Let’s think of tetrachords as a requisite for understanding modes. In order to do so, we should first consider the previous definition that I gave for a tetrachord: a group of four consecutive notes that make up either the lower or upper segment of a scale or mode and whose sum is equal to the interval of a fourth.
We’re going to change that definition slightly by putting a new condition on it, sort of, by adding that the sum of the notes must be equal to the interval of a perfect fourth. Eventually we’ll see that there are exceptions to this, but it’s important to understand that for now we’re concentrating on what are referred to as the three ancient tetrachords: Lydian, Dorian, and Phrygian.
The following examples illustrate the construction of three different modes. Each of these modes consists of two equal tetrachords separated from one another by the interval of a whole tone, or a major second. Each of the tetrachords complies with our current definition, that the sum of the four notes must be equal to the interval of a perfect fourth.
I realize that I haven’t explained yet the difference between the three tetrachords or how they are constructed. In the next post, we’ll take a closer look at the intervals that make up each. For now, it might be worth giving some consideration to the whole-tone interval that separates the tetrachords; those intervals are shown in green. Can we continue following this same pattern? What happens if we keep going? Will the tetrachords continue to keep the same distance apart?
In the final example below, I’ve put all of the modes that were created above into a single scale that spans four octaves. Unless we add an accidental to the final measure (an F#), our pattern comes to an abrupt stop when it runs into the semi-tone interval between the final two measures, highlighted in red. There are a couple of ways that this could be handled, but what happened to our nice little sequence? Where do we go from here?
I’m not sure that this answers many questions, or if anyone was even asking. If you’re curious about why there are twelve tones in western music and how those notes became organized into the scales and modes that we still use today, I hope that presenting the information in this way might begin to provide a little insight. I know I’m continually trying to get to the bottom of it.
There’s a lot more that could be said about this last example, but I think it might be best to come back to it in the future. In the meantime, your thoughts, comments, criticisms and/or questions are always welcomed.