Scala analysis: hexat11a
Hexatonic scale (2-2-2-2-1-2) in 11-tET
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 218.182 cents 218.181820 2: 436.364 cents 436.363640 3: 654.545 cents 654.545450 4: 872.727 cents 872.727270 5: 981.818 cents 981.818180 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 218.1818 cents 218.1818 1: 218.1818 cents 218.1818 2: 218.1818 cents 218.1818 3: 218.1818 cents 218.1818 4: 218.1818 cents 218.1818 5: 109.0909 cents 109.0909 6: 218.1818 cents 218.1818
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 109.09091 cents 1: 5 218.18182 cents 2: 2 327.27273 cents 2: 4 436.36364 cents 3: 3 545.45454 cents 3: 3 654.54545 cents 4: 4 763.63636 cents 4: 2 872.72727 cents 5: 5 981.81818 cents 5: 1 1090.90909 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 218.2 436.4 654.5 872.7 981.8 1200.0 218.2 : 218.2 436.4 654.5 763.6 981.8 1200.0 436.4 : 218.2 436.4 545.5 763.6 981.8 1200.0 654.5 : 218.2 327.3 545.5 763.6 981.8 1200.0 872.7 : 109.1 327.3 545.5 763.6 981.8 1200.0 981.8 : 218.2 436.4 654.5 872.7 1090.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 109.0909 .. 218.1818 cents 109.09091 cents 109.09091 cents 2: 327.2727 .. 436.3636 cents 109.09091 cents 109.09091 cents 3: 545.4545 .. 654.5454 cents 109.09091 cents 109.09090 cents 4: 763.6364 .. 872.7273 cents 109.09091 cents 109.09091 cents 5: 981.8182 .. 1090.9091 cents 109.09091 cents 109.09091 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 109.09091 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 218.18182 cents Average / Smallest step : 1.833333 Largest / Average step : 1.090909 Largest / Smallest step : 2.000000 Median interval of one step : 218.18182 cents, amount: 5 Most common interval of one step : 218.18182 cents, amount: 5 Least squares average step : 204.99500 cents, oct.: 1229.97003 cents Scale is strictly proper Scale has Myhill's property chromas: 109.09091 cents and 1/1, 0.0000 cents generators: 1 of 218.18182 cents and 5 of 981.81818 cents Scale is maximally even in 11-tone equal temperament ET pair of linear temperament : 11&59999989 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 11-tone equal temperament with octave 2/1 degrees: 2 4 6 8 9 11 generators: 2 and 9 Number of contiguous 1-step segments: 1 Scale is fully connected major-minor triadic in 11-tone equal temperament Scale is a Winograd/Gamer deep scale Step pattern alph. order: AAAABA Step pattern size order : LLLLSL Interval vector is [ 1 5 2 4 3 ] Scale is a Constant Structure, by a margin of 109.09090 cents Scale diversity : 1.338291 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.545455 Rothenberg efficiency : 0.777778 redundancy: 0.222222 Efficiency x scale size : 4.666667 Number of different interval sizes : 10 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 109.09090 cents Most common intervals : 218.18182 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 436.364 981.818 cents Most common triad is 0.0 218.182 981.818 cents, amount: 4 Number of recognisable fifths : 0 Formal octave complements present : 3 = 50.0000% Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 4-5 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 41.3278 c. M: 72.7273 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 8: 1 2 1 2 1 1 P D3 SD: 46.9086 c. M:-68.1818 c. 10: 2 1 2 2 1 2 SP B ME I SD: 42.4848 c. M: 76.3636 c. Lemba-6 11: 2 2 2 2 1 2 SP M ME SD: 0.0000 c. M:-0.0000 c. Schulter Hexatonic
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 23.7048 cents 3 x 4 x 5 x 6 S SD: 20.9228 cents 4 x 5:6 x 7:8 S SD: 17.5383 cents 5:6 x 7:8:9:10 S SD: 27.8948 cents 6:7:8:9:10:11:12 H SD: 19.0908 cents 7:8:9:10 x 12:14 S SD: 12.5129 cents 13:15:17:19:22:23:26 SD: 9.3560 cents 14:16:18:20:23:25:28 SD: 7.8232 cents 15:17:19:22:25:26:30 SD: 7.1084 cents 17:19:22:25:28:30:34 SD: 5.2956 cents 21:24:27:31:35:37:42 SD: 4.3962 cents 24:27:31:35:40:42:48 SD: 3.9255 cents 28:32:36:41:46:49:56 SD: 3.9014 cents 29:33:37:42:48:51:58 SD: 3.5028 cents 31:35:40:45:51:55:62 SD: 3.3784 cents 35:40:45:51:58:62:70 SD: 2.6157 cents 38:43:49:55:63:67:76 SD: 2.6144 cents 46:52:59:67:76:81:92 SD: 1.6219 cents 52:59:67:76:86:92:104 SD: 1.1805 cents 59:67:76:86:98:104:118 SD: 1.1288 cents 67:76:86:98:111:118:134 SD: 1.0151 cents 81:92:104:118:134:143:162 SD: 0.9880 cents 98:111:126:143:162:173:196 SD: 0.7279 cents 105:119:135:153:174:185:210 SD: 0.6682 cents 119:135:153:174:197:210:238 SD: 0.6280 cents 157:178:202:229:260:277:314 SD: 0.3077 cents 224:254:288:327:371:395:448 SD: 0.2785 cents 261:296:336:381:432:460:522 SD: 0.2189 cents 342:388:440:499:566:603:684 SD: 0.1361 cents 418:474:538:610:692:737:836 SD: 0.1310 cents 485:550:624:708:803:855:970 SD: 0.1129 cents 520:590:669:759:861:917:1040 SD: 0.1079 cents 566:642:728:826:937:998:1132 SD: 0.1038 cents