Tones

Tones are the basic building blocks of music. How these tones are arranged give a piece of music its particular sound. Tones come in all different kinds of sizes and colors, but they abide by certain mathematical principles. A tone is a soundwave vibrating at a particular frequency, the speed of the vibration in a wave. Frequency is measured by a unit called Hertz or Hz, meaning vibrations per second. The human ear can generally hear from 20 to 20,000 Hz.

In modern music there are twelve tones that exist, each with its own name (when a tone is named it is refered to as a pitch) and its own domain of Hz. For example, the pitch A has a value of 440 Hz. If this value is doubled to 880 Hz it will still be an A. If it is divided in half to 220 Hz it will also still be an A. This phenomena is called the octave, which is when the same tone appears but at different levels of the sound spectrum.

A in three octaves

     220 Hz (A3)              440 Hz (A4)               880Hz (A5)

 

The Overtone Series

In the nature of tones there is a phenomena refered to as the Overtone Series. If a taught string (such as one on a piano or guitar) is struck it will vibrate at a particular pitch. But what is heard is not only one tone but many. The most prominent of these tones will be the loudest and lowest in frequency, called the fundemental. But a string will not vibrate at only in way but in many different ways in all three dimensions: up, down, forward, and back. Every way it vibrates will conform to the frequecy that is the biggest, being the fundemental. These lesser frequencies are called overtones and make up the Overtone Series. The vibration of the fundemental creates the vibrations of these overtones.

The fundamental tone, which the pitch is named after.

The first among  the overtones is the frequency of the fundemental doubled, one octave above. When a frequency is doubled its wavelength is halved.

The second overtone is the frequency of the fundemental tripled, and octave and a fifth above.

The third overtone is the frequency of the fundemental quadrupled, two octaves above.

The forth overtone is the frequency of the fundemental quintupled, two octaves and a major third above.

Fundamental frequency and its first four overtones.

The next overtone will be the frequency of the fundamental multiplied by 6, then 7, then 8 and so on, each less prominent than the last. The Overtone Series is the basis of the relationship one pitch has with another, playing a vital role in music. It is also major reason why instruments sound different, because each instrument will emphasize different overtones.