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]]. | ||
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. | ||
[[Category:7-odd-limit]] | 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. | |||
There is also an archytas tetrad involving [[prime interval|prime]] [[5/1|5]]: | |||
* 1–8/7–5/4–10/7 with steps 8/7, 10/9, 8/7, 7/5. | |||
For a list of equal temperaments with archytas chords, see the optimal ET sequence in [[Archytas family #Archytas]]. | |||
== Ares chords == | |||
'''Ares chords''' are [[essentially tempered chord]]s tempered by any two of 64/63, [[100/99]], and [[176/175]]. There are exactly two ares chords in the [[11-odd-limit]], both being palindromic pentads: | |||
* 1–10/9–5/4–10/7–11/7 with steps 10/9, 8/7, 8/7, 10/9, 14/11. | |||
* 1–8/7–5/4–11/8–11/7 with steps 8/7, 10/9, 10/9, 8/7, 14/11. | |||
For a list of equal temperaments with ares chords, see the optimal ET sequence in [[Archytas family #Ares]]. | |||
[[Category:7-odd-limit chords]] | |||
[[Category:9-odd-limit chords]] | |||
[[Category:11-odd-limit chords]] | |||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||
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[[Category:Pentads]] | [[Category:Pentads]] | ||
[[Category:Archytas]] | [[Category:Archytas]] | ||
[[Category:Ares]] | |||
Latest revision as of 11:33, 16 December 2025
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.
There is also an archytas tetrad involving prime 5:
- 1–8/7–5/4–10/7 with steps 8/7, 10/9, 8/7, 7/5.
For a list of equal temperaments with archytas chords, see the optimal ET sequence in Archytas family #Archytas.
Ares chords
Ares chords are essentially tempered chords tempered by any two of 64/63, 100/99, and 176/175. There are exactly two ares chords in the 11-odd-limit, both being palindromic pentads:
- 1–10/9–5/4–10/7–11/7 with steps 10/9, 8/7, 8/7, 10/9, 14/11.
- 1–8/7–5/4–11/8–11/7 with steps 8/7, 10/9, 10/9, 8/7, 14/11.
For a list of equal temperaments with ares chords, see the optimal ET sequence in Archytas family #Ares.