Tetrachords: 4 plus 4 equals 7 (pt.5)

In the last post, we saw how inseparable the three basic tetrachords are. The Lydian, Dorian and Phrygian tetrachords co-exist with each other through a shared symmetry. When all three sets of notes are aligned with one another, they form a mirror-like image that adds up to the interval of a sixth.

Remember that what we’re trying to do here is use these tetrachords as an explanation for why the keyboard of a piano is set up the way that it is.

We’re going to continue on and complete the building of the keyboard by repeating each of our tetrachords with an identical tetrachord that begins on the next available white puzzle-piece. Scrolling through the images will illustrate that the keyboard is fully-realized through the combination of a lower and upper tetrachord.

lower_tetrachords

upper_tetrachords

upper_lower_tetrachords_combined

The lower and upper tetrachords are combined to form the completed version of the piano keyboard. The combination also results in the creation of the Ionian (two Lydian tetrachords), Dorian, and Phrygian modes.

Combining two equal tetrachords a whole-tone apart is the basis for the heptatonic scales of western harmony. The overlapping tetrachords account for the semi-tone that separates consecutive repetitions of two tetrachords; this is also the note that the creates tri-tone interval that splits the octave in half (count on more information about tri-tones later) and is the reason why black keys on a piano alternate between groups of two’s and three’s. Together, each of the equal pairings of tetrachords span seven unique notes; an octave now exists between the first of the lower and the last of the upper tetrachord notes.

I mentioned in an earlier post that regardless of the how the pieces appear arranged and organized by color or size, the distance between any two adjacent notes is an equal distance. The next step in making sense of the keyboard is to understand that our tetrachords can be created from any starting point by following the same logic of tone and semi-tone relationships for each tetrachord.

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