tetrachords iii

So here's another post concerning tetrachords (for the earlier posts: part i, part ii). This time we're going to work with the lydian tetrachord:

This tetrachord is different from all the others we've dealt with because it outlines an augmented fourth (the famed tritone) as opposed to a perfect fourth. This has some implications that we'll get to in a minute.

Our other tetrachords up to this point are as follows: major, minor, phrygian, harmonic. With the lydian tetrachord we have a pool of 5, meaning that we should be able to come up with 25 pairs altogether. We've accrued 16, meaning that the lydian will give us an additional 9. But not really...

Let's start with the lydian tetrachord as the lower tetrachord. We'll base these on C, but it could be any tone:

lyd tet + maj tet = c d e f# g a b c = Lydian mode
lyd tet + min tet = c d e f# g a bb c = Overtone aka Lydian b7 (mode IV of harmonic minor)
lyd tet + phryg tet = c d e f# g ab bb c
lyd tet + harm tet = c d e f# g ab b c

So let's put the lydian tetrachord on top now. Since it outlines an aug 4th we'll have to adjust the tetrachord's position if we want the last tone to be an octave of the first tone (in this case a c). We can do this by starting the lydian tetrachord a semitone (or half-step or minor second) above the lower tetrachord, as opposed to a full tone.

maj tet + lyd tet = c d e f gb ab bb c
min tet + lyd tet = c d eb f gb ab bb c = Aeolian b5 [mode III of melodic minor]
phryg tet + lyd tet = c db eb f gb ab bb c = Locrian mode
harm tet + lyd tet = c db e f gb ab bb c

There's one more combination: lyd tet + lyd tet. BUT there's a problem here.

lyd tet + lyd tet = c d e f# g a b c#

The last tone is an issue. It takes us into the realm of octatonic scales: 8 tone scales as opposed to the 7 note scales we've been dealing with. There's no easy fix in this situation, because if we lower the upper tetrachord's position by a semitone we'll simply duplicate the f#, and technically we'd end up with a hexatonic scale. Though this hexatonic scale is famous...see if you know it:

c d e f# ab bb c.

If we rename this enharmonically it's much more obvious:

c d e f# g# a# c, aka the whole tone scale.

Hopefully you'll find that tetrachords are somewhat helpful or at least interesting, as opposed to being unduly complicated. Play them and see...