I sort of dropped the ball on this series, but I’m back. Anyway…when I last left this discussion, we had defined 2 of our 4 answers to the question ofhow many unique triads there are (48 and 68). Today, as promised, we’ll talk about the next answer, which is 84.
To recap, we get 48 by simply multiplying the 12 unique tones of the octave by the 4 types of triads to get how many different sounding triads there are.
68 we got by adding in enharmonic spellings of black keys (e.g. F# and Gb are two different spellings of the same tone). This gave 17 possible roots x4 possible chord types. And this set is the set of chord spellings for every chord which cannot be spelled in a simpler way (but may have 2 equally simple spellings).
So, let’s talk 84. As it turns out, black keys aren’t the only ones that have multiple names. When you first start learning music theory you might have learned that there is no such thing as B#. But that’s not exactly true. B# does exist, it’s just enharmonic to C. To sharp a note really just means to raise it by half a step (the opposite is true of flatting). This can be done even if there is no adjacent white key to raise or lower it to. So the note B# is actually the white key we would normally call C. Like any note, though, we can build triads off of it. In this case, B# diminished would be (B#, D#, F#). C diminished on the other hand is (C, Eb, Gb). The same keys. Just as the two notes sound identical but are spelled differently, so too the chords we build off of them. So, to our list of possible roots, we can now add B# (enharmonic to C), E# (enharmonic to F), Cb (enharmonic to B), and Fb (enharmonic to E). 4 more roots x 4 triad types yields 16 more possible triads, which gets us to 84.
But the weirdest is yet to come. Next time we’ll talk about how there are actually an infinite number of triads.