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A '''gentle chord''' is an [[Dyadic chord|essentially tempered chord]] tempered by the gentle comma, [[364/363]].  
'''Gentle chords''' are [[Dyadic chord|essentially tempered chords]] 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.
There are 10 triads, 33 tetrads, 26 pentads and 6 hexads as 2.3.7.11.13 [[subgroup]] [[13-odd-limit]] essentially tempered chords.


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


The ''gentle major triad'' (or ''supermajor gentle triad'') is a tempering of  
The ''supermajor gentle triad'' (or ''gentle major triad'') is a tempering of  
* 1-14/11-3/2 with steps of 14/11-13/11-4/3;
* 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  
and its inversion the ''subminor gentle triad'' (or ''gentle minor triad'') is a tempering of  
* 1-13/11-3/2 with steps of 13/11-14/11-4/3.
* 1-13/11-3/2 with steps of 13/11-14/11-4/3.


The ''gothic gentle triads'' are temperings of  
The ''gothic gentle triads'' are temperings of  
* 1-7/6-11/8 with steps of 7/6-13/11-16/11;
* 1-13/11-11/8 with steps of 13/11-7/6-16/11,


and its inversion,  
and its inversion,  
* 1-13/11-11/8 with steps of 13/11-7/6-16/11.
* 1-7/6-11/8 with steps of 7/6-13/11-16/11.


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.  


The rest three inversely related pairs of triads contain semitones:  
The rest three inversely related pairs of triads contain semitones, such as 12/11 or 13/12:  
* 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;
* 1-14/11-18/13 with steps of 14/11-12/11-13/9, and its inverse  
* 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;
* 1-12/11-18/13 with steps of 12/11-14/11-13/9;
* 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.
* 1-14/11-11/8 with steps of 14/11-13/12-16/11, and its inverse  
* 1-13/12-11/8 with steps of 13/12-14/11-16/11;
* 1-13/11-9/7 with steps of 13/11-12/11-14/9, and its inverse  
* 1-12/11-9/7 with steps of 12/11-13/11-14/9.


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


The ''gentle major tetrad'' is a tempering of
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;  
* 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
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.
* 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
The ''gothic gentle tetrad'' is palindromic, a tempering of  
* 1-13/11-11/8-13/8 with steps of 13/11-7/6-13/11-16/13.
* 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.
The rest four palindromic tetrads contain semitones, such as 12/11, 13/12 or 14/13:
* 1-13/11-14/11-3/2 with steps of 13/11-14/13-13/11-4/3;
* 1-14/11-11/8-7/4 with steps of 14/11-13/12-14/11-8/7;
* 1-12/11-14/11-18/13 with steps of 12/11-7/6-12/11-13/9;
* 1-12/11-13/11-9/7 with steps of 12/11-13/12-12/11-14/9;


There are also pentads and hexads as gentle chords, all of them contain semitones.
as well as the rest thirteen inversely related pairs of tetrads:
* 1-14/11-3/2-24/13 with steps of 14/11-13/11-16/13-13/12, and its inverse
* 1-13/11-3/2-13/8 with steps of 13/11-14/11-13/12-16/13;
* 1-14/11-3/2-11/6 with steps of 14/11-13/11-11/9-12/11, and its inverse
* 1-13/11-3/2-18/11 with steps of 13/11-14/11-12/11-11/9;
* 1-14/11-3/2-18/11 with steps of 14/11-13/11-12/11-11/9, and its inverse
* 1-13/11-3/2-11/6 with steps of 13/11-14/11-11/9-12/11;
* 1-7/6-14/11-3/2 with steps of 7/6-12/11-13/11-4/3, and its inverse
* 1-13/11-9/7-3/2 with steps of 13/11-12/11-7/6-4/3;
* 1-7/6-11/8-3/2 with steps of 7/6-13/11-12/11-4/3, and its inverse
* 1-12/11-9/7-3/2 with steps of 12/11-13/11-7/6-4/3;
* 1-14/11-11/8-3/2 with steps of 14/11-13/12-12/11-4/3, and its inverse
* 1-12/11-13/11-3/2 with steps of 12/11-13/12-14/11-4/3;
* 1-14/11-18/13-3/2 with steps of 14/11-12/11-13/12-4/3, and its inverse
* 1-13/12-13/11-3/2 with steps of 13/12-12/11-14/11-4/3;
* 1-13/11-11/8-3/2 with steps of 13/11-7/6-12/11-4/3, and its inverse
* 1-12/11-14/11-3/2 with steps of 12/11-7/6-13/11-4/3;
* 1-12/11-18/13-3/2 with steps of 12/11-14/11-13/12-4/3, and its inverse
* 1-13/12-11/8-3/2 with steps of 13/12-14/11-12/11-4/3;
* 1-11/9-13/9-11/7 with steps of 11/9-13/11-12/11-14/11, and its inverse
* 1-12/11-9/7-11/7 with steps of 12/11-13/11-11/9-14/11;
* 1-12/11-9/7-18/13 with steps of 12/11-13/11-14/13-13/9, and its inverse
* 1-14/13-14/11-18/13 with steps of 14/13-13/11-12/11-13/9;
* 1-13/11-14/11-11/8 with steps of 13/11-14/13-13/12-16/11, and its inverse
* 1-13/12-7/6-11/8 with steps of 13/12-14/13-13/11-16/11;
* 1-7/6-14/11-11/8 with steps of 7/6-12/11-13/12-16/11, and its inverse
* 1-13/12-13/11-11/8 with steps of 13/12-12/11-7/6-16/11.
 
