What is pitch?

Pitch is one of the three subjective attributes of sound. That is to say our auditory system provides us with sensations caused by changes in air pressure, and those sensations seem to vary along three basic dimensions of loudness, pitch and timbre. Thus when we hear two sounds that are different, we can associate those differences to a change in loudness, a change in pitch, a change in timbre, or some combination of these.

Pitch is related to the "musical" quality of a sound, that aspect of sounds generated by musical instruments that we label with "notes" such as "middle-C". When we sing we try to make noises that change in pitch in the same proportions as musical instruments change in pitch. We also use these changes in pitch when we speak to indicate the "tone" of our voice, for contrast, for emphasis or for questions.

Acoustically, pitch is related to the repetition frequency of the sound wave; that is how many pattern cycles complete per second. A low-pitched sound has few repetition cycles per second: perhaps a hundred. A high-pitched sound has many repetition cycles per second: perhaps a few thousand. Pitch doesn't tell us about the shape of the cycles, only how often they repeat. To speak at different pitches, I control the tension of the vocal folds in my larynx: if I tense my folds they vibrate more frequently, have a higher repetition frequency and generate sounds that give a sensation of a higher pitch.


What is timbre?

Timbre has a technical and a non-technical definition. Non-technically it is to do with the 'quality' of a sound, rather than its pitch or loudness. Different musical instruments are said to have a different quality or timbre even for the same musical note: e.g. a trumpet and a flute, or a guitar and a violin. Technically, we can say that a difference in timbre is the name given to our perception of the difference between two sounds which have the same perceived pitch and perceived loudness. There are both spectral and temporal aspects to timbre: this is easy to show by playing a piece of music backwards: the musical notes will be the same loudness, the same pitch and have the same spectral properties, but the instruments will still sound different - this is due to our sensitivity to how a sound builds up and dies away as well as to its spectral content.


How do you find and measure the individual harmonics in a complex periodic waveform?

We can use a special system called a band-pass filter to selectively remove all but small frequency regions from the input signal. A band-pass filter, as its name suggests, passes only sinusoidal components of an input signal which happen to lie within its operating band. We can build a bank of band-pass filters to examine in turn each frequency region, then measure the amplitude of the output signal. This output amplitude will tell us the amplitude of the sinusoidal components of the input signal in that region.


Explain harmonic numbering

A harmonic is simply a sinewave component of a complex periodic waveform. One important characteristics of harmonics is that they only occur at frequencies which are whole number multiples of the fundamental frequency of the complex. This means that if we know the fundamental frequency, say F, then the harmonics must occur at 1F, 2F, 3F, 4F, etc. We adopt a simple numbering system to identify harmonics: the first harmonic occurs at the fundamental frequency; the second harmonic occurs at twice the fundamental frequency, the third at three times, etc. Using this terminology we can make statements such as: "damping the vibrations of a guitar string half way along its length removes the first harmonic and all odd harmonics, leaving mainly the second and other even harmonics, effectively doubling the fundamental frequency of the note produced."


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