Takasawa Dynamics / Engine Sim / Firing order and pitch

The formula

In a four-stroke engine, each cylinder fires once every two crank revolutions. So the number of firing events per second is:

Work an example. A V8 at 7,000 rpm: 7,000 ÷ 60 = 116.7 revolutions per second, times four firing events per revolution = 467 Hz. That is close to B♭4, just above the middle of a piano. An inline-four at the same 7,000 rpm produces half as many events, 233 Hz — B♭3, exactly one octave lower.

This is why the cylinder count is audible even to people who cannot name it. Doubling the cylinders at constant rpm raises the fundamental by an octave. It is also why the opening claim holds: 3,000 rpm ÷ 60 × 4 = 200 Hz for the V8, and 6,000 ÷ 60 × 2 = 200 Hz for the four. Identical fundamentals.

What every layout sounds like, in hertz

The fundamental firing frequency at a typical working rpm for each configuration, with the nearest musical note:

Two things jump out of that table. First, a W16 at a lazy 6,500 rpm is producing a higher fundamental than a V12 near its redline — sixteen cylinders is a lot of events. Second, the racing V10 at 19,000 rpm sits at 1,583 Hz, which is in the region where human hearing is at its most sensitive. There is more on that in why Formula 1 V10s screamed.

Engine orders: how NVH engineers say the same thing

People who measure vehicle noise for a living rarely talk in hertz, because hertz changes with every twitch of the throttle. They talk in orders: multiples of the crankshaft rotation rate. First order is once per revolution. A four-stroke V8 fires four times per revolution, so its dominant component is 4th order; an inline-four is 2nd order, a V10 5th order, a V12 6th order.

The advantage is that the order number stays fixed while the engine sweeps through the rev range, so a plot of 4th-order level against rpm describes an engine’s character in one line. It is also a compact way to state the rule above: a four-stroke engine’s firing order number is half its cylinder count.

Engines with uneven firing produce strong half-orders as well — 0.5, 1.5, 2.5 and so on — which is precisely the low-frequency content that gives a crossplane V8 or an unequal-header boxer its lope.

What the firing order actually controls

Note that the formula above does not contain the firing order. The sequence in which cylinders fire has no effect on the fundamental pitch at all. What it decides is everything else:

• Which cylinders share a manifold, and when. The firing order determines the intervals seen by each exhaust runner and each collector. Even intervals produce a clean harmonic stack; uneven ones produce sub-harmonics and beating. This is the whole story of the crossplane V8.
• Crankshaft loading. Firing adjacent cylinders back to back twists the crank hard between two nearby journals. The standard inline-six order 1-5-3-6-2-4 and the inline-four’s 1-3-4-2 both exist to spread that load along the shaft rather than concentrating it.
• Intake charge robbing. If two cylinders fed by the same plenum draw in quick succession, the second gets a thinner charge. Firing order is chosen to avoid it.
• Cooling and bearing life. Consecutive firings at one end of the block make a hot spot and hammer one main bearing.

So the firing order is fundamentally an engineering compromise about loads and gas flow. The sound is a side effect — an extremely conspicuous one that manufacturers have since learned to design around deliberately.

Change one variable at a time

Engine Sim computes each firing event from the crank angle rather than playing recordings, so holding the revs and changing the layout — or the exhaust — isolates exactly the variable you want to hear. Twenty-one engines, from a 450 cc single to a W16.

Why two engines at the same pitch still sound different

The V8 at 3,000 rpm and the four at 6,000 share a fundamental, but nobody would confuse them. Three things separate them:

1. Harmonic content. The pulse from a large, slow-turning cylinder has a different shape — a longer blowdown, a softer edge — than the pulse from a small, fast one. Sharper pulses put more energy into the upper harmonics, which reads as brightness or harshness.
2. Resonance. The exhaust and intake tracts are tubes with their own preferred frequencies. They amplify certain harmonics and suppress others, which is why the same engine sounds different through a different exhaust while the firing frequency has not moved a single hertz.
3. Mechanical noise. Valvetrain clatter, chain and gear whine, injector ticking and turbo spool all sit on top, and they scale with rpm differently from the firing frequency. An engine at 6,000 rpm has twice as much of it per second as the same engine at 3,000.

Pitch, in other words, is the easy part. Timbre is where the character lives — see how real-time engine sound synthesis works for how each of those layers is actually generated.

FAQ

How do I calculate an engine’s sound frequency?

For a four-stroke, multiply rpm by the number of cylinders and divide by 120. For a two-stroke, divide by 60 instead. The result is the fundamental firing frequency in hertz.

Why do engines sound higher as they rev?

Because the firing frequency is directly proportional to rpm. Doubling the revs doubles the frequency, which is exactly one octave. An engine sweeping from 2,000 to 8,000 rpm rises through two octaves.

Does the firing order change the pitch?

No. The fundamental pitch depends only on rpm and cylinder count. The firing order changes the spacing of pulses within each exhaust manifold, which changes the timbre and can add strong sub-harmonics, but not the fundamental itself.

Why does a motorcycle sound higher than a car with the same number of cylinders?

Mostly because it revs further. A four-cylinder sportbike at 14,000 rpm is at 467 Hz — the same fundamental as a car V8 at 7,000. Smaller cylinders also produce sharper pulses, adding brightness on top.