## Thursday, June 7, 2018

### Seventh Chords

What are seventh chords? Chords that contain the seventh note in a scale starting from the root of the chord! That's not a very practical answer, though, when experimenting with microtonality, where scales are not clearly defined. Here is an alternate definition: a seventh chord is a four note chord constructed by stacking thirds. The root note is the foundation. The next note is a third above the root. Another third above that is some sort of fifth note. Another third above that is some sort of seventh note. Typically the interval of a third is composed of two steps of a scale. So a seventh chord looks like 1-3-5-7 in terms of steps of a scale. But intervals are more fundamental than scales. The notion of a sequence of three intervals, each a third, makes sense even without any scale.

There are two different intervals of a third: a major third and a minor third. This gives eight different types of seventh chords, built from sequences of these different thirds, e.g. major-major-major, major-major-minor, major-minor-major, etc.

To find out how these seventh chords sound in the microtonal system where an octave is divided into 53 equal steps (rather than the conventional 12 steps), I wrote a little program that uses simulated annealing to construct a fractal pattern near a phase transition. The program builds a 12x12x12 toroidal mesh and places a seventh chord at each vertex. The total number of possible chords is 8x53=424. Each vertex can have any one of these 424 chords. Chords at neighboring vertices are probabilistically selected to be similar to each other. Chords are more similar the more notes they have in common.

The result, so far at least, is not very musical! But it's a lot of seventh chords! 1728 sevenths