Dicot: Difference between revisions
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{{About|the regular temperament|the ploidacot signature|Ploidacot/Dicot}} | {{About|the regular temperament|the ploidacot signature|Ploidacot/Dicot}} | ||
'''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. | '''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, with [[mos scale]]s [[3L 4s]] and [[7L 3s]]. | ||
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. | 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. | 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. | ||
For technical data, see [[Dicot family #Dicot]]. | For technical data, see [[Dicot family #Dicot]]. | ||
Revision as of 16:11, 22 November 2025
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- This page is about the regular temperament. For the ploidacot signature, see Ploidacot/Dicot.
Dicot is an exotemperament that tempers out 25/24. It is also the first fully prototypical 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, with mos scales 3L 4s and 7L 3s.
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.
For technical data, see Dicot family #Dicot.
Interval chain
In the following table, odd harmonics 1–9 are labeled in bold.
| # | Cents* | Approximate ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 351.1 | 5/4, 6/5 |
| 2 | 702.2 | 3/2 |
| 3 | 1053.3 | 9/5, 15/8 |
| 4 | 204.3 | 9/8 |
* In 5-limit CWE tuning