Scala analysis: ennon15
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: 250/189 484.250233 5: 10/7 617.487807 Euler's tritone 6: 54/35 750.725382 septimal semi-augmented fifth 7: 5/3 884.358713 major sixth, BP sixth 8: 9/5 1017.596288 just minor seventh, BP seventh 9: 35/18 1151.229619 septimal semi-diminished octave 10: 21/10 1284.467193 minor semitone +1 octave 11: 245/108 1418.100524 12: 50/21 1501.846520 BP second, quasi-equal minor third +1 octave 13: 18/7 1635.084095 septimal major 10th 14: 25/9 1768.717426 classic augmented eleventh, BP twelfth 15: 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: 12500/11907 84.1418 5: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 6: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 7: 175/162 133.6333 8: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 9: 175/162 133.6333 10: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 11: 175/162 133.6333 12: 360/343 83.7460 13: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 14: 175/162 133.6333 15: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 360/343 83.746 cents 1: 1 12500/11907 84.142 cents 1: 8 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 5 175/162 133.633 cents 2: 1 1944/1715 216.984 cents 2: 3 500/441 217.379 cents 2: 2 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 2: 9 7/6 266.871 cents septimal minor third 3: 5 60/49 350.617 cents smaller approximation to neutral third 3: 1 6250/5103 351.013 cents 3: 7 63/50 400.108 cents quasi-equal major third 3: 2 1225/972 400.504 cents 4: 3 324/245 483.854 cents 4: 5 250/189 484.250 cents 4: 3 1701/1250 533.346 cents 4: 4 49/36 533.742 cents Arabic lute acute fourth 5: 1 8748/6125 617.092 cents 5: 9 10/7 617.488 cents Euler's tritone 5: 4 147/100 666.979 cents 5: 1 8575/5832 667.375 cents 6: 7 54/35 750.725 cents septimal semi-augmented fifth 6: 5 125/81 751.121 cents 6: 2 3969/2500 800.217 cents two (quasi-equal major third) 6: 1 343/216 800.613 cents 7: 3 1458/875 883.963 cents 7: 11 5/3 884.359 cents major sixth, BP sixth 7: 1 343/200 933.850 cents 8: 1 600/343 968.105 cents 8: 11 9/5 1017.596 cents just minor seventh, BP seventh 8: 3 875/486 1017.992 cents 9: 1 648/343 1101.342 cents 9: 2 2500/1323 1101.738 cents 9: 5 243/125 1150.834 cents octave - maximal diesis 9: 7 35/18 1151.230 cents septimal semi-diminished octave 10: 1 17496/8575 1234.580 cents 10: 4 100/49 1234.976 cents Erlich's decatonic comma, tritonic diesis +1 octave 10: 9 21/10 1284.467 cents minor semitone +1 octave 10: 1 6125/2916 1284.863 cents 11: 4 108/49 1368.213 cents Zalzal's mujannab +1 octave 11: 3 1250/567 1368.609 cents BP great semitone, major BP chroma +1 octave 11: 5 567/250 1417.705 cents 11: 3 245/108 1418.101 cents 12: 2 2916/1225 1501.451 cents 12: 7 50/21 1501.847 cents BP second, quasi-equal minor third +1 octave 12: 1 15309/6250 1550.942 cents 12: 5 49/20 1551.338 cents larger approximation to neutral third +1 octave 13: 9 18/7 1635.084 cents septimal major 10th 13: 2 625/243 1635.480 cents 13: 3 1323/500 1684.576 cents 13: 1 1715/648 1684.971 cents 14: 5 486/175 1768.322 cents 14: 8 25/9 1768.717 cents classic augmented eleventh, BP twelfth 14: 1 35721/12500 1817.813 cents 14: 1 343/120 1818.209 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.85714 = 27/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 133.2 266.9 400.1 484.3 617.5 750.7 884.4 1017.6 1151.2 1284.5 1418.1 1501.8 1635.1 1768.7 1902.0 133.2 : 133.6 