Dicot: Difference between revisions
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No septimal dicot anymore! |
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{{Infobox regtemp | {{Infobox regtemp | ||
| Title = Dicot | | Title = Dicot | ||
| Subgroups = 2.3.5 | | Subgroups = 2.3.5, 2.3.5.11 | ||
| Comma basis = [[25/24]] | | Comma basis = [[25/24]] (2.3.5);<br>[[25/24]], [[45/44]] (2.3.5.11) | ||
| Edo join 1 = | | Edo join 1 = 7 | Edo join 2 = 10 | ||
| Mapping = 1; 2 1 | | Mapping = 1; 2 1 5 | ||
| Generators = 6/5 | Generators tuning = 351.1 | Optimization method = CWE | | Generators = 6/5 | Generators tuning = 351.1 | Optimization method = CWE | ||
| MOS scales = [[3L 1s]], [[3L 4s]], [[7L 3s]] | | MOS scales = [[3L 1s]], [[3L 4s]], [[7L 3s]] | ||
| Pergen = (P8, P5/2) | | Pergen = (P8, P5/2) | ||
| Odd limit 1 = 5 | Mistuning 1 = 35.3 | Complexity 1 = 3 | | Odd limit 1 = 5 | Mistuning 1 = 35.3 | Complexity 1 = 3 | ||
| Odd limit 2 = 5 | | Odd limit 2 = 2.3.5.11 15 | Mistuning 2 = 35.3 | Complexity 2 = 7 | ||
}} | }} | ||
{{About|the regular temperament|the ploidacot signature|Ploidacot/Dicot}} | {{About|the regular temperament|the ploidacot signature|Ploidacot/Dicot}} | ||
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'''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]]. | '''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]], 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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== Tunings == | == Tunings == | ||
=== Norm-based tunings === | === Norm-based tunings === | ||
{{ | {| class="wikitable mw-collapsible mw-collapsed" | ||
|+ style="font-size: 105%; white-space: nowrap;" | 5-limit norm-based tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~5/4 = 354.664{{C}} | |||
| CWE: ~5/4 = 351.086{{C}} | |||
| POTE: ~5/4 = 348.594{{C}} | |||
|} | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | 2.3.5.11-subgroup norm-based tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~5/4 = 352.287{{C}} | |||
| CWE: ~5/4 = 348.954{{C}} | |||
| POTE: ~5/4 = 346.734{{C}} | |||
|} | |||
=== Tuning spectrum === | === Tuning spectrum === | ||
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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]] | ||