Scala analysis: triskabree12
Twelvth 16807/12800&117649/100000 scale = inverse triskabree13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/25 196.198479 middle second 2: 8/7 231.174094 septimal whole tone 3: 2401/2000 316.362484 4: 64/49 462.348187 2 septatones or septatonic major third 5: 3200/2401 497.323802 6: 343/250 547.536578 7: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 8: 8/5 813.686286 minor sixth 9: 80/49 848.661901 smaller approximation to neutral sixth 10: 16807/10000 898.874677 11: 640/343 1079.835994 12: 49/25 1165.024385 BP eighth 13: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 1: 28/25 196.1985 middle second 2: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 3: 16807/16000 85.1884 4: 128000/117649 145.9857 5: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 6: 823543/800000 50.2128 7: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 8: 8/7 231.1741 septimal whole tone 9: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 10: 823543/800000 50.2128 11: 6400000/5764801 180.9613 12: 16807/16000 85.1884 13: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 2 823543/800000 50.213 cents 1: 2 16807/16000 85.188 cents 1: 1 128000/117649 145.986 cents 1: 1 6400000/5764801 180.961 cents 1: 1 28/25 196.198 cents middle second 1: 1 8/7 231.174 cents septimal whole tone 2: 3 16807/16000 85.188 cents 2: 2 343/320 120.164 cents 2: 1 6400000/5764801 180.961 cents 2: 4 8/7 231.174 cents septimal whole tone 2: 3 400/343 266.150 cents 3: 1 343/320 120.164 cents 3: 1 8/7 231.174 cents septimal whole tone 3: 4 400/343 266.150 cents 3: 2 20000/16807 301.125 cents 3: 5 2401/2000 316.362 cents 4: 1 400/343 266.150 cents 4: 1 20000/16807 301.125 cents 4: 1 2401/2000 316.362 cents 4: 7 49/40 351.338 cents larger approximation to neutral third 4: 1 64/49 462.348 cents 2 septatones or septatonic major third 4: 2 3200/2401 497.324 cents 5: 2 49/40 351.338 cents larger approximation to neutral third 5: 2 5/4 386.314 cents major third 5: 1 40353607/32000000 401.551 cents 5: 1 823543/640000 436.526 cents 5: 3 3200/2401 497.324 cents 5: 2 160000/117649 532.299 cents 5: 1 343/250 547.537 cents 5: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 1 5/4 386.314 cents major third 6: 1 823543/640000 436.526 cents 6: 2 160000/117649 532.299 cents 6: 1 343/250 547.537 cents 6: 5 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 3 10/7 617.488 cents Euler's tritone 7: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 7: 5 10/7 617.488 cents Euler's tritone 7: 1 500/343 652.463 cents 7: 2 117649/80000 667.701 cents 7: 1 1280000/823543 763.474 cents 7: 1 8/5 813.686 cents minor sixth 8: 1 10/7 617.488 cents Euler's tritone 8: 1 500/343 652.463 cents 8: 2 117649/80000 667.701 cents 