 751.1 884.4 1101.7 1235.0 1368.6 1501.8 1635.1 1768.7 1902.0 617.5 : 133.2 266.9 400.1 533.7 667.0 884.4 1017.6 1151.2 1284.5 1417.7 1551.3 1684.6 1902.0 750.7 : 133.6 266.9 400.5 533.7 751.1 884.4 1018.0 1151.2 1284.5 1418.1 1551.3 1768.7 1902.0 884.4 : 133.2 266.9 400.1 617.5 750.7 884.4 1017.6 1150.8 1284.5 1417.7 1635.1 1768.3 1902.0 1017.6: 133.6 266.9 484.3 617.5 751.1 884.4 1017.6 1151.2 1284.5 1501.8 1635.1 1768.7 1902.0 1151.2: 133.2 350.6 483.9 617.5 750.7 884.0 1017.6 1150.8 1368.2 1501.5 1635.1 1768.3 1902.0 1284.5: 217.4 350.6 484.3 617.5 750.7 884.4 1017.6 1235.0 1368.2 1501.8 1635.1 1768.7 1902.0 1501.8: 133.2 266.9 400.1 533.3 667.0 800.2 1017.6 1150.8 1284.5 1417.7 1551.3 1684.6 1902.0 1635.1: 133.6 266.9 400.1 533.7 667.0 884.4 1017.6 1151.2 1284.5 1418.1 1551.3 1768.7 1902.0 1768.7: 133.2 266.5 400.1 533.3 750.7 884.0 1017.6 1150.8 1284.5 1417.7 1635.1 1768.3 1902.0 1902.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 217.3793 cents 12500/11907, 84.1418 cents 27/25, 133.2376 cents 2: 266.4751 .. 350.6169 cents 12500/11907, 84.1418 cents 321489/312500, 49.0958 cents 3: 400.1085 .. 484.2502 cents 12500/11907, 84.1418 cents 1029/1000, 49.4916 cents 4: 533.3461 .. 617.4878 cents 12500/11907, 84.1418 cents 321489/312500, 49.0958 cents 5: 666.9794 .. 751.1211 cents 12500/11907, 84.1418 cents 1029/1000, 49.4916 cents 6: 800.2170 .. 884.3587 cents 12500/11907, 84.1418 cents 321489/312500, 49.0958 cents 7: 1017.5963 .. 1101.7380 cents 12500/11907, 84.1418 cents 27/25, 133.2376 cents 8: 1150.8339 .. 1234.9756 cents 12500/11907, 84.1418 cents 321489/312500, 49.0958 cents 9: 1284.4672 .. 1368.6089 cents 12500/11907, 84.1418 cents 1029/1000, 49.4916 cents 10: 1417.7048 .. 1501.8465 cents 12500/11907, 84.1418 cents 321489/312500, 49.0958 cents 11: 1551.3381 .. 1635.4799 cents 12500/11907, 84.1418 cents 1029/1000, 49.4916 cents 12: 1684.5757 .. 1768.7174 cents 12500/11907, 84.1418 cents 321489/312500, 49.0958 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 27/25, 133.2376 cents, class 1 Average step (divided formal octave): 146.3042 cents Largest one step interval : 500/441, 217.3793 cents Average / Smallest step : 1.098070 Largest / Average step : 1.485803 Largest / Smallest step : 1.631517 Median interval of one step : 27/25, 133.2376 cents, amount: 7 Most common interval of one step : 27/25, 133.2376 cents, amount: 7 Least squares average step : 146.81888 cents, oct.: 1908.64548 cents Scale is strictly proper Step pattern alph. order: ABACABABACABA Step pattern size order : SMSLSMSMSLSMS Scale is a Constant Structure, by a margin of 49.09582 cents Scale diversity : 0.295362 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.469125 Number of different interval sizes : 38 = 3.16667 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.16667 = 19/6 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 