42edo: Difference between revisions
Tag: Undo |
fix step size in infobox, formatting |
||
| Line 1: | Line 1: | ||
{{Infobox ET | {{Infobox ET | ||
| Prime factorization = 2 × 3 × 7 | | Prime factorization = 2 × 3 × 7 | ||
| Step size = | | Step size = 28.57143¢ | ||
| Fifth = 25\42 | | Fifth = 25\42 (714¢) | ||
| Major 2nd = 8\42 = | | Major 2nd = 8\42 = (229¢) (→[[21edo|4\21]]) | ||
| Minor 2nd = 1\42 = | | Minor 2nd = 1\42 = (29¢) | ||
| Augmented 1sn = 7\42 = 200¢ (→[[6edo|1\6]]) | | Augmented 1sn = 7\42 = (200¢) (→[[6edo|1\6]]) | ||
}} | }} | ||
The '''42edo''' is the equal division of the octave into 42 equal parts of 28. | The '''42edo''' is the equal division of the octave into 42 equal parts of 28.6 [[cent]]s each. It has a fifth (the step of which being coprime to its cardinality, this being a first for a composite equal division of cardinality 7''n'') and a third both over 12 cents sharp, using the same 400 cent interval to represent [[5/4]] as does [[12edo]], which means it [[tempering out|tempers out]] 128/125. In the [[7-limit]], it tempers out 64/63 and [[126/125]], making it a tuning supporting [[augene]] temperament. | ||
While not an accurate tuning on the full 7-limit, it does an excellent job on the 2.9.15.7.33.39 [[k*N subgroups|2*42 subgroup]], having the same tuning on it as does [[84edo]]. On this subgroup 42 has the same [[comma]]s as 84. | While not an accurate tuning on the full 7-limit, it does an excellent job on the 2.9.15.7.33.39 [[k*N subgroups|2*42 subgroup]], having the same tuning on it as does [[84edo]]. On this subgroup 42 has the same [[comma]]s as 84. | ||