Dicot: Difference between revisions

Line 8:

| Mapping = 1; 2 1

| Pergen = (P8, P5/2)

| Odd limit 1 = 5 | Mistuning 1 = 35.4 | Complexity 1 = 5

| Odd limit 1 = 5 | Mistuning 1 = 35.3 | Complexity 1 = 3

| Odd limit 2 = (5-limit) 9 | Mistuning 1 = 35.4 | Complexity 2 = 9

| 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]].

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.

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

@@ Line 8: / Line 8: @@
 | Mapping = 1; 2 1
 | Pergen = (P8, P5/2)
-| Odd limit 1 = 5 | Mistuning 1 = 35.4 | Complexity 1 = 5
+| Odd limit 1 = 5 | Mistuning 1 = 35.3 | Complexity 1 = 3
-| Odd limit 2 = (5-limit) 9 | Mistuning 1 = 35.4 | Complexity 2 = 9
+| 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]].
+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.
 For technical data, see [[Dicot family #Dicot]].