Minor minthmic chords: Difference between revisions

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A '''gentle chord''' is ~~a [[13-odd-limit]]~~ [[Dyadic chord|essentially tempered chord]] ~~in the gentle temperament, tempering out~~ the gentle comma, [[364/363]].

A '''gentle chord''' is an [[Dyadic chord|essentially tempered chord]] tempered by the gentle comma, [[364/363]].

~~A gentle triad is any of four~~ 13-odd-limit essentially tempered ~~triads in the gentle temperament~~.

Gentle chords are numerous, including 10 triads and 33 tetrads as 2.3.7.11.13 [[subgroup]] [[13-odd-limit]] essentially tempered chords.

~~The ''supermajor gentle triad'' is a tempering~~ of

For triads, there are five pairs of chords in inverse relationship.

* 1-14/11-3/2

~~and its inversion the~~ ''~~subminor~~ gentle triad'' is a tempering of

The ''gentle major triad'' (or ''supermajor gentle triad'') is a tempering of

* 1-13/11-3/2

* 1-14/11-3/2 with steps of 14/11-13/11-4/3;

~~The~~ ''~~gothic~~ gentle ~~triads~~'' ~~are the temperings~~ of

and its inversion the ''gentle minor triad'' (or ''subminor gentle triad'') is a tempering of

* 1-7/6-11/8

* 1-13/11-3/2 with steps of 13/11-14/11-4/3.

and its inversion

The ''gothic gentle triads'' are temperings of

* 1-13/11-11/8.

* 1-7/6-11/8 with steps of 7/6-13/11-16/11;

and its inversion,

* 1-13/11-11/8 with steps of 13/11-7/6-16/11.

The names refer to [[Margo Schulter]]'s [[Neo-gothic]] theory of harmony, which features a [[gentle region]] with a slightly sharpened fifth in which gentle triads and neogothic triads flourish.

A gentle tetrad is ~~any~~ of ~~three~~ 13-~~limit essentially tempered tetrads in~~ the gentle ~~temperament~~.

The rest three inversely related pairs of triads contain semitones:

* 1-14/11-18/13 with steps 14/11-12/11-13/9 and its inverse 1-12/11-18/13 with steps 12/11-14/11-13/9;

* 1-14/11-11/8 with steps 14/11-13/12-16/11 and its inverse 1-13/12-11/8 with steps 13/12-14/11-16/11;

* 1-13/11-9/7 with steps 13/11-12/11-14/9 and its inverse 1-12/11-9/7 with steps 12/11-13/11-14/9.

For tetrads, there are five palindromic chords and fourteen pairs of chords in inverse relationship.

The ''gentle major tetrad'' is a tempering of

* 1-14/11-3/2-7/4 with steps of 14/11-13/11-7/6-8/7;

and its inversion the ''gentle minor tetrad'' is a tempering of

* 1-13/11-3/2-12/7 with steps of 13/11-14/11-8/7-7/6.

The ''gothic gentle tetrad'' is palindromic, a tempering of pairs of

* 1-13/11-11/8-13/8 with steps of 13/11-7/6-13/11-16/13.

The rest four palindromic tetrads and thirteen inversely related pairs of tetrads contain semitones such as 12/11, 13/12 or 14/13.

~~In close position, these~~ are ~~temperings of~~

There are also pentads and hexads as gentle chords, all of them contain semitones.

* 1-14/11-3/2-7/4, with steps of 14/11-13/11-7/6-8/7

* 1-13/11-3/2-12/7, with steps of 13/11-14/11-8/7-7/6

* 1-13/11-11/8-13/8, ~~with steps~~ of ~~13/11-7/6-13/11-16/13~~

~~Edo~~ with gentle chords include {{~~EDOs~~| 17, 22, 29, 41, 46, 58, 72, 87, 104, 121, 130, 217, 232, 234, 289 and 456 }}.

Equal temperaments with gentle chords include {{Optimal ET sequence| 17, 22, 29, 41, 46, 58, 72, 87, 104, 121, 130, 217, 232, 234, 289 and 456 }}.

