The Telharmonium was a polyphonic instrument with a touch-sensitive keyboard that produced sine waves by using a series of rapidly spinning alternators. The alternators were driven by banks of electric motors that rotated at fixed speeds and controlled the frequency of the alternators and thus the pitch of the sound. The instrument predated the invention of the amplifier, however, and was a monstrosity that weighed over tons and needed six railroad cars to transport.
Because of this and other technological problems, the Telharmonium wasn't an enduring success. B-4 the B-3 When Laurens Hammond took the rotating-disk system of the Telharmonium and combined it with more modern electrical technology, the first commercially successful electric musical instrument became available.
The Hammond organ was invented in and first reached the public in It sported an electric motor that rotated a shaft containing 91 metal disks, each patterned with specific grooves, that were used to control note frequencies. Its additive synthesis-related features came in the form of switches called drawbars, each of which corresponded to a specific partial, and which together could be used to produce over , different sounds.
But the Hammond organ along with its predecessors still lacked two very important features for the creation of truly complex sounds. First, the organ produced sounds with nonvarying amplitudes, meaning you preset the volume of each partial and then every note had the same amplitude. The volume settings could be changed, but not while a note was sounding. More serious, however, was the fact that the range of sounds the Hammond could produce was, in a sense, limited.
Let's look at a little more theory to understand why. Part and Partial The partials that make up a sound's spectrum come in two forms: harmonic and inharmonic. Harmonic partials are defined mathematically as whole-number multiples of the fundamental frequency. For example, by doubling a fundamental frequency of Hz, we get a harmonic partial with a frequency of Hz, and tripling it produces another harmonic partial at 1, Hz.
These frequencies are known as the second and third partials, and so on. Inharmonic partials, on the other hand, are those sine waves whose frequencies are not whole-number multiples of the fundamental. For example, partials at Hz and Hz would be inharmonic relative to a fundamental of Hz. The Hammond organ was limited to harmonic partials, which is why it produced such pure and smooth tones. To create truly complex sounds, any synthesizer should be able to produce both harmonic and inharmonic partials.
And it should have the ability to combine several dozen to several hundred sine waves. Each of those waves requires its own oscillator, set to a unique frequency and amplitude.
Because the loudness of most complex sounds varies over time, the amplitude of every sine wave must be dynamically controlled by an envelope generator. Each envelope generator requires at least an attack, decay, sustain, and release segment, so even with only 30 sine waves to manage, that's over parameters that have to be controlled and created in real time in order to create a single note. This task was beyond the reach of any instrument in the s and was something that could only be performed by the power of computing.
The Computer as Synth During the s and '60s, digital mainframe computers found in research institutions were first used to generate complex sounds by manipulating specific partials. Researcher Max Matthews at Bell Labs is credited with developing the first sound programming language. Matthews called his program Music I, and though the first version was a simple, 1-voice generation utility, it quickly evolved into an application that provided an unlimited number of voices.
The program didn't work in real time, however. Sound parameters had to be fed into the computer, which then took a certain amount of time for processing, and the results had to be converted into an analog signal before being played. Then, in the late s, David Luce built a machine that would analyze a set number of partials for any complex sound and display their individual envelopes as plots on an oscilloscope screen in real time.
These plots were photographed, and Luce would then manipulate the partials of the sound by redrawing the envelopes and having the machine scan his drawings using an optical scanner.
The machine would then play back the altered sound in real time. This was one of the first demonstrations of what is known as resynthesis. Resynthesis Today, pure additive synthesis is still very scarce even with all of the computing power available on the desktop. That's because the sheer number of parameters that have to be set in order to accomplish even a fairly complex sound is overwhelming.
And to accurately mimic acoustic instruments, you need to set the partials for every note because the partial characteristics change for every fundamental frequency, and to a lesser extent, for different loudness levels. Here is a single spoken word as shown in the analysis screen of Steinberg's Wavelab.
Sure, you may not think of it in this way, and you may be surprised to discover that it predates what we now think of as 'conventional' VCO-VCF-VCA analogue synthesis by about 30 years. This instrument is the Hammond Tonewheel Additive Synthesizer.
Oops, sorry. I mean, it's the Hammond Organ. This means that you will now have two sine waves per note. Figure 9: The classic Hammond configuration of nine drawbars per registration. Each of these has nine amplitude positions 1 to 8, plus 'off' so many millions of possible combinations more usually called 'registrations' are available.
So there you have it: nine harmonically related pitches, each with nine possible volumes, and you can combine these in any way you choose. But surely this can't be the be-all and end-all of additive synthesis? There's obviously something missing. In my discussions about filters and envelopes, I postulated that sounds will always sound static and uninteresting if they do not change in time. So let's encapsulate this in another Synth Secret: Organs sound like organs not because of the simplicity or not of their waveform generators, but because their sounds do not change over time.
Or, to put this another way: No matter how clever the method of synthesis, and no matter how complex an initial waveform may be, any timbre will sound static and 'organ-like' if it does not change in time. One way to add interest is by applying 'effects' such as phasers, flangers, or echo units to the basic signal.