8: 3 2401/1600 702.676 cents two (larger approximation to neutral third) 8: 1 1280000/823543 763.474 cents 8: 1 64000000/40353607 798.449 cents 8: 2 8/5 813.686 cents minor sixth 8: 2 80/49 848.662 cents smaller approximation to neutral sixth 9: 2 2401/1600 702.676 cents two (larger approximation to neutral third) 9: 1 49/32 737.652 cents 9: 7 80/49 848.662 cents smaller approximation to neutral sixth 9: 1 4000/2401 883.638 cents 9: 1 16807/10000 898.875 cents 9: 1 343/200 933.850 cents 10: 5 4000/2401 883.638 cents 10: 2 16807/10000 898.875 cents 10: 4 343/200 933.850 cents 10: 1 7/4 968.826 cents harmonic seventh 10: 1 640/343 1079.836 cents 11: 3 343/200 933.850 cents 11: 4 7/4 968.826 cents harmonic seventh 11: 1 5764801/3200000 1019.039 cents 11: 2 640/343 1079.836 cents 11: 3 32000/16807 1114.812 cents 12: 1 7/4 968.826 cents harmonic seventh 12: 1 25/14 1003.802 cents middle minor seventh 12: 1 5764801/3200000 1019.039 cents 12: 1 117649/64000 1054.014 cents 12: 2 32000/16807 1114.812 cents 12: 2 1600000/823543 1149.787 cents 12: 5 49/25 1165.024 cents BP eighth Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.16667 = 37/6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 0.0 : 196.2 231.2 316.4 462.3 497.3 547.5 582.5 813.7 848.7 898.9 1079.8 1165.0 1200.0 196.2 : 35.0 120.2 266.1 301.1 351.3 386.3 617.5 652.5 702.7 883.6 968.8 1003.8 1200.0 231.2 : 85.2 231.2 266.1 316.4 351.3 582.5 617.5 667.7 848.7 933.9 968.8 1165.0 1200.0 316.4 : 146.0 181.0 231.2 266.1 497.3 532.3 582.5 763.5 848.7 883.6 1079.8 1114.8 1200.0 462.3 : 35.0 85.2 120.2 351.3 386.3 436.5 617.5 702.7 737.7 933.9 968.8 1054.0 1200.0 497.3 : 50.2 85.2 316.4 351.3 401.6 582.5 667.7 702.7 898.9 933.9 1019.0 1165.0 1200.0 547.5 : 35.0 266.1 301.1 351.3 532.3 617.5 652.5 848.7 883.6 968.8 1114.8 1149.8 1200.0 582.5 : 231.2 266.1 316.4 497.3 582.5 617.5 813.7 848.7 933.9 1079.8 1114.8 1165.0 1200.0 813.7 : 35.0 85.2 266.1 351.3 386.3 582.5 617.5 702.7 848.7 883.6 933.9 968.8 1200.0 848.7 : 50.2 231.2 316.4 351.3 547.5 582.5 667.7 813.7 848.7 898.9 933.9 1165.0 1200.0 898.9 : 181.0 266.1 301.1 497.3 532.3 617.5 763.5 798.4 848.7 883.6 1114.8 1149.8 1200.0 1079.8: 85.2 120.2 316.4 351.3 436.5 582.5 617.5 667.7 702.7 933.9 968.8 1019.0 1200.0 1165.0: 35.0 231.2 266.1 351.3 497.3 532.3 582.5 617.5 848.7 883.6 933.9 1114.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.9756 .. 231.1741 cents 28/25, 196.1985 cents 50/49, 34.9756 cents 2: 85.1884 .. 266.1497 cents 6400000/5764801, 180.9613 cents 117649/128000,-145.9857 cents 3: 120.1640 .. 316.3625 cents 28/25, 196.1985 cents 117649/128000,-145.9857 cents 4: 266.1497 .. 497.3238 cents 8/7, 231.1741 cents 800000/823543,-50.2128 cents 5: 351.3381 .. 