For pentads, there are thirteen pairs of chords in inverse relationship, all of them involve semitones and the perfect fifth:
* 1-14/11-11/8-3/2-7/4 with steps of 14/11-13/12-12/11-7/6-8/7, and its inverse
* 1-12/11-13/11-3/2-12/7 with steps of 12/11-13/12-14/11-8/7-7/6;
* 1-13/11-9/7-3/2-12/7 with steps of 13/11-12/11-7/6-8/7-7/6, and its inverse
* 1-7/6-14/11-3/2-7/4 with steps of 7/6-12/11-13/11-7/6-8/7;
* 1-14/11-11/8-3/2-11/6 with steps of 14/11-13/12-12/11-11/9-12/11, and its inverse
* 1-12/11-13/11-3/2-18/11 with steps of 12/11-13/12-14/11-12/11-11/9;
* 1-14/11-18/13-3/2-18/11 with steps of 14/11-12/11-13/12-12/11-11/9, and its inverse
* 1-13/12-13/11-3/2-11/6 with steps of 13/12-12/11-14/11-11/9-12/11;
* 1-13/11-14/11-3/2-11/6 with steps of 13/11-14/13-13/11-11/9-12/11, and its inverse
* 1-13/11-14/11-3/2-18/11 with steps of 13/11-14/13-13/11-12/11-11/9;
* 1-13/11-9/7-3/2-18/11 with steps of 13/11-12/11-7/6-12/11-11/9, and its inverse
* 1-7/6-14/11-3/2-11/6 with steps of 7/6-12/11-13/11-11/9-12/11;
* 1-13/11-11/8-3/2-11/6 with steps of 13/11-7/6-12/11-11/9-12/11, and its inverse
* 1-12/11-14/11-3/2-18/11 with steps of 12/11-7/6-13/11-12/11-11/9;
* 1-14/11-18/13-3/2-24/13 with steps of 14/11-12/11-13/12-16/13-13/12, and its inverse
* 1-13/12-13/11-3/2-13/8 with steps of 13/12-12/11-14/11-13/12-16/13;
* 1-13/11-11/8-3/2-13/8 with steps of 13/11-7/6-12/11-13/12-16/13, and its inverse
* 1-12/11-14/11-3/2-24/13 with steps of 12/11-7/6-13/11-16/13-13/12;
* 1-13/11-14/11-11/8-3/2 with steps of 13/11-14/13-13/12-12/11-4/3, and its inverse
* 1-12/11-13/11-14/11-3/2 with steps of 12/11-13/12-14/13-13/11-4/3;
* 1-7/6-14/11-11/8-3/2 with steps of 7/6-12/11-13/12-12/11-4/3, and its inverse
* 1-12/11-13/11-9/7-3/2 with steps of 12/11-13/12-12/11-7/6-4/3;
* 1-12/11-9/7-18/13-3/2 with steps of 12/11-13/11-14/13-13/12-4/3, and its inverse
* 1-13/12-7/6-11/8-3/2 with steps of 13/12-14/13-13/11-12/11-4/3;
* 1-12/11-14/11-18/13-3/2 with steps of 12/11-7/6-12/11-13/12-4/3, and its inverse
* 1-13/12-13/11-11/8-3/2 with steps of 13/12-12/11-7/6-12/11-4/3.
 
For hexads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
* 1-7/6-14/11-11/8-3/2-7/4 with steps of 7/6-12/11-13/12-12/11-7/6-8/7;
* 1-12/11-14/11-18/13-3/2-24/13 with steps of 12/11-7/6-12/11-13/12-16/13-13/12.
 
The inversely related pairs of chords are
* 1-7/6-14/11-11/8-3/2-11/6 with steps of 7/6-12/11-13/12-12/11-11/9-12/11, and its inverse
* 1-12/11-13/11-9/7-3/2-18/11 with steps of 12/11-13/12-12/11-7/6-12/11-11/9;
* 1-13/11-14/11-11/8-3/2-11/6 with steps of 13/11-14/13-13/12-12/11-11/9-12/11, and its inverse
* 1-12/11-13/11-14/11-3/2-18/11 with steps of 12/11-13/12-14/13-13/11-12/11-11/9.


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 }}.
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 }}.
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[[Category:Triads]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]
[[Category:Gentle]]
[[Category:Gentle]]
[[Category:Neo-gothic]]
[[Category:Neo-gothic]]
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