266.9 351.0 484.3 617.5 751.1 884.4 1018.0 1151.2 1284.9 1368.6 1501.8 1635.5 1768.7 1902.0 266.9 : 133.2 217.4 350.6 483.9 617.5 750.7 884.4 1017.6 1151.2 1235.0 1368.2 1501.8 1635.1 1768.3 1902.0 400.1 : 84.1 217.4 350.6 484.3 617.5 751.1 884.4 1018.0 1101.7 1235.0 1368.6 1501.8 1635.1 1768.7 1902.0 484.3 : 133.2 266.5 400.1 533.3 667.0 800.2 933.9 1017.6 1150.8 1284.5 1417.7 1550.9 1684.6 1817.8 1902.0 617.5 : 133.2 266.9 400.1 533.7 667.0 800.6 884.4 1017.6 1151.2 1284.5 1417.7 1551.3 1684.6 1768.7 1902.0 750.7 : 133.6 266.9 400.5 533.7 667.4 751.1 884.4 1018.0 1151.2 1284.5 1418.1 1551.3 1635.5 1768.7 1902.0 884.4 : 133.2 266.9 400.1 533.7 617.5 750.7 884.4 1017.6 1150.8 1284.5 1417.7 1501.8 1635.1 1768.3 1902.0 1017.6: 133.6 266.9 400.5 484.3 617.5 751.1 884.4 1017.6 1151.2 1284.5 1368.6 1501.8 1635.1 1768.7 1902.0 1151.2: 133.2 266.9 350.6 483.9 617.5 750.7 884.0 1017.6 1150.8 1235.0 1368.2 1501.5 1635.1 1768.3 1902.0 1284.5: 133.6 217.4 350.6 484.3 617.5 750.7 884.4 1017.6 1101.7 1235.0 1368.2 1501.8 1635.1 1768.7 1902.0 1418.1: 83.7 217.0 350.6 483.9 617.1 750.7 884.0 968.1 1101.3 1234.6 1368.2 1501.5 1635.1 1768.3 1902.0 1501.8: 133.2 266.9 400.1 533.3 667.0 800.2 884.4 1017.6 1150.8 1284.5 1417.7 1551.3 1684.6 1818.2 1902.0 1635.1: 133.6 266.9 400.1 533.7 667.0 751.1 884.4 1017.6 1151.2 1284.5 1418.1 1551.3 1685.0 1768.7 1902.0 1768.7: 133.2 266.5 400.1 533.3 617.5 750.7 884.0 1017.6 1150.8 1284.5 1417.7 1551.3 1635.1 1768.3 1902.0 1902.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 83.7460 .. 133.6333 cents 12005/11664, 49.8873 cents 360/343, 83.7460 cents 2: 216.9836 .. 266.8709 cents 12005/11664, 49.8873 cents 314928/300125, 83.3502 cents 3: 350.6169 .. 400.5042 cents 12005/11664, 49.8873 cents 360/343, 83.7460 cents 4: 483.8545 .. 533.7418 cents 12005/11664, 49.8873 cents 314928/300125, 83.3502 cents 5: 617.0921 .. 667.3751 cents 52521875/51018336, 50.2831 cents 314928/300125, 83.3502 cents 6: 750.7254 .. 800.6127 cents 12005/11664, 49.8873 cents 314928/300125, 83.3502 cents 7: 883.9630 .. 933.8503 cents 12005/11664, 49.8873 cents 314928/300125, 83.3502 cents 8: 968.1047 .. 1017.9920 cents 12005/11664, 49.8873 cents 120000/117649, 34.2544 cents 9: 1101.3423 .. 1151.2296 cents 12005/11664, 49.8873 cents 314928/300125, 83.3502 cents 10: 1234.5799 .. 1284.8629 cents 52521875/51018336, 50.2831 cents 314928/300125, 83.3502 cents 11: 1368.2132 .. 1418.1005 cents 12005/11664, 49.8873 cents 314928/300125, 83.3502 cents 12: 1501.4508 .. 1551.3381 cents 12005/11664, 49.8873 cents 314928/300125, 83.3502 cents 13: 1635.0841 .. 1684.9714 cents 12005/11664, 49.8873 cents 360/343, 83.7460 cents 14: 1768.3217 .. 1818.2090 cents 12005/11664, 49.8873 cents 314928/300125, 83.3502 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 360/343, 83.7460 cents, class 1 Average step (divided formal octave): 126.7970 cents Largest one step interval : 175/162, 133.6333 cents Average / Smallest step : 1.514066 Largest / Average step : 1.053916 Largest / Smallest step : 1.595698 Median interval of one step : 27/25, 133.2376 cents, amount: 8 Most common interval of one step : 27/25, 133.2376 cents, amount: 8 Least squares average step : 126.69503 cents, oct.: 1900.42552 cents Scale is strictly proper Step pattern alph. order: ABACAABABABDABA Step pattern size order : CDCBCCDCDCDACDC Scale is a Constant Structure, by a margin of 34.25442 cents Scale diversity : 0.311350 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.632371 