The tetrachord

Harmony tutorial

This time we are going to talk about harmony. A basic harmony concept is the tetrachord. This word means "4 notes". To understand tetrachords will help us to understand music scales later.

Steps and half steps.

The distance between two adjacent notes in the chromatic scale is called a half step. For example: the distance between C and C# or between F and F#. This is also the case between G and Ab and so on. This is easier to understand looking at a music keyboard. The closest key is a half step away, it doesn't matter if it's a black or white key. Now, two half steps make a step (whole step). For example, there is a step between C and D. From E to F there is a half step, but from Eb to F there's a whole step. Another example would be the distance from B to C#, a step.

The tetrachord formula.

Ok, so to create a tetrachord we have to use this formula:
S - S - HS
Where: S = Step and HS = Half Step. We can make tetrachords from any note. For example, let's start from C, following the formula we get:
  1. Our first note: C
  2. We count one Step ahead: D
  3. We count another Step ahead: E
  4. We count one Half Step now: F
The formula S - S - HS gives us the notes: C, D, E and F. These notes make the C tetrachord. Easy huh? Let's see another example. Now the D tetrachord:
  1. We start from D
  2. One Step ahead: E
  3. One Step ahead: F#
  4. One Half Step ahead: G
So, the D tetrachord is built with the notes: D, E, F# and G.

 Now, let's build the F tetrachord:
  1. We start with F
  2. One Step: G
  3. One Step: A
  4. One Half Step: Bb
So, the F tetrachord is made with the notes: F, G, A and Bb. A common question is why to use Bb and not A# instead? Well, the answer is that the tetrachords MUST be made with consecutive letter names, we cannot repeat nor skip any. So in a tetrachord we cannot find an A and an A#, nor an Eb and an E, etc. In the same way, we cannot have E and skip to Gb instead of F#. In this fashion, we can (and we should) create tetrachords from every single note. This exercise will give us a lot of fluency to better understand scales and other harmony topics later.

Finally, to grasp tetrachords requires practice. It's very important to play them with a musical instrument so we can hear how they sound. The tetrachord "sound" will be our base for the major scales.


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