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Sound, vibrations, frequency and period

• Sound moves in air as a vibration causing a disturbance in air particles
• The basic and most fundamental building block of sound is the sine wave
• We can use degrees to describe progress through the wave cycle; a full wave cycle is 360 degrees
• Waves have a positive and a negative maximum (peak and trough)
• The amplitude is the amount of displacement from the 0 line; we measure this in an upwards direction
• We measure frequency in Hertz; 1Hz is when one wave cycle takes one second
• We hear frequency as pitch or timbre; we hear amplitude as volume
• Period is written as T; t is the time in seconds that it takes for one complete wave cycle;  T = 1/f and F = 1/t
• You can also use this calculation to work out the rate of an effect; for any effect that has a cyclic modulation, if you can estimate the period, you can calculate the rate.

Harmonics

• It is very rare for a signal or sound to consist of a single frequency; the combination of different frequencies that make up an overall signal or sound is like an individual fingerprint, giving its timbre
• The lowest sine wave we hear is known as the fundamental frequency – this gives us the overall pitch of the note
• The harmonics are also sine waves; they are always higher in pitch than the fundamental
• The geometric waveforms we see on a synthesiser are created using different combinations of sine wave
• Humans can hear between 20Hz and 20,000Hz (or 20kHz); our ears are more sensitive to some frequencies
• Higher frequency hearing tends to deteriorate as we get older
• Doubling the frequency of a wave means that the pitch goes an octave up
• Most musical intervals are based on a logarithmic scale (more on this later) and therefore are not easily calculable; we can calculate a perfect fifth as is the mid-point between two octaves
• The harmonic series is the order of notes that sounds when you cause a string to vibrate or blow across a tube
• We can calculate any harmonic from higher up the series if we know the fundamental by multiplying the fundamental by the harmonic number.

Phase and polarity

• Phase describes how ‘in time’ two waveforms are; these timing differences are very small
• If sound waves are in phase, then their peaks and troughs line up
• If sound waves are out of phase then the peaks and troughs do not line up and cause destructive interference, which causes some degree of cancellation
• Phase can become a problem when we are recording with multiple microphones that are close together
• The sound waves hit the microphones at different times, and we get slight time differences between each signal
• When the signals are combined, some frequencies construct or more often, destruct
• Sometimes, moving microphones further apart can fix phase issues
• As a solution to phase issues, mixers and DAWs have polarity buttons
• These switch the polarity of the signal to solve this problem
• We can calculate phase difference in terms of degrees; 0^o is the start of a cycle and 360^o is the end
• You can normally tell if you’ve got a phase issue when recording if something sounds thin and lacking in bass.

Linear and logarithmic scales

• A logarithmic scale is used to represent very large numerical changes in a linear way, going up in powers of 10 rather than units of 1
• The decibel is a unit of sound pressure level; it presents big changes in sound pressure in a linear way because even though we think they do, our ears don’t respond to sound pressure like that
• There are a few different variations of the dB scale; dBA is used for environmental noise, dBFS is used on Logic
• Digital distortion occurs at 0dBFS so everything we mix in Logic should be lower than that value
• If the scale on our EQ plugins and hardware units was linear, we would devote lots of space to parts of the frequency range that don’t really matter to our ears
• A logarithmic scale means that each octave is spaced equally despite the doublings and better represents how we perceive the frequency spectrum.

Revision checklist

Displaying and interpreting information graphically

Waveforms

EQ curves

Technical numeracy

Level in decibels

Frequency in Hertz

Understanding how logarithms are used in terms of decibels and EQ scales

Understanding the fundamental frequency and higher harmonics

Calculations

Converting between frequency and period

Finding the frequency of the octave higher and lower

Finding the frequency of the fifth above or the fourth lower

Calculating higher harmonics from a fundamental or given harmonic number

Calculating phase difference

Microphone techniques

Understanding phase relationships between multiple microphones