Archytas chords: Difference between revisions

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'''Archytas chords''' are [[essentially tempered chord]]s tempered by the archytas comma, [[64/63]].  
'''Archytas chords''' are [[essentially tempered chord]]s tempered by the archytas comma, [[64/63]].  


These include the following palindromic triad in the [[7-odd-limit]]:  
The only archytas triad is the following palindromic triad in the [[7-odd-limit]], presented as a stack of two fourths here:  
* 1–4/3–7/4 with steps 4/3, 4/3, 8/7.  
* 1–4/3–7/4 with steps 4/3, 4/3, 8/7.  


as well as the following palindromic tetrad:  
Note that one rotation is the sus2 chord (1–8/7–3/2) and the other is the sus4 chord (1–4/3–3/2). In any case, it becomes an essentially just chord in the [[9-odd-limit]].
 
Another archytas chord is the following palindromic tetrad that could be called the archy sus4/7 chord:  
* 1–4/3–3/2–7/4 with steps 4/3, 8/7, 7/6, 8/7.  
* 1–4/3–3/2–7/4 with steps 4/3, 8/7, 7/6, 8/7.  


In the [[9-odd-limit]], we have an additional palindromic pentad:  
Unlike the triad above, this chord remains essentially tempered in the 9-odd-limit. It makes for an interesting comparison with the [[didymic chords|meantone sus2/6 chord]].
 
In the 9-odd-limit, we have an additional palindromic pentad, which also happens to be the [[2L 3s|pentic]] scale [[archy5|Archy[5]]]:  
* 1–7/6–4/3–3/2–7/4 with steps 7/6, 8/7, 8/7, 7/6, 8/7.  
* 1–7/6–4/3–3/2–7/4 with steps 7/6, 8/7, 8/7, 7/6, 8/7.  


[[Category:7-odd-limit chords]]
[[Category:7-odd-limit chords]]
[[Category:9-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Triads]]

Revision as of 10:08, 9 October 2024

Archytas chords are essentially tempered chords tempered by the archytas comma, 64/63.

The only archytas triad is the following palindromic triad in the 7-odd-limit, presented as a stack of two fourths here:

  • 1–4/3–7/4 with steps 4/3, 4/3, 8/7.

Note that one rotation is the sus2 chord (1–8/7–3/2) and the other is the sus4 chord (1–4/3–3/2). In any case, it becomes an essentially just chord in the 9-odd-limit.

Another archytas chord is the following palindromic tetrad that could be called the archy sus4/7 chord:

  • 1–4/3–3/2–7/4 with steps 4/3, 8/7, 7/6, 8/7.

Unlike the triad above, this chord remains essentially tempered in the 9-odd-limit. It makes for an interesting comparison with the meantone sus2/6 chord.

In the 9-odd-limit, we have an additional palindromic pentad, which also happens to be the pentic scale Archy[5]:

  • 1–7/6–4/3–3/2–7/4 with steps 7/6, 8/7, 8/7, 7/6, 8/7.