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Update: adding 1-25/24-27/14 chord and its derivation
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'''Ragismic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the ragisma, [[4375/4374]].
'''Ragismic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the ragisma, [[4375/4374]].


The [[Ragismic microtemperaments|ragismic temperament]] has 4 triads, 11 tetrads, 9 pentads and 2 hexads as essentially tempered chords.
Since the temperament is complex, even the simplest ragismic chords are [[27-odd-limit]], although they contain only [[7-limit|7-prime-limit]] intervals. There are 6 triads, 21 tetrads, 22 pentads and 7 hexads as essentially tempered chords.


For triads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are
For triads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
* 1-27/25-7/6 chord with steps of 27/25-27/25-12/7;
* 1-27/25-7/6 chord with steps of 27/25-27/25-12/7;
* 1-25/18-27/14 chord with steps of 25/18-25/18-28/27.
* 1-25/18-27/14 chord with steps of 25/18-25/18-28/27.


The inversely related pair of chords is
The inversely related pairs of chords are
* 1-9/7-25/18 with steps of 9/7-27/25-36/25 and its inverse 1-27/25-25/18 with steps of 27/25-9/7-36/25.
* 1-9/7-25/18 with steps of 9/7-27/25-36/25 and its inverse 1-27/25-25/18 with steps of 27/25-9/7-36/25;
* 1-25/24-27/25 with steps of 25/24-28/27-50/27 and its inverse 1-25/24-27/14 with steps of 25/24-50/27-28/27.


For tetrads, there are three palindromic chords and four pairs of chords in inverse relationship. The palindromic chords are
For tetrads, there are five palindromic chords and eight pairs of chords in inverse relationship. The palindromic chords are
* 1-27/25-25/18-14/9 chord with steps of 27/25-9/7-28/25-9/7;
* 1-27/25-25/18-3/2 chord with steps of 27/25-9/7-27/25-4/3;
* 1-27/25-25/18-3/2 chord with steps of 27/25-9/7-27/25-4/3;
* 1-27/25-25/18-14/9 chord with steps of 27/25-9/7-28/25-9/7;
* 1-27/25-9/7-25/18 chord with steps of 27/25-25/21-27/25-36/25;
* 1-27/25-9/7-25/18 chord with steps of 27/25-25/21-27/25-36/25.
* 1-25/24-27/25-9/8 chord with steps of 25/24-28/27-25/24-16/9;
* 1-25/24-27/25-27/14 chord with steps of 25/24-28/27-25/14-28/27.


The inversely related pairs of chords are
The inversely related pairs of chords are
* 1-27/25-7/6-14/9 with steps of 27/25-27/25-4/3-9/7 and its inverse 1-27/25-7/6-3/2 with steps of 27/25-27/25-9/7-4/3;
* 1-27/25-7/6-3/2 with steps of 27/25-27/25-9/7-4/3 and its inverse 1-27/25-7/6-14/9 with steps of 27/25-27/25-4/3-9/7;
* 1-27/25-7/6-25/18 with steps of 27/25-27/25-25/21-36/25 and its inverse 1-25/21-9/7-25/18 with steps of 25/21-27/25-27/25-36/25;
* 1-27/25-7/6-25/18 with steps of 27/25-27/25-25/21-36/25 and its inverse 1-25/21-9/7-25/18 with steps of 25/21-27/25-27/25-36/25;
* 1-25/18-3/2-27/14 with steps of 25/18-27/25-9/7-28/27 and its inverse 1-27/25-3/2-14/9 with steps of 27/25-25/18-28/27-9/7;
* 1-27/25-3/2-14/9 with steps of 27/25-25/18-28/27-9/7 and its inverse 1-25/18-3/2-27/14 with steps of 25/18-27/25-9/7-28/27;
* 1-27/25-25/18-27/14 with steps of 27/25-9/7-25/18-28/27 and its inverse 1-25/18-25/14-27/14 with steps of 25/18-9/7-27/25-28/27.
* 1-25/18-25/14-27/14 with steps of 25/18-9/7-27/25-28/27 and its inverse 1-27/25-25/18-27/14 with steps of 27/25-9/7-25/18-28/27;
* 1-25/24-27/25-3/2 with steps of 25/24-28/27-25/18-4/3 and its inverse 1-25/24-25/18-27/14 with steps of 25/24-4/3-25/18-28/27;
* 1-25/24-27/25-25/18 with steps of 25/24-28/27-9/7-36/25 and its inverse 1-25/24-3/2-27/14 with steps of 25/24-36/25-9/7-28/27;
* 1-27/25-9/8-7/6 with steps of 27/25-25/24-28/27-12/7 and its inverse 1-25/24-9/8-27/14 with steps of 25/24-27/25-12/7-28/27;
* 1-25/24-27/25-7/6 with steps of 25/24-28/27-27/25-12/7 and its inverse 1-25/24-25/14-27/14 with steps of 25/24-12/7-27/25-28/27.


For pentads, there are one palindromic chord and four pairs of chords in inverse relationship. The palindromic chord is
For pentads, there are two palindromic chords and ten pairs of chords in inverse relationship. The palindromic chords are
* 1-27/25-7/6-3/2-14/9 chord with steps of 27/25-27/25-9/7-28/27-9/7.
* 1-27/25-7/6-3/2-14/9 chord with steps of 27/25-27/25-9/7-28/27-9/7;
* 1-25/24-27/25-9/8-3/2 chord with steps of 25/24-28/27-25/24-4/3-4/3.


