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# Phase

## Introduction

In order to understand how phase works clearly, it is necessary to be able to picture exactly how sound waves work. therefore, this article begins with a discussion of the theory of sound, which should help.

It is possible to be aware of some of the effects of phase without grasping all the details of the theory, so the second part of the article will go through the practical implications of phase, both its potential benefits and negative consequences.

## The Theory

Picture an a4 piece of paper on which someone has drawn a sound wave. In order to represent it accurately, they would need to draw time along the bottom and amplitude, (The sounds intensity), up the side. Crucially, the point of 0 amplitude would have to be in the middle of the graph paper rather than at the bottom. this is because we are trying to represent vibrating air, which vibrates both back and forth. If 0 was at the bottom, the graph would only be able to represent the forward motion of the air molecules. In order to represent both, we need to think in terms of negative amplitude. Positive amplitude, strictly when considering pictures of sound waves, is forward motion, negative amplitude is backward motion.

A sine wave drawn in this way might curve up to +6 amplitude from 0, and then curve down through 0 to -6 and repeat. The number of times it repeated this pattern in a second would be the sound's frequency. It is crucial to understand that we could start our drawing at any point during this vibration and the sound wave would still be the same. Same frequency, same amplitude.

Now, let's draw the interaction of two identical sound waves. This is where phase comes in. Phase describes a relationship between two or more sounds. One sound on its own cannot be said to be in or out of phase, because there is nothing for it to be in or out of phase with. If they are in phase, they go at the same direction at the same time and add together, meaning that the resulting sound is twice as loud.

If, however, one sine wave were vibrating backwards, while the other were vibrating forwards with equal and opposite intensity, the net result would be no sound at all. So one sine wave would go down through 0 to -6 amplitude, while the other would go up to plus 6 amplitude at the same time. 6 -6 is 0, i.e. no sound at all. The air cannot move in two opposite directions at once. It stays still. This state is called being half a cycle out of phase or 180 degrees out of phase. It is also called phase cancelation because the two sounds cancel each other out.

There are any number of possibilities in between these two extremes of phase. One wave might just be reaching 0 as the other is reaching its peak or its trough. One wave might be half way between the 0 and the trough or the 0 and the peak, while the other has reached either extreme of its oscillation or the 0-crossing. The 0-crossing is the point at which a wave's cycle crosses through 0 amplitude and is an important term to remember when editing.

All these different phase possibilities will have differing effects on the resulting sound's volume, either attenuating or increasing it by varying extents ranging between the result being twice as loud as either of the waves on their own, right the way down to there being no sound at all.

## Phase in the Real World

### In Tune with Phase

You will probably have heard the effects of phase more often than you think and used it for something very important - telling if two or more instruments, vocalists or strings on the same instrument are in tune. When two pitches are slightly out of tune, it sounds strange. You can hear a kind of throbbing or pulsing. Now we are dealing with sound waves that are not quite the same frequency but very similar. Think of two clocks ticking at slightly different rates. Their ticks go in and out of phase, i.e. sometimes they tick at precisely the same time but they also go through most of the degrees of phase in-between until they come back to ticking at the same time again. Their phase relationship is constantly changing.

Sounds do the same thing. Two sounds at slightly different frequencies slip in and out of phase and we hear this as a pulsing sound as the resulting amplitude produced by the two sounds rises and falls.

This phenomenon is called beats in music. Binaural beats are created by using two tones of slightly different frequencies, one on the left channel and one on the right. These sounds are believed to have beneficial effects such as helping people sleep etc. Many examples can be heard on youtube.

The following sound was created by varying the pitch of two sine waves very slightly so that the pulsing varies in speed. when we do this, we vary the rate of change of the phase relationship.

you will notice that the stereo image of the above example kept changing as both sine waves moved back and forth across the stereo field. If you were wearing headphones though, you will notice that the movement didn't seem to be horizontal, that the sound appeared to travel around your head.

Both tones, when played on their own, only move horizontally left and right. What causes the perception of more complex movement? The answer is phase and, crucially, the distance between our headphohnes, which is, also, of course, the difference between our ears.

