# Exercise D

## Exercise D: Modulation

One of the more important synthesis techniques is modulation. Last semester we learned how to use an LFO to change the pitch of an oscillator slowly, creating vibrato. This week, we learn how to build that structure from the ground up using native Max audio objects. The basic modulation scheme can be applied to any parameter, not just oscillator frequency. Any waveform, including band-limited noise (as generated by rand~), can act as a modulation source.

If you raise the frequency of a periodic modulation source, such as a sine wave oscillator, so that it is higher than 20 Hz, you create timbral changes. This technique of modulation synthesis comes in two basic forms: amplitude modulation (AM) and frequency modulation (FM), depending on whether the modulation source (the modulator) controls the amplitude or the frequency of the oscillator we hear (the carrier).

We will try ring modulation (RM), which is a more commonly used special case of amplitude modulation. Then we will explore FM synthesis, which is more complex than either AM or RM.

### Goals

We’re learning how to...

• perform ring modulation by multiplying the outputs of two oscillators,
• create a sub-audio rate (i.e., less than 20 Hz) modulation structure to produce vibrato, and
• use that same structure to implement FM synthesis.

### How to Do This Exercise

Working on the assignment is a three-stage process.

1. Download Exercise D Max Tips. This folder of Max patches shows you how to implement two kinds of modulation synthesis.
2. Take your detuned oscillator patch from Exercise C, and ring modulate it. You can reduce the detuned patch to mono before ring modulating it with a sine wave oscillator. It’s better to omit the noise layer of Exercise C for this.

You should insert your ring modulator into the signal chain directly above the master volume fader (the live.gain~ that connects to ezdac~).

3. Make a patch that uses the FM structure shown in Part 2 of the ExD Max Tips: create two layers, one for the left channel, one for the right channel. So, two copies of what you see in the Part 2 example patch.

Specific requirements...

• Save several settings of the parameters (number boxes) to get contrasting sounds. You can use the simple preset box (without pattrstorage) to do this.
• Be sure that the modulating oscillator frequency is well above 20 Hz. We want FM synthesis, not vibrato.
• Try simple ratios between the carrier and modulator frequencies.
• Try setting the modulation depth (the number fed to *~) to a very high value (above 10,000), in order to get bright FM timbres. The depth must be much higher than you would ever use for vibrato.

In a complete implementation of FM synthesis, we would express the modulation depth in terms of a modulation index, which combines with the modulator frequency to produce consistent brightness when you change pitch. But we won’t bother with that here.

### Submission

• