Scala analysis: prop19_7a
Diatonic major
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 189.474 cents 189.473684 2: 378.947 cents 378.947368 3: 505.263 cents 505.263158 4: 694.737 cents 694.736842 5: 884.211 cents 884.210526 6: 1073.684 cents 1073.684211 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 126.3158 cents 126.3158 1: 189.4737 cents 189.4737 2: 189.4737 cents 189.4737 3: 126.3158 cents 126.3158 4: 189.4737 cents 189.4737 5: 189.4737 cents 189.4737 6: 189.4737 cents 189.4737 7: 126.3158 cents 126.3158
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 126.31579 cents 1: 5 189.47368 cents 2: 4 315.78947 cents 2: 3 378.94737 cents 3: 6 505.26316 cents 3: 1 568.42105 cents 4: 1 631.57895 cents 4: 6 694.73684 cents 5: 3 821.05263 cents 5: 4 884.21053 cents 6: 5 1010.52632 cents 6: 2 1073.68421 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 : 189.5 378.9 505.3 694.7 884.2 1073.7 1200.0 189.5 : 189.5 315.8 505.3 694.7 884.2 1010.5 1200.0 378.9 : 126.3 315.8 505.3 694.7 821.1 1010.5 1200.0 505.3 : 189.5 378.9 568.4 694.7 884.2 1073.7 1200.0 694.7 : 189.5 378.9 505.3 694.7 884.2 1010.5 1200.0 884.2 : 189.5 315.8 505.3 694.7 821.1 1010.5 1200.0 1073.7: 126.3 315.8 505.3 631.6 821.1 1010.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 126.3158 .. 189.4737 cents 63.15789 cents 126.31579 cents 2: 315.7895 .. 378.9474 cents 63.15789 cents 126.31579 cents 3: 505.2632 .. 568.4211 cents 63.15790 cents 126.31579 cents 4: 631.5789 .. 694.7368 cents 63.15790 cents 63.15789 cents 5: 821.0526 .. 884.2105 cents 63.15789 cents 126.31579 cents 6: 1010.5263 .. 1073.6842 cents 63.15790 cents 126.31579 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 126.31579 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 189.47368 cents Average / Smallest step : 1.357143 Largest / Average step : 1.105263 Largest / Smallest step : 1.500000 Median interval of one step : 189.47368 cents, amount: 5 Most common interval of one step : 189.47368 cents, amount: 5 Least squares average step : 175.03759 cents, oct.: 1225.26316 cents Scale is strictly proper Scale has Myhill's property chromas: 63.15789 cents and 63.15790 cents, ratio: 1.000000 generators: 3 of 505.26316 cents and 4 of 694.73684 cents Scale is maximally even in 19-tone equal temperament ET pair of linear temperament : 19&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 19-tone equal temperament with octave 1200.000 cents degrees: 3 6 8 11 14 17 19 generators: 8 and 11 Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 19-tone equal temperament Step pattern alph. order: AABAAAB Step pattern size order : LLSLLLS Interval vector is [ 0 2 5 0 4 3 0 6 1 ] Scale is a Constant Structure, by a margin of 63.15789 cents Ratio Whole / Half tone : 1.500000 ( 3/2 ) Scale diversity : 1.261564 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.684211 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 : 63.15789 cents Most common intervals : 505.26316 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 505.263 1010.526 cents Most common triad is 0.0 505.263 694.737 cents, amount: 5 Number of recognisable fifths : 6, average 694.7368 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 : 3 = 42.8571% Limited inverse transpositions : 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 4-5 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 25.5196 c. M: 45.1128 c. Lebeng 12: 2 2 1 2 2 2 1 P M ME S SD: 14.8865 c. M:-26.3158 c. G.Lydian, M.Ionian, M.Hypolydian, Major, Bilaval That, Mela Shankarabharanam, Raga Atana, Ghana Heptatonic, Peruvian Major, Matzore, Rast ascending: Greece, 4th plagal Byzantine, Ararai: Ethiopia, Makam Cargah, Ajam Ashiran, Dastgah-e Mahur, Dastgah-e Rast Panjgah, Xin: China, DS2, Heptatonia prima 19: 3 3 2 3 3 3 2 SP M ME S SD: 0.0000 c. M: 0.0000 c. Nineteen-tone Major, Ionian
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 3.6091 cents 3 x x 4 x 5 x 6 S SD: 2.4066 cents 4 x 5 x 6:7 x 8 S SD: 21.3104 cents 5 x 6:7 x 8:9:10 S SD: 26.9032 cents 6:7 x 8:9:10:11:12 S SD: 13.6281 cents 7:8:9 x 10:12:13:14 S SD: 19.1881 cents 8:9:10:11:12:13:15:16 SD: 9.6433 cents 12:13:15:16:18:20:22:24 SD: 8.2573 cents 15:17:19:20:22:25:28:30 SD: 7.5077 cents 16:18:20:21:24:27:30:32 S SD: 6.6784 cents 17:19:21:23:25:28:32:34 SD: 6.5624 cents 18:20:22:24:27:30:33:36 S SD: 5.9598 cents 20:22:25:27:30:33:37:40 SD: 5.1145 cents 24:27:30:32:36:40:45:48 S SD: 3.4393 cents 33:37:41:44:49:55:61:66 SD: 2.6525 cents 36:40:45:48:54:60:67:72 SD: 2.0771 cents 44:49:55:59:66:73:82:88 SD: 2.0168 cents 45:50:56:60:67:75:84:90 SD: 1.9242 cents 53:59:66:71:79:88:99:106 SD: 1.6617 cents 61:68:76:82:91:102:113:122 SD: 1.6409 cents 69:77:86:92:103:115:128:138 SD: 1.2328 cents 77:86:96:103:115:128:143:154 SD: 0.8733 cents 114:127:142:153:170:190:212:228 SD: 0.8311 cents 122:136:152:163:182:203:227:244 SD: 0.8125 cents 123:137:153:165:184:205:229:246 SD: 0.8099 cents 127:142:158:170:190:212:236:254 SD: 0.8025 cents 130:145:162:174:194:217:242:260 SD: 0.6359 cents 138:154:172:185:206:230:257:276 SD: 0.6354 cents 147:164:183:197:220:245:273:294 SD: 0.5956 cents 148:165:184:198:221:247:275:296 SD: 0.5569 cents 156:174:194:209:233:260:290:312 SD: 0.2803 cents 233:260:290:312:348:388:433:466 SD: 0.2353 cents 336:375:418:450:502:560:625:672 SD: 0.2127 cents 348:388:433:466:520:580:647:696 SD: 0.2027 cents 363:405:452:486:542:605:675:726 SD: 0.1497 cents 510:569:635:683:762:850:948:1020 SD: 0.1317 cents 519:579:646:695:775:865:965:1038 SD: 0.0954 cents