1547edo: Difference between revisions

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In the 5-limit, it supports [[gross]], which is a very high-accuracy temperament. The 118-tone [[maximal evenness]] scale produced by gross is [[concoctic]], since it uses 118\1547 as the generator. In addition, 1547edo tempers out the [[septendecima]] and thus supports the [[chlorine]] temperament in 5-limit and also in the 7-limit. 1547edo tempers out the 5-limit comma {{monzo| 236 -61 -60 }}, thus associating a stack of sixty [[15/8]]'s with [[4/3]], and sixty-one of them make [[5/4]].

In the 7-limit, it provides the [[optimal patent val]] for 7-limit [[brahmagupta]], the 441 & 1106 temperament, and supports an alternative 11-limit extension to it. It also supports [[semidimi]], the 171 & 1376 temperament. In the 11-limit, it tempers out 117649/117612, and is a tuning for the rank-3 temperament [[heimdall]]. In higher limits, it supports 91th-octave temperament [[protactinium]].

In the 7-limit, it provides the [[optimal patent val]] for 7-limit [[brahmagupta]], the 441 & 1106 temperament, and supports an alternative 11-limit extension to it. It also supports [[semidimi]], the 171 & 1376 temperament.

In the 11-limit, 1547edo provides the optimal patent val for the [[aluminium]] temperament, which maps 135/128 to 1/13th of the occtave. It also tempers out 117649/117612, and is a tuning for the rank-3 temperament [[heimdall]]. In higher limits, it supports 91th-octave temperament [[protactinium]].

=== Prime harmonics ===

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 In the 5-limit, it supports [[gross]], which is a very high-accuracy temperament. The 118-tone [[maximal evenness]] scale produced by gross is [[concoctic]], since it uses 118\1547 as the generator. In addition, 1547edo tempers out the [[septendecima]] and thus supports the [[chlorine]] temperament in 5-limit and also in the 7-limit. 1547edo tempers out the 5-limit comma {{monzo| 236 -61 -60 }}, thus associating a stack of sixty [[15/8]]'s with [[4/3]], and sixty-one of them make [[5/4]].
-In the 7-limit, it provides the [[optimal patent val]] for 7-limit [[brahmagupta]], the 441 & 1106 temperament, and supports an alternative 11-limit extension to it. It also supports [[semidimi]], the 171 & 1376 temperament. In the 11-limit, it tempers out 117649/117612, and is a tuning for the rank-3 temperament [[heimdall]]. In higher limits, it supports 91th-octave temperament [[protactinium]].
+In the 7-limit, it provides the [[optimal patent val]] for 7-limit [[brahmagupta]], the 441 & 1106 temperament, and supports an alternative 11-limit extension to it. It also supports [[semidimi]], the 171 & 1376 temperament.
+In the 11-limit, 1547edo provides the optimal patent val for the [[aluminium]] temperament, which maps 135/128 to 1/13th of the occtave. It also tempers out 117649/117612, and is a tuning for the rank-3 temperament [[heimdall]]. In higher limits, it supports 91th-octave temperament [[protactinium]].
 === Prime harmonics ===