Scala analysis: xen18-erlich-helmholtz-07
5L 2s MOS for Helmholtz, L=203.51, s=91.26
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 203.510 cents 203.510000 2: 294.770 cents 294.770000 3: 498.280 cents 498.280000 4: 701.790 cents 701.790000 5: 905.300 cents 905.300000 6: 996.560 cents 996.560000 7: 1200.070 cents 1200.070000
SHOW/INTERVAL
0: 203.5100 cents 203.5100 1: 203.5100 cents 203.5100 2: 91.2600 cents 91.2600 3: 203.5100 cents 203.5100 4: 203.5100 cents 203.5100 5: 203.5100 cents 203.5100 6: 91.2600 cents 91.2600 7: 203.5100 cents 203.5100
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 91.26000 cents 1: 5 203.51000 cents 2: 4 294.77000 cents 2: 3 407.02000 cents 3: 6 498.28000 cents 3: 1 610.53000 cents 4: 1 589.54000 cents 4: 6 701.79000 cents 5: 3 793.05000 cents 5: 4 905.30000 cents 6: 5 996.56000 cents 6: 2 1108.81000 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 7 0.0 : 203.5 294.8 498.3 701.8 905.3 996.6 1200.1 203.5 : 91.3 294.8 498.3 701.8 793.0 996.6 1200.1 294.8 : 203.5 407.0 610.5 701.8 905.3 1108.8 1200.1 498.3 : 203.5 407.0 498.3 701.8 905.3 996.6 1200.1 701.8 : 203.5 294.8 498.3 701.8 793.0 996.6 1200.1 905.3 : 91.3 294.8 498.3 589.5 793.0 996.6 1200.1 996.6 : 203.5 407.0 498.3 701.8 905.3 1108.8 1200.1 1200.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 91.2600 .. 203.5100 cents 112.25000 cents 91.26000 cents 2: 294.7700 .. 407.0200 cents 112.25000 cents 91.26000 cents 3: 498.2800 .. 610.5300 cents 112.25000 cents 91.26000 cents 4: 589.5400 .. 701.7900 cents 112.25000 cents -20.99000 cents 5: 793.0500 .. 905.3000 cents 112.25000 cents 91.26000 cents 6: 996.5600 .. 1108.8100 cents 112.25000 cents 91.26000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 91.26000 cents, class 1 Average step (divided formal octave): 171.4386 cents Largest one step interval : 203.51000 cents Average / Smallest step : 1.878573 Largest / Average step : 1.187072 Largest / Smallest step : 2.230002 Median interval of one step : 203.51000 cents, amount: 5 Most common interval of one step : 203.51000 cents, amount: 5 Least squares average step : 171.43857 cents, oct.: 1200.07000 cents Scale is not proper Scale has Myhill's property chromas: 112.25000 cents and 20.99000 cents, ratio: 5.347785 generators: 3 of 498.28000 cents and 4 of 701.79000 cents ET pair of linear temperament : 12&53 Scale is distributional even Scale is a mode of a 973-tone equal temperament with octave 1200.070 cents degrees: 165 239 404 569 734 808 973 generators: 404 and 569 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAABA Step pattern size order : LSLLLSL Scale is a Constant Structure, by a margin of 20.99000 cents Ratio Whole / Half tone : 2.230002 Scale diversity : 1.287953 Lumma stability : 0.456273 Lumma impropriety factor : 0.017491 Rothenberg efficiency : 0.761905 redundancy: 0.238095 Efficiency x scale size : 5.333333 Number of different interval sizes : 12 = 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 : 20.99000 cents Most common intervals : 498.28000 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 498.280 996.560 cents Most common triad is 0.0 498.280 701.790 cents, amount: 5 Number of recognisable fifths : 6, average 701.7900 cents Number of recognisable fourths : 6, average 498.2800 cents Scale contains two identical disjunct tetrachords Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 7 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 32.0714 c. M: 48.1071 c. Lebeng 11: 2 1 2 1 2 1 2 P M ME I SD: 31.6307 c. M: 47.2064 c. Superkleismic-7 12: 2 1 2 2 2 1 2 P M ME I SD: 3.4983 c. M: 5.2475 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 29: 5 2 5 5 5 2 5 N M DE I SD: 3.3986 c. M: 5.0979 c. 41: 7 3 7 7 7 3 7 N M DE I SD: 1.3800 c. M: 2.0700 c. 53: 9 4 9 9 9 4 9 N M DE I SD: 0.2755 c. M: 0.4132 c. 118: 20 9 20 20 20 9 20 N M DE I SD: 0.1083 c. M: 0.1625 c. 171: 29 13 29 29 29 13 29 N M DE I SD: 0.0106 c. M: 0.0160 c. 802: 136 61 136 136 136 61 136 N M DE I SD: 0.0069 c. M: 0.0103 c. 973: 165 74 165 165 165 74 165 N M DE I SD: 0.0038 c. M: 0.0057 c. 1144: 194 87 194 194 194 87 194 N M DE I SD: 0.0016 c. M: 0.0024 c. 1315: 223 100 223 223 223 100 223 N M DE I SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0700 cents 2 x x x 3 x x 4 S SD: 0.0896 cents 3 x x 4 x 5 x 6 S SD: 6.9809 cents 4 x 5 x 6 x 7:8 S SD: 23.9132 cents 5 x 6:7 x 8:9:10 S SD: 25.5861 cents 6 x 7:8:9:10:11:12 S SD: 10.5477 cents 7:8 x 9:11:12 x 14 SD: 21.9511 cents 8:9 x 11:12 x 14:16 SD: 11.9706 cents 10:11:12:13:15:17:18:20 SD: 9.5626 cents 12 x 14:16:18:20:21:24 S SD: 7.4277 cents 13:15 x 17:20:22:23:26 SD: 11.9557 cents 14:16:17:19:21:24:25:28 SD: 9.2884 cents 15:17:18:20:23:25:27:30 SD: 7.7602 cents 16:18:19:21:24:27:28:32 SD: 5.5941 cents 22:25:26:29:33:37:39:44 SD: 4.0545 cents 26:29:31:35:39:44:46:52 SD: 3.7212 cents 32:36:38:43:48:54:57:64 SD: 1.9781 cents 48:54:57:64:72:81:85:96 SD: 1.1120 cents 54:61:64:72:81:91:96:108 SD: 1.1102 cents 80:90:95:107:120:135:142:160 SD: 0.9564 cents 90:101:107:120:135:152:160:180 SD: 0.9263 cents 96:108:114:128:144:162:171:192 SD: 0.5811 cents 144:162:171:192:216:243:256:288 SD: 0.4119 cents 162:182:192:216:243:273:288:324 SD: 0.4015 cents 210:236:249:280:315:354:373:420 SD: 0.3998 cents 216:243:256:288:324:364:384:432 SD: 0.2911 cents 258:290:306:344:387:435:459:516 SD: 0.2534 cents 306:344:363:408:459:516:544:612 SD: 0.2230 cents 312:351:370:416:468:526:555:624 SD: 0.1970 cents 360:405:427:480:540:607:640:720 SD: 0.1875 cents 432:486:512:576:648:729:768:864 SD: 0.1559 cents 474:533:562:632:711:800:843:948 SD: 0.1431 cents 528:594:626:704:792:891:939:1056 SD: 0.1095 cents