Mr.X:
Este artículo de Wikipedia es bastante bueno y claro (los que encontré en español más que aclarar oscurecen):
http://en.wikipedia.org/wiki/Overtone Este otro es un poco más técnico (sólo un póco), pero biene bien hojearlo también:
http://en.wikipedia.org/wiki/Harmonic Por otro lado, un buen libro al respecto es
The Physics and psychophysics of music de
Juan G. Roederer (a quien tuve el gusto de conocer). Creo que es bastante usado en la materia Acústica en los conservatorios y universidades, y está escrito de manera bastante accesible.
Por último, aquí podés generar ondas estacionarias (por ej., una cuerda vibrando) eligiendo sus componentes armónicos:
http://www.seriedefourier.com.ar/Graficar.html. Probalo con una fundamental de frecuencia 3 o 4, porque si no queda muy chiquito.
Cualquier duda no dejes de preguntar, que en la medida en que lo sepa te contestaré. Igual abajo copio el primer artículo y hago un par de acotaciones.
Saludos,
Fernando.
An overtone is a natural resonance or vibration frequency of a system. Systems described by overtones are often sound systems, for example, blown pipes or plucked strings. If such a system is excited, a number of sound frequencies may be produced [al tocar cualquier nota en el contrabajo siempre suenan simultáneamente la fundamental y unos cuantos
overtones]. These frequencies, are usually, but not always, a close approximation to an integer multiple of a lowest resonance frequency. Thus, overtones and harmonics should not be confused or interchanged [no obstante lo cual en música se habla siempre de
armónicos]. By definition a harmonic is an exact integer multiple of a fundamental frequency, where as in most systems, overtones are never exact integer multiples of a root frequency. For example, the first overtone of a circular drum is approximately 2.4 times its fundamental resonance frequency.
Explanation
Most oscillators, from a guitar string to a bell (or even the hydrogen atom or a periodic variable star) will naturally vibrate at a series of distinct frequencies known as normal modes. The lowest normal mode frequency is known as the fundamental frequency, while the higher frequencies are called overtones. Often, when these oscillators are excited, by, for example, plucking a guitar string, it will oscillate at several of its modal frequencies at the same time. In music, this gives the sensation of hearing other frequencies (overtones) above the lowest frequency (the fundamental). The overall combination of the instrument's specific overtones is what determines the timbre ("flavor of sound") of that instrument. Timbre is what gives the listener the ability to distinguish different instruments that play the same note at the same volume in a band or orchestra.
A driven non-linear oscillator, such as the human voice, a blown wind instrument, or a bowed violin string (but not a struck guitar string or bell) will oscillate in a periodic, non-sinusoidal manner. This generates the impression of sound at integer multiple frequencies of the fundamental known as harmonics. For most string instruments and other long and thin instruments such as a trombone or bassoon, the first few overtones are quite close to integer multiples of the fundamental frequency, producing an approximation to a harmonic series. Thus, in music, overtones are often called harmonics. Depending upon how the string is plucked or bowed, different overtones can be emphasized.
However, some overtones in some instruments may not be of a close integer multiplication of the fundamental frequency, thus causing a small dissonance. "High quality" instruments are usually built in such a manner that their individual notes do not create disharmonious overtones. In fact, the flared end of a brass instrument is not to make the instrument sound louder, but to correct for tube length ?end effects? that would otherwise make the overtones significantly different from integer harmonics. [...]
The intensity of each of the overtones is rarely constant during the duration of the overall sound. Over time, different overtones may decay at different rates causing the relative intensity of each overtone to rise or fall independent of the overall volume of the sound, and a carefully trained ear can hear these changes even in a single note. This is why the timbre of a note may be perceived differently when played staccato or legato, dampened or lengthened. [O sea: si tocamos cualquier nota pizzicato y la dejamos vibrar no sólo suena cada vez más bajita, sino que el color de la nota, su timbre, va cambiando).
Musical usage term
An 'overtone' is a partial (a "partial wave" or "constituent frequency") that can be either a harmonic or an inharmonic. A harmonic is an integer multiple of the fundamental frequency. An inharmonic overtone is a non-integer multiple of a fundamental frequency.
An example of harmonic overtones: (absolute harmony)
f 440 Hz fundamental tone first harmonic
2f 880 Hz first overtone second harmonic
3f 1320 Hz second overtone third harmonic
4f 1760 Hz third overtone fourth harmonic
Not all overtones are necessarily harmonics, or exact multiples of the fundamental frequency. Some musical instruments produce overtones that are slightly sharper or flatter than the true harmonics. The sharpness or flatness of their overtones is one of the elements that contributes to their unique sound. This also has the effect of making their waveforms not perfectly periodic. Some instruments, such as tuning forks or flutes produce a clear or near perfect sound because their overtones are in very good approximation of "absolute" harmony with the base frequency.
