Nicolic chords: Difference between revisions

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~~The~~ '''nicolic ~~tetrad~~''' ~~in close position~~ is a [[~~Unison|1~~]]-[[15/13]]-[[15/11]]-[[11/7]] ~~in a temperament where the~~ [[~~nicola~~]], ~~1575~~/~~1573, is~~ [[~~tempering out|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 ~~[[58edo]]~~, ~~[[72edo]]~~, ~~[[87edo]]~~, ~~[[103edo]]~~, ~~[[121edo]]~~, ~~[[130edo]]~~, ~~[[190edo]]~~, ~~[[217edo]]~~, ~~[[224edo]]~~, ~~[[311edo]]~~, ~~[[414edo]]~~, ~~[[441edo]]~~, ~~[[665edo]]~~ and ~~[[855edo]]~~.

A '''nicolic chord''' is a [[15-odd-limit]] [[essentially tempered dyadic chord]] which is tempered by [[1575/1573]], the nicola.

The nicolic triads include the following palindromic form,

* 1-[[15/11]]-[[13/7]] with steps 15/11-15/11-[[14/13]],

and a pair in inverse relationship,

* 1-15/11-[[11/7]] with steps 15/11-[[15/13]]-[[14/11]], and

* 1-15/11-[[26/15]] with steps 15/11-14/11-15/13.

Any of these leads to a tetrad, in close position,

* 1-15/13-15/11-11/7, with steps of 15/13-[[13/11]]-15/13-14/11.

[[Equal temperament]]s with nicolic chords include {{EDOs| 58, 72, 87, 103, 121, 130, 190, 217, 224, 311, 414, 441, 665 and 855 }}.

Here is a listening sample. Although it is non-tempered, it may be regarded as close enough.

{| class="wikitable center-all" style="column-width:10em"

! Ratio

! [[~~Unison|~~1/1]] || [[15/13]] || [[15/11]] || [[11/7]]

! [[1/1]] || [[15/13]] || [[15/11]] || [[11/7]]

|-

! [[Cent]]s

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Line 26:

|}

[[Category:15-odd-limit]]

[[Category:15-limit]]

[[Category:Dyadic]]

[[Category:~~Nicola~~]]

[[Category:Triad]]

[[Category:Tetrad]]

[[Category:Nicolic]]

~~[[Category:Tetrad]]~~

[[Category:Listen]]

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-The '''nicolic tetrad''' in close position is a [[Unison|1]]-[[15/13]]-[[15/11]]-[[11/7]] in a temperament where the [[nicola]], 1575/1573, is [[tempering out|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 [[58edo]], [[72edo]], [[87edo]], [[103edo]], [[121edo]], [[130edo]], [[190edo]], [[217edo]], [[224edo]], [[311edo]], [[414edo]], [[441edo]], [[665edo]] and [[855edo]].
+A '''nicolic chord''' is a [[15-odd-limit]] [[essentially tempered dyadic chord]] which is tempered by [[1575/1573]], the nicola.
+The nicolic triads include the following palindromic form,
+* 1-[[15/11]]-[[13/7]] with steps 15/11-15/11-[[14/13]],
+and a pair in inverse relationship,
+* 1-15/11-[[11/7]] with steps 15/11-[[15/13]]-[[14/11]], and
+* 1-15/11-[[26/15]] with steps 15/11-14/11-15/13.
+Any of these leads to a tetrad, in close position,
+* 1-15/13-15/11-11/7, with steps of 15/13-[[13/11]]-15/13-14/11.
+[[Equal temperament]]s with nicolic chords include {{EDOs| 58, 72, 87, 103, 121, 130, 190, 217, 224, 311, 414, 441, 665 and 855 }}.
+Here is a listening sample. Although it is non-tempered, it may be regarded as close enough.
 {| class="wikitable center-all" style="column-width:10em"
 ! Ratio
-! [[Unison|1/1]] || [[15/13]] || [[15/11]] || [[11/7]]
+! [[1/1]] || [[15/13]] || [[15/11]] || [[11/7]]
 |-
 ! [[Cent]]s
@@ Line 12: / Line 26: @@
 |}
+[[Category:15-odd-limit]]
-[[Category:15-limit]]
 [[Category:Dyadic]]
-[[Category:Nicola]]
+[[Category:Triad]]
+[[Category:Tetrad]]
 [[Category:Nicolic]]
-[[Category:Tetrad]]
 [[Category:Listen]]