Ben Duncan explains Absolute Phase & Phase Inversion and highlights its significance with respect to good recordings and hot monitoring.

In Martin Gardner's classic, 'The Ambidextrous Universe', he develops the theme of mathematical puzzles into the realms of symmetry. Casting his symmetry detector around the cosmos (from complete poems which read the same backwards, the peculiarities of mirrors, through to the symmetrical qualities in cantilever bridges, plants and atoms), he asks whether we can distinguish left-handed versions from right-handed ones? Is one original and the other a mutant, or are left and right absolute qualities? In other words, does the cosmos have parity? This question can arise in music too. Figure 1 shows the symmetry of a sinewave like, a continuous tone from a signal generator.

In air, the continually fluctuating amplitude of the waveform is acted-out as an alternate rarification and pressurisation (ie. compression) of the air (Figure 2). This in itself belies a fundamental assymmetry: at high sound levels, the air can ultimately only thin out to zero (a vacuum), whereas the scope for compressing air is fairly limitless. So in music's louder passages, we can expect the positive, pressurised parts of a soundwave to convey the peak excursions more faithfully than the opposite, rarified motions.

As soon as it reaches our mic, the sound wave is converted to an electrical analogue. Here, analogue means we ideally copy the shape of the waveform, though we may vary its size. The word 'analogue,' by the way, shares the same semantic roots as 'analogy' and 'analogous'.

So the rarified portions of the wave-in-air ideally become the negative going portions in the new, electrical waveform. Likewise, the pressurised portions of the acoustic wave become the positive half of the electrical signal travelling through the wires in your recording gear (Figure 3). And so on, until it's finally projected from the speaker, as a pressure wave in free air, many electron-miles and light-seconds later. I say 'ideally', because the problem we're abut to confront is that there are several places in the signal chain where the positive and negative portions of the (music) waveform can get transposed.

One comforting facet of electricity is that it's positive and negative inflexions are wholly symmetrical: they display parity. So from a purely electrical viewpoint, it really doesn't matter whether the initial pressurised (positive air blast from a saxophone, for instance, is conveyed as the positive or negative portion of the waveform (except that in half-dead equipment, one half of the waveform may distort at lower levels than the other). But we'll shortly discover that ill consequences can befall the signal if it's still 'upside down' when it exits from the speaker, or is mixed in with other signals.

Figure 4 shows assymmetry in a sample of music waveform. Unlike the sinewave in Figure 1, the negative and positive portions differ. If the positive inflexion is inverted at some stage within the recording chain (Figure 5), the reproduced sound may be perceived differently, even without reference to any other sound. The natural harmonic distortion of sound in air above some 90dB (acoustic decibels) manifests as assymmetry, and exaggerates the effects of an inversion, when an already assymmetric musical sound is turned on its head and thrust back into the air at 110dB, by punchy monitor speakers.

Drums, horns, woodwind instruments and pianos are the hallmarks of assymmetry in musical waveforms. In fact, any instrument played percussively will produce assymmetry. The human voice is another major contributor, beginning with Serjeant Majors and other vocal performers who let-rip with raunchy, croaky or throaty sounds. If, on the other hand, you're seeking pure and perfect pitch, you're really seeking to emulate the symmetry of a perfect sinewave, like a stringed instrument. Which leads to a rule of thumb: the music containing the biggest proportion of assymmetric components is rock (the more so if it's particularly percussive or 'spikey'), while 'smooth' orchestral music contains the least.

Polarity and Phase

Figure 6 sums up the effect of what's loosely (and misleading) called phase reversal or (better) phase inversion, using a continous sinewave as our reference. After asking a few people awkward questions, you might encounter nothing more than monosyllabic replies, because matters of polarity and absolute phase are rarely discussed in audio textbooks. But somewhere along the line, you might get the drift that the magic words inversion or reversal are involved. So let's not be too hasty to call the out-of-step waveform in Figure 6 an 'absolute phase shift', even if many people already do. That's because the condition we're discussing, has strictly nothing to do with phase shifts.

First, phase shifts are continuous functions, meaning they can be any number of degrees, like 27½°, 156° or 555¾°. A phase shift can certianly mimic the effect in Figure 6 but at just one point, where it reaches exactly ±180.00°. Second, phase shift comes hand-in-hand with convulsions in the time domain, namely varying amounts of time delay at different frequencies. This kind of behaviour is natural in EQs, crossovers, or any other kind of filter.

The same isn't true of the circuits and situations we're about to look at: because their apparent phase 'shift' alters our signal's phase reference (ie. any phase we care to take our measurements against) by exactly + or -180° at all frequencies, and courts no appreciable time delay, it's much less ambiguous if we simply call it what it really is: a reversal of signal polarity. But, if you're really sure it won't mislead you, be proud to call it a phase inversion.

