Dicot: Difference between revisions
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add it in the infobox then |
"It is also the first fully prototypical dicot temperament" only makes sense due to the hyperlink |
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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]]. | '''Dicot''' is an [[exotemperament]] that [[tempering out|tempers out]] [[25/24]]. This means 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]], called ''[[mujannabic]]'', 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. | ||
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<nowiki/>* Besides the octave | <nowiki/>* Besides the octave | ||
[[Category:Dicot| ]] <!-- main article --> | |||
[[Category:Rank-2 temperaments]] | [[Category:Rank-2 temperaments]] | ||
[[Category:Exotemperaments]] | [[Category:Exotemperaments]] | ||
[[Category:Dicot family]] | [[Category:Dicot family]] | ||
Latest revision as of 10:27, 28 June 2026
| Dicot |
25/24, 45/44 (2.3.5.11)
2.3.5.11 15-odd-limit: 35.3 ¢
2.3.5.11 15-odd-limit: 7 notes
- This page is about the regular temperament. For the ploidacot signature, see Ploidacot/Dicot.
Dicot is an exotemperament that tempers out 25/24. This means 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, called mujannabic, 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
Tunings
Norm-based tunings
| Euclidean | |||
|---|---|---|---|
| Constrained | Constrained & skewed | Destretched | |
| Tenney | CTE: ~5/4 = 354.664 ¢ | CWE: ~5/4 = 351.086 ¢ | POTE: ~5/4 = 348.594 ¢ |
| Euclidean | |||
|---|---|---|---|
| Constrained | Constrained & skewed | Destretched | |
| Tenney | CTE: ~5/4 = 352.287 ¢ | CWE: ~5/4 = 348.954 ¢ | POTE: ~5/4 = 346.734 ¢ |
Tuning spectrum
| Edo generator |
Eigenmonzo (Unchanged-interval)* |
Generator (¢) | Comments |
|---|---|---|---|
| 1\4 | 300.000 | Lower bound of 5-odd-limit diamond monotone | |
| 5/3 | 315.641 | Full comma | |
| 3\11 | 327.273 | 11c val | |
| 9/5 | 339.199 | 2/3-comma | |
| 2\7 | 342.857 | Lower bound of 5-limit 9-odd-limit diamond monotone | |
| 27/20 | 343.910 | 3/5-comma | |
| 7\24 | 350.000 | 24c val | |
| 3/2 | 350.978 | 1/2-comma | |
| 5\17 | 352.941 | ||
| 45/32 | 358.045 | 2/5-comma | |
| 3\10 | 360.000 | ||
| 15/8 | 362.756 | 1/3-comma | |
| 4\13 | 369.231 | ||
| 5/4 | 386.314 | Untempered tuning | |
| 1\3 | 400.000 | Upper bound of 5-odd-limit, and 5-limit 9-odd-limit diamond monotone |
* Besides the octave