Sensamagic clan: Difference between revisions

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== BPS ==

''BPS'', for ''Bohlen–Pierce–Stearns'', is the 3.5.7 subgroup temperament tempering out 245/243. This subgroup temperament was formerly called the ''lambda'' temperament, which was named after the [[4L 5s (tritave-equivalent)|lambda scale]].

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'''[[Bohpier]]''' is named after its [[Relationship between Bohlen-Pierce and octave-ful temperaments|interesting relationship with the non-octave ~~Bohlen-Pierce~~ equal temperament]].

'''[[Bohpier]]''' is named after its [[Relationship between Bohlen-Pierce and octave-ful temperaments|interesting relationship with the non-octave Bohlen–Pierce equal temperament]].

[[Subgroup]]: 2.3.5.7

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=== Triboh ===

'''Triboh''' is named after "[[39edt|Triple ~~Bohlen-Pierce~~ scale]]", which divides each step of the [[13edt|equal-tempered]] [[~~Bohlen-Pierce~~]] scale into three equal parts.

'''Triboh''' is named after "[[39edt|Triple Bohlen–Pierce scale]]", which divides each step of the [[13edt|equal-tempered]] [[Bohlen–Pierce]] scale into three equal parts.

Subgroup: 2.3.5.7.11

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: ''For the 5-limit version of this temperament, see [[High badness temperaments #Magus]].''

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 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]] ({{nowrap|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]])3, 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)2 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]].

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]])3, that is, {{nowrap|2 + 3 × 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)2 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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 == BPS ==
-{{Main|Bohlen-Pierce-Stearns}}
+{{Main|Bohlen–Pierce–Stearns}}
 ''BPS'', for ''Bohlen–Pierce–Stearns'', is the 3.5.7 subgroup temperament tempering out 245/243. This subgroup temperament was formerly called the ''lambda'' temperament, which was named after the [[4L 5s (tritave-equivalent)|lambda scale]].
@@ Line 51: / Line 51: @@
 {{Main| Bohpier }}
-'''[[Bohpier]]''' is named after its [[Relationship between Bohlen-Pierce and octave-ful temperaments|interesting relationship with the non-octave Bohlen-Pierce equal temperament]].
+'''[[Bohpier]]''' is named after its [[Relationship between Bohlen-Pierce and octave-ful temperaments|interesting relationship with the non-octave Bohlen–Pierce equal temperament]].
 [[Subgroup]]: 2.3.5.7
@@ Line 113: / Line 113: @@
 === Triboh ===
-'''Triboh''' is named after "[[39edt|Triple Bohlen-Pierce scale]]", which divides each step of the [[13edt|equal-tempered]] [[Bohlen-Pierce]] scale into three equal parts.
+'''Triboh''' is named after "[[39edt|Triple Bohlen–Pierce scale]]", which divides each step of the [[13edt|equal-tempered]] [[Bohlen–Pierce]] scale into three equal parts.
 Subgroup: 2.3.5.7.11
@@ Line 289: / Line 289: @@
 : ''For the 5-limit version of this temperament, see [[High badness temperaments #Magus]].''
-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 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]] ({{nowrap|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]].
+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, {{nowrap|2 + 3 × 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