If you're still perplexed, here's a photographic analogy to sum up the difference: there are broadly two ways to pervert the image of a familiar object. One is to distort the film base, or 'paint' the emulsion (as in Polaroid Art), and the other is to employ some elaborate distorting lens, like a fish-eye. These effects involve continuous gradations, just as with the phase shifts and time delays in equalisers, and taken far enough, they can soon make an object all but unrecognisable. But there's a simpler way to make it look startingly different, without any effort. The answer is reversal, namely, printing a negative image. In an everday studio context, this is equivalent to a polarity inversion: when there's a kickdrum hit (for example), the speaker cone 'sucks' backwards, instead of biffing the air up front.

Some Consequences of Polarity Reversal

Having got to grips with the nature of polarity inversion, it's time to explore situations in which it can arise, and the consequences occurring.

Beginning with simple stereo playback, Figure 7 shows two speakers wired in opposition. The left speaker is wired conventionally, so the positive terminal comes from the positive terminal on the power amplifier, but the right speaker's positive terminal comes from the right channel's negative output terminal. Anyone who's had to hook up to a stereo system has done this at some time, and there are no prizes for guessing what happens: there's no low bass, and the sound may take on a hollow, 'phasey' quality. But if we disconnect either speaker, the remaining one will sound quite normal. Essentially, each speaker is trying to cancel the output of the other; but they can succeed only in so far as the original, incoming left and right signals have the same content and instantaneous polarity. It follows that the cancellation effect is strongest on a mono feed, or with the monophonic components in the mix, where the left and right signals are one and the same, so the reversed speaker connections has the effect of making them direct opposites.

When one speaker's polarity is reversed, cancellation of the mono components is always strongest at low frequencies. It's less effective higher up, and varies as we walk around the room, because it ultimately depends on the acoustic phase relationship between the two sounds in air. For example, at 100Hz, where the wavelength of a sound is 22½ feet, a pair of speakers placed six feet apart and wired with opposing polarities are acoustically close enough to cancel each other. The closer the speakers, the higher the 'bass' frequency at which it all begins to take effect. Up at 3kHz though, where the wavelength is five inches, cancellation happens every five inches, but not in between. This just underlines the fact that phase shifts are continuous functions. Cancellation also occurs in the mid-range and above, whether the speakers polarity is correct, or not. Either way, identical sounds mixing from two sources beget 'peaky' colouration, the exact effect depending on where we're standing. A polarity reversal just makes matters worse, by stirring up needless interactions in the low frequencies. Thirdly, on a pure stereo signal, a polarity inversion takes out the centre image, pushing it sideways or backwards, depending on the speakers. It also boosts the sense of stereo space (at the expense of solidity and a gaping hole), by emphasising incoherent ambient information, which being of low level, isn't picked up by the polarity detector inside our ears. This sort of behaviour has no place in everyday stereo monitoring, but it does have its uses when we're originally creating and mixing sound; ask the Cocteau Twins.

Considering the ease with which just two speakers can suffer hidden polarity transpositions, it's no surprise that the scope for errors in 3-way active monitors, or PA systems with dozens of drivers can approach nightmarish proportions! In either case, where the adjacent drivers are driven in tandem, over the same frequency range (albeit from separate amplifiers), a polarity reversal on one can leave both speakers expending hundreds of watts cancelling each other out.

Cockups in the Rigging

Signal polarity can be transposed wherever the signal's two wires can be swopped over without loss of signal. So while it can easily happen to balanced lines, and mic and speaker leads, (because speakers, like mics, are usually un-earthed, floating sources), it doesn't apply to unbalanced connections, since they share their return path with signal ground, which means the signal is shorted (and therefore muted) if your interconnect's screening braid and the inner (hot) wire, are transposed in error.

Kicking off with balanced interconnects then, Figure 8 reminds us ofthe perils of the pin conventions, namely pin 2 hot vs pin 3 hot, for balanced inputs and outputs. Let's begin by assuming that pin 2 is the normal 'hot' (or +) side of the balanced XLR connection, as is normal. But looking carefully, notice that input 1 has been wired to the old USA standard, so pin 3 is the 'hot' side. It doesn't matter much whether this happens at the source end, or in the lead, or because the equipment's internal wiring is wrong or has been inadvertedly swopped over during a repair job. In any event, channel 1's polarity is at odds with any other signals it's directly related to. In the studio, this could apply to the monitoring's stereo signal path, with the same result as getting our speaker connections out-of-polarity with one another. But if it happens in the mixing stage, it's far more insidious, typically leading to surreptitious cancellation, and a weakening of the instrument's sounds). Figure 9, for example, portrays a pair of close spaced mics, feeding the console's balanced inputs. The XLR on one of the mics (it doesn't matter which) is wired back to front. Therefore the opposing polarities clash when mixed down in equal portions. As you adjust the faders on channels 1 and 2, behold a curious sensation: as either fader heads up, the cancellation increases, occasionally enough for the sound to disappear altogether about ½ way up to the fader's travel. Bizarre.