Unfortunately, these do not affect the essential nature of the sound. Now consider playing this sample through the contoured filters and amplifiers that no doubt reside within your sampler. Figure [top] Adding filter and amplitude contours to our basic additive synthesizer. Figure [bottom] A more complex and useful additive synthesizer. It's just that we have nine oscillators instead of three. We know from experience that this is loud and bright at the start of the note, and becomes quieter and 'darker' as time passes.
Firstly, we must assign the pitches of the oscillators to imitate the harmonic nature of the string. Secondly, we must consider how each of these harmonics changes in time. This is also simple: we know that the sound becomes duller as time passes, so the higher-frequency harmonics must decay more rapidly than the lower ones.
Thirdly, we must determine how the overall brightness and loudness of the sound changes as the note progresses, and create filter and amplifier profiles that emulate this. Figure [top] The four contours controlling the amplifiers in Figure Figure [bottom] The four decaying harmonics defined by the contours in Figure So let's now design our simple plucked string sound.
Note also that, because the higher frequencies are decaying more quickly, the sound becomes 'darker' as time passes. Figure [top] The final waveform output by our 'additive' synthesizer. Starting with the fundamental frequency, odd harmonics are added that decrease in amplitude proportional to the harmonic number. So if we start at Hz at a normalized amplitude of 1. Next would be the 5th harmonic tone at Hz at an amplitude of. The more odd harmonics added using the same proportional amplitude adjustment, the more distinct the square wave becomes.
Notice how the waveforms below change as more harmonics are added: 8 Harmonics 16 Harmonics 24 Harmonics Again, the more harmonics used, the more distinct the resulting shape and sound becomes.The use of sine waves make the process highly predictable and controllable. The wave set can be either partials 1 to 64 or partials 65 to of the naturally occurring harmonic series. Below is an example of a square wave built from sine waves. Main article: Wavetable synthesis In the case of harmonic, quasi-periodic musical tones, wavetable synthesis can be as general as time-varying additive synthesis, but requires less computation during synthesis. Given a source set of values and a set of algorithmic rules, the control parameters reference the previous value entered into the system to determine the result of the next one.
In order to make up for this, the instrument provides PCM samples that can be combined with the wave sets to create more complex waveforms. Figure [bottom] The four decaying harmonics defined by the contours in Figure So yes each partial is a sine wave of a given frequency pitch. This is also simple: we know that the sound becomes duller as time passes, so the higher-frequency harmonics must decay more rapidly than the lower ones.
For a review, see the January issue of EM. Given the massive range of frequencies that can appear in a sound and the fact that these frequencies change in strength as the sound evolves, you can see why "sound quality," or timbre, is so difficult to define.
That's a sine wave. The Fourier Theorem During the early nineteenth century, a French mathematician named Jean Baptiste Joseph Fourier theorized that any complex sound can be broken down into a series of simple sounds. The instrument predated the invention of the amplifier, however, and was a monstrosity that weighed over tons and needed six railroad cars to transport. Volumes have been written on Additive Synthesis and you should have no problem digging deeper if you so choose. See Markov chains.
Figure [bottom] A more complex and useful additive synthesizer. This means all subtractive synths must have at minimum one filter. Moreover, certain sounds, such as brass instruments, have a spectrum in which the upper partials enter after the lower ones and disappear sooner. Inharmonic partials, on the other hand, are those sine waves whose frequencies are not whole-number multiples of the fundamental. A harmonic sound could be restructured to sound inharmonic, and vice versa. So, despite everything, we need at least one filter in our additive synth.
Next would be the 5th harmonic tone at Hz at an amplitude of. Mind you, the noise produced by orchestral instruments is far from 'white' or 'pink'; it is heavily filtered by the nature of the instrument itself. B-4 the B-3 When Laurens Hammond took the rotating-disk system of the Telharmonium and combined it with more modern electrical technology, the first commercially successful electric musical instrument became available. More serious, however, was the fact that the range of sounds the Hammond could produce was, in a sense, limited. Moving on, let's ask ourselves the following question.
So is 'sinusoids plus noise' synthesis. Older techniques rely on banks of filters to separate each sinusoid; their varying amplitudes are used as control functions for a new set of oscillators under the user's control. This powerful application is the latest in a long line of sound-programming languages that extend directly back to Max Matthews's original Music program. You can even put simple amplitude envelopes on the partials to vary the sound as it evolves.
The Telharmonium was a polyphonic instrument with a touch-sensitive keyboard that produced sine waves by using a series of rapidly spinning alternators.
Additive synthesis is a sound technique that uses sine waves to produce a certain timbre the sounds quality. If you have the appropriate expensive equipment, you can separate their sounds into their component harmonics. Given the massive range of frequencies that can appear in a sound and the fact that these frequencies change in strength as the sound evolves, you can see why "sound quality," or timbre, is so difficult to define.
This makes it easy to take apart any sound, like a spoken word, and find the structure of its spectrum see Fig. Static waveforms, for example the square or sawtooth, contain partials whose amplitudes are fixed, which is why these tones have, for the most part, a lifeless quality. As soon as you have done this, you've entering the weird and wonderful world of additive synthesis.
Just how much do the partials in a natural sound fluctuate? By summing several sine waves of varying frequency, amplitude and phase, we can create more complex sonorities. This representation can be re-synthesized using additive synthesis.
The results can be truly remarkable.