Theory Level: Intermediate
Ok, so let’s put our Bb Augmented chord aside. We’ll come back to it. Two weeks ago, I posed the question: How many different triads are there, and I proposed 4 different answers. Those answers were 48, 68, 84, and infinitely many. So let’s look at each of those answers in turn.
Answer #1: 48.
This one is simple. As we discussed last week, there are 4 different triad qualities, diminished, minor, major, and augmented, which each come from stacking a combination of two thirds on top of one another, (min+min), (min+maj), (maj+min) and (maj+maj) respectively. These are the only possible ways to stack two thirds. There are 12 tones in the octave, 4x12=48. So there are only 48 possible combinations of tones that create a triad (again excluding inversions, doublings and spread voicings but that was part of the original rules).
Answer #2: 68
The first answer is good enough if what you want to know is how many combinations of tones can be combined to create triads. But that isn’t the full story because sometimes 1 set of tones can have 2 different names, and what you call it matters to how you understand the role of a particular chord in a particular piece of music (I’m going to come back to this concept but for now just trust me. It matters). For instance, if I build a major chord (4+3) from an F# root I get F#,A#,C#. But that root note can also be called Gb, and if I spell it that way I get Gb,Bb,Db. These chords sound exactly the same because they contain the same tones (sounds) but are spelled differently.
This is what we mean by musical homophones. In linguistics we can have two different words that sound the same but are spelled differently and have different meanings (e.g. right and write). In speech they are interchangeable, but if you write(wink) the wrong one, you are wrong. Music works the same way. F# Major and Gb Major sound the same but are spelled differently and have different meanings (function).
So, if we treat each black key as having 2 common names, we get 17 possible roots (5 black keys with 2 names each and 7 white keys with 1 name each). 17x4=68.
Those other two answers get even stranger. But I’ll get to that next week.