Figure 10 concentrates on floating balanced sources with transformers, like mics and DI boxes, which have been converted to feed unbalanced inputs in an ad-hoc fashion. In either case, it's done by shorting one output to ground (pin 1), but here, different people have evidently gone for different conventions, using either pin 2 or pin 3 to convey the signal. It probably won't matter if the signals are unrelated, but if they are, you can anticipate colouration. To make matters more complicated, the polarity of the mic capsule's connections may vary, depending on any previous repairs, and whether the mic originates from the USA, Europe or Japan.

Absolute Polarity

In general, polarity reversals are only audible in themselves when the solo instrument has a universally defined polarity for the ear to refer to, as with the kick drum, slapped bass and similarly percussive bass sounds. Thanks to what Robert Fripp calls multitrack madness, together with a historical lack of awareness about the consequences of absolute polarity inversion, composite (ie. mixed down) music is (with few exceptions) executed with random absolute polarity; a cheerful mess, in other words. But if you have a track which features some forthright bass percussion to hand, you can evaluate your own sensitivity to absolute polarity as follows:

1. Play the track at the originally recorded, live level, or at least as loud as you can.

2. Listen attentively to the bass instrument, paying special attention to the harmonics and inflexions.

3. Now swap the connections to both speakers, and repeat the track.

4. For objectivity's sake, it's good practice to counteract perceptual bias, by leaving the monitors in the 'all reversed' state all day, then repeating the test the next day (if this worries you, bear in mind that swapped over wiring stand a ⁵⁰/₅₀ chance of being the correct polarity, relative to the random polarity of most recordings). Then repeat steps 1-3, going from 'all reversed', back to the original connections.

People vary in their sensitivity to audio symmetry. Like stereo perception, whether you hear a difference or not may depend on how long you concentrate, on your state of health, or on medication... So if you don't hear any difference first time around, don't waste any more time, but simply try it out another time. Equally, if you're convinced that you can't hear a difference, don't go leaping to the conclusion that the rest of the world can't!

Some Polar Remedies

Though twisted polarities in a big recording set-up can be invidious and tiresome to disentangle, individual polarity reversals are easily put right, and even identified on a trial basis. For example, when an engineer gets a sound that differs from the expected, there's often a switch you can fling on every one of a console's channels. Marked Phase Invert (or words to that effect), it commonly works on the mic input only, and has the same polarity transposing effect as swapping the hot and cold leads on the mic's plug. Except that it's quicker, and you don't have to do any soldering. It applies particularly when you'vejust miked up an unfamiliar combination, and whenever there's two or more mics on an instrument.

To check or correct a balanced line interconnection, it's normal to drop in a polarity inversion lead. For an XLR setup, this gizmo comprises a short length of cable linking pin 2 on one plug to pin 3 on the other, and vice-versa (Figure 11). Note that pin 1 is connected normally.

Phase inversion leads are best wrapped in stripy red tape, so they're unmistakable, thus saving disappearances in the general spaghetti.

For stereo speakers, a test inversion is achieved by simply swapping over the leads on one unit. In my own monitoring set-up, I find it handy to have a polarity inversion switch (Figure 12), since listening with a reversed polarity can help critical assessments, in revealing a recording's hidden, ambient and antiphase facets. Sometimes, recordings sound better with the polarity inverted; if for example, the polarity of the bass or kick drum was back-to-front when they were originally set on tape. Sometimes the producer intends it to be this way, but it's not unknown for it to happen by accident, and then pass unnoticed until the moment of trial mixdown, when it's not quite so easy to sort out. So beware!

Testing the polarity of speakers is easily accomplished with a 4½ volt cycle battery, the traditional oblong sort, with screw terminals. Alternatively, some test meters provide 4½ volts when set to their 'low ohms' range. Either way, you need to identify the positive terminal of the voltage source. This is obvious enough on a battery, but it's commonly the negative (black) leads on analogue test meters, when set to the 'ohms' range. Now pulse the voltage across the speaker's terminals, so the positive side goes into the speaker's positive terminal. If correct, the bass-mid driver's cone should pulse forwards. In fact, it makes quite a loud thud, but don't panic! The 4½ volts we're employing is harmless to speakers rated in excess of 10W. If the cone sucks on one speaker, but pulses forward on the other, it's obvious that one needs its leads swopping over inside. This can be awkward, so if both enclosures turn out to be wired so a positive voltage on the red (or positive, or pin 2) terminal makes the cone suck backwards, you can avoid the carpentry and soldering act by just marking the cabinet to this effect (ie.'+ polarity = pin 1'), so that future users are aware of the peculiarity.

Testing mics for polarity requires special equipment, since we need to be able to define the waveform's polarity at the point it strikes the mic, or else generate a unambiguously assymmetric waveform.