Buzurgismic chords: Difference between revisions

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'''Buzurgismic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the buzurgisma, [[169/168]].
'''Buzurgismic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the buzurgisma, [[169/168]].


The [[buzurgismic]] temperament is very comparable to the [[biyatismic]] temperament. It has 2 triads and 6 tetrads in the [[13-odd-limit]] of the 2.3.7.13 subgroup, but these all become essentially just in the [[21-odd-limit]].  
The [[buzurgismic]] temperament is very comparable to the [[biyatismic]] temperament. It has two triads, nine tetrads, seven pentads and one hexad in the 2.3.7.13 subgroup [[13-odd-limit]].  


The two buzurgismic triads are in inverse relationship:  
The two buzurgismic triads are in inverse relationship:  
* 1-16/13-12/7 with steps of 16/13-18/13-7/6;  
* 1-7/6-13/8 with steps 7/6-18/13-16/13;  
* 1-7/6-13/8 with steps of 7/6-18/13-16/13.
* 1-18/13-13/8 with steps 18/13-7/6-16/13.


For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are  
For tetrads, there are three palindromic chords and three pairs of chords in inverse relationship. The palindromic chords are  
* 1-16/13-18/13-12/7 with steps of 16/13-9/8-16/13-7/6;  
* 1-9/8-18/13-13/8 with steps 9/8-16/13-7/6-16/13;  
* 1-3/2-13/8-13/7 with steps of 3/2-13/12-8/7-13/12.  
* 1-3/2-13/8-13/7 with steps 3/2-13/12-8/7-13/12;
* 1-13/12-18/13-3/2 with steps 13/12-9/7-13/12-4/3.  


The inversely related pairs of chords are
The inversely related pairs of chords are
* 1-18/13-3/2-13/8 with steps of 18/13-13/12-13/12-16/13 and 1-13/12-3/2-13/7 with steps of 13/12-18/13-16/13-13/12;  
* 1-18/13-3/2-13/8 with steps 18/13-13/12-13/12-16/13, and its inverse
* 1-7/6-3/2-13/8 with steps of 7/6-9/7-13/12-16/13 and 1-9/7-3/2-13/7 with steps of 9/7-7/6-16/13-13/12.  
* 1-13/12-3/2-13/7 with steps 13/12-18/13-16/13-13/12;
* 1-13/12-3/2-7/4 with steps 13/12-18/13-7/6-8/7, and its inverse
* 1-18/13-3/2-12/7 with steps 18/13-13/12-8/7-7/6;
* 1-7/6-3/2-13/8 with steps 7/6-9/7-13/12-16/13, and its inverse
* 1-9/7-3/2-13/7 with steps 9/7-7/6-16/13-13/12.
 
For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is
* 1-9/8-18/13-3/2-13/8 with steps 9/8-16/13-13/12-13/12-16/13.
 
The inversely related pairs of chords are
* 1-13/12-7/6-3/2-13/8 with steps 13/12-13/12-9/7-13/12-16/13, and its inverse
* 1-9/7-18/13-3/2-13/7 with steps 9/7-13/12-13/12-16/13-13/12;
* 1-13/12-7/6-3/2-7/4 with steps 13/12-13/12-9/7-7/6-8/7, and its inverse
* 1-9/7-18/13-3/2-12/7 with steps 9/7-13/12-13/12-8/7-7/6;
* 1-13/12-3/2-13/8-7/4 with steps 13/12-18/13-13/12-13/12-8/7, and its inverse
* 1-18/13-3/2-12/7-13/7 with steps 18/13-13/12-8/7-13/12-13/12;
 
Finally, there is a palindromic hexad,
* 1-13/12-7/6-3/2-13/8-7/4 with steps 13/12-13/12-9/7-13/12-13/12-8/7.  


[[Category:13-odd-limit]]
[[Category:13-odd-limit]]
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[[Category:Triads]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]
[[Category:Buzurgismic]]
[[Category:Buzurgismic]]

Revision as of 12:44, 9 September 2023

Buzurgismic chords are essentially tempered dyadic chords tempered by the buzurgisma, 169/168.

The buzurgismic temperament is very comparable to the biyatismic temperament. It has two triads, nine tetrads, seven pentads and one hexad in the 2.3.7.13 subgroup 13-odd-limit.

The two buzurgismic triads are in inverse relationship:

  • 1-7/6-13/8 with steps 7/6-18/13-16/13;
  • 1-18/13-13/8 with steps 18/13-7/6-16/13.

For tetrads, there are three palindromic chords and three pairs of chords in inverse relationship. The palindromic chords are

  • 1-9/8-18/13-13/8 with steps 9/8-16/13-7/6-16/13;
  • 1-3/2-13/8-13/7 with steps 3/2-13/12-8/7-13/12;
  • 1-13/12-18/13-3/2 with steps 13/12-9/7-13/12-4/3.

The inversely related pairs of chords are

  • 1-18/13-3/2-13/8 with steps 18/13-13/12-13/12-16/13, and its inverse
  • 1-13/12-3/2-13/7 with steps 13/12-18/13-16/13-13/12;
  • 1-13/12-3/2-7/4 with steps 13/12-18/13-7/6-8/7, and its inverse
  • 1-18/13-3/2-12/7 with steps 18/13-13/12-8/7-7/6;
  • 1-7/6-3/2-13/8 with steps 7/6-9/7-13/12-16/13, and its inverse
  • 1-9/7-3/2-13/7 with steps 9/7-7/6-16/13-13/12.

For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is

  • 1-9/8-18/13-3/2-13/8 with steps 9/8-16/13-13/12-13/12-16/13.

The inversely related pairs of chords are

  • 1-13/12-7/6-3/2-13/8 with steps 13/12-13/12-9/7-13/12-16/13, and its inverse
  • 1-9/7-18/13-3/2-13/7 with steps 9/7-13/12-13/12-16/13-13/12;
  • 1-13/12-7/6-3/2-7/4 with steps 13/12-13/12-9/7-7/6-8/7, and its inverse
  • 1-9/7-18/13-3/2-12/7 with steps 9/7-13/12-13/12-8/7-7/6;
  • 1-13/12-3/2-13/8-7/4 with steps 13/12-18/13-13/12-13/12-8/7, and its inverse
  • 1-18/13-3/2-12/7-13/7 with steps 18/13-13/12-8/7-13/12-13/12;

Finally, there is a palindromic hexad,

  • 1-13/12-7/6-3/2-13/8-7/4 with steps 13/12-13/12-9/7-13/12-13/12-8/7.
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