1547edo: Difference between revisions

Line 7:

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 ~~supports~~ [[~~semidimi~~]]~~. Another edo which is quite strong in the~~ 7-limit ~~is like 1547edo is 441edo~~, and ~~1547edo thus~~ supports ~~the~~ [[~~brahmagupta~~]] temperament ~~produced by merging 441 & 1547~~.

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 11-limit, it is a tuning for the rank-3 temperament [[heimdall]].

In higher limits, it supports 91th-octave temperament [[protactinium]].

=== Prime harmonics ===

Line 17:

Line 13:

=== Divisors ===

1547 has subset edos {{EDOs| 7, 13, 17, 91, 119, and 221 }}.

== Regular temperament properties ==

@@ Line 7: / Line 7: @@
 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 supports [[semidimi]]. Another edo which is quite strong in the 7-limit is like 1547edo is 441edo, and 1547edo thus supports the [[brahmagupta]] temperament produced by merging 441 & 1547.
+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 11-limit, it is a tuning for the rank-3 temperament [[heimdall]].
-In higher limits, it supports 91th-octave temperament [[protactinium]].
 === Prime harmonics ===
@@ Line 17: / Line 13: @@
 === Divisors ===
 has subset edos {{EDOs| 7, 13, 17, 91, 119, and 221 }}.
 == Regular temperament properties ==