#### UNDER CONSTRUCTION!

##### The Fundamentals: What are harmonics and overtones?

From Wikipedia, the free online encyclopedia:

##### Harmonic

In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integral multiple of the fundamental frequency. For a sine wave, it is an integral multiple of the frequency of the wave. For example, if the frequency is f, the harmonics have frequency 2f, 3f, 4f, etc.

In musical terms, harmonics are component pitches of a harmonic tone which sound at whole number multiples above, or "within", the named note being played on a musical instrument. Non-whole number multiples are called partials or inharmonic overtones. It is the amplitude and placement of harmonics and partials which give different instruments different timbre (despite not usually being detected separately by the untrained human ear), and the separate trajectories of the overtones of two instruments playing in unison is what allows one to perceive them as separate. Bells have more clearly perceptible partials than most instruments.

The name of the note played is the fundamental frequency or the first harmonic, the second harmonic is twice the fundamental frequency, the third harmonic is thrice the fundamental frequency, and so on. This series is called the harmonic series. For instance, when one plays an A440Hz, "A" refers to the fundamental or first harmonic, but this sound also contains the second harmonic, 880Hz, the third, 1320Hz, and so on, at varying amplitudes.

In many musical instruments, it is possible to play the upper harmonics without the fundamental note being present. In a simple case (e.g.recorder) this has the effect of making the note go up in pitch by an octave; but in more complex cases many other pitch variations are obtained. In some cases it also changes the timbre of the note. This is part of the normal method of obtaining higher notes in wind instruments, where it is called overblowing. On string instruments it is often used to produce very pure sounding notes which have an eerie quality, as well as being high in pitch.

The fundamental frequency is the reciprocal of the period of the periodic phenomenon.

##### Some interesting Harmonics facts:
• Sine waves contain only the fundamental with no harmonic or harmonic overtones.
• Lower pitches can potentialy produce more overtones within our ranges of hearing. A tone with a 30 Hz fundamental may produce many overtones but a note high on the piano with a fundamental at about 4000 will pass our hearing range at about 2 octaves leaving only a few audible overtones.
• Doubling the frequency (Hz) of a pitch will raise the pitch one octave.
• Doubling the frequency of any harmonic (Hz) will raise the harmonic one octave.
• Repeated doubling the frequency of an harmonic will continue to raise the harmonics by octaves. Example: if the fundamental of a note is a "C", so are harmonics 2, 4, 8, 16...etc.
• The number of any harmonic indicates how many times that harmonic is a multiple of the fundamental.

##### Some Good Harmonics References:

The Harmonic Series A path to understanding musical intervals, scales, tuning and timbre by Reginald Bain - University of South Carolina. This is a great reference with lots of harmonic-related info, sounds, graphics, and links. Very cool!

Harmonic Series Rice College Summary: The harmonic series is the key to understanding not only harmonics, but also timbre and the basic functioning of many musical instruments. A good online lesson in harmonics and overtones.

Why two notes of the harmonic series sound well together Cool sound samples