# Harmonics & Additive Synthesis

Harmonics & Additive Synthesis A waveform is a periodic mathematical function (or sum of functions) defined by frequency, amplitude and phase. Frequency is the number of full cycles or periods that the waveform goes through in one second. And a harmonic is a waveform with a frequency that is a perfect integer multiple of the frequency of any given fundamental waveform. When the frequency is not an integer multiple of the fundamental frequency, we call it an inharmonic. Harmonics and inharmonics are both grouped into a larger category that we call partials. Partials are all of the simple component waveforms […]

# Audio Signal Filtering

Audio Signal Filtering Your pool guy would tell you they keep things out of your pool. Your car guy would tell you they keep things out of your engine. Your computational fluid dynamics guy (you have one of those, right?) would tell you they keep things out of your Navier-Stokes equations. And I’d tell you that filters keep things out of your audio signal. Fourier analysis and theory says that a signal (electrical, audio, electromagnetic, etc.) can be decomposed into an infinite number of different sinusoidal waveforms all with different frequencies, amplitudes, and phases. A filter in electrical engineering, communications, […]

# Frequency Modulation

Frequency Modulation Frequency modulation, also known as FM, is a signal processing method used around the world in radio broadcasting, radar, medicine, music production, and a load of other technologies. And yes, that’s what the “FM” stands for in FM radio. But what is it exactly, and how does it work? This article will demystify the concept for you. Modulation The word “modulate” really just means to instantaneously change some property of a signal waveform using a different waveform. When one signal waveform “modulates” another, it changes a property of the signal being modulated. We call the signal being modulated […]

# Waveform Phase & Phase Cancellation

Waveform Phase & Phase Cancellation In order to understand music production, we first need to understand how waveform phase and phase cancellation can effect the interactions between waveforms. Without a fundamental understanding of this subject, it may become difficult to identify and pinpoint phase problems, especially when we’re dealing with audio. Sinusoidal Functions Sine waves are periodic mathematical functions represented by the equation y(t) = A sin(ωt + θ). It may look confusing to those of us who have never been exposed to it, but this equation basically says that the y-value (height) in a time-versus-height graph depends on the […]

# Spectral Analysis & Fast Fourier Transforms

The Fourier Transform Arguably one of the most important developments in applied mathematics in modern times is the Fourier transform. The Fourier transform is a mathematical operation that takes any waveform and breaks it down into individual component sine waves at different frequencies and amplitudes. These are then represented by peaks in a frequency spectrum, and this whole process is called spectral analysis. A waveform as a summation of many simple sine waves is a concept seen in all oscillatory physical phenomena, including electromagnetic radiation, AC electricity, rotational motion, and the most important one for our purposes… sound. Let’s dig […]

# How Speakers Work

How Speakers Work In the article on the sound physics, we talked about how sound sources create and transmit vibration at given frequencies and intensities through a medium. Special hairs in the ear then change the vibration into electrical signals in the brain, causing the perception of sound by the listener. A speaker is just one example of a sound source, and this article will cover the science and theory behind how speakers work to make sound. History of Speakers The modern-day dynamic loudspeaker is an ingenious feat of engineering. British physicist Oliver Lodge invented it in 1898 and two Americans […]

# Physics of Sound

Our objective as musicians and music producers is to manipulate sound within the spectrum of human hearing to ultimately create something appealing to the listener. To learn how, we need to understand the physics of sound and what exactly is happening in the space between the ears of the musician and the ears of the listener. In this article, we’ll cover the following questions: What is sound and what are sound waves? What is frequency? How are frequency and wavelength related? What is amplitude? What is sound intensity? How do we hear? What is Sound? Sound is a physical phenomenon […]