Sensamagic clan: Difference between revisions

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Magus temperament tempers out 50331648/48828125 (salegu) in the 5-limit. This temperament can be described as 46 & 49 temperament, which tempers out the sensamagic and 28672/28125 (sazoquingu). The alternative extension [[Starling temperaments #Amigo|amigo]] (43 & 46) tempers out the same 5-limit comma as the magus, but with the [[126/125|starling comma]] (126/125) rather than the sensamagic tempered out.

Magus has a generator of a sharp ~5/4 (so that ~[[25/16]] is twice as sharp so that it makes sense to equate with [[11/7]] by tempering [[176/175]]), so that three reaches [[128/125]] short of the octave (where 128/125 is tuned narrow); this is significant because magus reaches [[3/2]] as ([[25/16]])/([[128/125]])<sup>3</sup>, that is, 2 plus 3 times 3 = 11 generators. Therefore, it implies that [[25/24]] is split into three [[128/125]]'s. Therefore, in the 5-limit, Magus can be thought of as a higher-complexity and sharper analogue of [[Würschmidt]] (which reaches [[3/2]] as (25/16)/(128/125)<sup>2</sup> implying 25/24 is split into two 128/125's thus having a guaranteed neutral third), which itself is a higher-complexity and sharper analogue of [[Magic]] (which equates 25/24 with 128/125 by flattening 5). For more details on these connections see [[Würschmidt comma]].

[[Subgroup]]: 2.3.5.7

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 Magus temperament tempers out 50331648/48828125 (salegu) in the 5-limit. This temperament can be described as 46 &amp; 49 temperament, which tempers out the sensamagic and 28672/28125 (sazoquingu). The alternative extension [[Starling temperaments #Amigo|amigo]] (43 &amp; 46) tempers out the same 5-limit comma as the magus, but with the [[126/125|starling comma]] (126/125) rather than the sensamagic tempered out.
+Magus has a generator of a sharp ~5/4 (so that ~[[25/16]] is twice as sharp so that it makes sense to equate with [[11/7]] by tempering [[176/175]]), so that three reaches [[128/125]] short of the octave (where 128/125 is tuned narrow); this is significant because magus reaches [[3/2]] as ([[25/16]])/([[128/125]])<sup>3</sup>, that is, 2 plus 3 times 3 = 11 generators. Therefore, it implies that [[25/24]] is split into three [[128/125]]'s. Therefore, in the 5-limit, Magus can be thought of as a higher-complexity and sharper analogue of [[Würschmidt]] (which reaches [[3/2]] as (25/16)/(128/125)<sup>2</sup> implying 25/24 is split into two 128/125's thus having a guaranteed neutral third), which itself is a higher-complexity and sharper analogue of [[Magic]] (which equates 25/24 with 128/125 by flattening 5). For more details on these connections see [[Würschmidt comma]].
 [[Subgroup]]: 2.3.5.7