| |

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┬ámajor 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.┬áBut 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…