An octave is eight notes (whole tones).

In the physics realm of music, going up one octave is the doubling of the frequency of the pitch.

Concert B flat (standard pitch tuning for concert bands and orchestras) uses 440 HZ (Herz – cycles per second) for the A, otherwise known as A440. The next octave up, the A would have 880Hz.

The bagpipe Low A is tuned near the B flat of the A440 scale which would be about 477Hz.

What is Sound

Sound is vibrations that are within the range of human hearing. When an object vibrates, it displaces a medium like air. The moving air then moves parts of your ear which is translated into an auditory signal in your brain.

On the bagpipes, sound is created by the air moving past the lips of the reed. This causes the lips to vibrate, leading to the sound produced.

If an object vibrates at one frequency it has what is called a pure tone. When the object vibrates at multiple frequencies at the same time and there is a mathmatical relationship between the frequencies, you have a rich tone. If the ratios between frequencies is not whole numbers, you end up with noise.

The pitch of the sound

The pitch is determined by the frequency or frequencies of the vibrating object. Since the speed of sound is constant in a medium, the frequency is strictly dependent on the wavelength.

frequency = speed / wavelength

In an instrument, the wavelength is determined by the length of the tube that the vibrating air is passing through. The longer the tube, the smaller the frequency (less vibrations per second) and therefore the lower the pitch of the sound. Another example of this though not sound producing is a pendulum (think clock). The longer the pendulum arm, the slower the swing. A guitar string is the same; the shorter the string, the higher the frequency.

Further details as it applies to bagpipes can be found at https://secure.wikimedia.org/wikipedia/en/w/index.php?title=Acoustic_resonance .

While the pipe chanter is a cone, the open tube is close enough for both the chanter and the drones. The theory around False Tones also applies, as you can get harmonics out of the drones if the tuning aligns just right.

On the chanter, we alter the length of the tube by covering or uncovering the holes with our fingers. The more fingers that are down sequentially, the longer the tube and therefore the longer the wavelength resulting in a lower frequency.

The Tone of the sound

A musical note is more than just the base frequency – there are overtones that make up the tone of the note. The first (strongest) harmonic is a perfect octave (2x the frequency) of the main frequency. The next overtone is 3/2 the frequency. The exact mix of the overtones is what changes the tone (overall sound i.e. tonal quality) of the note from warm to cold. When all of the overtones are added together you end up with the waveform of the sound.

Computer generated waveforms are square, but non square ones can be simulated by adding a whole bunch of really short square ones at appropriately different strengths to make the round/triangle/ waveforms desired.