Scala analysis: strangeion
19-limit "dodekaphonic" scale (19 & 17).
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/16 104.955410 17th harmonic 2: 19/17 192.557607 quasi-meantone 3: 19/16 297.513016 19th harmonic 4: 323/256 402.468426 5: 8192/6137 500.018558 6: 361/256 595.026032 two (19th harmonic) 7: 6137/4096 699.981442 8: 512/323 797.531574 9: 32/19 902.486984 19th subharmonic 10: 34/19 1007.442393 quasi-mean seventh 11: 32/17 1095.044590 17th subharmonic 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 17/16 104.9554 17th harmonic 1: 17/16 104.9554 17th harmonic 2: 304/289 87.6022 3: 17/16 104.9554 17th harmonic 4: 17/16 104.9554 17th harmonic 5: 2097152/1982251 97.5501 6: 2215457/2097152 95.0075 7: 17/16 104.9554 17th harmonic 8: 2097152/1982251 97.5501 9: 17/16 104.9554 17th harmonic 10: 17/16 104.9554 17th harmonic 11: 304/289 87.6022 12: 17/16 104.9554 17th harmonic
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 304/289 87.602 cents 1: 1 2215457/2097152 95.007 cents 1: 2 2097152/1982251 97.550 cents 1: 7 17/16 104.955 cents 17th harmonic 2: 5 19/17 192.558 cents quasi-meantone 2: 1 37662769/33554432 199.963 cents 2: 3 131072/116603 202.506 cents 2: 3 289/256 209.911 cents two (17th harmonic) 3: 9 19/16 297.513 cents 19th harmonic 3: 3 8192/6859 307.461 cents 4: 1 361/289 385.115 cents two (quasi-meantone) 4: 3 131072/104329 395.063 cents 4: 7 323/256 402.468 cents 4: 1 8704/6859 412.416 cents 5: 3 361/272 490.071 cents 5: 5 8192/6137 500.019 cents 5: 4 5491/4096 507.424 cents 6: 6 361/256 595.026 cents two (19th harmonic) 6: 6 512/361 604.974 cents 7: 4 8192/5491 692.576 cents 7: 5 6137/4096 699.981 cents 7: 3 544/361 709.929 cents 8: 1 6859/4352 787.584 cents 8: 7 512/323 797.532 cents 8: 3 104329/65536 804.937 cents 8: 1 578/361 814.885 cents 9: 3 6859/4096 892.539 cents 9: 9 32/19 902.487 cents 19th subharmonic 10: 3 512/289 990.089 cents 10: 3 116603/65536 997.494 cents 10: 1 67108864/37662769 1000.037 cents 10: 5 34/19 1007.442 cents quasi-mean seventh 11: 7 32/17 1095.045 cents 17th subharmonic 11: 2 1982251/1048576 1102.450 cents 11: 1 4194304/2215457 1104.993 cents 11: 2 289/152 1112.398 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 105.0 192.6 297.5 402.5 500.0 595.0 700.0 797.5 902.5 1007.4 1095.0 1200.0 105.0 : 87.6 192.6 297.5 395.1 490.1 595.0 692.6 797.5 902.5 990.1 1095.0 1200.0 192.6 : 105.0 209.9 307.5 402.5 507.4 605.0 709.9 814.9 902.5 1007.4 1112.4 1200.0 297.5 : 105.0 202.5 297.5 402.5 500.0 605.0 709.9 797.5 902.5 1007.4 1095.0 1200.0 402.5 : 97.6 192.6 297.5 395.1 500.0 605.0 692.6 797.5 902.5 990.1 1095.0 1200.0 500.0 : 95.0 200.0 297.5 402.5 507.4 595.0 700.0 804.9 892.5 997.5 1102.4 1200.0 595.0 : 105.0 202.5 307.5 412.4 500.0 605.0 709.9 797.5 902.5 1007.4 1105.0 1200.0 700.0 : 97.6 202.5 307.5 395.1 500.0 605.0 692.6 797.5 902.5 1000.0 1095.0 1200.0 797.5 : 105.0 209.9 297.5 402.5 507.4 595.0 700.0 804.9 902.5 997.5 1102.4 1200.0 902.5 : 105.0 192.6 297.5 402.5 490.1 595.0 700.0 797.5 892.5 997.5 1095.0 1200.0 1007.4: 87.6 192.6 297.5 385.1 490.1 595.0 692.6 787.6 892.5 990.1 1095.0 1200.0 1095.0: 105.0 209.9 297.5 402.5 507.4 605.0 700.0 804.9 902.5 1007.4 1112.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 87.6022 .. 104.9554 cents 4913/4864, 17.3532 cents 304/289, 87.6022 cents 2: 192.5576 .. 209.9108 cents 4913/4864, 17.3532 cents 304/289, 87.6022 cents 3: 297.5130 .. 307.4610 cents 131072/130321, 9.9479 cents 304/289, 87.6022 cents 4: 385.1152 .. 412.4164 cents 2515456/2476099, 27.3011 cents 2476099/2367488, 77.6543 cents 5: 490.0706 .. 507.4238 cents 4913/4864, 17.3532 cents 2476099/2367488, 77.6543 cents 6: 595.0260 .. 