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.  
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:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Gentle]]
[[Category:Gentle]]
[[Category:Neo-gothic]]
[[Category:Neo-gothic]]

Revision as of 11:34, 3 September 2023

A gentle chord is an essentially tempered chord tempered by the gentle comma, 364/363.

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

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

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

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

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

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

The gothic gentle triads are temperings of

  • 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.

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.

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

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

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