4375/4374, 0.3958 cents Most common intervals : 5/3, 884.3587 cents & inv., amount: 10 Most common triad is 0.0 884.359 1017.596 cents, amount: 7 Number of recognisable fifths : 0 Number of recognisable fourths : 6, average 484.1183 cents Number of appreciable fourths : 0 Scale contains two identical disjunct tetrachords Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 13 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 6-7 -- Rational properties -- Prime limit : 7 Odd number limit : 3969 (O: 3969 U: 1323) Highest odd numerator or denominator: 63 Scale harmonicity : 0.016259 Average absolute harmonicity : 0.081924 Specific harmonicity : 0.085787 Fundamental : 1/3150, -11.6211 octaves, 0.0831 Hz. Guide tone : 9450, 13.2061 octaves, 2472361.592 Hz. Exponens Consonantiae : 2.976750E+07, 24.82723 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 262.0, average 20.15385 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 15.21171, average 1.17013 Sum of Tenney's harmonic distance : 28.97415, average 2.22878 Vogel's harmonic complexity : 25.61538 Wille's k value : 3307 Wilson's harmonic complexity : 49 Rectangular lattice diameter : 11 Triangular lattice diameter : 5 Lattice compactness : 288.37890, average 3.16900 Lattice compactness (without 2's) : 269.32838, average 2.95965 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.00000 8 3: -2 .. 3 0.53846 21 1 5: -2 .. 2 0.00000 14 4 7: -1 .. 1 0.00000 8 8 Average exponent except 2's : 7 / 13 = 0.53846 Average absolute exponent except 2's: 43 / 13 = 3.30769 Scale is JI-epimorphic with val: <7 13 19 22| Scale is weakly epimorphic with val: <7 13 19 24| Scale is weakly epimorphic with val: <7 13 21 21| Scale is JI-epimorphic with val: <8 13 19 23| = patent Scale is weakly epimorphic with val: <8 13 19 25| Scale is weakly epimorphic with val: <8 13 21 22| Scale is weakly epimorphic with val: <9 13 18 21| Scale is JI-epimorphic with val: <9 13 19 24| Scale is weakly epimorphic with val: <9 13 21 23|
FIT/MODE
13: 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 24.1528 c. M: 38.8042 c. 15: 1 1 1 2 1 1 1 1 1 2 1 1 1 P M ME I SD: 12.3425 c. M: 19.7175 c. 28: 2 2 2 3 2 2 2 2 2 3 2 2 2 SP M ME I SD: 4.6030 c. M: 7.4533 c. 43: 3 3 3 5 3 3 3 3 3 5 3 3 3 SP M DE I SD: 1.3129 c. M: 2.0249 c. 71: 5 5 5 8 5 5 5 5 5 8 5 5 5 SP M DE I SD: 1.0273 c. M:-1.7130 c. 114: 8 8 8 13 8 8 8 8 8 13 8 8 8 SP M DE I SD: 0.1761 c. M:-0.3031 c. 271: 19 19 19 31 19 19 19 19 19 31 19 19 19 SP M DE I SD: 0.1350 c. M: 0.2310 c. 385: 27 27 27 44 27 27 27 27 27 44 27 27 27 SP M DE I SD: 0.1047 c. M: 0.1763 c. 499: 35 35 35 57 35 35 35 35 35 57 35 35 35 SP M DE I SD: 0.1044 c. M:-0.1661 c. 884: 62 62 62 101 62 62 62 62 62 101 62 62 62 SP M DE I SD: 0.1029 c. M: 0.1596 c. 2267: 159 159 159 259 159 159 159 159 159 259 159 159 159 SP M DE I SD: 0.1030 c. M: 0.1594 c.
