Here’s an interesting and perhaps misunderstood note. It’s a compound move on the lattice: down a third and up a fifth. Or up a fifth and down a third, it doesn’t matter what order. So the ratio is 3/5, or 6/5, octave reduced. The note is the minor third. I call it b3. It lives a…
There are four basic moves available on the lattice of fifths and thirds. They are: Up a fifth (x3) Down a fifth (÷3) Up a major third (x5) Down a major third (÷5) Each of these moves has its own harmonic flavor, and they can be combined to create new flavors. The major scale only…
The harmonic lattice can be divided into four quadrants. Northeast is pure overtonal energy. All these notes are reached by multiplication alone. Powers of 3 and 5 are in the numerators, and the denominators are all powers of 2. Southwest is pure reciprocal energy. You get there by dividing. All the 3’s and 5’s are…
All the notes I’ve discussed so far are found above and to the right of the tonic, in the northeast quadrant of the map. These notes are generated by multiplication alone. What about the notes that are generated by division? These are found to the left and down on the lattice. The closer a note is…