The three primary tetrachords that we’ve been focusing on have been the Lydian, Dorian, and Phrygian. Each of these tetrachords collectively span six unique pitches that are an equal distance apart. By using a combination of tone and semi-tone intervals, the four-note tetrachords are formed. Each of these three tetrachords are equal to the interval of a perfect fourth, and given the criteria outlined above, these are the only three possible combination.
The one exception to the above conditions belongs to the Locrian tetrachord. We encountered this when we combined the lower and upper tetrachords together to form the completed keyboard, which accounted for the appearance of the group of three black keys. The addition of the seventh pitch in this cluster forced the arrangement of white keys to become augmented because of the extra semi-tone interval. The notes of the the Locrian tetrachord are comprised of only whole-tone intervals.
Below are the remaining Lydian, Dorian, and Phrygian tetrachords as they can be found on the keyboard. These two segments of perfect fourth intervals occur between two black keys. These are the last of the isolated tetrachords that can be formed.
This won’t be the last we’ll hear from the tetrachords, but they will likely take a back seat for a while. For one thing, I’m getting a bit exhausted thinking about them and need a break just from typing the word.
Before long, modes will have to be addressed and will bring us back around to the tetrachords again. Something to think about before that time comes is to consider that modes are not just major scales that begin from a note other than the tonic. Part of looking at the tetrachords with such detail is so that we can eventually look at how they work with modes to create changes of key and modulation; especially true in polyphonic music.