604.9740 cents 131072/130321, 9.9479 cents 304/289, 87.6022 cents 7: 692.5762 .. 709.9294 cents 4913/4864, 17.3532 cents 304/289, 87.6022 cents 8: 787.5836 .. 814.8848 cents 2515456/2476099, 27.3011 cents 2476099/2367488, 77.6543 cents 9: 892.5390 .. 902.4870 cents 131072/130321, 9.9479 cents 2476099/2367488, 77.6543 cents 10: 990.0892 .. 1007.4424 cents 4913/4864, 17.3532 cents 304/289, 87.6022 cents 11: 1095.0446 .. 1112.3978 cents 4913/4864, 17.3532 cents 304/289, 87.6022 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 304/289, 87.6022 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 17/16, 104.9554 cents Average / Smallest step : 1.141524 Largest / Average step : 1.049554 Largest / Smallest step : 1.198091 Median interval of one step : 17/16, 104.9554 cents, amount: 7 Most common interval of one step : 17/16, 104.9554 cents, amount: 7 Least squares average step : 99.97716 cents, oct.: 1199.72589 cents Scale is strictly proper Step pattern alph. order: ABAACDACAABA Step pattern size order : DADDCBDCDDAD Scale is a Constant Structure, by a margin of 77.65426 cents Scale diversity : 1.129006 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.842862 Rothenberg efficiency : 0.419108 redundancy: 0.580892 Efficiency x scale size : 5.029293 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 2.54266 cents Most common intervals : 19/16, 297.5130 cents & inv., amount: 9 Most common triad is 0.0 297.513 902.487 cents, amount: 6 Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Scale contains a complete diamond : 1 17 19 323 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 11 = 91.6667% Limited transpositions with margin 17.3532 cents: 3 5 6 7 9 Limited inverse transpositions with margin 17.3532 cents: 3 5 6 7 9 -- Rational properties -- Prime limit : 19 Odd number limit : 37662769 (O: 37662769 U: 37662769) Highest odd numerator or denominator: 6137 Scale harmonicity : 0.004511 Average absolute harmonicity : 0.099931 Specific harmonicity : 0.025722 Fundamental : 1/25137152, -24.5833 octaves, 0.0000 Hz. Guide tone : 50274304, 25.5833 octaves, 13153043204.114 Hz. Exponens Consonantiae : 1.263753E+15, 50.16664 octaves Euler's gradus suavitatis : 130 Sum of Mann's harmonic distance : 13426.5, average 1118.87500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 22.72774, average 1.89398 Sum of Tenney's harmonic distance : 46.26073, average 3.85506 Vogel's harmonic complexity : 70.00000 Wille's k value : 18831384 Wilson's harmonic complexity : 110 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 675.66085, average 8.66232 Lattice compactness (without 2's) : 147.17367, average 1.88684 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -12 .. 13 -0.16667 70 1 17: -1 .. 1 0.00000 8 2 19: -2 .. 2 0.16667 12 9 Average exponent except 2's : 2 / 12 = 0.16667 Average absolute exponent except 2's: 20 / 12 = 1.66667 Scale is weakly epimorphic with val: <12 46 51| Scale is weakly epimorphic with val: <12 47 51| Scale is JI-epimorphic with val: <12 49 51| = patent Scale is weakly epimorphic with val: <12 50 51|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 4.1752 c. M: 7.4424 c. Twelve-tone Chromatic (1/11-comma) 56: 5 4 5 5 4 5 5 4 5 5 4 5 SP B ME I SD: 4.0118 c. M: 7.1614 c. 57: 5 4 5 5 5 4 5 5 5 5 4 5 SP D3 SD: 3.3248 c. M: 5.5523 c. 69: 6 5 6 6 6 5 6 6 6 6 5 6 SP D3 SD: 2.4888 c. M: 4.3293 c. 81: 7 6 7 7 7 6 7 7 7 7 6 7 SP D3 SD: 2.0689 c. M: 3.6851 c. 93: 8 7 8 8 8 7 8 8 8 8 7 8 SP D3 SD: 1.9144 c. M: 3.2072 c. 101: 9 7 9 9 8 8 9 8 9 9 7 9 SP SD: 1.5215 c. M: 2.4586 c. 113: 10 8 10 10 9 9 10 9 10 10 8 10 SP SD: 0.9630 c. M: 1.4072 c. 125: 11 9 11 11 10 10 11 10 11 11 9 11 SP SD: 0.5707 c. M: 0.8186 c. 137: 12 10 12 12 11 11 12 11 