Meet the Trichords

Under certain assumptions (which I'll talk about in a moment) there are only 12 three-note chords. I'm hoping to dig into some of the more unusual ones in later posts so here's a quick survey of them.

In jazz we often like chords with four rather than three notes, but there are a lot more tetrachords so starting with trichords seemed sensible. Plus, when playing with others these smaller chords can be extremely useful.

The chords are considered here as pitch class sets, which means we don't care about transpositions or inversions. Ignoring transpositions is uncontroversial enough; after all, we want these concepts at the level of "augmented triad", not something specific like "Eb aug".

Ignoring inversions is a bit weirder-looking. The motivation for this is that the sound of a chord comes largely from the total set of intervals between its notes, and inverting a chord doesn't change this. But this collapses together some things that really do sound different: for example, the major triad inverts to a minor triad, so in this approach they count as the same thing. I'll chart a middle course on this and treat a trichord and its inversion as different but closely-related things.

Here's a complete list of all the possibilities, grouped into three types according to whether their smallest interval is a minor second (Type 1), a major second (Type 2) or something bigger (Type 3). I've added the standard Forte numbers (3-1 etc), and used "I" to flag up the ones that are inversions.

The Type 3 chords are already familiar: from left to right they're just the diminished, minor, major and augmented triads. So these are not so interesting. It's the other 15 that offer some opportunities for further exploration. More to follow on this...

Incidentally, although classics like Forte's book are great the most useful book I know of on this stuff is Friedmann's Ear Training for Twentieth Century Music. When I feel lazy or suspect I've made a mistake, this calculator is extremely helpful.