Archytas chords

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.