Understanding Sythesis - Part 1

Understanding Synthesis Part 1 - Frequency and Pitch
By Kirk Spencer

Welcome to Sound Synthesis. This month we will be setting the foundations for our look into synthesis.

We'll start by discussing the basics of sound and how we can describe it, this will provide us with the tools we need to talk about shaping the sound and creating new sounds.

In this blog post we will be looking at ways of describing sound and what sound is. 
Technically sound can be described as a vibration through a medium - this means that sound can travel through air or water or anything that can propagate waves of energy.

Sound can also be described through several key properties - Frequency, Pitch, Amplitude, Duration and Envelope, Harmonic and Timbre. We will be focussing on Frequency and Pitch on this blog post.

Sound Properties - Frequency

Think of plucked guitar string, when we release the string it begins to move away from us until it reaches a maximum and which point it comes back towards us almost reaching its original position. This cycle is repeated again and again at the same rate or period (the number of the these periods in one second is known as the frequency)

Frequency is measured in Hz (hertz) so = 1 Hz is a single 1 period in 1 second a single back and forth which is a very slow frequency. Using these ideas we can accurately describe how many times a second a sound is vibrating the air around us.

A 100hz wave takes 0.01 seconds or 10 milliseconds, to complete a single period.
If 100hz is 100 Periods / 1 Second, then the time it takes for one period is 1 Second / 100 Hertz, or 0.01 seconds.

Frequency can also tell us about the length of a wave. Sound has a speed at which it travels through materials in air sound travels at a speed of 1138 feet per second. This means that a 1hz wave will travel 1138 feet in a single period. This also means that a room would need to be that large in order to accommodate the full cycle of that frequency. This is often why small rooms might have a poor bass response

Sound Properties - Pitch

Another critical property is pitch - while frequency enables us to describe the rate at which a sound is vibrating as humans we are generally interested in the ordering of frequencies from low to high. We describe the ordering of these frequencies as pitch. With a high pitch corresponding to a high frequency and a low pitch corresponding to a low frequency.

When talking about pitch we are also interested in relationship between sounds.
If we hear a frequency of 440hz in isolation then we are not likely to hear that as a middle A on a keyboard however if you first play a sound of 440hz and then play a second sound of at 880hz we will hear that as a specific relationship known as a octave. If the two pitches played at the same time we perceive the relationship between the two.

For example when a the frequencies have a 2.1 or a doubling we say they are an octave apart. When they have a relationship of 5.4 we say they are a major third apart. This means that we are perceptually interested in things like the doubling or halving of frequencies rather than a fixed number of frequencies in between a interval.

For example lets listen to the sound of a octave.
If we start at a frequency of 220hz (Low A) the octave above that would be 440hz which is also a A and the octave above that is 880hz.

We can also hear what a major third is which is a 5.4 relationship we can hear this by playing a C and a E on a keyboard.

If we play a A at 440 HZ, what is the frequency of the A four octaves higher?

The simple way to do this is to double the value at each octave so 440 * 2= 880, then 880 *2 = 1760, then 1760 *2 = 3520, and finally 3520 * 2 = 7040.

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