Dicot: Difference between revisions

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| Odd limit 2 = (5-limit) 9 | Mistuning 2 = 35.3 | Complexity 2 = 7

}}

~~'''~~Dicot~~''' is an exotemperament that tempers out 25/24. It is also~~ the ~~first fully prototypical [[~~Ploidacot/Dicot|dicot]] temperament. It tempers out 6/5 and 5/4 into the same "neutral third" interval, which, when the fifth is tuned pure, is [[sqrt(3/2)]]. It is useful to represent the structure of 5-limit harmonies without fully representing them in its greater accuracy.

It can be extended by tempering out [[15/14]] and [[36/35]] in the 7-limit, though ~~in practice~~ this ~~turns~~ the [[3L 4s]] [[~~MOS~~]] into a [[4L 3s]] [[~~MOS~~]]. This makes [[7/6]] and [[9/7]] equated to the neutral third, viewing [[6:7:9]] as a tertian chord. Another notable extension of dicot is [[decimal]], which splits the octave in two for [[7/5]]~[[10/7]] by tempering out [[50/49]], and equates [[7/6]] and [[8/7]] to the tritone complement of 5/4~6/5, neutralizing the 6:7:8 chord as well. This represents the structure of 7-limit harmonies in a way that ~~isn't~~ based on tertian harmony and a heptatonic system, but rather a decatonic one. A more accurate system based on 10 interval classes that ~~doesn't~~ neutralize these chords is [[pajara]]. An even more accurate one is [[miracle]], though its structure is more complex than that of pajara.

'''Dicot''' is an [[exotemperament]] that [[tempering out|tempers out]] [[25/24]]. It is also the first fully prototypical [[ploidacot/Dicot|dicot]] temperament. It tempers [[6/5]] and [[5/4]] into the same [[neutral third]] interval, which, when the fifth is tuned pure, is [[sqrt(3/2)]]. It is useful to represent the structure of [[5-limit]] harmonies without fully representing them in its greater accuracy.

It can be extended by tempering out [[15/14]] and [[36/35]] in the [[7-limit]], though this could turn the [[3L 4s]] [[mos]] into a [[4L 3s]] [[mos]]. This makes [[7/6]] and [[9/7]] equated to the neutral third, viewing [[6:7:9]] as a tertian chord.

Another notable extension of dicot is [[decimal]], which splits the octave in two for [[7/5]][[~]][[10/7]] by tempering out [[50/49]], and equates [[7/6]] and [[8/7]] to the tritone complement of 5/4~6/5, neutralizing the 6:7:8 chord as well. This represents the structure of 7-limit harmonies in a way that is not based on tertian harmony and a heptatonic system, but rather a decatonic one. A more accurate system based on 10 interval classes that does not neutralize these chords is [[pajara]]. An even more accurate one is [[miracle]], though its structure is more complex than that of pajara.

For technical data, see [[Dicot family #Dicot]].

@@ Line 11: / Line 11: @@
 | Odd limit 2 = (5-limit) 9 | Mistuning 2 = 35.3 | Complexity 2 = 7
 }}
-'''Dicot''' is an exotemperament that tempers out 25/24. It is also the first fully prototypical [[Ploidacot/Dicot|dicot]] temperament. It tempers out 6/5 and 5/4 into the same "neutral third" interval, which, when the fifth is tuned pure, is [[sqrt(3/2)]]. It is useful to represent the structure of 5-limit harmonies without fully representing them in its greater accuracy.
+{{Redirect|Dicot|the ploidacot signature|Ploidacot/Dicot}}
-It can be extended by tempering out [[15/14]] and [[36/35]] in the 7-limit, though in practice this turns the [[3L 4s]] [[MOS]] into a [[4L 3s]] [[MOS]]. This makes [[7/6]] and [[9/7]] equated to the neutral third, viewing [[6:7:9]] as a tertian chord. Another notable extension of dicot is [[decimal]], which splits the octave in two for [[7/5]]~[[10/7]] by tempering out [[50/49]], and equates [[7/6]] and [[8/7]] to the tritone complement of 5/4~6/5, neutralizing the 6:7:8 chord as well. This represents the structure of 7-limit harmonies in a way that isn't based on tertian harmony and a heptatonic system, but rather a decatonic one. A more accurate system based on 10 interval classes that doesn't neutralize these chords is [[pajara]]. An even more accurate one is [[miracle]], though its structure is more complex than that of pajara.
+'''Dicot''' is an [[exotemperament]] that [[tempering out|tempers out]] [[25/24]]. It is also the first fully prototypical [[ploidacot/Dicot|dicot]] temperament. It tempers [[6/5]] and [[5/4]] into the same [[neutral third]] interval, which, when the fifth is tuned pure, is [[sqrt(3/2)]]. It is useful to represent the structure of [[5-limit]] harmonies without fully representing them in its greater accuracy.
+It can be extended by tempering out [[15/14]] and [[36/35]] in the [[7-limit]], though this could turn the [[3L 4s]] [[mos]] into a [[4L 3s]] [[mos]]. This makes [[7/6]] and [[9/7]] equated to the neutral third, viewing [[6:7:9]] as a tertian chord.
+Another notable extension of dicot is [[decimal]], which splits the octave in two for [[7/5]][[~]][[10/7]] by tempering out [[50/49]], and equates [[7/6]] and [[8/7]] to the tritone complement of 5/4~6/5, neutralizing the 6:7:8 chord as well. This represents the structure of 7-limit harmonies in a way that is not based on tertian harmony and a heptatonic system, but rather a decatonic one. A more accurate system based on 10 interval classes that does not neutralize these chords is [[pajara]]. An even more accurate one is [[miracle]], though its structure is more complex than that of pajara.
 For technical data, see [[Dicot family #Dicot]].