12 12 10 12 SP SD: 0.4229 c. M: 0.7485 c. 319: 28 23 28 28 26 25 28 26 28 28 23 28 SP SD: 0.4213 c. M: 0.7081 c. 331: 29 24 29 29 27 26 29 27 29 29 24 29 SP SD: 0.2731 c. M: 0.4641 c. 343: 30 25 30 30 28 27 30 28 30 30 25 30 SP SD: 0.1675 c. M: 0.2738 c. 355: 31 26 31 31 29 28 31 29 31 31 26 31 SP SD: 0.1654 c. M: 0.2631 c. 468: 41 34 41 41 38 37 41 38 41 41 34 41 SP SD: 0.1412 c. M:-0.2499 c. 480: 42 35 42 42 39 38 42 39 42 42 35 42 SP SD: 0.0345 c. M: 0.0576 c. 972: 85 71 85 85 79 77 85 79 85 85 71 85 SP SD: 0.0217 c. M:-0.0357 c. 1452: 127 106 127 127 118 115 127 118 127 127 106 127 SP SD: 0.0106 c. M: 0.0186 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: 0.9868 cents 3 x x x x 4 x x x 5 x x 6 S SD: 6.0785 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 10.4765 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 5.8286 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 9.1783 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.8660 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.4290 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.5228 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.5057 cents 11 x 12:13:14:15 x 16:17:19:20:21:22 SD: 10.6022 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.5576 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.8103 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.1247 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.8803 cents 20:21:22:24:25:27:28:30:32:34:36:38:40 SD: 4.7115 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.5603 cents 24:26:27:29:30:32:34:36:38:40:43:45:48 SD: 4.4728 cents 26:28:29:31:33:35:37:39:41:44:47:49:52 SD: 3.3744 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.1557 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.2942 cents 34:36:38:40:43:45:48:51:54:57:61:64:68 SD: 2.0987 cents 42:45:47:50:53:56:59:63:67:71:75:79:84 SD: 1.7919 cents 48:51:54:57:61:64:68:72:76:81:86:90:96 SD: 1.7104 cents 51:54:57:61:64:68:72:76:81:86:91:96:102 SD: 1.6995 cents 53:56:59:63:67:71:75:79:84:89:95:100:106 SD: 1.5818 cents 58:62:65:69:73:77:82:87:92:98:104:109:116 SD: 1.5053 cents 60:64:67:71:76:80:85:90:95:101:107:113:120 SD: 1.3003 cents 66:70:74:78:83:88:93:99:105:111:118:124:132 SD: 1.2064 cents 68:72:76:81:86:91:96:102:108:115:122:128:136 SD: 1.1516 cents 76:81:85:90:96:101:107:114:120:128:136:143:152 SD: 1.0993 cents 80:85:89:95:101:107:113:120:127:135:143:151:160 SD: 0.9609 cents 92:98:103:109:116:123:130:138:146:155:165:173:184 SD: 0.7979 cents 95:101:106:113:120:127:134:142:151:160:170:179:190 SD: 0.7003 cents 110:117:123:131:139:147:155:165:174:185:197:207:220 SD: 0.6796 cents 111:118:124:132:140:148:157:166:176:187:199:209:222 SD: 0.6485 cents 127:135:142:151:160:170:179:190:201:214:227:239:254 SD: 0.6197 cents 129:137:144:153:163:172:182:193:204:217:231:243:258 SD: 0.5956 cents 143:152:160:170:180:191:202:214:227:241:256:269:286 SD: 0.5776 cents 144:153:161:171:182:192:203:216:228:243:258:271:288 SD: 0.5087 cents 161:171:180:191:203:215:227:241:255:271:288:303:322 SD: 0.2846 cents 256:272:286:304:323:342:361:384:406:431:458:482:512 SD: 0.2338 cents 305:324:341:362:385:407:430:457:483:514:546:574:610 SD: 0.2185 cents 367:390:410:436:463:490:518:550:582:618:657:691:734 SD: 0.1930 cents 383:407:428:455:483:511:540:574:607:645:685:721:766 SD: 0.1532 cents 400:425:447:475:505:534:564:599:634:674:716:753:800 SD: 0.1460 cents 475:505:531:564:599:634:670:712:753:800:850:894:950 SD: 0.1454 cents 528:561:590:627:666:705:745:791:837:889:945:994:1056 SD: 0.1198 cents 561:596:627:666:708:749:791:841:889:945:1004:1056:1122 SD: 0.1145 cents 576:612:644:684:727:769:812:863:913:970:1031:1084:1152 SD: 0.1019 cents