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Frequency modulation synthesis is capable of creating a broad, detailed, highly nuanced range of tones which can be controlled with a fine.
Table of contents
- Where to Get the Book
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- How to Make a Noise: Frequency Modulation Synthesis on Apple Books
- Operators and Algorithms
- See a Problem?
Figure 1: [top] Amplitude Modulation. Figure 2: [bottom] Frequency Modulation. At this point, you would be completely justified in running, screaming, for the hills. You will, therefore, be delighted to know that I'm not even going to try to solve the equation. Unfortunately, that means that you will have to take many of the following facts on trust. But hey In this example, the frequency of that Modulator is significantly lower than that of the Carrier. Figure 3: [top] The effect of vibrato on a triangle wave. Figure 4: [bottom] A short segment of a Carrier waveform. Now let's ask ourselves what happens as we increase the Modulator's frequency until it approaches, equals, or even exceeds that of the Carrier.
As you will appreciate, this sounds nothing like vibrato. But what does it sound like?
Figure 5: [top] Modulating the Carrier in Figure 4 with a high-frequency, low-amplitude Modulator. Figure 6: [bottom] A Carrier and a Modulator.
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If you refer back to Equation 5, you'll see that the equation for A 1 has two 'alien' terms within it: a 2 and w 2. These are, of course, the gain maximum amplitude and the frequency of the Modulator. So it's fair to assume that each of these will have an affect on the nature of the modulated signal. Let's look first at w 2 , and see what attribute of the output is influenced by the Modulator's frequency. John Chowning discovered that FM, like AM, generates side bands — additional components, not necessarily harmonically related to the frequency of the Carrier or Modulator — in the frequency spectrum of the output signal.
For an explanation of what side bands are, please refer back to last month. So far, so good In the real world, however, no system has infinite bandwidth, and analogue systems are limited to producing side bands within their finite bandwidth see later for more on bandwidth. Similarly, manufacturers of digital FM systems constrain the mathematics to those values that they deem significant.
Figure 7: The positions of the side bands. Fortunately, and despite this possible complication, the simple formula in Equation 6 makes it easy to see where the side bands are located. Now, what about the amplitudes of these side bands? OK, we now know that frequency modulation generates side bands, and that the Modulator's frequency determines where they lie. But what is the 'shape' of the resulting spectrum? Figure 8: [top] A simple analogue FM vibrato patch. Figure 9: [bottom] FM side bands with low Modulation Index.
Don't forget that in this case, the Modulator frequency w m is very much lower than the Carrier frequency w c. Consider the case where the gain of the VCA is zero. Now let's increase the gain of the VCA slightly. What we learn from this is that the sound we hear is not only determined by the frequency of the Modulator, but also by its gain or maximum amplitude.
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We write this as follows:. Let's take that case where the Modulation Index is low — say in the region of 0. Figure [top] FM of the same signals when the Modulation Index is increased. Now look at Equation 7 again and you'll see that the denominator the bit 'below the line' is the frequency of the Modulator. The consequences of this are very far-reaching. This will require both the Carrier and the Modulator to track the keyboard equally so that the harmonic relationship between the spectral components the side bands remains constant.
Mind you, this configuration is almost impossibly difficult to calibrate perfectly, and the vagaries of analogue components ensure that it will, at best, be inconsistent. This is the reason why FM is almost always implemented using digital technology.
So let's discuss what the real bandwidth of an FM'd signal might be. The FM Synth is an instrument doing frequency modulation synthesis. This is very different than our other synthesizers like the Simple, which is doing subtractive synthesis. FM synthesis means that you create a complex waveform by modulating a simple waveform with another simple waveform. This is done using waveforms of different frequencies and amplitudes to kind of mangle, distort and change the sound into something more complex and interesting.
The FM Synth is quite a complex synthesizer so read on get a better understanding of how it works. We wont dig to deep here in how to use it to create complex sounds. But you can find lots of great material on FM synthesis using a search engine! The DX7 have six so-called Operators.
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Each Operator is a sine wave and is used to create your more complex waveform. You can think of them as six different sine wave oscillators. A carrier is something that you can hear. Whether an Operator is a carrier or a modulator is decided by the Algorithm setting. Operator number 1 is always a carrier.
Then each algorithm connects the rest of the Operators in different configurations as carriers or modulators to make up your finished sound. The bottom row shows the carriers while the rows above show the modulators.
How to Make a Noise: Frequency Modulation Synthesis on Apple Books
In this case Operator 2, 4 and 6 are the modulators. Click here for a full view of all Algorithms.
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For carriers this level knob controls the output volume. For modulators however the level knob decides the amount of change it does to the carrier. And the more you turn it up the brighter the sound will be.
Operators and Algorithms
So for modulators you can think of the level knob as something similar to the cutoff frequency in a lowpass filter. We control the pitch with the coarse, fine and detune parameters. The settings represent different frequency ratios. Starting from 0 to 31, where 1 is the fundamental frequency and 0 is one octave below it. So the detune knob is very subtle and has a lesser effect than the fine settings. This is usually most useful if the operator is acting as a modulator.
In fixed mode you can set the frequency between 1Hz and 9,Hz using the course and fine settings.
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All operators have the same envelope settings. If an operator is a carrier, where the sound is routed directly to the output of the instrument, then the envelope will affect the amplitude of what you hear. If an operator is a modulator, meaning if affects another operator, then the envelope affects the tone and timbre of the sound. Envelopes in this synth are different than those found in our other instruments.
Simply put the envelope Levels are reached at different Rates. For example R1 controls how long it takes for it to reach the amplitude level of L1. Each knob can be set between 0 and You can think of the Rate knob, as a speeding vehicle where 0 is moving very slow and 99 is very fast. R1 controls the time it takes to reach the level of L1.