Nicolic chords: Difference between revisions

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**Imported revision 244448463 - Original comment: **
 
This is of pattern 1b
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
'''Nicolic chords''' are [[dyadic chord|essentially tempered chords]] tempered by the nicola, [[1575/1573]].
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
 
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-05 03:08:12 UTC</tt>.<br>
Nicolic chords are of [[dyadic chord/Pattern of essentially tempered chords|pattern 1b]] in the [[15-odd-limit]]. There are 3 triads, 6 tetrads and 2 pentads for a total of 11 distinct chord structures.  
: The original revision id was <tt>244448463</tt>.<br>
 
: The revision comment was: <tt></tt><br>
The nicolic triads include the following palindromic form since it identifies [[13/7]] by a stack of two [[15/11]]'s:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
* 1–15/11–13/7 with steps of 15/11, 15/11, [[14/13]].  
<h4>Original Wikitext content:</h4>
 
<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">The //nicolic tetrad// in close position is a 1-15/13-15/11-11/7 in a temperament where the nicola, 1575/1573, is tempered out. It therefore has steps of 15/13-13/11-15/13-14/11, and is a 15-limit chord. Equal divisions with nicolic tetrads include 58, 72, 87, 103, 121, 130, 190, 217, 224, 311, 414, 441, 665 and 855.</pre></div>
And a pair in inverse relationship:  
<h4>Original HTML content:</h4>
* 1–15/11–[[11/7]] with steps of 15/11, [[15/13]], [[14/11]], and its inverse
<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;nicolic tetrad&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;nicolic tetrad&lt;/em&gt; in close position is a 1-15/13-15/11-11/7 in a temperament where the nicola, 1575/1573, is tempered out. It therefore has steps of 15/13-13/11-15/13-14/11, and is a 15-limit chord. Equal divisions with nicolic tetrads include 58, 72, 87, 103, 121, 130, 190, 217, 224, 311, 414, 441, 665 and 855.&lt;/body&gt;&lt;/html&gt;</pre></div>
* 1–15/11–[[26/15]] with steps of 15/11, 14/11, 15/13.
 
For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
* 1–15/13–15/11–11/7 with steps of 15/13, [[13/11]], 15/13, 14/11;
* 1–15/13–[[22/15]]–11/7 with steps of 15/13, 14/11, [[15/14]], 14/11.
 
The inversely related pairs of chords are
* 1–15/11–11/7–13/7 with steps of 15/11, 15/13, 13/11, 14/13, and its inverse
* 1–15/11–22/15–26/15 with steps of 15/11, 14/13, 13/11, 15/13;
* 1–15/11–26/15–13/7 with steps of 15/11, 14/11, 15/14, 14/13, and its inverse
* 1–15/11–22/15–11/7 with steps of 15/11, 14/13, 15/14, 14/11.
 
They can be extended to pentads:  
* 1–15/14–15/13–15/11–11/7 with steps of 15/14, 14/13, 13/11, 15/13, 14/11, and its inverse
* 1–15/13–15/11–22/15–11/7 with steps of 15/13, 13/11, 14/13, 15/14, 14/11.
 
[[Equal temperament]]s with nicolic chords include {{Optimal ET sequence| 29, 31, 43, 58, 72, 87, 94, 103, 121, 130, 159, 190, 217, 224, 311, 414, 441, 665 and 855 }}.
 
Here is a listening sample, tempered to TE tuning of nicolic.
 
{| class="wikitable center-all"
! Ratio
! [[1/1]] || [[15/13]] || [[15/11]] || [[11/7]]
|-
! [[Cent]]s
| 0.000 || 247.099 || 536.086 || 783.185
|-
! Sound <br> <small>[[:File:Nicolic tetrad.mp3|[info]]]</small>
| colspan="4" | [[File:Nicolic tetrad.mp3]]
|}
 
[[Category:15-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Nicolic]]
[[Category:Listen]]

Latest revision as of 14:29, 20 March 2025

Nicolic chords are essentially tempered chords tempered by the nicola, 1575/1573.

Nicolic chords are of pattern 1b in the 15-odd-limit. There are 3 triads, 6 tetrads and 2 pentads for a total of 11 distinct chord structures.

The nicolic triads include the following palindromic form since it identifies 13/7 by a stack of two 15/11's:

  • 1–15/11–13/7 with steps of 15/11, 15/11, 14/13.

And a pair in inverse relationship:

  • 1–15/11–11/7 with steps of 15/11, 15/13, 14/11, and its inverse
  • 1–15/11–26/15 with steps of 15/11, 14/11, 15/13.

For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are

  • 1–15/13–15/11–11/7 with steps of 15/13, 13/11, 15/13, 14/11;
  • 1–15/13–22/15–11/7 with steps of 15/13, 14/11, 15/14, 14/11.

The inversely related pairs of chords are

  • 1–15/11–11/7–13/7 with steps of 15/11, 15/13, 13/11, 14/13, and its inverse
  • 1–15/11–22/15–26/15 with steps of 15/11, 14/13, 13/11, 15/13;
  • 1–15/11–26/15–13/7 with steps of 15/11, 14/11, 15/14, 14/13, and its inverse
  • 1–15/11–22/15–11/7 with steps of 15/11, 14/13, 15/14, 14/11.

They can be extended to pentads:

  • 1–15/14–15/13–15/11–11/7 with steps of 15/14, 14/13, 13/11, 15/13, 14/11, and its inverse
  • 1–15/13–15/11–22/15–11/7 with steps of 15/13, 13/11, 14/13, 15/14, 14/11.

Equal temperaments with nicolic chords include 29, 31, 43, 58, 72, 87, 94, 103, 121, 130, 159, 190, 217, 224, 311, 414, 441, 665 and 855.

Here is a listening sample, tempered to TE tuning of nicolic.

Ratio 1/1 15/13 15/11 11/7
Cents 0.000 247.099 536.086 783.185
Sound
[info]
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