## Harmonic Distance

Harmonic distance is the total length of the connection between two notes on the lattice, as measured on the solid lines. The more tinkertoy sticks you traverse to get from one note to the other, the greater the harmonic distance. It’s not the same thing as melodic distance, which is a difference in pitch. Two notes can…

## Polarity Experiment

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…

## Consonance Experiment

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,…

## Consonance and Dissonance

I just passed the 10,000 photo mark on the stop motion animations, good thing I’m not hand-drawing them like Winsor McCay! The one I’m working on, Real Girl, has a lot of dissonant notes in it. The melody ranges far from the roots and makes some slightly dizzying harmonic jumps. I want to use it…

## Mixolydian Matchsticks

In yesterday’s post I mentioned matchstick harmony. This concept is from Mathieu’s book Harmonic Experience, which I’ve discussed a lot on this blog. Matchstick harmony is governed by a rule: It’s easiest for the ear to follow harmonies that move short distances on the lattice. Imagine that the lines of the lattice are matchsticks. The…

## The Compass Points

There are two basic directions on the lattice: multiplication and division. If I start with a note, and then multiply it by 3, or 5, or 7, I will get a harmony note with overtonal energy. Such a note is in the natural overtone series of the original note. Overtonal energy is stable, restful, it…

## Intervals

An interval, in music, is the difference in pitch between two notes. Here’s Wikipedia’s definition: In music theory, an interval is the difference between two pitches. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic…

## Tonal Gravity

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…