showstack

The confusion

Polarity is not phase

These two words are used interchangeably by people who know better, and the distinction is worth being pedantic about because the fix is different.

Polarity is a sign flip. Every positive becomes negative and every negative positive, identically at every frequency, instantly. It is what the ø button on a preamp does, what swapping pins 2 and 3 does, and what wiring a loudspeaker backwards does. It is completely reversible: press the button again and you are exactly where you were.

Phase is a time relationship, and here is the part that matters — a fixed delay is a different number of degrees at every frequency. Three metres of air is about 8.7 ms, which is a full cycle at 115 Hz, half a cycle at 57 Hz, and dozens of cycles at 4 kHz. So two mics on one source are not “out of phase” by some amount you can dial out. They are in a different phase relationship at every single frequency, and the comb filtering that results has peaks and nulls spaced by the reciprocal of that delay.

Which is why the polarity button sometimes helps and never fixes it. Flipping polarity turns every cancellation into a reinforcement and vice versa — it moves the comb rather than removing it, and whether that is an improvement depends entirely on where the nulls land relative to what you wanted to hear. The actual fix is time: move the microphone, or delay the other one. The speaker delay calculator is the same arithmetic pointed at loudspeakers.

Absolute polarity

The third thing, and the one worth the least argument

There is a further question hiding under the first one, and it gets more heat than it deserves: not whether two sources agree with each other, but whether the whole chain agrees with the world. If a drum skin moving towards the microphone ends with a loudspeaker cone moving towards the audience, the system has correct absolute polarity. If everything is flipped together, it does not.

It is largely inaudible on most material, for a good reason: a symmetrical waveform sounds the same either way up, and most sustained musical sound is close to symmetrical. Where it becomes audible is on asymmetrical waveforms — a kick drum, a bass guitar, brass, the human voice on plosives — where the pressure excursion is genuinely larger in one direction than the other. There the flip changes which way the loudspeaker moves first, and on a system with real low-frequency authority some people reliably hear the difference on those sources and nothing else.

The practical position is the honest one. It is worth getting right because it costs nothing to get right, it is worth checking with a polarity popper when a system is commissioned, and it is not worth an argument at eleven at night. What is worth an argument at eleven at night is relative polarity between two boxes in the same array, because that is not subtle, it cancels real output, and it reads as a room problem rather than a wiring one.

The recipe

What a square, a saw and a triangle actually are

Every periodic wave is a sum of sines at whole multiples of its fundamental. That is not an approximation or a way of thinking about it — it is what the wave is, and the four classic synthesiser shapes have famously tidy recipes.

A sine is the fundamental and nothing else, which is why it is featureless and why it is the only shape that survives any linear system unchanged. A sawtooth has every harmonic, falling off as 1/n, which makes it the brightest and the most useful raw material for subtractive synthesis — there is plenty there for a filter to remove. A square has odd harmonics only, also at 1/n: no octaves at all, which is exactly what makes it sound hollow and clarinet-ish rather than bright. And a triangle has odd harmonics at 1/n², which falls away so fast that the third is already down at a ninth and the shape is very nearly a sine.

The connection worth carrying off this page: those odd harmonics on a square include the third, which is a triplen — the same harmonic that arrives in phase on all three legs of a supply and fills up a neutral conductor. An oscillator generating a square wave and a switch-mode power supply drawing a spiky current are not analogous, they are the same fact pointed at different jobs, and the same arithmetic describes both.

Making one

Subtractive, additive, FM, and why one of them won

Subtractive synthesis starts with something harmonically rich — a saw, usually — and takes away. A filter with a cutoff and a resonance removes the top, an envelope moves the cutoff over time, and that is most of the sound of electronic music. It won because it maps onto how the ear hears change: a filter sweep is a single gesture that alters an enormous number of harmonics at once, and it is one knob.

Additive synthesis goes the other way, building a sound by summing sines with individual envelopes. It can theoretically make anything, and it is almost unusable by hand: a convincing sound needs dozens of partials each with their own amplitude curve, which is a lot of parameters for one note and no gesture that moves them together meaningfully.

FM uses one oscillator to modulate the frequency of another. The result is a sideband spectrum that is not obvious from the controls at all — small changes in the modulation index reorganise the harmonic content wholesale, which is why FM is famous for metallic and bell-like sounds and for being difficult to steer. It is enormously efficient, which is why it appeared in hardware when memory and processing were expensive.

All three are still around, and the distinction blurs in software where nothing costs what it used to. What survives is the ergonomic point: subtractive won not because it sounds better but because one knob moves the whole spectrum in a way a person can predict.

The two knobs

What an envelope and a filter are actually doing

Subtractive synthesis is two ideas wearing a lot of front panel. Everything else is a variation.

The envelope describes how something changes from the moment a key goes down to after it comes up, and the standard four stages are attack, decay, sustain and release — ADSR, which is what the four knobs are labelled on almost every instrument ever made. Three of those are times and one is not: sustain is a level. Attack is how long to reach full, decay is how long to fall from full to the sustain level, sustain is the level it holds at while the key is held, and release is how long to fall from wherever it is to silence once the key is let go. Almost every confused synth patch is somebody turning sustain expecting a duration. A plucked sound is a fast attack, a short decay and a sustain of zero — the note ends while your finger is still down, and it is the sustain level that ends it.

The filter is usually a low-pass with two controls. Cutoff is the frequency above which it starts removing, and it is the single most expressive control on the instrument because moving it changes every harmonic at once in a way the ear reads as a sound opening or closing. Resonance is feedback around the filter that boosts a narrow band right at the cutoff, which makes the sweep audible as a distinct tone travelling through the sound rather than as a dulling. Turn it far enough and the loop sustains itself: the filter oscillates with no input, which is a sine source you get for free and a very effective way to make an unpleasant noise at full level.

Then the two are joined, and that join is the whole instrument: an envelope routed to the filter cutoff rather than to volume. Now the sound is bright at its start and darkens as it decays, which is what nearly every struck or plucked physical object does, and it is why that patch sounds like something happened rather than like a tone was switched on.

Placing it

Three ways, and they fail differently

Putting a sound somewhere in a room is not one problem with three solutions. It is three different bargains.

Where this goes next

The calculators on this page

Waveform harmonics shows the recipe for each shape and hands it to the distortion maths. VBAP and DBAP does both panning laws, including the rolloff trade in DBAP. Wave field synthesis gives the aliasing frequency and what a target would cost in loudspeakers. And how each sense tells things apart is why any of it works — two ears, a delay of a few hundred microseconds, and a great deal of inference.