## 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…

## Cents

Musical notes can be mapped onto many different spaces. The two I find useful so far are: — Harmonic space, the space of the lattice, organized by harmonic connections (ratios of whole numbers). — Melodic space, the space of the scale, organized by pitch, or frequency. Both maps show the location of a note relative…

## The Major Third

Multiplying a note by 2 creates an octave, and multiplying it by 3 creates a perfect fifth. Multiplying by 5 gives yet another new note, the pure major third.5-1 5/1 is over two octaves above the original note, so you have to reduce it twice (divide by 4) to get it down into the same octave.5-4…

## Octave Reduction

Doubling the frequency of a note certainly changes it. The ear hears a higher-pitched note. But there is something in the essence of the note that does not change, a character that stays consistent through the octaves. This allows a process called octave reduction. When you’re working with notes as ratios, it’s convenient to multiply or…

## Pythagoras’ Epiphany

Pythagoras was a Greek philosopher who lived about a century before Athens’ golden age. Some time before 530 BC, he had an epiphany. He had been investigating vibrating strings, and found that when you cut the length of the string in half, the note it makes is an octave higher. Sound is vibration. When one…