Number of different interval sizes : 54 = 3.85714 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.85714 = 27/7 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: 11 Most common triad is 0.0 884.359 1017.596 cents, amount: 8 Number of recognisable fifths : 0 Number of recognisable fourths : 8, average 484.1018 cents Number of appreciable fourths : 0 Formal octave complements present : 13 = 86.6667% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 7-8 -- Rational properties -- Prime limit : 7 Odd number limit : 35721 (O: 35721 U: 11907) Highest odd numerator or denominator: 245 Scale harmonicity : 0.012216 Average absolute harmonicity : 0.074536 Specific harmonicity : 0.074187 Fundamental : 1/18900, -14.2061 octaves, 0.0138 Hz. Guide tone : 330750, 18.3354 octaves, 86532655.723 Hz. Exponens Consonantiae : 6.251175E+09, 32.54148 octaves Euler's gradus suavitatis : 54 Sum of Mann's harmonic distance : 658.0, average 43.86667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 19.87734, average 1.32516 Sum of Tenney's harmonic distance : 38.07114, average 2.53808 Vogel's harmonic complexity : 29.93333 Wille's k value : 21437 Wilson's harmonic complexity : 64 Rectangular lattice diameter : 14 Triangular lattice diameter : 7 Lattice compactness : 431.94782, average 3.59957 Lattice compactness (without 2's) : 402.44335, average 3.35369 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.06667 11 3: -3 .. 3 0.06667 27 1 5: -2 .. 3 0.26667 18 4 7: -1 .. 2 0.06667 11 10 Average exponent except 2's : 6 / 15 = 0.40000 Average absolute exponent except 2's: 56 / 15 = 3.73333 Scale is JI-epimorphic with val: <8 15 22 25| Scale is JI-epimorphic with val: <9 15 22 26| Scale is JI-epimorphic with val: <10 15 22 27|
FIT/MODE
15: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 14.2618 c. M: 23.3335 c. 28: 2 2 2 1 2 2 2 2 2 2 2 1 2 2 2 P M ME I SD: 5.3053 c. M: 8.7615 c. 43: 3 3 3 2 3 3 3 3 3 3 3 2 3 3 3 SP M ME I SD: 1.5260 c. M: 2.6922 c. 71: 5 5 5 3 5 5 5 5 5 5 5 3 5 5 5 SP M DE I SD: 1.1766 c. M: 2.0645 c. 114: 8 8 8 5 8 8 8 8 8 8 8 5 8 8 8 SP M DE I SD: 0.1966 c. M: 0.4196 c. 271: 19 19 19 12 19 19 19 19 19 19 19 12 19 19 19 SP M DE I SD: 0.1639 c. M: 0.4071 c. 385: 27 27 27 17 27 27 27 27 27 27 27 17 27 27 27 SP M DE I SD: 0.1249 c. M: 0.2795 c. 499: 35 35 35 22 35 35 35 35 35 35 35 22 35 35 35 SP M DE I SD: 0.1212 c. M: 0.2102 c. 884: 62 62 62 39 62 62 62 62 62 62 62 39 62 62 62 SP M DE I SD: 0.1210 c. M: 0.2404 c. 1112: 78 78 78 49 78 78 78 78 78 78 78 49 78 78 78 SP M DE I SD: 0.1234 c. M: 0.2095 c. 1269: 89 89 89 56 89 89 89 89 89 89 89 56 89 89 89 SP M DE I SD: 0.1217 c. M: 0.2523 c. 1383: 97 97 97 61 97 97 97 97 97 97 97 61 97 97 97 SP M DE I SD: 0.1208 c. M: 0.2295 c. 1611: 113 113 113 71 113 113 113 113 113 113 113 71 113 113 113 SP M DE I SD: 0.1226 c. M: 0.2021 c. 1654: 116 116 116 73 116 116 116 116 116 116 116 73 116 116 116 SP M DE I SD: 0.1223 c. M: 0.2586 c. 1882: 132 132 132 83 132 132 132 132 132 132 132 83 132 132 132 SP M DE I SD: 0.1208 c. M: 0.2244 c. 2110: 148 148 148 93 148 148 148 148 148 148 148 93 148 148 148 SP M DE I SD: 0.1222 c. M: 0.1982 c. 2153: 151 151 151 95 151 151 151 151 151 151 151 95 151 151 151 SP M DE I SD: 0.1214 c. M: 0.2474 c. 2267: 159 159 159 100 159 159 159 159 159 159 159 100 159 159 159 SP M DE I SD: 0.1208 c. M: 0.2338 c. 2381: 167 167 167 105 167 167 167 167 167 167 167 105 167 167 167 SP M DE I SD: 0.1208 c. M: 0.2214 c.
