Scala analysis: moh
Rational mohajira, 11/9 generator
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 1458/1331 157.776178 2: 11/9 347.407941 undecimal neutral third 3: 162/121 505.184119 4: 121/81 694.815881 two (undecimal neutral third) 5: 18/11 852.592059 undecimal neutral sixth 6: 1331/729 1042.223822 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 1458/1331 157.7762 1: 1458/1331 157.7762 2: 14641/13122 189.6318 3: 1458/1331 157.7762 4: 14641/13122 189.6318 5: 1458/1331 157.7762 6: 14641/13122 189.6318 7: 1458/1331 157.7762
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 1458/1331 157.776 cents 1: 3 14641/13122 189.632 cents 2: 1 2125764/1771561 315.552 cents 2: 6 11/9 347.408 cents undecimal neutral third 3: 5 162/121 505.184 cents 3: 2 161051/118098 537.040 cents 4: 2 236196/161051 662.960 cents 4: 5 121/81 694.816 cents two (undecimal neutral third) 5: 6 18/11 852.592 cents undecimal neutral sixth 5: 1 1771561/1062882 884.448 cents 6: 3 26244/14641 1010.368 cents 6: 4 1331/729 1042.224 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 : 157.8 347.4 505.2 694.8 852.6 1042.2 1200.0 157.8 : 189.6 347.4 537.0 694.8 884.4 1042.2 1200.0 347.4 : 157.8 347.4 505.2 694.8 852.6 1010.4 1200.0 505.2 : 189.6 347.4 537.0 694.8 852.6 1042.2 1200.0 694.8 : 157.8 347.4 505.2 663.0 852.6 1010.4 1200.0 852.6 : 189.6 347.4 505.2 694.8 852.6 1042.2 1200.0 1042.2: 157.8 315.6 505.2 663.0 852.6 1010.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 157.7762 .. 189.6318 cents 19487171/19131876, 31.8556 cents 1458/1331, 157.7762 cents 2: 315.5524 .. 347.4079 cents 19487171/19131876, 31.8556 cents 125.92059 cents 3: 505.1841 .. 537.0397 cents 19487171/19131876, 31.8556 cents 1458/1331, 157.7762 cents 4: 662.9603 .. 694.8159 cents 19487171/19131876, 31.8556 cents 125.92059 cents 5: 852.5921 .. 884.4476 cents 19487171/19131876, 31.8556 cents 1458/1331, 157.7762 cents 6: 1010.3682 .. 1042.2238 cents 19487171/19131876, 31.8556 cents 125.92059 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 1458/1331, 157.7762 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 14641/13122, 189.6318 cents Average / Smallest step : 1.086530 Largest / Average step : 1.106185 Largest / Smallest step : 1.201904 Median interval of one step : 1458/1331, 157.7762 cents, amount: 4 Most common interval of one step : 1458/1331, 157.7762 cents, amount: 4 Least squares average step : 171.88365 cents, oct.: 1203.18556 cents Scale is strictly proper Scale has Myhill's property chromas: 19487171/19131876, 31.8556 cents and 125.92059 cents, ratio: 3.952858 generators: 2 of 347.40794 cents and 5 of 852.59206 cents ET pair of linear temperament : 31&38 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 791-tone equal temperament with octave 2/1 degrees: 104 229 333 458 562 687 791 generators: 229 and 562 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABA Step pattern size order : SLSLSLS Scale is a Constant Structure, by a margin of 125.92059 cents Scale diversity : 1.151368 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.840722 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 : 19487171/19131876, 31.8556 cents Most common intervals : 11/9, 347.4079 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 347.408 694.816 cents Most common triad is 0.0 347.408 852.592 cents, amount: 5 Number of recognisable fifths : 5, average 694.8159 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 Scale contains a complete diamond : 9 11 Formal octave complements present : 7 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 11 Odd number limit : 1771561 (O: 1771561 U: 1771561) Highest odd numerator or denominator: 1331 Scale harmonicity : 0.007038 Average absolute harmonicity : 0.164793 Specific harmonicity : 0.039627 Fundamental : 1/970299, -19.8881 octaves, 0.0003 Hz. Guide tone : 1940598, 20.8881 octaves, 507710048.772 Hz. Exponens