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.

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.

Equal temperaments with archytas chords include 5, 10, 12, 15, 17, 22, 27, and 49.

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.

Equal temperaments with ares chords include 12, 15, 22, and 49.