Scala analysis: xen18-erlich-meantone-07
5L 2s MOS for Meantone, L=193.44, s=117.25
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: 310.690 cents 310.690000 3: 504.130 cents 504.130000 4: 697.570 cents 697.570000 5: 891.010 cents 891.010000 6: 1008.260 cents 1008.260000 7: 1201.700 cents 1201.700000
SHOW/INTERVAL
0: 193.4400 cents 193.4400 1: 193.4400 cents 193.4400 2: 117.2500 cents 117.2500 3: 193.4400 cents 193.4400 4: 193.4400 cents 193.4400 5: 193.4400 cents 193.4400 6: 117.2500 cents 117.2500 7: 193.4400 cents 193.4400
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 117.25000 cents 1: 5 193.44000 cents 2: 4 310.69000 cents 2: 3 386.88000 cents 3: 6 504.13000 cents 3: 1 580.32000 cents 4: 1 621.38000 cents 4: 6 697.57000 cents 5: 3 814.82000 cents 5: 4 891.01000 cents 6: 5 1008.26000 cents 6: 2 1084.45000 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 : 193.4 310.7 504.1 697.6 891.0 1008.3 1201.7 193.4 : 117.3 310.7 504.1 697.6 814.8 1008.3 1201.7 310.7 : 193.4 386.9 580.3 697.6 891.0 1084.4 1201.7 504.1 : 193.4 386.9 504.1 697.6 891.0 1008.3 1201.7 697.6 : 193.4 310.7 504.1 697.6 814.8 1008.3 1201.7 891.0 : 117.2 310.7 504.1 621.4 814.8 1008.3 1201.7 1008.3: 193.4 386.9 504.1 697.6 891.0 1084.5 1201.7 1201.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 117.2500 .. 193.4400 cents 76.19000 cents 117.25000 cents 2: 310.6900 .. 386.8800 cents 76.19000 cents 117.25000 cents 3: 504.1300 .. 580.3200 cents 76.19000 cents 117.25000 cents 4: 621.3800 .. 697.5700 cents 76.19000 cents 41.06000 cents 5: 814.8200 .. 891.0100 cents 76.19000 cents 117.25000 cents 6: 1008.2600 .. 1084.4500 cents 76.19000 cents 117.25000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 117.25000 cents, class 1 Average step (divided formal octave): 171.6714 cents Largest one step interval : 193.44000 cents Average / Smallest step : 1.464149 Largest / Average step : 1.126804 Largest / Smallest step : 1.649808 Median interval of one step : 193.44000 cents, amount: 5 Most common interval of one step : 193.44000 cents, amount: 5 Least squares average step : 171.67143 cents, oct.: 1201.70000 cents Scale is strictly proper Scale has Myhill's property chromas: 76.19000 cents and 41.06000 cents, ratio: 1.855577 generators: 3 of 504.13000 cents and 4 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 1404-tone equal temperament with octave 1201.700 cents degrees: 226 363 589 815 1041 1178 1404 generators: 589 and 815 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 41.06000 cents Scale diversity : 1.281008 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.619589 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 : 41.06000 cents Most common intervals : 504.13000 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 504.130 1008.260 cents Most common triad is 0.0 504.130 697.570 cents, amount: 5 Number of recognisable fifths : 6, average 697.5700 cents Number of recognisable fourths : 6, average 504.1300 cents Scale contains two identical disjunct tetrachords Best fifths form a closed circle 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: 21.7686 c. M: 32.6529 c. Lebeng 12: 2 1 2 2 2 1 2 P M ME I SD: 6.8433 c. M: 10.2650 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 19: 3 2 3 3 3 2 3 SP M ME I SD: 3.6979 c. M: 5.5468 c. Nineteen-tone Dorian 31: 5 3 5 5 5 3 5 SP M DE I SD: 0.3826 c. M: 0.5739 c. Intense Diatonic Phrygian, M.Dorian 112: 18 11 18 18 18 11 18 SP M DE I SD: 0.3096 c. M: 0.4645 c. 143: 23 14 23 23 23 14 23 SP M DE I SD: 0.1596 c. M: 0.2394 c. 174: 28 17 28 28 28 17 28 SP M DE I SD: 0.0630 c. M: 0.0945 c. 205: 33 20 33 33 33 20 33 SP M DE I SD: 0.0044 c. M: 0.0066 c. 1404: 226 137 226 226 226 137 226 SP M DE I SD: 0.0040 c. M: 0.0059 c. 1609: 259 157 259 259 259 157 259 SP M DE I SD: 0.0029 c. M: 0.0043 c. 1814: 292 177 292 292 292 177 292 SP M DE I SD: 0.0021 c. M: 0.0031 c. 2019: 325 197 325 325 325 197 325 SP M DE I SD: 0.0014 c. M: 0.0021 c. 2224: 358 217 358 358 358 217 358 SP M DE I SD: 0.0009 c. M: 0.0013 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 1.7000 cents 2 x x x 3 x x 4 S SD: 2.3515 cents 3 x x 4 x 5 x 6 S SD: 3.0579 cents 4 x 5 x 6 x 7:8 S SD: 21.3543 cents 5 x 6:7 x 8:9:10 S SD: 22.1245 cents 6 x 7:8:9:10:11:12 S SD: 10.1557 cents 7:8 x 9:10:12:13:14 S SD: 22.6115 cents 8:9:10:11:12:13:14:16 S SD: 15.7667 cents 9:10:11:12:13:15:16:18 SD: 10.5148 cents 10:11:12:13:15:17:18:20 SD: 9.2555 cents 14:16:17:19:21:23:25:28 SD: 8.7040 cents 15:17:18:20:22:25:27:30 SD: 6.2726 cents 18:20:22:24:27:30:32:36 S SD: 5.9273 cents 24:27:29:32:36:40:43:48 SD: 3.1989 cents 36:40:43:48:54:60:64:72 SD: 2.7950 cents 41:46:49:55:61:69:73:82 SD: 2.6702 cents 42:47:50:56:63:70:75:84 SD: 2.0360 cents 50:56:60:67:75:84:90:100 SD: 2.0149 cents 51:57:61:68:76:85:91:102 SD: 1.8507 cents 61:68:73:82:91:102:109:122 SD: 1.6572 cents 62:69:74:83:93:104:111:124 SD: 1.6300 cents 67:75:80:90:100:112:120:134 SD: 1.3299 cents 76:85:91:102:114:127:136:152 SD: 1.0726 cents 77:86:92:103:115:129:138:154 SD: 0.8133 cents 101:113:121:135:151:169:181:202 SD: 0.5731 cents 153:171:183:205:229:256:274:306 SD: 0.4629 cents 177:198:212:237:265:296:317:354 SD: 0.4511 cents 204:228:244:273:305:341:365:408 SD: 0.4401 cents 254:284:304:340:380:425:455:508 SD: 0.3069 cents 296:331:354:396:443:495:530:593 SD: 0.2602 cents 355:397:425:475:531:594:636:711 SD: 0.2487 cents 373:417:446:499:558:624:668:747 SD: 0.2294 cents 391:437:468:523:585:654:700:783 SD: 0.1938 cents 397:444:475:531:594:664:711:795 SD: 0.1687 cents 447:500:535:598:669:748:800:895 SD: 0.1638 cents 514:575:615:688:769:860:920:1029 SD: 0.1513 cents 524:586:627:701:784:877:938:1049 SD: 0.1054 cents