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Dicot: Difference between revisions

VisualWikitext
Wikispaces>keenanpepper
**Imported revision 260687030 - Original comment: **
 
No septimal dicot anymore!
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox regtemp
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Title = Dicot
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-10-02 17:02:08 UTC</tt>.<br>
| Subgroups = 2.3.5, 2.3.5.11
: The original revision id was <tt>260687030</tt>.<br>
| Comma basis = [[25/24]] (2.3.5);<br>[[25/24]], [[45/44]] (2.3.5.11)
: The revision comment was: <tt></tt><br>
| Edo join 1 = 7 | Edo join 2 = 10
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Mapping = 1; 2 1 5
<h4>Original Wikitext content:</h4>
| Generators = 6/5 | Generators tuning = 351.1 | Optimization method = CWE
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">See [[Dicot family]].</pre></div>
| MOS scales = [[3L 1s]], [[3L 4s]], [[7L 3s]]
<h4>Original HTML content:</h4>
| Pergen = (P8, P5/2)
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Dicot&lt;/title&gt;&lt;/head&gt;&lt;body&gt;See &lt;a class="wiki_link" href="/Dicot%20family"&gt;Dicot family&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
| Odd limit 1 = 5 | Mistuning 1 = 35.3 | Complexity 1 = 3
| Odd limit 2 = 2.3.5.11 15 | Mistuning 2 = 35.3 | Complexity 2 = 7
}}
{{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, 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]], 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'''.
 
{| class="wikitable center-1 right-2"
|-
! # !! 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'''
|}
<nowiki/>* In 5-limit CWE tuning
 
== 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 ===
{| class="wikitable center-all left-4"
|-
! Edo<br>generator !! Eigenmonzo<br>(Unchanged-interval)* !! Generator (¢) !! Comments
|-
| '''[[4edo|1\4]]''' ||  || '''300.000''' || '''Lower bound of 5-odd-limit diamond monotone'''
|-
|  || [[5/3]] || 315.641 || Full comma
|-
| [[11edo|3\11]] || || 327.273 || 11c val
|-
|  || [[9/5]] || 339.199 || 2/3-comma
|-
| '''[[7edo|2\7]]''' ||  || '''342.857''' || '''Lower bound of 5-limit 9-odd-limit diamond monotone'''
|-
|  || [[27/20]] || 343.910 || 3/5-comma
|-
| [[24edo|7\24]] ||  || 350.000 || 24c val
|-
|  || [[3/2]] || 350.978 || 1/2-comma
|-
| [[17edo|5\17]] ||  || 352.941 ||
|-
|  || [[45/32]] || 358.045 || 2/5-comma
|-
| [[10edo|3\10]] ||  || 360.000 ||
|-
|  || [[15/8]] || 362.756 || 1/3-comma
|-
| [[13edo|4\13]] || || 369.231 ||
|-
|  || [[5/4]] || 386.314 || Untempered tuning
|-
| '''[[3edo|1\3]]''' ||  || '''400.000''' || '''Upper bound of 5-odd-limit, <br>and 5-limit 9-odd-limit diamond monotone'''
|}
<nowiki/>* Besides the octave
 
[[Category:Dicot| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Exotemperaments]]
[[Category:Dicot family]]
Retrieved from "https://en.xen.wiki/w/Dicot"