582.5122 cents 8/7, 231.1741 cents 117649/128000,-145.9857 cents 6: 386.3137 .. 617.4878 cents 8/7, 231.1741 cents 25/28,-196.1985 cents 7: 582.5122 .. 813.6863 cents 8/7, 231.1741 cents 49/50,-34.9756 cents 8: 617.4878 .. 848.6619 cents 8/7, 231.1741 cents 25/28,-196.1985 cents 9: 702.6762 .. 933.8503 cents 8/7, 231.1741 cents 117649/128000,-145.9857 cents 10: 883.6375 .. 1079.8360 cents 28/25, 196.1985 cents 800000/823543,-50.2128 cents 11: 933.8503 .. 1114.8116 cents 6400000/5764801, 180.9613 cents 117649/128000,-145.9857 cents 12: 968.8259 .. 1165.0244 cents 28/25, 196.1985 cents 117649/128000,-145.9857 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 50/49, 34.9756 cents, class 1 Average step (divided formal octave): 92.3077 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.639201 Largest / Average step : 2.504386 Largest / Smallest step : 6.609579 Median interval of one step : 823543/800000, 50.2128 cents, amount: 2 Most common interval of one step : 50/49, 34.9756 cents, amount: 5 Least squares average step : 95.11738 cents, oct.: 1236.52593 cents Scale is not proper Step pattern alph. order: ABCDBEBFBEGCB Step pattern size order : FACDABAGABECA Scale is not a Constant Structure Scale diversity : 1.416927 Lumma stability : 0.058293 Lumma impropriety factor : 0.799727 Number of different interval sizes : 40 = 3.33333 / class Number of one step interval sizes : 7 Highest interval variety : 8 Mean interval variety : 6.16667 = 37/6 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 40353607/40000000, 15.2372 cents Number of recognisable fifths : 5, average 702.6762 cents Formal octave complements present : 1 = 7.6923% -- Rational properties -- Prime limit : 7 Odd number limit : 40353607 (O: 40353607 U: 40353607) Highest odd numerator or denominator: 16807 Scale harmonicity : 0.007044 Average absolute harmonicity : 0.112908 Specific harmonicity : 0.044041 Fundamental : 1/24010000, -24.5171 octaves, 0.0000 Hz. Guide tone : 53782400, 25.6806 octaves, 14070850803.245 Hz. Exponens Consonantiae : 1.291315E+15, 50.19776 octaves Euler's gradus suavitatis : 90 Sum of Mann's harmonic distance : 19398.5, average 1492.19231 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 24.91456, average 1.91650 Sum of Tenney's harmonic distance : 50.28541, average 3.86811 Vogel's harmonic complexity : 51.38462 Wille's k value : 20176803 Wilson's harmonic complexity : 93 Rectangular lattice diameter : 15 Triangular lattice diameter : 9 Lattice compactness : 525.03852, average 5.76965 Lattice compactness (without 2's) : 342.33343, average 3.76191 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 7 1.84615 42 1 5: -4 .. 2 -0.92308 20 1 7: -4 .. 5 0.30769 28 11 Average exponent except 2's :-8 / 13 =-0.61538 Average absolute exponent except 2's: 48 / 13 = 3.69231 Scale is weakly epimorphic with val: <13 29 35| Scale is weakly epimorphic with val: <13 30 38| Scale is weakly epimorphic with val: <13 33 34|