The inversely related pairs of chords are
The inversely related pairs of chords are
* 1-27/25-25/18-3/2-27/14 with steps of 27/25-9/7-27/25-9/7-28/27 and its inverse 1-9/7-25/18-25/14-27/14 with steps of 9/7-27/25-9/7-27/25-28/27;
* 1-27/25-7/6-25/18-14/9 with steps of 27/25-27/25-25/21-28/25-9/7 and its inverse 1-27/25-7/6-3/2-42/25 with steps of 27/25-27/25-9/7-28/25-25/21;
* 1-27/25-7/6-25/18-3/2 with steps of 27/25-27/25-25/21-27/25-4/3 and its inverse 1-27/25-7/6-14/9-42/25 with steps of 27/25-27/25-4/3-27/25-25/21;
* 1-27/25-7/6-25/18-3/2 with steps of 27/25-27/25-25/21-27/25-4/3 and its inverse 1-27/25-7/6-14/9-42/25 with steps of 27/25-27/25-4/3-27/25-25/21;
* 1-27/25-7/6-25/18-14/9 with steps of 27/25-27/25-25/21-28/25-9/7 and its inverse 1-27/25-7/6-3/2-42/25 with steps of 27/25-27/25-9/7-28/25-25/21;
* 1-9/7-25/18-25/14-27/14 with steps of 9/7-27/25-9/7-27/25-28/27 and its inverse 1-27/25-25/18-3/2-27/14 with steps of 27/25-9/7-27/25-9/7-28/27;
* 1-25/18-3/2-25/14-27/14 with steps of 25/18-27/25-25/21-27/25-28/27 and its inverse 1-27/25-3/2-14/9-42/25 with steps of 27/25-25/18-28/27-27/25-25/21.
* 1-25/18-3/2-25/14-27/14 with steps of 25/18-27/25-25/21-27/25-28/27 and its inverse 1-27/25-3/2-14/9-42/25 with steps of 27/25-25/18-28/27-27/25-25/21;
* 1-27/25-9/8-7/6-3/2 with steps of 27/25-25/24-28/27-9/7-4/3 and its inverse 1-9/7-4/3-25/18-3/2 with steps of 9/7-28/27-25/24-27/25-4/3;
* 1-25/24-27/25-7/6-3/2 with steps of 25/24-28/27-27/25-9/7-4/3 and its inverse 1-9/7-25/18-36/25-3/2 with steps of 9/7-27/25-28/27-25/24-4/3;
* 1-25/24-27/25-25/18-3/2 with steps of 25/24-28/27-9/7-27/25-4/3 and its inverse 1-27/25-25/18-36/25-3/2 with steps of 27/25-9/7-28/27-25/24-4/3;
* 1-25/24-27/25-7/6-25/18 with steps of 25/24-28/27-27/25-25/21-36/25 and its inverse 1-25/21-9/7-4/3-25/18 with steps of 25/21-27/25-28/27-25/24-36/25.
* 1-25/24-27/25-25/18-27/14 with steps of 25/24-28/27-9/7-25/18-28/27 and its inverse 1-25/24-27/25-3/2-27/14 with steps of 25/24-28/27-25/18-9/7-28/27.
* 1-25/24-27/25-9/8-7/6 with steps of 25/24-28/27-25/24-28/27-12/7 and its inverse 1-25/24-27/25-9/8-27/14 with steps of 25/24-28/27-25/24-12/7-28/27.
 
For hexads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is
* 1-25/24-27/25-25/18-3/2-27/14 chord with steps of 25/24-28/27-9/7-27/25-9/7-28/27.


They can be extended to hexads as
The inversely related pairs of chords are
* 1-27/25-7/6-25/18-3/2-14/9 with steps of 27/25-27/25-25/21-27/25-28/27-9/7 and its inverse 1-27/25-7/6-3/2-14/9-42/25 with steps of 27/25-27/25-9/7-28/27-27/25-25/21.
* 1-27/25-7/6-25/18-3/2-14/9 with steps of 27/25-27/25-25/21-27/25-28/27-9/7 and its inverse 1-27/25-7/6-3/2-14/9-42/25 with steps of 27/25-27/25-9/7-28/27-27/25-25/21;
* 1-25/24-27/25-7/6-25/18-3/2 with steps of 25/24-28/27-27/25-25/21-27/25-4/3 and its inverse 1-27/25-9/7-25/18-36/25-3/2 with steps of 27/25-25/21-27/25-28/27-25/24-4/3;
* 1-25/24-27/25-9/8-7/6-3/2 with steps of 25/24-28/27-25/24-28/27-9/7-4/3 and its inverse 1-25/24-27/25-9/8-3/2-27/14 with steps of 25/24-28/27-25/24-4/3-9/7-28/27.


Equal temperaments with ragismic chords include {{Optimal ET sequence|19, 53, 72, 99, 118, 152, 171, 224, 270, 323, 441, 494, 612, 665, 783, 935, 1106, 1277 and 1547}}.
Equal temperaments with ragismic chords include {{Optimal ET sequence|19, 53, 72, 99, 118, 152, 171, 224, 270, 323, 441, 494, 612, 665, 783, 935, 1106, 1277 and 1547}}.
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