FIT/HARMONIC
1 x x x x x x x 2 x x x x 3 S SD: 24.3852 cents 2 x x x x 3 x x 4 x x 5 x 6 S SD: 21.1182 cents 3 x x 4 x x 5 x 6 x 7:8 x 9 S SD: 21.8311 cents 4 x x 5 x 6 x 7:8 x x 10:11:12 S SD: 14.2909 cents 5 x 6 x 7:8 x 9:10:11:12:13:14:15 S SD: 13.1062 cents 6 x 7:8 x 9:10:11:12:13:14:15:17:18 SD: 13.8057 cents 7 x 8:9:10:11:12:13:14:15:17:18:19:21 SD: 10.2714 cents 8 x 9:10:11:12:13:14:16:17:19:21:22:24 SD: 11.6682 cents 9:10 x 11:13:14:15:16:18:19:21:23:25:27 SD: 8.3436 cents 11:12:13:14:16:17:18:20:21:23:26:28:31:33 SD: 5.7343 cents 12:13:14:15:17:19:20:22:23:25:29:31:33:36 SD: 5.5946 cents 16:17:19:20:23:25:27:29:31:34:38:41:44:48 SD: 4.8328 cents 18:19:21:23:26:28:30:32:35:38:43:46:50:54 SD: 4.4990 cents 19:21:22:24:27:29:32:34:37:40:45:49:53:57 SD: 4.1014 cents 22:24:26:28:31:34:37:40:43:46:52:57:61:66 SD: 3.9996 cents 23:25:27:29:33:35:38:41:45:48:55:59:64:69 SD: 3.1632 cents 24:26:28:30:34:37:40:43:47:50:57:62:67:72 SD: 2.4257 cents 30:32:35:38:43:46:50:54:58:63:71:77:83:90 SD: 2.3828 cents 35:38:41:44:50:54:58:63:68:74:83:90:97:105 SD: 1.6330 cents 42:45:49:53:60:65:70:76:82:88:100:108:117:126 SD: 1.5358 cents 49:53:57:62:70:76:82:88:95:103:117:126:136:147 SD: 1.3071 cents 54:58:63:68:77:83:90:97:105:113:129:139:150:162 SD: 1.1701 cents 61:66:71:77:87:94:102:110:119:128:145:157:169:183 SD: 0.9609 cents 72:78:84:91:103:111:120:130:140:151:171:185:200:216 SD: 0.8383 cents 77:83:90:97:110:119:128:139:150:162:183:198:214:231 SD: 0.7939 cents 84:91:98:106:120:130:140:151:163:176:200:216:233:252 SD: 0.7810 cents 89:96:104:112:127:137:148:160:173:187:212:229:247:267 SD: 0.6047 cents 112:121:131:141:160:173:187:202:218:235:267:288:311:336 SD: 0.5839 cents 114:123:133:144:163:176:190:205:222:239:271:293:317:342 SD: 0.5690 cents 126:136:147:159:180:194:210:227:245:265:300:324:350:378 SD: 0.4196 cents 138:149:161:174:197:213:230:248:268:290:329:355:383:414 SD: 0.3876 cents 149:161:174:188:213:230:248:268:290:313:355:383:414:447 SD: 0.3724 cents 161:174:188:203:230:248:268:290:313:338:383:414:447:483 SD: 0.3642 cents 186:201:217:234:266:287:310:335:362:391:443:478:517:558 SD: 0.3527 cents 199:215:232:251:284:307:332:358:387:418:474:512:553:597 SD: 0.2912 cents 210:227:245:265:300:324:350:378:408:441:500:540:583:630 SD: 0.2681 cents 234:253:273:295:334:361:390:421:455:491:557:602:650:702 SD: 0.2469 cents 250:270:292:315:357:386:417:450:486:525:595:643:694:750 SD: 0.2428 cents 276:298:322:348:394:426:460:497:537:580:657:710:767:828 SD: 0.2171 cents 289:312:337:364:413:446:482:520:562:607:688:743:803:867 SD: 0.1643 cents 324:350:378:408:463:500:540:583:630:680:771:833:900:972 SD: 0.1546 cents 378:408:441:476:540:583:630:680:735:794:900:972:1050:1134 SD: 0.1470 cents 420:454:490:529:600:648:700:756:817:882:1000:1080:1167:1260 SD: 0.1439 cents 427:461:498:538:610:659:712:769:830:897:1017:1098:1186:1281 SD: 0.1432 cents 438:473:511:552:626:676:730:788:852:920:1043:1126:1217:1314 SD: 0.1327 cents 450:486:525:567:643:694:750:810:875:945:1071:1157:1250:1350 SD: 0.0836 cents 588:635:686:741:840:907:980:1058:1143:1235:1400:1512:1633:1764 SD: 0.0815 cents 600:648:700:756:857:926:1000:1080:1167:1260:1429:1543:1667:1800 SD: 0.0780 cents