Consonantiae : 1.882960E+12, 40.77614 octaves Euler's gradus suavitatis : 86 Sum of Mann's harmonic distance : 2693.0, average 384.71429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.49671, average 1.78524 Sum of Tenney's harmonic distance : 25.15174, average 3.59311 Vogel's harmonic complexity : 51.57143 Wille's k value : 885780 Wilson's harmonic complexity : 102 Rectangular lattice diameter : 18 Triangular lattice diameter : 12 Lattice compactness : 154.40095, average 5.51432 Lattice compactness (without 2's) : 152.05262, average 5.43045 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.57143 4 1 3: -6 .. 6 0.00000 24 11: -3 .. 3 0.00000 12 6 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 36 / 7 = 5.14286 Scale is JI-epimorphic with val: <7 10 22| Scale is weakly epimorphic with val: <7 10 23| Scale is weakly epimorphic with val: <7 10 24| Scale is weakly epimorphic with val: <7 10 25| Scale is weakly epimorphic with val: <7 10 26| Scale is weakly epimorphic with val: <7 11 23| Scale is JI-epimorphic with val: <7 11 24| = patent Scale is weakly epimorphic with val: <7 11 25| Scale is weakly epimorphic with val: <7 11 26| Scale is weakly epimorphic with val: <7 12 22| Scale is weakly epimorphic with val: <7 12 23| Scale is weakly epimorphic with val: <7 12 25| Scale is JI-epimorphic with val: <7 12 26|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 9.1016 c. M:-13.6524 c. Lebeng 24: 3 4 3 4 3 4 3 SP M ME I SD: 5.1841 c. M:-7.7762 c. Neutral Dorian, Misaelides 2nd Byzantine mode, Iced Fridgian, Maqam Sikah Baladi, Maqamic-7 31: 4 5 4 5 4 5 4 SP M ME I SD: 1.9583 c. M:-2.9375 c. Neutral Dorian, Maqamic-7 38: 5 6 5 6 5 6 5 SP M ME I SD: 0.0790 c. M:-0.1186 c. 411: 54 65 54 65 54 65 54 SP M DE I SD: 0.0746 c. M:-0.1119 c. 449: 59 71 59 71 59 71 59 SP M DE I SD: 0.0616 c. M:-0.0924 c. 487: 64 77 64 77 64 77 64 SP M DE I SD: 0.0506 c. M:-0.0760 c. 525: 69 83 69 83 69 83 69 SP M DE I SD: 0.0413 c. M:-0.0619 c. 563: 74 89 74 89 74 89 74 SP M DE I SD: 0.0331 c. M:-0.0497 c. 601: 79 95 79 95 79 95 79 SP M DE I SD: 0.0260 c. M:-0.0391 c. 639: 84 101 84 101 84 101 84 SP M DE I SD: 0.0198 c. M:-0.0297 c. 677: 89 107 89 107 89 107 89 SP M DE I SD: 0.0143 c. M:-0.0214 c. 715: 94 113 94 113 94 113 94 SP M DE I SD: 0.0093 c. M:-0.0139 c. 753: 99 119 99 119 99 119 99 SP M DE I SD: 0.0048 c. M: 0.0073 c. 791: 104 125 104 125 104 125 104 SP M DE I SD: 0.0008 c. M:-0.0012 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: 3.5696 cents 3 x x 4 x 5 x 6 S SD: 10.8530 cents 4 x 5 x 6 x 7:8 S SD: 20.8445 cents 5 x 6:7 x 8:9:10 S SD: 19.0881 cents 6 x 7:8:9:10:11:12 S SD: 14.5757 cents 7:8 x 9:10:11:13:14 SD: 24.7565 cents 8:9:10:11:12:13:15:16 SD: 12.8468 cents 9:10:11:12:13:15:16:18 SD: 12.1066 cents 10:11:12:13:15:16:18:20 SD: 10.9082 cents 12:13:15:16:18:20:22:24 SD: 7.8824 cents 17:19:21:23:25:28:31:34 SD: 7.4866 cents 18:20:22:24:27:29:33:36 SD: 5.5039 cents 22:24:27:29:33:36:40:44 SD: 4.3568 cents 30:33:37:40:45:49:55:60 SD: 3.0670 cents 32:35:39:43:48:52:58:64 SD: 2.9547 cents 41:45:50:55:61:67:75:82 SD: 1.4496 cents 53:58:65:71:79:87:97:106 SD: 1.4307 cents 63:69:77:84:94:103:115:126 SD: 1.0852 cents 85:93:104:114:127:139:155:170 SD: 0.6810 cents 126:138:154:169:188:206:230:252 SD: 0.5814 cents 148:162:181:198:221:242:270:296 SD: 0.4187 cents 189:207:231:253:282:309:345:378 SD: 0.3729 cents 239:262:292:320:357:391:436:478 SD: 0.2985 cents 251:275:307:336:375:411:458:502 SD: 0.2919 cents 275:301:336:368:411:450:502:550 SD: 0.2767 cents 283:310:346:379:423:463:517:566 SD: 0.2352 cents 292:320:357:391:436:478:533:584 SD: 0.2092 cents 316:346:386:423:472:517:577:632 SD: 0.1922 cents 401:439:490:537:599:656:732:802 SD: 0.1879 cents 419:459:512:561:626:686:765:838 SD: 0.1466 cents 504:552:616:675:753:825:920:1008 SD: 0.1384 cents 522:572:638:699:780:854:953:1044 SD: 0.1298 cents 567:621:693:759:847:928:1035:1134 SD: 0.0918 cents