Refining Sound: A Practical Guide to Synthesis and Synthesizers by Brian K. Shepard

Companion Website Materials
Instructions for using the interactive demonstrations

Chapter 1: Synthesis and Synthesizers

Demo Group Icon
Download all Chapter 1 Interactive Demonstrations (4.9 MB)
Interactive Demo Icon Demo 1.1: Sound Basics (1.1 MB)
This demonstration illustrates the basics of sound and sound waves. Sound is an oscillation of high and low (usually air) pressures known as compression and rarefaction respectively. The magnitude of the pressure change is the sound's amplitude, and the number of times the sound wave oscillates (both compression and rarefaction) per second is the sound's frequency. There is a common misperception that we hear frequencies. What we hear are changes in amplitude. It is our ears and brain that interpret the rapidity of the changes in amplitude as frequencies. Note that amplitude is measured from the 0% position outward to either the top of the compression phase or the bottom of the rarefaction phase, not from top-to-bottom of the sound wave.

In this demonstration, the Frequency slider increases and decreases the number of wave oscillations per second, measured in Hertz. The Amplitude slider increases and decreases the magnitude of the oscillation. Here, an amplitude of 100% represents the maximum capability of the computer's sound card without distorting.
Sound Basics
Interactive Demo Icon Demo 1.2: Equal Loudness (1.0 MB)
For a variety of physical and psychoacoustic reasons, humans do not perceive all frequencies of sound with the same sensitivity. Even when sound waves are generated at the exact same amplitude level, we tend to perceive some frequencies as being louder than others. In general, we are much more sensitive to frequencies within the 500Hz to 5kHz range than we are to frequencies outside of that range. Use the Equal Loudness demonstration at left to hear it for yourself. When you activate the two oscillators, you will hear a low (100 Hz) and a high (3 kHz) frequency tone. For most people, the 3 kHz tone will sound considerably louder than the 100 Hz tone. With both tones sounding, use the Down arrow key on your computer keyboard to adjust the high frequency tone until they both sound equally loud to you. Then, after you reveal the meters, you can see how much you had to reduce the amplitude of the high frequency tone to make it sound at the same level as the low frequency tone. Keep in mind that for every drop of 6dB, you have cut the sound's amplitude in half.

The "Equal-Loudness Contours" chart at right shows that, to maintain the same perceived loudness level (often called phons) over frequency, the average listener needs to continuously turn the amplitude (SPL) down (red curved lines) as the sound's frequency rises. As frequency begins to rise above 5 kHz, the average listener needs to turn the amplitude back up to maintain the same perceived loudness. Notice, also, that the phon lines have a much greater curvature when the phon level is low. Not only are humans more sensitive to frequencies in the 500 Hz - 5 kHz range, but also the amount of that sensitivity is greater when the sound is very quiet (20 phons) than when it is very loud (100 phons).
Equal Loudness     Equal Loudness Contours

Interactive Demo Icon Demo 1.3: Decibel Calculator (1.8 MB)
There is probably no audio term that creates more confusion, and is so poorly understood among students of sound and audio, than the decibel. Adding to that confusion and misunderstanding is the fact that there are multiple versions of decibels (dB SPL, dBu, dBV, dBm), and two different formulas for calculating them. This demonstration illustrates the calculations for Power Quantity decibels (current flow, wattage, intensity, etc.) and Field Quantity decibels (amplitude, voltage, sound pressure level, etc.). It also provides a real-world demonstration of how changing the dB level on an audio fader changes the amplitude of the sound wave (field quantity).
Interactive Demo Icon Demo 1.4: Aliasing Demonstration (967 KB)
Sound energy extends well above our hearing range of approximately 20 kHz (just ask your dog). With digital audio, frequencies above the Nyquist frequency (1/2 the sampling rate frequency) are improperly rendered, or aliased, producing artificial lower frequencies that were not part of the original sound. Digital recording devices typically prevent aliasing by passing the incoming audio through a filter that prevents any frequencies above the Nyquist frequency from entering the recording chain. However, digital synthesizers can easily create aliasing with oscillator wave forms like sawtooth and pulse waves that produce a large number of high partials. Even though the fundamental frequency of these oscillator waves is well below the Nyquist frequency, the upper partials go well above it. Generally, the amplitudes of these high partials are so low that we do not hear the aliasing. However, as you raise the fundamental frequency of these oscillators, some of the more prominent partials also go above the Nyquist frequency, producing odd, noise-like frequencies that sound a bit like a badly tuned AM radio. In order to avoid aliasing, many digital synthesizers use waveshaping and lowpass filters to prevent partials from exceeding the Nyquist frequency.

In the Aliasing Demonstration, first slowly increase the frequency of the Aliased sawtooth oscillator and note the odd sounds that you hear as you move the frequency knob. Repeat the process with the Anti-Aliased sawtooth oscillator and note that the odd tones have disappeared from the oscillator wave. Other than the missing odd noises in the anti-aliased version, do you hear differences in the timbre between the aliased and anti-aliased versions of the sawtooth wave?
Related Links Music and Computers - a user-friendly, web-based introductory course in computer music and synthesis from the Music Department at Dartmouth College and the Computer Music Center at Columbia University
Sound and Acoustics Animations - an excellent resource for understanding sound and sound waves, created by the Institute of Sound and Vibration Research at the University of Southampton, UK
Acoustics and Vibrations Animations - another excellent source of animations that explain the properties of sound and acoustics
Vintage Synth Explorer - detailed descriptions, photographs, and audio examples of more than 750 commercial synthesizers produced in the late 20th century
Telharmonium Article from McClure's Magazine - published in July, 1906, this is a fascinating contemporary account of Thaddeus Cahill's "Dynamophone" before he renamed it the "Telharmonium"

Introduction | Chapter 1: Synthesis and Synthesizers | Chapter 2: Oscillators | Chapter 3: Oscillator Combinations | Chapter 4: Amplitude Envelope Generators
Chapter 5: Audio Filters | Chapter 6: Internal Modulation Sources | Chapter 7: External Control Sources | Chapter 8: Effects Processors | Chapter 9: Putting It All Together

Refining Sound