The Artsulli Blog

Theory Thursday: Musical Homophones Part 3

May 28, 2020

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.

How to Get More Music Fans in 8 Steps

May 26, 2020

Music publicist, Kari Zalik, explains how to grow your fanbase using an 8-step public relations campaign formula.

Theory Thursday: Musical Homophones Part 2

May 21, 2020

Theory Level: Intermediate It’s Bb Augmented. That’s the answer to last week’s question. The only triad that is properly spelled with both a sharp and a flat. In this case Bb, D, F#. But why is such a seemingly normal chord the one exception? Well, right off the bat, if you know a little theory, you probably should have guessed it would be an augmented chord. After all, every major, minor or diminished chord is diatonic in at least one major key, and since no major key signature contains both sharps and flats, it stands to reason that no major, minor, or diminished chord could possibly satisfy the requirement. And that only leaves augmented chords as possible answers. But I’ve already lost half of you, so let’s back up. The building block chords of tertian harmony (the most common system of western harmony) are triads, made by stacking two thirds on top of one another, that is starting on a root note, going up two letters, then going up two more letters (e.g. C, E, G, which is C Major). However, knowing that we go up two scale degrees (letters) doesn’t tell us everything we need to know about a chord, because notes can be sharp, natural, or flat. And thirds can be either 3 half steps (a minor third) or 4 half steps (a major third). Half steps are the smallest interval in standard western tuning, equal to a single piano key (white or black) or a single fret on the guitar. The closest two notes can be to one another in standard tuning is one half step, and a third can contain EITHER 3 OR 4 half steps. So if I go up a minor third (3 half steps) from A I’ll get C but if I go up a major third (4 half steps) I’ll get C#. Both are thirds and both are 2 letters apart. This is an important concept for later. So, if we go up a third and then another third, there are 4 possible combinations of distances between our 3 notes. 3+3 (which we call a diminished chord), 3+4 (minor), 4+3 (major), or 4+4 (augmented). Using the example root C we can get C diminished (C, Eb, Gb), C minor (C, Eb, G), C major (C, E, G), or C augmented (C, E, G#). But notice that no matter which triad we build off the root C we will end up with the same 3 letters: C, E, and G. That means that since there are only 7 letters in our musical alphabet there are only 7 combinations of letters that can form triads, and memorizing them is pretty easy. This makes tertian harmony very intuitive if you understand the basic theory, and is really quite a brilliant way to organize pitches and the chords formed from them. It also means that even though two notes might be enharmonic to one another (the same piano key), for instance C# and Db, the two are not interchangeable when spelling chords. Hence, in our Bb augmented, we cannot spell the chord Bb, D, Gb, because even though F# and Gb are the same key on the keyboard, from a spelling standpoint, Gb is three letters above D, not 2 like F#. No G note can ever be part of a triad with Bb as the root. So F# is the only correct spelling. But that still doesn’t tell us why this one chord is so special. Next week…

Theory Thursday: Musical Homophones Part 1

May 14, 2020

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.