extended triad types iii

In this post we're going to look at extended triads in the way in which some might believe we should have done at the beginning: analytically or simply mathematically. The reason we didn't begin this way is because I wanted to demonstrate that there are real (and not just conceptual/theoretical) reasons why one needs the idea of extended triads, viz. the fact that they are produced naturally in certain scales.

So let's consider triads this way: chords consisting of a root, 3rd and 5th (as opposed to a harmonic structure that has just any 3 tones). As for 3rds we will allow diminished, minor, major and augmented; and for 5ths we'll allow diminished, perfect and augmented. The reason for "will allow" is that these intervals are all found naturally occurring in scales (such as the whole-half diminished and ionian flat-2, etc). We aren't going to examine triads which are comprised of a quadruply diminished 3rd and a quintuply augmented 5th (which triad would produce a third lower than the root and the like -- this could be interesting in a modern physics/mathematical kind of way but it's not extremely useful to us at present.

So based on our options of intervals we can simplify the triad families based on the 5th: there are only three kinds (diminished, perfect and augmented). Each family will have 4 types of third (diminished, minor, major and augmented). You won't have to resort to your calculator to figure, then, that there are, all in all, 12 triads. Here's a 1000 words:


The 3rds in blue denote that that chord is a basic triad type (diminished, minor, major or augmented) -- for example, the min 3rd in the diminished 5th family is blue because that chord is your garden variety diminished triad. And another 1000 words follow here with actual instantiations of all of the chord types:



Finally some issues of nomenclature. A M3P5 chord is simply called a major chord, so all chords containing a major or minor 3rd could be likewise appelled (a major diminished chord for M3dim5). Also since perfect 5ths are somewhat privileged we could drop that part of the name when it occurs: a diminished 3rd chord, an augmented 3rd chord.

Lastly -- and as promised -- let's look at the °3dim chord again. It has another name and is actually an extremely common chord in common practice "classical" music. Here it is in first inversion, showing its outer voice resolution:



Yes, that's right! An It+6 chord! For our purposes, then, the It+6 chord in root position is simply an It°3 chord. More on augmented 6th chords to come.

Play through these chords: some of these triads will undoubtedly be (or become) sonically interesting to you...

see also extended triads i, extended triads ii, basic triads