[[Category:13-odd-limit]]

[[Category:Essentially tempered chords]]

[[Category:Triads]]

[[Category:Tetrads]]

[[Category:Gentle]]

[[Category:Neo-gothic]]

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-A '''gentle chord''' is a [[13-odd-limit]] [[Dyadic chord|essentially tempered chord]] in the gentle temperament, tempering out the gentle comma, [[364/363]].
+A '''gentle chord''' is an [[Dyadic chord|essentially tempered chord]] tempered by the gentle comma, [[364/363]].
-A gentle triad is any of four 13-odd-limit essentially tempered triads in the gentle temperament.
+Gentle chords are numerous, including 10 triads and 33 tetrads as 2.3.7.11.13 [[subgroup]] [[13-odd-limit]] essentially tempered chords.
-The ''supermajor gentle triad'' is a tempering of
+For triads, there are five pairs of chords in inverse relationship.
-* 1-14/11-3/2
-and its inversion the ''subminor gentle triad'' is a tempering of
+The ''gentle major triad'' (or ''supermajor gentle triad'') is a tempering of
-* 1-13/11-3/2
+* 1-14/11-3/2 with steps of 14/11-13/11-4/3;
-The ''gothic gentle triads'' are the temperings of
+and its inversion the ''gentle minor triad'' (or ''subminor gentle triad'') is a tempering of
-* 1-7/6-11/8
+* 1-13/11-3/2 with steps of 13/11-14/11-4/3.
-and its inversion
+The ''gothic gentle triads'' are temperings of
-* 1-13/11-11/8.
+* 1-7/6-11/8 with steps of 7/6-13/11-16/11;
+and its inversion,
+* 1-13/11-11/8 with steps of 13/11-7/6-16/11.
 The names refer to [[Margo Schulter]]'s [[Neo-gothic]] theory of harmony, which features a [[gentle region]] with a slightly sharpened fifth in which gentle triads and neogothic triads flourish.
-A gentle tetrad is any of three 13-limit essentially tempered tetrads in the gentle temperament.
+The rest three inversely related pairs of triads contain semitones:
+* 1-14/11-18/13 with steps 14/11-12/11-13/9 and its inverse 1-12/11-18/13 with steps 12/11-14/11-13/9;
+* 1-14/11-11/8 with steps 14/11-13/12-16/11 and its inverse 1-13/12-11/8 with steps 13/12-14/11-16/11;
+* 1-13/11-9/7 with steps 13/11-12/11-14/9 and its inverse 1-12/11-9/7 with steps 12/11-13/11-14/9.
+For tetrads, there are five palindromic chords and fourteen pairs of chords in inverse relationship.
+The ''gentle major tetrad'' is a tempering of
+* 1-14/11-3/2-7/4 with steps of 14/11-13/11-7/6-8/7;
+and its inversion the ''gentle minor tetrad'' is a tempering of
+* 1-13/11-3/2-12/7 with steps of 13/11-14/11-8/7-7/6.
+The ''gothic gentle tetrad'' is palindromic, a tempering of pairs of
+* 1-13/11-11/8-13/8 with steps of 13/11-7/6-13/11-16/13.
+The rest four palindromic tetrads and thirteen inversely related pairs of tetrads contain semitones such as 12/11, 13/12 or 14/13.
-In close position, these are temperings of
+There are also pentads and hexads as gentle chords, all of them contain semitones.
-* 1-14/11-3/2-7/4, with steps of 14/11-13/11-7/6-8/7
-* 1-13/11-3/2-12/7, with steps of 13/11-14/11-8/7-7/6
-* 1-13/11-11/8-13/8, with steps of 13/11-7/6-13/11-16/13
-Edo with gentle chords include {{EDOs| 17, 22, 29, 41, 46, 58, 72, 87, 104, 121, 130, 217, 232, 234, 289 and 456 }}.
+Equal temperaments with gentle chords include {{Optimal ET sequence| 17, 22, 29, 41, 46, 58, 72, 87, 104, 121, 130, 217, 232, 234, 289 and 456 }}.
+[[Category:13-odd-limit]]
 [[Category:Essentially tempered chords]]
+[[Category:Triads]]
+[[Category:Tetrads]]
 [[Category:Gentle]]
 [[Category:Neo-gothic]]