Scala analysis: xen18-erlich-meantone-05
2L 3s MOS for Meantone, L=310.69, s=193.44
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 193.440 cents 193.440000 2: 504.130 cents 504.130000 3: 697.570 cents 697.570000 4: 1008.260 cents 1008.260000 5: 1201.700 cents 1201.700000
SHOW/INTERVAL
0: 193.4400 cents 193.4400 1: 193.4400 cents 193.4400 2: 310.6900 cents 310.6900 3: 193.4400 cents 193.4400 4: 310.6900 cents 310.6900 5: 193.4400 cents 193.4400
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 193.44000 cents 1: 2 310.69000 cents 2: 1 386.88000 cents 2: 4 504.13000 cents 3: 4 697.57000 cents 3: 1 814.82000 cents 4: 2 891.01000 cents 4: 3 1008.26000 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 0.0 : 193.4 504.1 697.6 1008.3 1201.7 193.4 : 310.7 504.1 814.8 1008.3 1201.7 504.1 : 193.4 504.1 697.6 891.0 1201.7 697.6 : 310.7 504.1 697.6 1008.3 1201.7 1008.3: 193.4 386.9 697.6 891.0 1201.7 1201.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 193.4400 .. 310.6900 cents 117.25000 cents 193.44000 cents 2: 386.8800 .. 504.1300 cents 117.25000 cents 76.19000 cents 3: 697.5700 .. 814.8200 cents 117.25000 cents 193.44000 cents 4: 891.0100 .. 1008.2600 cents 117.25000 cents 76.19000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 193.44000 cents, class 1 Average step (divided formal octave): 240.3400 cents Largest one step interval : 310.69000 cents Average / Smallest step : 1.242452 Largest / Average step : 1.292710 Largest / Smallest step : 1.606131 Median interval of one step : 193.44000 cents, amount: 3 Most common interval of one step : 193.44000 cents, amount: 3 Least squares average step : 242.47182 cents, oct.: 1212.35909 cents Scale is strictly proper Scale has Myhill's property chromas: 117.25000 cents and 76.19000 cents, ratio: 1.538916 generators: 2 of 504.13000 cents and 3 of 697.57000 cents ET pair of linear temperament : 12&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 205-tone equal temperament with octave 1201.700 cents degrees: 33 86 119 172 205 generators: 86 and 119 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABA Step pattern size order : SLSLS Scale is a Constant Structure, by a margin of 76.19000 cents Scale diversity : 1.295452 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.609720 Rothenberg efficiency : 0.800000 redundancy: 0.200000 Efficiency x scale size : 4.000000 Number of different interval sizes : 8 = 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 : 76.19000 cents Most common intervals : 504.13000 cents & inv., amount: 4 Scale is a chain of 2 triads 0.0 504.130 1008.260 cents Most common triad is 0.0 504.130 697.570 cents, amount: 3 Number of recognisable fifths : 4, average 697.5700 cents Number of recognisable fourths : 4, average 504.1300 cents Best fifths form a closed circle Formal octave complements present : 5 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 2-3 -- Rational properties --
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 33.1633 c. M:-46.9000 c. 7: 1 2 1 2 1 P M ME I SD: 15.3927 c. M:-21.7686 c. Thai mode 2 12: 2 3 2 3 2 SP M ME I SD: 4.8390 c. M:-6.8433 c. Suspended Pentatonic, Raga Madhyamavati, Madhmat Sarang, Megh, Egyptian, Shang, Rui Bin, Jin Yu, Qing Yu: China, Yo: Japan, Ngu Cung Dao: Vietnam, Yematebela wofe: Ethiopia 19: 3 5 3 5 3 SP M DE I SD: 2.6148 c. M:-3.6979 c. Nineteen-tone Suspended Pentatonic 31: 5 8 5 8 5 SP M DE I SD: 0.2705 c. M:-0.3826 c. 112: 18 29 18 29 18 SP M DE I SD: 0.2190 c. M:-0.3096 c. 143: 23 37 23 37 23 SP M DE I SD: 0.1128 c. M:-0.1596 c. 174: 28 45 28 45 28 SP M DE I SD: 0.0445 c. M: 0.0630 c. 205: 33 53 33 53 33 SP M DE I SD: 0.0031 c. M:-0.0044 c. 1404: 226 363 226 363 226 SP M DE I SD: 0.0028 c. M: 0.0040 c. 1609: 259 416 259 416 259 SP M DE I SD: 0.0020 c. M: 0.0029 c. 1814: 292 469 292 469 292 SP M DE I SD: 0.0015 c. M:-0.0021 c. 2019: 325 522 325 522 325 SP M DE I SD: 0.0010 c. M:-0.0014 c. 2224: 358 575 358 575 358 SP M DE I SD: 0.0006 c. M:-0.0009 c.
FIT/HARMONIC
1 x x x x 2 S SD: 1.7000 cents 2 x x 3 x 4 S SD: 2.3515 cents 3 x 4 x 5:6 S SD: 41.3541 cents 4 x 5:6:7:8 S SD: 31.0824 cents 5:6:7 x 9:10 SD: 36.3722 cents 6:7:8:9:11:12 SD: 16.9005 cents 8:9:11:12:14:16 SD: 12.5116 cents 10:11:13:15:18:20 SD: 11.6782 cents 14:16:19:21:25:28 SD: 9.0971 cents 15:17:20:22:27:30 SD: 8.6236 cents 16:18:21:24:29:32 SD: 8.2421 cents 18:20:24:27:32:36 SD: 3.6280 cents 24:27:32:36:43:48 SD: 2.6112 cents 42:47:56:63:75:84 SD: 1.7964 cents 59:66:79:88:106:118 SD: 1.6870 cents 67:75:90:100:120:134 SD: 1.6837 cents 68:76:91:102:122:136 SD: 1.2072 cents 77:86:103:115:138:154 SD: 0.9052 cents 101:113:135:151:181:202 SD: 0.6836 cents 109:122:146:163:195:218 SD: 0.6752 cents 119:133:159:178:213:238 SD: 0.6342 cents 153:171:205:229:274:306 SD: 0.6315 cents 177:198:237:265:317:354 SD: 0.5097 cents 195:218:261:292:349:390 SD: 0.4780 cents 228:255:305:341:408:456 SD: 0.4141 cents 272:304:364:407:487:545 SD: 0.3505 cents 296:331:396:443:530:593 SD: 0.2708 cents 373:417:499:558:668:747 SD: 0.1992 cents 381:426:510:570:682:763 SD: 0.1975 cents 405:453:542:606:725:811 SD: 0.1489 cents 482:539:645:721:863:965 SD: 0.0970 cents 524:586:701:784:938:1049 SD: 0.0853 cents