FIT/HARMONIC
1 x x x x x x x x 2 x x x x x 3 S SD: 24.3852 cents 2 x x x x x 3 x x 4 x x x 5 x 6 S SD: 21.1182 cents 3 x x x 4 x x 5 x 6 x x 7:8 x 9 S SD: 14.6782 cents 4 x x 5 x x 6 x 7:8 x 9 x 10:11:12 S SD: 12.6297 cents 5 x 6 x x 7:8 x 9:10 x 11:12:13:14:15 S SD: 11.6234 cents 6 x 7 x 8 x 9:10:11:12:13 x 14:15:17:18 SD: 10.6255 cents 7 x 8:9 x 10:11:12:13:14:15:16:17:18:19:21 SD: 9.5345 cents 8 x 9:10 x 11:12:13:14:16:17:18:19:21:22:24 SD: 10.8258 cents 9:10 x 11:12:13:14:15:16:18:19:20:21:23:25:27 SD: 7.6563 cents 10:11:12 x 13:14:15:17:18:19:21:23:24:26:28:30 SD: 7.8198 cents 11:12:13:14:15:16:17:18:20:21:23:25:26:28:31:33 SD: 6.0900 cents 12:13:14:15:16:17:19:20:22:23:25:27:29:31:33:36 SD: 5.0250 cents 16:17:19:20:21:23:25:27:29:31:34:36:38:41:44:48 SD: 4.3868 cents 18:19:21:23:24:26:28:30:32:35:38:41:43:46:50:54 SD: 4.0336 cents 19:21:22:24:25:27:29:32:34:37:40:43:45:49:53:57 SD: 3.6167 cents 22:24:26:28:29:31:34:37:40:43:46:50:52:57:61:66 SD: 3.4958 cents 23:25:27:29:30:33:35:38:41:45:48:52:55:59:64:69 SD: 3.2066 cents 24:26:28:30:32:34:37:40:43:47:50:54:57:62:67:72 SD: 2.4820 cents 30:32:35:38:40:43:46:50:54:58:63:68:71:77:83:90 SD: 2.2626 cents 35:38:41:44:46:50:54:58:63:68:74:79:83:90:97:105 SD: 1.6996 cents 37:40:43:47:49:53:57:62:67:72:78:84:88:95:103:111 SD: 1.5565 cents 49:53:57:62:65:70:76:82:88:95:103:111:117:126:136:147 SD: 1.1910 cents 59:64:69:74:78:84:91:98:106:115:124:134:140:152:164:177 SD: 1.1338 cents 61:66:71:77:81:87:94:102:110:119:128:138:145:157:169:183 SD: 0.9963 cents 66:71:77:83:87:94:102:110:119:128:139:150:157:170:183:198 SD: 0.9761 cents 72:78:84:91:95:103:111:120:130:140:151:163:171:185:200:216 SD: 0.8166 cents 77:83:90:97:102:110:119:128:139:150:162:175:183:198:214:231 SD: 0.7398 cents 84:91:98:106:111:120:130:140:151:163:176:191:200:216:233:252 SD: 0.7375 cents 89:96:104:112:118:127:137:148:160:173:187:202:212:229:247:267 SD: 0.5921 cents 96:104:112:121:127:137:148:160:173:187:202:218:229:247:267:288 SD: 0.5907 cents 108:117:126:136:143:154:167:180:194:210:227:245:257:278:300:324 SD: 0.5842 cents 112:121:131:141:148:160:173:187:202:218:235:254:267:288:311:336 SD: 0.5202 cents 126:136:147:159:167:180:194:210:227:245:265:286:300:324:350:378 SD: 0.4358 cents 149:161:174:188:197:213:230:248:268:290:313:338:355:383:414:447 SD: 0.3270 cents 161:174:188:203:213:230:248:268:290:313:338:365:383:414:447:483 SD: 0.3246 cents 186:201:217:234:246:266:287:310:335:362:391:422:443:478:517:558 SD: 0.3064 cents 199:215:232:251:263:284:307:332:358:387:418:451:474:512:553:597 SD: 0.2933 cents 210:227:245:265:278:300:324:350:378:408:441:476:500:540:583:630 SD: 0.2672 cents 238:257:278:300:315:340:367:397:428:463:500:540:567:612:661:714 SD: 0.2486 cents 250:270:292:315:331:357:386:417:450:486:525:567:595:643:694:750 SD: 0.2384 cents 276:298:322:348:365:394:426:460:497:537:580:626:657:710:767:828 SD: 0.1909 cents 289:312:337:364:382:413:446:482:520:562:607:656:688:743:803:867 SD: 0.1791 cents 324:350:378:408:429:463:500:540:583:630:680:735:771:833:900:972 SD: 0.1768 cents 350:378:408:441:463:500:540:583:630:681:735:794:833:900:972:1050 SD: 0.1478 cents 378:408:441:476:500:540:583:630:680:735:794:858:900:972:1050:1134 SD: 0.1441 cents 396:428:462:499:524:566:611:660:713:770:832:898:943:1018:1100:1188 SD: 0.1416 cents 415:448:484:523:549:593:640:692:747:807:872:941:988:1067:1153:1245 SD: 0.1398 cents 427:461:498:538:565:610:659:712:769:830:897:969:1017:1098:1186:1281 SD: 0.1360 cents 450:486:525:567:595:643:694:750:810:875:945:1021:1071:1157:1250:1350 SD: 0.0880 cents 588:635:686:741:778:840:907:980:1058:1143:1235:1334:1400:1512:1633:1764 SD: 0.0785 cents