Triad names

Aha!

Consider the traditional naming of triads (built by stacking thirds from the root upwards):
- m3, m3: diminished triad
- m3, M3: minor triad
- M3, m3: major triad
- M3, M3: augmented triad

What is "diminished" about a diminished triad? Its diminished fifth, according to the traditional interval-naming scheme.

What is "augmented" about an augmented triad? Its augmented fifth, according to the traditional interval-naming scheme.

That is, the traditional naming-rule for triads is:
- If both of the triad's thirds are the same width, name the triad after the width of the fifth.
- Else, name the triad after the width of its bottom third interval (i.e., the one between the chord's mode's 1st and 3rd degrees).

If JIMS re-names the narrow fifth "minor" and the width fifth "major," as discussed below, then the traditional triad-naming rule doesn't make sense within JIMS. That means that JIMS either needs to (a) not rename the fifths, (b) rename the triads, or (c) redefine the triad-naming rule.

I like the latter option best (re-defining the triad-naming rule). With this approach, JIMS' rule for naming triads would be:
- If both thirds are minor, the triad is "diminished."
- If the thirds differ, name the triad after the width of its bottom third.
- If both thirds are major, then the triad is "augmented."

This rule produces the same triad names as the traditional rule, but without relying on the name of the triad's fifth.

I like this approach because it recognizes that the triad is what is diminished or augmented, not the triad's fifth, which is as independently major or minor as the thirds are.

I'll have to think about the naming of seventh chords, too. There seems to be a lot of variation in seventh-chord naming anyway, between classical and jazz traditions, so a little more variation wouldn't be shocking.