Intervals and Steps
What makes intervals and steps so important in music? Well, basically, they are the fundamental building blocks. I like to think of them as letters. When you put them together in the right order they spell out a scale, much like a word. And, while note names are tied to certain frequencies (440hz for standard A4), intervals express the relationship between them. This way you can start on any pitch, even one not technically “in tune” and still build out any scale. Understanding intervals with your ears is especially useful as it is the first step to developing a solid foundation for relative pitch. Once you develop relative pitch you can figure music out by ear quite easily.
In this article about major chords and this one about minor chords we talked a little about intervals. Mostly we cover distances between triad notes in half-steps and the importance of the 3rd of the scale. You can check those articles out if any of that feels confusing.
Knowing the importance of the interval of a 3rd in chords transfers right on over to scales. Just like chords, if the 3rd is major, then the scale is major. Likewise for minor 3rds and scales.
Theory and Language
I like to always acknowledge that all music theory is after-the-fact. Music doesn’t come from the theory, instead the theory comes from the music. Much like language, it is a natural and chaotic force for which we come up with grammar and syntax rules as best we can. All we can really do is nail down a few general concepts and set out some guidelines based on what has worked before. Much of the time it is even just describing a style. In this way standard classical music theory can greatly differ from, say, contemporary jazz. Again with the language comparison, we could say classical is French and jazz is Spanish. They share a lot of sounds and basic ideas, but pronunciation and vocabulary are very much idiosyncratic.
A Few Steps to Major
Ok, so what is this all about then? Let’s have a look at what steps make the major scale. Here we’re going use only half-steps and whole-steps to build out a kind of equation. We’ll start with a scale, though, and figure out the equation from there. The music comes first, right?
Since it has no sharps or flats, here is C Major:
As you can see, we just go from ‘C’ to ‘C’ in alphabetical order. Remember that ‘G’ is the last letter in the musical alphabet, so we jump back to ‘A’ afterwards.
Going from C to D calls for us to pass by a C# on the way. Remembering that a half-step is the smallest movement from one note to the next, we get 2 half steps in order to reach D. One half step from C to C#, and one more from C# to D. Now for some simple math
1/2 + 1/2 = ?
Eh… well, math was never my strong suit, but I believe it comes out to 1. In other words, 2 half steps = 1 whole step. Ok, I follow. So, that means for every time we have a whole step, we are passing by a note along the way. On the other hand, a half step means we go from one note to the next without skipping any.
Now, what about D to E? There is a D# between them, so we have another whole step. Ok, so far we have 2 whole steps.
E to F? E# and F are enharmonic equivalents (the same frequency, just different use cases), so we don’t skip any notes here. A half step it is.
F to G = whole step after skipping over F#.
G to A? Whole step.
A to B? Whole step.
B to C? Ah, here we have another half step, since B# would be the same as C. Alright then, I think we have it.
We can build out any scale using this approach, but let’s leave that for next time where we’ll have a look at minor scales. I would suggest trying out building up scales from different start notes and see what you come up with. Don’t forget, in some cases, depending on what note you choose to start with, you can end up having what are called ‘double sharps’ or ‘double flats’. That shouldn’t be an issue if you stick to the standard major scales for now. When in doubt, your scales should never have repeated notes. So, if you have A – A#, you’ll most likely want to change the A# to a Bb. That way you end up with A – Bb.
Go ahead and give it a try! Just remember the formula: W – W – H – W – W – W – H.