MTC191 / E.Walker Sound & Waveforms Understanding how sound works will help us learn to manipulate it in the form of audio signals, such as an analog voltage or a digital signal that is stored and played back from a hard drive or device. We need this skill in the art of electronic music sound design. Like any waveform, sound has the characteristics of wavelength, frequency, amplitude and speed or velocity. In music, the velocity is constant (the speed of sound) so we donʼt worry about it. Itʼs a good thing, since weʼve reserved the term velocity in the MIDI realm to refer to the speed at which we strike a piano key. With a constant speed of sound, wavelength and frequency are intimately related, so we donʼt worry about the wavelength. That leaves amplitude and frequency. Sound requires a medium in which to travel - like air. When an object vibrates, air molecules are disturbed. Sound propagates a wave of energy that disturbs air molecules. Air is elastic - it returns to its original position after being disturbed. When an object, such as a speaker, pushes outward, it causes air to compress. When it pulls back, itʼs called rarefaction. Pictured in figure 2, the sound wave is shown as air molecules and the audio signal that represents it is underneath. The arrow represents time. Fig 1. Fig 2. The louder the sound, the taller the waveform, and this is referred to as the amplitude. (see Fig 2.) Where the wave crosses the zero point (the timeline arrow) there is no movement of air molecules. That represents silence. The peaks and valleys represent the loudest parts of the waveform. An analog audio signal represents silence as zero volts and the loudest part as the maximum voltage. The higher the pitch of the sound, the shorter the wavelength will be, and this is referred to as the frequency, or cycles per second. Imagine the speaker cone moving faster or slower. Fig. 3 Fig 4. So far weʼve only looked at sine waves, the simplest motion. Usually, there is more than one sine wave happening at a time. They add together as air molecules get pulled and pushed in different directions and interract (Fig 4.). Imagine the speaker cone moving in a complex motion. We refer to the complex waveform as the timbre, and this is associated with the tone quality, or what instrument it sounds like. Now letʼs take a look at these three aspects of sound: Amplitude, Frequency and Timbre. These are the three aspects of sound we are concerned with as electronic musicians.
Amplitude (loudness) The taller the waveform is, the higher the amplitude. This is usually associated with loudness. Decibels Fig 5. A common measurement of loudness is the decibel (db). It is 1/10 of a bel, which was named after the inventor of the telephone, Alexander Graham Bell. One decibel measures the limit of human hearing, the softest threshold point where a change in loudness can be detected by the ear and recognized by the brain. The difference between silence and a single leaf falling is one decibel. Our ability to hear spans an enormous range of pressure amplitudes - a vary large dynamic range. A logarithmic response compresses this range so that our response to variations in weak sounds is similar to the response to variations in loud sounds. Our ears are awesome compressors! Fig 6. Because our ears are such amazing compressors, the human hearing system has an incredible dynamic range of about 120 db between the threshold of hearing and threshold of pain. The difference in intensity between the softest and loudest sounds we can hear is unfathomably large - a trillion times - but is perceived as only 120 times as loud by the human ear. Type of Sound Intensity Perceived loudness in db rustle of leaves 10 10 whisper 100 20 soft conversation 1,000 30 average residence 10,000 40 average office 100,000 50 telephone conversation 10,000,000 70 heavy traffic 1,000,000,000 90 subway traffic 10,000,000,000 100 fighter jet at takeoff 1,000,000,000,000 120 Tip: If your track is just a bit too soft, ask the mix engineer to turn it up 3dB, since it will be noticable but not drastic. If one band member wants something louder and another doesnʼt, try 1dB as a good compromise.
Frequency (Pitch) The shorter the waveform is, the higher the frequency. Frequency is usually associated with pitch. 1. 2. 3. 4. 5. Hertz 6. Fig 7. Each repetition of a wave is called a cycle. The frequency is the number of cycles per second. For example, when a tuning fork sounds the note A4, its tines vibrate 440 times per second. Its frequency is 440 cycles per second, which is usually written as 440 Hertz or 440 Hz. Cents The higher the frequency is, the higher the pitch. However, we do not hear pitch linearly, just as we do not perceive loudness linearly. For instance, pitch differences depend on the ratio of frequencies. If the frequency is doubled (2/1), we hear the pitch rise by an octave. For this reason, in electronic music the scale of cents is often used instead of Hertz because it is easier to think about. 100 cents equals a half step, and 1200 cents equals an octave (because there are 12 half steps in one octave). Harmonic series In nearly every musical instrument, the fundamental tone is always accompanied by other, higherfrequency tones that are generally called overtones. In pitched instruments, these shorter, faster waves are reflected between the two ends of the string or air column, etc. As the reflected waves interact, frequencies whose wavelengths do not divide evenly into the length of the string or air column are suppressed, and the vibrations that persist are called harmonics. Their wavelengths are 1, 1/2, 1/3, 1/4, 1/5, 1/6, etc. of the length of the string or air column. Theoretically, these wavelengths produce vibrations at frequencies that are 2, 3, 4, 5, 6, etc. times the fundamental frequency. (see Fig 7.) In terms of frequency (measured in cycles per second, or hertz (Hz), the difference between consecutive harmonics is therefore constant. But because our ears respond to sound logarithmically, we perceive higher harmonics as "closer together" than lower ones. In the same sense, the octave series is an exponential progression (2xf, 4xf, 8xf, 16xf,...), and we hear these distances as "the same" in all ranges. You find more and more as you program electronic instruments that it makes more sense to use cents. However, you will still find instances where a synthesizer refers to Hertz. Be familiar with both.
Timbre (tone quality) Multiple sine waves add to make complex waveforms, referred to as the timbre. Timbre is the quality of a musical note or sound that distinguishes different types of sounds, such as voices or different musical instruments. Fig 9. sine wave triangle wave square wave sawtooth wave Shown in figure 9 are some simple waveforms that we deal with a lot in electronic music. These are periodic, meaning they repeat exactly the same over time. Weʼll learn how to modify them over time to make them more interesting. We do this with amplitude changes, and also filtering tequniques. To understand how filtering works, we need to understand the spectrum, which are the underlying sine waves that were added to create these waveforms. Spectrum The spectrum of a sound refers to the specific frequencies (sine waves) that make up the sound and respective amplitude of each one. The graph of a spectrum is usually shown in this form: Fig 10. The lowest loudest sine wave is the fundamental frequency. The fundamental is usually the loudest and loudest, and is the pitch (or note) that you hear. The harmonics above the fundamental are what give the sound its tone quality, or timbre. Another way to view this is to look at the individual harmonics and to view the more complex waveform that is created when they are added together. The sine waves added together create the square wave. A square wave contains only odd
harmonics. In musical terms, square waves are often described as sounding hollow, and are used as the basis for wind instrument sounds. Triangle wave Like the square wave, a triangle wave contains only odd harmonics. However, the higher harmonics roll off much faster than in a square wave. Because it has softer high frequencies, its sound is smoother than a square wave and is nearer to that of a sine wave.
Non-Periodic Waveforms: Voice Spectrum over time A waveform of a voice (in blue) is an example of a non-periodic waveform. It doesnʼt have a set pitch, as the pitch is constantly changing. The harmonic spectrum shown in green is very filled in because it is all of the frequencies that occurred in a 15 second timeframe, with the respective amplitudes. 3D spectral plot over time This 3 dimensional display shows a note being played, over time, combining the spectral plot (odd harmonics in this case) and an amplitude envelope for each individual harmonic over time.