Scala analysis: pelog_pa
"Blown fifth" pelog, von Hornbostel, type a.
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 156.000 cents 156.000000 2: 312.000 cents 312.000000 3: 468.000 cents 468.000000 4: 678.000 cents 678.000000 5: 834.000 cents 834.000000 6: 990.000 cents 990.000000 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 210.0000 cents 210.0000 1: 156.0000 cents 156.0000 2: 156.0000 cents 156.0000 3: 156.0000 cents 156.0000 4: 210.0000 cents 210.0000 5: 156.0000 cents 156.0000 6: 156.0000 cents 156.0000 7: 210.0000 cents 210.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 156.00000 cents 1: 2 210.00000 cents 2: 3 312.00000 cents 2: 4 366.00000 cents 3: 1 468.00000 cents 3: 6 522.00000 cents 4: 6 678.00000 cents 4: 1 732.00000 cents 5: 4 834.00000 cents 5: 3 888.00000 cents 6: 2 990.00000 cents 6: 5 1044.00000 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 : 156.0 312.0 468.0 678.0 834.0 990.0 1200.0 156.0 : 156.0 312.0 522.0 678.0 834.0 1044.0 1200.0 312.0 : 156.0 366.0 522.0 678.0 888.0 1044.0 1200.0 468.0 : 210.0 366.0 522.0 732.0 888.0 1044.0 1200.0 678.0 : 156.0 312.0 522.0 678.0 834.0 990.0 1200.0 834.0 : 156.0 366.0 522.0 678.0 834.0 1044.0 1200.0 990.0 : 210.0 366.0 522.0 678.0 888.0 1044.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 156.0000 .. 210.0000 cents 54.00000 cents 156.00000 cents 2: 312.0000 .. 366.0000 cents 54.00000 cents 102.00000 cents 3: 468.0000 .. 522.0000 cents 54.00000 cents 102.00000 cents 4: 678.0000 .. 732.0000 cents 54.00000 cents 156.00000 cents 5: 834.0000 .. 888.0000 cents 54.00000 cents 102.00000 cents 6: 990.0000 .. 1044.0000 cents 54.00000 cents 102.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 156.00000 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 210.00000 cents Average / Smallest step : 1.098901 Largest / Average step : 1.225000 Largest / Smallest step : 1.346154 Median interval of one step : 156.00000 cents, amount: 5 Most common interval of one step : 156.00000 cents, amount: 5 Least squares average step : 167.18571 cents, oct.: 1170.30000 cents Scale is strictly proper Scale has Myhill's property chromas: 54.00000 cents and 102.00000 cents, ratio: 1.888889 generators: 522.00000 cents and 4 of 678.00000 cents ET pair of linear temperament : 16&23 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 200-tone equal temperament with octave 2/1 degrees: 26 52 78 113 139 165 200 generators: 87 and 113 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABAAB Step pattern size order : SSSLSSL Interval vector is [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 ] Scale is a Constant Structure, by a margin of 102.00000 cents Scale diversity : 1.227543 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.730000 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 : 54.00000 cents Most common intervals : 522.00000 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 522.000 1044.000 cents Most common triad is 0.0 522.000 678.000 cents, amount: 5 Number of recognisable fifths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% Limited inverse transpositions : 3 Inversional symmetry on degrees : 5 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 27.8143 c. M:-46.2857 c. Lebeng 12: 2 1 2 2 1 2 2 P M ME S SD: 26.3059 c. M:-44.0000 c. G.M.Hypodorian, G.M.Aeolian, G.Hyperphrygian, Natural Minor, Melodic Minor descending, Asavari That, Mela Natabhairavi, Raga Jaunpuri, Adana, Darbari, Dhanyasi, Jingla, Gregorian nr.2, Makam Buselik, Nihavend, Peruvian Minor, Se, Chiao: China, Geez, Ezel: Ethiopia, Kiourdi descending: Greece, Cushak: Armenia 13: 2 1 2 2 2 2 2 SP M ME S SD: 23.1763 c. M: 35.0769 c. Tamashian 15: 2 2 2 2 2 2 3 SP M ME S SD: 23.0651 c. M: 38.0000 c. 16: 2 2 2 3 2 2 3 SP M ME S SD: 10.8167 c. M: 18.0000 c. Antilydian 23: 3 3 3 4 3 3 4 SP M ME S SD: 0.9406 c. M:-1.5652 c. Pelogic-7, Antilydian 108: 14 14 14 19 14 14 19 SP M DE S SD: 0.8012 c. M: 1.3333 c. 131: 17 17 17 23 17 17 23 SP M DE S SD: 0.4954 c. M: 0.8244 c. 154: 20 20 20 27 20 20 27 SP M DE S SD: 0.2810 c. M: 0.4675 c. 177: 23 23 23 31 23 23 31 SP M DE S SD: 0.1222 c. M: 0.2034 c. 200: 26 26 26 35 26 26 35 SP M DE S SD: 0.0000 c. M:-0.0000 c.
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: 11.9775 cents 3 x x 4 x 5 x 6 S SD: 19.5468 cents 4 x 5 x 6 x 7:8 S SD: 20.2248 cents 5 x 6 x 7:8:9:10 S SD: 20.3031 cents 6 x 7:8:9:10:11:12 S SD: 16.3071 cents 7:8 x 9:10:11:12:14 S SD: 21.2679 cents 8:9:10 x 12:13:14:16 S SD: 15.7080 cents 9:10:11:12:13:15:16:18 SD: 12.0705 cents 10:11:12:13:15:16:18:20 SD: 6.4404 cents 19:21:23:25:28:31:34:38 SD: 5.0155 cents 21:23:25:28:31:34:37:42 SD: 4.7620 cents 29:32:35:38:43:47:51:58 SD: 3.4156 cents 31:34:37:41:46:50:55:62 SD: 2.7843 cents 40:44:48:52:59:65:71:80 SD: 2.7289 cents 42:46:50:55:62:68:74:84 SD: 2.0690 cents 52:57:62:68:77:84:92:104 SD: 1.4233 cents 61:67:73:80:90:99:108:122 SD: 1.3257 cents 65:71:78:85:96:105:115:130 SD: 1.1371 cents 71:78:85:93:105:115:126:142 SD: 1.0798 cents 87:95:104:114:129:141:154:174 SD: 0.9470 cents 96:105:115:126:142:155:170:192 SD: 0.7906 cents 106:116:127:139:157:172:188:212 SD: 0.7371 cents 126:138:151:165:186:204:223:252 SD: 0.6727 cents 136:149:163:178:201:220:241:272 SD: 0.5657 cents 157:172:188:206:232:254:278:314 SD: 0.5492 cents 158:173:189:207:234:256:280:316 SD: 0.4669 cents 171:187:205:224:253:277:303:342 SD: 0.3728 cents 202:221:242:265:299:327:358:404 SD: 0.3511 cents 213:233:255:279:315:345:377:426 SD: 0.3072 cents 223:244:267:292:330:361:395:446 SD: 0.2058 cents 380:416:455:498:562:615:673:760 SD: 0.1617 cents 415:454:497:544:614:672:735:830 SD: 0.1447 cents 425:465:509:557:629:688:753:850 SD: 0.1255 cents 486:532:582:637:719:787:861:972 SD: 0.1223 cents 551:603:660:722:815:892:976:1102 SD: 0.0904 cents