Theory Level: Intermediate
Here’s a question with an ambiguous answer. Ignoring inversions and doubled voicings and multi-octave range, how many distinct triads are there?
There are at least four legitimate answers to this question, and maybe more (if you come up with a different answer, I’d love to hear about it in the comments). The four possible answers are: 48, 68, 84, and infinitely many. The difference depends on what you count as a legitimate chord root, and whether you care about your answer’s real-world usefulness. BTW "There are multiple answers and one of them is infinity but that answer is a philosophical thought experiment with no practical application” is a commonly recurring theme in music theory. We’ll get to the why of each of those answers a little later in this series.
But first, I want to ask another question that only has one right (and very odd) answer. How many triads have both a sharp and a flat in them?
No matter what your answer to the first question is, the answer to this one is 1. There is exactly 1 triad that is correctly spelled with both a sharp and a flat. And that’s weird. Music is math and math generally hates rules that are universal except for a single exception. How can it be that “triads may contain either sharps OR flats but not both” is a maxim that holds in all cases except 1? And how can it be that that single exception exists whether the whole set is 48 or infinity? What is going on here?
To answer that question, we’re going to have to dive deep into the internal structure of tertian harmony, and talk not just about music and math but also about language and symbolic structures, and we’re going to make pit stops at a number of other weird, anomalous musical roadside attractions, before finally winding up talking about one of my favorite all-time theoretical concepts, and how to use it to make your composition/songwriting better. See you next week.
Oh, but before I go…any guesses what it is? What is the one and only triad that is correctly spelled with both a flat and a sharp?
Comment with the answer. You have seven days.