tetrachords i

I mentioned tetrachords in passing before. Tetra in Greek means four, and chordos means string, but as in a lyre (or harp) string, so we can also read this as note. We won't go into Greek music theory here (where the 2 outside parts of the tetrachord were constant while the middle two changed): suffice to say that a tetrachord is 4 contiguous notes. I'd say it's a perfect 4th, but we're going to use the tetrachord as a way of analyzing parts of modes/scales, and in the instance of the Lydian mode (say) it's an augmented 4th.

A major scale (or any 7-note scale) can be seen as 2 disjunct (not overlapping) tetrachords:

In this case both tetrachords are a P4 in span, and are exactly the same in terms of intervals:
W, W, H, or M2, M2, m2. Let's call this the major tetrachord.
A major scale therefore = major tetrachord + major tetrachord.

If we examine a melodic minor scale we see these 2 tetrachords:

These tetrachords are different: the lower one is M2, m2, M2. Let's call this the minor tetrachord. The upper tetrachord is the same as in the major scale. So we can say that a melodic minor scale is a minor tetrachord + major tetrachord.

If we stick with just these 2 types of tetrachords let's see what other combinations we can can come up with.

Try a minor tetrachord + minor tetrachord:
Look familiar? This is the Dorian mode.


How about a major tetrachord + minor tetrachord:
This is the Mixolydian mode.

Let's look at one more scale today: the natural minor/aeolian.
Here the lower tetrachord is the familiar minor tetrachord but the upper one is different. Based on the Phrygian mode (with it's lowered 2nd and 3rd) let's call this the phrygian tetrachord.
So a natural minor/aeolian scale is a minor tetrachord + phrygian tetrachord.

In fact the Phrygian mode can be seen as 2 phrygian tetrachords:

By adding this third type of tetrachord let's see what scales we can generate. Play these so that you can hear them:

major tetrachord + phrygian tetrachord = Mixolydian b6 (mode V of a melodic minor scale).

phrygian tetrachord + major tetrachord = Neapolitan Major

phrygian tetrachord + minor tetrachord = Dorian b2 (mode II of a melodic minor scale).

So from just 3 different tetrachords we've been able to come up with 9 different modes. In fact I discussed this with a physicist friend of mine who informed me that the formula for determining how n objects can be arranged into a pair is simply n². We could, therefore, arrange 6 different tetrachords into 36 different scales!

I bring up tetrachords because since they're small they're easier to deal with conceptually. Also, at least for guitarists a tetrachord is easy to finger, and therefore it's easy to string them together. Try playing a major tetrachord starting on C then play a major tetrachord starting on G: you get the major scale (as above) and it's super easy to play.

Next tetrachord session we'll look at the Harmonic Minor and Lydian modes to see what tetrachords they possess and what we can generate then with all of our various tetrachords.