FIT/MODE
13: 2 1 0 2 0 1 0 3 0 1 2 1 0 N SD: 26.4900 c. M:-45.7490 c. 15: 2 1 1 2 0 1 0 3 0 1 2 1 1 N SD: 26.6039 c. M: 48.6619 c. 16: 3 0 1 2 1 0 1 3 0 1 2 2 0 N SD: 20.8846 c. M:-34.9756 c. 18: 3 0 2 2 0 1 1 3 1 0 3 1 1 N SD: 20.5069 c. M: 32.2080 c. 19: 3 1 1 2 1 1 0 4 0 1 3 1 1 N SD: 16.3546 c. M: 28.1823 c. 20: 3 1 1 3 0 1 1 4 0 1 3 1 1 N SD: 15.1335 c. M:-26.3137 c. 24: 4 1 1 3 1 1 1 4 1 1 4 1 1 N SD: 12.1871 c. M:-20.1640 c. 27: 4 1 2 3 1 1 1 5 1 1 4 2 1 N SD: 11.2002 c. M: 18.4207 c. 28: 5 0 2 4 1 1 1 5 1 1 4 2 1 N SD: 11.9445 c. M:-18.0872 c. 29: 5 1 2 3 1 1 1 6 1 1 4 2 1 N SD: 10.9916 c. M:-20.3036 c. 31: 5 1 2 4 1 1 1 6 1 1 5 2 1 N SD: 4.2964 c. M: 8.5521 c. 57: 9 2 4 7 2 2 2 11 1 3 8 4 2 N SD: 5.4394 c. M:-7.9394 c. 60: 10 2 4 7 2 2 2 12 1 3 9 4 2 N SD: 4.9830 c. M:-8.8259 c. 68: 11 2 5 8 2 3 2 13 2 3 10 5 2 N SD: 1.9806 c. M: 3.5247 c. 99: 16 3 7 12 3 4 3 19 3 4 15 7 3 N SD: 1.3711 c. M: 2.2591 c. 140: 23 4 10 17 4 6 4 27 4 6 21 10 4 N SD: 0.6315 c. M:-1.1253 c. 171: 28 5 12 21 5 7 5 33 5 7 26 12 5 N SD: 0.5267 c. M:-0.9218 c. 239: 39 7 17 29 7 10 7 46 7 10 36 17 7 N SD: 0.2440 c. M: 0.4235 c. 379: 62 11 27 46 11 16 11 73 11 16 57 27 11 N SD: 0.1670 c. M:-0.3338 c. 550: 90 16 39 67 16 23 16 106 16 23 83 39 16 N SD: 0.1103 c. M:-0.1973 c. 789: 129 23 56 96 23 33 23 152 23 33 119 56 23 N SD: 0.0088 c. M: 0.0154 c.
FIT/HARMONIC
1 x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x 3 x x x x 4 S SD: 55.8656 cents 3 x x x x 4 x x x x 5 x x 6 S SD: 4.8446 cents 4 x x 5 x x x x 6 x 7 x x 8 S SD: 37.3080 cents 5 x x 6 x x x 7:8 x x 9 x 10 S SD: 12.4488 cents 6 x 7 x x 8 x x x x 10:11 x 12 S SD: 9.8267 cents 7 x 8 x 9 x x 10:11 x 12:13 x 14 S SD: 9.2353 cents 8:9 x 10 x x 11 x x 13 x 15 x 16 SD: 11.9073 cents 9:10 x 11 x 12 x 13:14 x 15:17 x 18 SD: 10.5484 cents 10:11 x 12:13 x x 14:16 x 17:19 x 20 SD: 6.1418 cents 11:12 x 13:14 x 15 x x 18 x 21 x 22 S SD: 11.5366 cents 12:13:14 x x 16 x 17:19 x 20:22 x 24 SD: 10.0648 cents 13 x 15:16:17 x 18 x 21 x 22:24:25:26 SD: 7.2245 cents 14 x 16:17:18 x 19:20:22:23:24:26:27:28 S SD: 6.9382 cents 15 x 17:18 x 20 x 21:24 x 25:28:29:30 SD: 3.4865 cents 16:18 x 19:21 x 22 x x 26:27:30:31:32 SD: 3.6614 cents 17:19 x 20:22 x 23:24:27:28:29:32:33:34 SD: 5.6469 cents 18:20:21:22 x 24 x 25:29 x 30:34:35:36 SD: 6.0113 cents 19:21:22:23:25 x 26:27:30:31:32:35:37:38 SD: 4.7545 cents 20:22:23:24:26:27 x 28:32:33:34:37:39:40 SD: 4.3087 cents 21 x 24:25:27:28:29 x x 34:35:39:41:42 SD: 4.0169 cents 22 x 25:26:29 x 30:31:35:36:37:41:43:44 SD: 3.4821 cents 23:26 x 28:30:31 x 32:37:38:39:43:45:46 SD: 4.1761 