An engine is, in principle, a giant air pump that mixes fuel and air to create motion. All of this air moves through tubes, mechanical parts vibrate, and all of that works together to produce sound. While it is not a musical instrument, some of the best cars I have driven and witnessed have a musical quality to the sounds they create. In the process of creating the Lexus LFA V10, engineers from Yamaha and Lexus used the flowchart above to describe the role of engine sound to serve a proper driver's car. Let's dive in. 

As the crankshaft spins, the sounds it and parts associated with it provides the fundamental or dominant note. The secondary engine note is driven by the actual ignition of fuel and the pulses that move through the intake and exhaust. There are many variables that influence this sound, including engine layout (inline, flat, V, VR), engine bank angle, displacement per cylinder, intake and exhaust systems, even versus odd firing ignition and many more.

The higher the engine revs, the more frequently the gas pulses travel through the exhaust, increasing the pitch (low versus high frequency) and volume of the sound. However, that sound still stems from the fundamental engine note.Let's listen to a Ferrari V8 engine compared to one from a Mercedes AMG.

There are several reasons why they sound so different despite being the same engine layout. The main one is that the Ferrari uses a flat-plane crankshaft which has an even firing interval and less rotating mass than the uneven firing cross plane crank in the AMG. As the ferrari has less displacement volume per cylinder, and is engineered to rev high, this also contributes to the higher pitch of the engine note. Combining all this together (and many other factors) we can see that exhaust pulses and velocity of gasses of the Ferrari (red) are higher than the AMG (blue). 

In a four cylinder engine, there is a total of two ignitions per revolution, in a 6 cylinder 3 ignitions per revolution, and 8 cylinder 4 ignitions per revolution. Below is a wonderful diagram by the mind garage describing this relationship. Let's make a slight detour to what I think is the most musical of all engine sounds, even-firing V10 engines. 5 ignitions per revolution means that they align closely with the perfect fifth which primitive and modern musical systems are built on. 

The fifth is one of the easiest intervals for humans to learn to sing, meaning it is a strong sound that most people can learn to hear naturally. Almost all chords have a perfect fifth above the root. I do not get the music theory deeply, but it seems to be a natural sound that humans are drawn to. Here is the Lexus LFA V10 accelerating:

The Lexus LFA was designed around a high revving, even firing V10 engine and sound design was provided by Yamaha's music tuning division. The way engineers describe the engine sound of the LFA is “the roar of an angel”. The press release for the Lexus LFA's engine by Yamaha had this interesting nugget:

“We studied and used the surge tank (note 1) as part of the intake system to radiate the sound. The vibration mode of this tank was controlled by optimizing thickness, rib configuration, and other aspects of its design. When accelerating at an engine speed of about 3,000rpm, the driver hears a powerful harmonic sound structure centered around 250Hz, which is the primary component of combustion tone (note 2). At a high engine speed of about 6,000rpm, the harmonic sound structure is centered around 500Hz. This produces a sound that is rich and smooth. For even higher engine speeds, we further increased the number of high frequencies to create a sound that clearly reflects how the engine speed is climbing.”

In their technical paper, they spoke about the importance of tuning the surge tank, which is their carbon intake airbox to a 400hz frequency. My (possibly incorrect) understanding of the small orange graph in the paper below is that they are trying to use the surge tank to move the dominant frequency higher at higher rpms. Given Yamaha's expertise in musical instrument creation, this was a highly interesting collaborative development.

The large red graphs in the image are FFT plots. Fast Fourier Transform (FFT) plots express the frequencies recorded from the car during acceleration. It is important to note that the fundamental or dominant note is not always simple to isolate from harmonics and other noises. The color in the graph indicates the loudness in decibels (yellow is the loudest, indicative of the fundamental tone or dominant frequencies), while the Y-axis shows the frequencies (a higher frequency creates a higher pitch). We can see how Lexus and Yamaha engineers focused on the 400-600 Hz sound range through the rpm. On the left below, you can see a surge tank displayed in a museum somewhere in Japan. 

Lessons for Enthusiast Cars.

1. Start with the fundamental note.

Tuning the sound of your engine will first begin with whatever fundamental tone or dominant note that the engine comes with. One of the reasons I chose to develop a Mazda KL engine was the engineers' focus on reduction of unwanted frequencies through stiffening several areas of the block.

This serves to clean up the unwanted sounds adjacent to the fundamental note. In addition to increasing the rigidity of the block, application of friction reduction coatings and technology can reduce other sources of noise in the engine as well.

2. Intake velocity stacks and airbox tuning.

As seen in the LFA, the design of the air-box itself can promote and reduce different frequencies. In the case of intake stacks for individual throttle bodies, the rule of thumb is that longer stacks will produce lower frequencies and more torque down low, and shorter stacks will produce higher pitched sounds.

The surge tank or carbon air-box design itself is an extremely complex endeavour, and the only clues we have from Yamaha is to use sensory analysis to adjust the thickness of the top of the tank, and to direct that sound using the rough shape of the LFA surge tank with stiffening ribs placed in the same area. 

3. Use the headers and exhaust design to shape engine note.

The one area in which engine sound can be tuned is through the exhaust system. Thinking of a trombone, the sound pitch can be changed by lengthening or shortening the path that the air pulses flow through. The firing order pressure waves are interpreted through the exhaust system.

An exhaust system serves an optimal rpm range. When engine speed increases, time between exhaust pulses will reduce which suits shorter headers. If the diameter of the pipes is larger, the sound will have a lower pitch, and if they are smaller, there will be a higher pitched sound. The resonator and muffler can also serve to reduce or amplify frequencies.

In the case of engines with two exhaust banks, one bank can be over-pressured with exhaust pulses and the other side empty, reducing overall exhaust flow and therefore pitch. By creating an x-pipe design, both sides are allowed to merge into one and split again, allowing an equalization of pressure and it helps increase the exhaust pulse speed and therefore the pitch of the exhaust.

Personal Conclusion

For the Mazda KL V6 engined miata I am building, I will be adding a semi closed deck insert to the open deck block to increase block stiffness and raise natural frequency. I will also be running 12:1 comp pistons for higher exhaust frequency, and reducing weight from the rotating mass and valve train. Friction reduction technologies will be applied. I will be going for an equal-length exhaust manifold with 6 into 1 primaries that will run in front of the engine. Each primary will be 42.7mm and they will merge into a 74mm merge collector. The intake stacks on the itb between 80mm to 180mm. These stacks will be contained within a carbon air-box designed to amplify high-frequency sound.

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Sources:

https://www.carthrottle.com/post/weoo82y/

https://www.caranddriver.com/features/a15107374/this-is-why-various-engine-types-sound-so-different-feature/

https://decarreteres.wordpress.com/2019/10/22/engine-technology-exhaust-noise/

https://archive.yamaha.com/en/news_release/2009/20091021.html