The following video compares the perfect fifth with the perfect fourth. These notes are the next-door neighbors of the tonic. They are equally close to the center. They are both harmonious. Yet there is a great difference in their character. The difference between these two intervals is polarity. I learned this term from W.A. Mathieu,…
For every note on the lattice (except the 1), there is another note, the same distance away from the center and exactly opposite it. The harmonic moves for the two notes are the same, but the directions are opposite. Mirror twins are reciprocals of each other. Flipping a note’s ratio upside down will produce its…
In the last post I did a consonance experiment, listening to intervals with wider and wider spacing. In that experiment, I kept the axis (3) and direction (multiplication, overtonal) the same, and increased the distance. This time I’ll keep the axis and the distance the same, and switch direction. Each illustration will compare a note with…
In my last post I raised the idea that the consonance of an interval is not just one thing, but has two distinct parts: The sensation created by the sound of the two notes played together — smooth or rough, pleasant or unpleasant The sense of stability of the note — does it feel restful,…
I believe that the great driving force in tonal music, that creates the drama and story of the music itself (independently of any lyrics), is the longing for home. Home is the tonic. If a song is in the key of A, all the A’s in their various octaves will sound like home. Although there are…
The last three notes (b6, b3 and b7) are related to each other. They all contain a reciprocal third. There is a family resemblance of sound and function. (They also all happen to be a little flat in equal temperament. On a guitar it’s a nice trick to bend them a little to sweeten them.)…
The notes get more exotic as you move outward from the center. The ninth is quite consonant, but not nearly as consonant as the fifth. (Consonance and dissonance are descriptions of feelings; they are part of the flavor of an interval, and I don’t think the last word has been written on them yet. I’ll be…