You might be wondering why I continue to write so much about tetrachords. Are they really that important?
I’ve brought up the idea that we’re trying to solve a puzzle, one that we already have the answer to if we just look at the keyboard of any piano. It’s really more like a puzzle that we’re un-building. By focusing on the construction of tetrachords, we’re actually looking at the structure of the keyboard, which is an arguably perfect visualization for the western tonal system.
Perhaps one of the more significant things to keep in mind as we continue with tetrachords is that the sum distance of these six-note patterns is equal to the interval of a perfect 4th. We may argue later about just how perfect the 4th may or may not actually be, but we cannot argue its importance.
Keep in mind that so far we’ve managed to avoid giving our puzzle pieces any of the letter names that we associate with specific keys or pitches. We can continue to do this so long as we still agree that the distance between each neighboring note is equal to any other neighboring note. In seeing the keyboard this way, without assigning a conventional naming system, then no single pitch has more importance than any other; we’re simply concentrating on seeing the patterns where ever they exist on the keyboard. Letter names will be added soon enough when we look at where the pitches come from and how those pitches are notated; music is a language is a language after all, and all languages need an alphabet.
Scrolling through the images below will illustrate how the Lydian, Dorian and Phrygian tetrachords are part of the larger puzzle that we’re un-building. As they are put together, ee can see that each of the tetrachords are inseparable from one another.
Judging from this last image that combines all three tetrachords, our keyboard is near completion with ten of the twelve pieces in place. We have ten notes and are just short of an octave. How are we going to explain the two missing pieces?