cents 24:27 x 29:31:32:33:34:38:39:40:45:47:48 SD: 3.4064 cents 25:28:29:30 x 33:34:35:40:41:42:47:49:50 SD: 3.1241 cents 26:29:30:31:34:35:36 x 42 x 44:49:51:52 SD: 3.7895 cents 27:30:31:32:35:36:37:38:43:44:45:50:53:54 SD: 2.9500 cents 28:31:32:34 x 37:38:39:45:46:47:52:55:56 SD: 3.4403 cents 29:32:33:35:38:39:40:41:46:47:49:54:57:58 SD: 3.4050 cents 30 x 34:36:39:40:41:42:48:49:50:56:59:60 SD: 1.9876 cents 31:35 x 37:40:41 x 43:50:51:52:58:61:62 SD: 3.6593 cents 32:36:37:38:42:43:44:45:51:52:54:60:63:64 SD: 2.9387 cents 33:37:38:40:43:44:45:46:53:54:55:62:65:66 SD: 2.5772 cents 35:39:40:42:46:47:48:49:56:57:59:65:69:70 SD: 1.8506 cents 38 x 43:46:50:51:52:53:61:62:64:71:74:76 SD: 2.7020 cents 40:45:46:48:52:53:55:56:64:65:67:75:78:80 SD: 1.8995 cents 43:48:49:52:56:57:59:60:69:70:72:80:84:86 SD: 1.7478 cents 49:55:56:59:64:65:67:69:78:80:82:91:96:98 SD: 1.6205 cents 50:56:57:60:65:67:69:70:80:82:84:93:98:100 SD: 1.4700 cents 60:67:69:72:78:80:82:84:96:98:101:112:118:120 SD: 1.3292 cents 65:73:74:78:85:87:89:91:104:106:109:121:127:130 SD: 1.0975 cents 75:84:86:90:98:100:103:105:120:122:126:140:147:150 SD: 0.6840 cents 118:132:135:142:154:157:162:165:189:193:198:220:231:236 SD: 0.6372 cents 120:134:137:144:157:160:165:168:192:196:202:224:235:240 SD: 0.6171 cents 125:140:143:150:163:167:172:175:200:204:210:233:245:250 SD: 0.5878 cents 135:151:154:162:176:180:185:189:216:220:227:252:265:270 SD: 0.5408 cents 140:157:160:168:183:187:192:196:224:229:235:261:274:280 SD: 0.5227 cents 150:168:171:180:196:200:206:210:240:245:252:280:294:300 SD: 0.3825 cents 175:196:200:210:229:233:240:245:280:286:294:327:343:350 SD: 0.3794 cents 210:235:240:252:274:280:288:294:336:343:353:392:412:420 SD: 0.2542 cents 225:252:257:270:294:300:309:315:360:367:378:420:441:450 SD: 0.2312 cents 300:336:343:360:392:400:412:420:480:490:504:560:588:600 SD: 0.1956 cents 373:418:426:448:487:497:512:522:597:609:627:696:731:746 SD: 0.1756 cents 385:431:440:462:503:513:528:539:616:629:647:718:755:770 SD: 0.1744 cents 400:448:457:480:522:533:549:560:640:653:672:746:784:800 SD: 0.1683 cents 425:476:486:510:555:566:583:595:680:694:714:793:833:850 SD: 0.1556 cents 433:485:495:520:566:577:594:606:693:707:728:808:849:866 SD: 0.1553 cents 435:487:497:522:568:580:597:609:696:710:731:812:853:870 SD: 0.1500 cents 460:515:526:552:601:613:631:644:736:751:773:858:902:920 SD: 0.1408 cents 490:549:560:588:640:653:672:686:784:800:824:914:960:980 SD: 0.1376 cents 523:586:598:628:683:697:718:732:837:854:879:976:1025:1046 SD: 0.1353 cents 532:596:608:639:695:709:730:745:851:869:894:993:1043:1064 SD: 0.1328 cents 568:636:649:682:742:757:779:795:909:927:955:1060:1113:1136 SD: 0.1190 cents 575:644:657:690:751:766:789:805:920:939:966:1073:1127:1150 SD: 0.1102 cents