Nicolic chords: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Update
This is of pattern 1b
 
(4 intermediate revisions by 2 users not shown)
Line 1: Line 1:
A '''nicolic chord''' is a [[15-odd-limit]] [[essentially tempered dyadic chord]] which is tempered by [[1575/1573]], the nicola.  
'''Nicolic chords''' are [[dyadic chord|essentially tempered chords]] tempered by the nicola, [[1575/1573]].


The nicolic triads include the following palindromic form,
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.
* 1-[[15/11]]-[[13/7]] with steps 15/11-15/11-[[14/13]],  


and a pair in inverse relationship,
The nicolic triads include the following palindromic form since it identifies [[13/7]] by a stack of two [[15/11]]'s:
* 1-15/11-[[11/7]] with steps 15/11-[[15/13]]-[[14/11]], and
* 1–15/11–13/7 with steps of 15/11, 15/11, [[14/13]].  
* 1-15/11-[[26/15]] with steps 15/11-14/11-15/13.  


Any of these leads to a tetrad, in close position,
And a pair in inverse relationship:
* 1-15/13-15/11-11/7, with steps of 15/13-[[13/11]]-15/13-14/11.  
* 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.


[[Equal temperament]]s with nicolic chords include {{EDOs| 58, 72, 87, 103, 121, 130, 190, 217, 224, 311, 414, 441, 665 and 855 }}.
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.  
Here is a listening sample, tempered to TE tuning of nicolic.  


{| class="wikitable center-all" style="column-width:10em"
{| class="wikitable center-all"
! Ratio
! Ratio
! [[1/1]] || [[15/13]] || [[15/11]] || [[11/7]]
! [[1/1]] || [[15/13]] || [[15/11]] || [[11/7]]
Line 26: Line 39:
|}
|}


[[Category:15-odd-limit]]
[[Category:15-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Essentially tempered chords]]
[[Category:Triad]]
[[Category:Triads]]
[[Category:Tetrad]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Nicolic]]
[[Category:Nicolic]]
[[Category:Listen]]
[[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]
Retrieved from "https://en.xen.wiki/index.php?title=Nicolic_chords&oldid=187286"