Didacus: Difference between revisions
m Text replacement - "Prime-optimized" to "Norm-based" Tags: Mobile edit Mobile web edit |
m Added subroups to odd limits of infobox |
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| MOS scales = [[1L 5s]], [[6L 1s]], [[6L 7s]], [[6L 13s]], [[6L 19s]] | | MOS scales = [[1L 5s]], [[6L 1s]], [[6L 7s]], [[6L 13s]], [[6L 19s]] | ||
| Mapping = 1; 2 5 9 | | Mapping = 1; 2 5 9 | ||
| Odd limit 1 = 7 | Mistuning 1 = 1.22 | Complexity 1 = 13 | | Odd limit 1 = (2.5.7) 7 | Mistuning 1 = 1.22 | Complexity 1 = 13 | ||
| Odd limit 2 = 11 | Mistuning 2 = 4.13 | Complexity 2 = 19 | | Odd limit 2 = (2.5.7.11) 11 | Mistuning 2 = 4.13 | Complexity 2 = 19 | ||
}} | }} | ||
'''Didacus''' is a temperament of the [[2.5.7 subgroup]], tempering out [[3136/3125]], the hemimean comma, such that two intervals of [[7/5]] reach the same point as three intervals of [[5/4]]; the generator is therefore (7/5)/(5/4) = [[28/25]], two of which stack to 5/4 and three of which stack to 7/5, meaning that the [[4:5:7]] chord is "locked" to (0 2 5) in terms of logarithmic size and generator steps. It presents one of the most efficient traversals of the no-threes subgroup, especially considering that some tunings of didacus extend neatly to 11 and 13 (as explained below). | '''Didacus''' is a temperament of the [[2.5.7 subgroup]], tempering out [[3136/3125]], the hemimean comma, such that two intervals of [[7/5]] reach the same point as three intervals of [[5/4]]; the generator is therefore (7/5)/(5/4) = [[28/25]], two of which stack to 5/4 and three of which stack to 7/5, meaning that the [[4:5:7]] chord is "locked" to (0 2 5) in terms of logarithmic size and generator steps. It presents one of the most efficient traversals of the no-threes subgroup, especially considering that some tunings of didacus extend neatly to 11 and 13 (as explained below). | ||