Scala analysis: hemi6
Hemiwuerschmidt[6] in pure 7s tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 193.765 cents 193.765181 2: 387.530 cents 387.530363 3: 581.296 cents 581.295544 4: 775.061 cents 775.060725 5: 968.826 cents 968.825906 6: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 231.1741 cents 231.1741 1: 193.7652 cents 193.7652 2: 193.7652 cents 193.7652 3: 193.7652 cents 193.7652 4: 193.7652 cents 193.7652 5: 193.7652 cents 193.7652 6: 231.1741 cents 231.1741
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 193.76518 cents 1: 1 231.17409 cents 2: 4 387.53036 cents 2: 2 424.93927 cents 3: 3 581.29554 cents 3: 3 618.70446 cents 4: 2 775.06073 cents 4: 4 812.46964 cents 5: 1 968.82591 cents 5: 5 1006.23482 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 : 193.8 387.5 581.3 775.1 968.8 1200.0 193.8 : 193.8 387.5 581.3 775.1 1006.2 1200.0 387.5 : 193.8 387.5 581.3 812.5 1006.2 1200.0 581.3 : 193.8 387.5 618.7 812.5 1006.2 1200.0 775.1 : 193.8 424.9 618.7 812.5 1006.2 1200.0 968.8 : 231.2 424.9 618.7 812.5 1006.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 193.7652 .. 231.1741 cents 37.40891 cents 193.76518 cents 2: 387.5304 .. 424.9393 cents 37.40891 cents 156.35627 cents 3: 581.2955 .. 618.7045 cents 37.40891 cents 156.35627 cents 4: 775.0607 .. 812.4696 cents 37.40891 cents 156.35627 cents 5: 968.8259 .. 1006.2348 cents 37.40891 cents 156.35627 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 193.76518 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 231.17409 cents Average / Smallest step : 1.032177 Largest / Average step : 1.155870 Largest / Smallest step : 1.193063 Median interval of one step : 193.76518 cents, amount: 5 Most common interval of one step : 193.76518 cents, amount: 5 Least squares average step : 196.23170 cents, oct.: 1177.39022 cents Scale is strictly proper Scale has Myhill's property chromas: 37.40891 cents and 156.35627 cents, ratio: 4.179653 generators: 1 of 193.76518 cents and 1006.23482 cents ET pair of linear temperament : 31&161 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1251-tone equal temperament with octave 1200.000 cents degrees: 202 404 606 808 1010 1251 generators: 202 and 1049 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAAAAB Step pattern size order : SSSSSL Scale is a Constant Structure, by a margin of 156.35627 cents Scale diversity : 1.160943 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.844130 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 : 37.40891 cents Most common intervals : 193.76518 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 387.530 1006.235 cents Number of recognisable fifths : 0 Steps are increasing Formal octave complements present : 1 = 16.6667% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 5-6 -- Rational properties --
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 18.8769 c. M:-31.1741 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 19: 3 3 3 3 3 4 SP M ME SD: 12.9932 c. M: 21.4575 c. Yasser's Hexad, Spell-6 25: 4 4 4 4 4 5 SP M ME SD: 5.3444 c. M: 8.8259 c. Hemithirds-6, Spell-6 31: 5 5 5 5 5 6 SP M ME SD: 0.6564 c. M: 1.0840 c. Hemithirds-6, Roulette-6 99: 16 16 16 16 16 19 SP M DE SD: 0.5275 c. M:-0.8711 c. Hemithirds-6 130: 21 21 21 21 21 25 SP M DE SD: 0.2452 c. M:-0.4049 c. 161: 26 26 26 26 26 31 SP M DE SD: 0.0716 c. M:-0.1182 c. 192: 31 31 31 31 31 37 SP M DE SD: 0.0460 c. M: 0.0759 c. 353: 57 57 57 57 57 68 SP M DE SD: 0.0076 c. M:-0.0126 c. 898: 145 145 145 145 145 173 SP M DE SD: 0.0038 c. M: 0.0063 c. 1251: 202 202 202 202 202 241 SP M DE SD: 0.0006 c. M: 0.0010 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x 4 S SD: 36.5529 cents 3 x x 4 x 5:6 S SD: 39.5325 cents 4 x 5 x 6:7:8 S SD: 18.2790 cents 5 x 6:7:8:9:10 S SD: 19.0158 cents 6:7 x 8:9:11:12 SD: 31.0521 cents 7:8:9:10:11:12:14 S SD: 13.2289 cents 8:9:10:11:13:14:16 SD: 12.1209 cents 12:13:15:17:19:21:24 SD: 10.4602 cents 15:17:19:21:23:26:30 SD: 8.3362 cents 16:18:20:22:25:28:32 SD: 5.2941 cents 23:26:29:32:36:40:46 SD: 4.5331 cents 25:28:31:35:39:44:50 SD: 3.1644 cents 32:36:40:45:50:56:64 SD: 2.2975 cents 43:48:54:60:67:75:86 SD: 2.1361 cents 48:54:60:67:75:84:96 SD: 1.8699 cents 52:58:65:73:81:91:104 SD: 1.8232 cents 60:67:75:84:94:105:120 SD: 0.6484 cents 108:121:135:151:169:189:216 SD: 0.5698 cents 128:143:160:179:200:224:256 SD: 0.5676 cents 135:151:169:189:211:236:270 SD: 0.5365 cents 143:160:179:200:224:250:286 SD: 0.4968 cents 168:188:210:235:263:294:336 SD: 0.2986 cents 228:255:285:319:357:399:456 SD: 0.2865 cents 271:303:339:379:424:474:542 SD: 0.2050 cents 303:339:379:424:474:530:606 SD: 0.1922 cents 363:406:454:508:568:635:726 SD: 0.1513 cents 439:491:549:614:687:768:878 SD: 0.1479 cents 549:614:687:768:859:961:1098 SD: 0.1374 cents