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]].

'''Nicolic chords''' are [[dyadic chord|essentially tempered chords]] tempered by the nicola, [[1575/1573]].

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

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 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 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

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

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

|-

! ~~Cents~~

! [[Cent]]s

| 0 || ~~248~~ || ~~537~~ || ~~782~~

| 0.000 || 247.099 || 536.086 || 783.185

|-

! Sound

! Sound <br> <small>[[:File:Nicolic tetrad.mp3|[info]]]</small>

| colspan="4" | [[File:~~Nocolic~~ tetrad.mp3]]

| colspan="4" | [[File:Nicolic tetrad.mp3]]

|}

[[Category:15-limit]]

[[Category:15-odd-limit chords]]

[[Category:~~Dyadic~~]]

[[Category:Essentially tempered chords]]

[[Category:~~Nicola~~]]

[[Category:Triads]]

[[Category:Tetrads]]

[[Category:Pentads]]

[[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]].
+'''Nicolic chords''' are [[dyadic chord|essentially tempered chords]] tempered by the nicola, [[1575/1573]].
-{| class="wikitable center-all" style="column-width:10em"
+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 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 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
-! [[Unison|1/1]] || [[15/13]] || [[15/11]] || [[11/7]]
+! [[1/1]] || [[15/13]] || [[15/11]] || [[11/7]]
 |-
-! Cents
+! [[Cent]]s
-| 0 || 248 || 537 || 782
+| 0.000 || 247.099 || 536.086 || 783.185
 |-
-! Sound
+! Sound <br> <small>[[:File:Nicolic tetrad.mp3|[info]]]</small>
-| colspan="4" | [[File:Nocolic tetrad.mp3]]
+| colspan="4" | [[File:Nicolic tetrad.mp3]]
 |}
-[[Category:15-limit]]
+[[Category:15-odd-limit chords]]
-[[Category:Dyadic]]
+[[Category:Essentially tempered chords]]
-[[Category:Nicola]]
+[[Category:Triads]]
+[[Category:Tetrads]]
+[[Category:Pentads]]
 [[Category:Nicolic]]
-[[Category:Tetrad]]
 [[Category:Listen]]