Our ears triangulate the position of things surrounding us, partly by using something called the inter-oral time difference, which is the tiny interval between a sound reaching one ear and the other. This difference in time dictates the phase relationship between the two sounds.

### Mono Compatibility: a Mixing Menace

Moving beyond sine waves and single musical notes in to the world of complex sounds with wide and constantly varying spectra, phase becomes much more difficult to manage. Things like 3d panning, which is the term or the phased stereo manipulation discussed above, while sounding great on headphones, can fall apart in a mono environment.

A binaural phase relationship's audible effect will usually be an effect on our perception of where the result is in the stereo or pseudo-surround field. In mono or when both sounds are trying to occupy the same part of the stereo field, the result can be far less pleasant. As well as undesirable changes in volume or parts of sounds disappearing altogether, a phenomenon called comb filtering may be introduced.

#### Comb Filtering

A complex sound is made up of many different frequency components. When you combine them in the same space in the stereo field, a situation may arise where some frequency components are in phase and some are out of phase. This causes exaggerated frequency peaks in the sound that make it sound as though it is stuck in a tube. It is called comb filtering because the resulting spectrum of two sounds with the right, or wrong phase relationship depending on your point of view, looks like the teeth of a comb, the points being the peaks where components are in phase, the gaps representing the parts where phase cancelation occurs.

this {{|Clip}} is an example of comb filtered speech.

Always listen to anything you create in mono at least once and preferably much more. This will allow you to identify such problems and take appropriate steps to deal with them. These steps might include:

• Changing the panning of one or both of the sounds involved.
• inverting the phase of one of the sounds, which basically means making its wave form go up above the 0 line when it had been going down first before or vice versa.
• changing the spectrum of one of the sounds using equalization.
• Adding a delay effect to one of the sounds so that, even though the original will be cancelled out by its opponent, the delayed copy will not.

### The Benefits of Phase

Sometimes, all the peculiar characteristics of phase relationships between complex sounds are exactly what we want, so plug-ins and hardware units have been created to deliberately introduce them.

#### Flanging

We have established that phase is how the vibrations of two sound waves interact. If you shift one in time, it will be at a different point in its vibration than before relative to the sound with which it is being combined. Its phase relationship to the other will have changed. Delay one copy of a sound by just a few milliseconds and you will get comb filtering. Vary the delay time between the two sounds and you will change the nature of that comb filtering. This is called flanging and it sounds like this It is an extremely popular and recognizable effect.

#### Phasing

This phaser clip demonstrates how speech sounds when put through a phaser.

Like flanging, phase involves creating a delayed copy of the sound but it goes a step further. The delayed copy is filtered in such a way that the phase relationship between the two copies is no longer linear. the series of filters applied to the delayed copy cause different amounts of phase shift. In other words, the phase relationship between the original sound's bass frequencies and the delayed copy's bass frequencies is not the same as that between the treble frequencies of the two sounds. As a result, phasing sounds different and less tonal because its effects do not follow the harmonic series of a spectrum.

#### Phase cancellation as a Tool

If used skillfully, phase cancellation can be used to make unwanted sounds completely disappear from a mix. It can also be used to determine whether a process has preserved the quality of the original sound.

If you open a sound in an audio application and save it again without performing any operations on it, but give it a different file name, and you open up both copies and mix them together with the phase of one copy inverted as discussed earlier, the result should be complete silence. Likewise, you could prove that flac is a lossless compression format by taking a wav copy of a sound and a flac and flipping them out of phase with each other in the same way. If the result is complete silence, the audio in the two files is exactly identical and no quality has been lost.

If you flip a wav out of phase with identical audio encoded in mp3 however, the result will not be complete silence. The result will be that all the identical components of the two sounds will be silenced but the differences between the files will remain, proving that changes do occur when you convert to MP3.

## Conclusion

Phase can rob your mix of bass, make it sound like parts of it were recorded inside a toilet roll tube, make sounds disappear entirely and generally make a nuisance of itself. Learn to identify the audio effects of phase and always audition your mix in mono.

Phase can also be a blessing - reducing or eliminating unwanted noise, creating appealing, ear-catching effects and making our stereo field more interesting. It can be made to work for you, even effects such as 3d panning. The trick is to know the dangers and to manage your audio carefully.