The Chromatic Scale: Another Geometric Sequence

As seen in the previous post, "modern" music is based off of a Geometric sequence where a=440Hz. When this frequency is doubled or halved, our ears recognize it as having the same tonal quality. These notes of the same tonal quality are denoted "octaves" Any frequency, when halved or doubled, provides a frequency that our ears perceive as the same note, just in a different octave. In the previous example we covered the geometric sequence of the octave. But what about the rest of the notes used in music besides "A"? You know, A#, B, C, C#, D, D#, E, F, F#, G and G#. Well these intervals are all part of a geometric sequence that is known by musicians as the chromatic scale. It has a very simple formula, and this sequence is often called "equal temperament", a reference to the equal spacing of the musical intervals on a logarithmic scale; the base 2 logarithm, aka the binary logarithm. The geometric series can be denoted by the following:

This results in a total of 126 tones used in "modern" (chromatic western) music, from C0 to C10, which covers over half of the range of frequencies perceivable by the human ear.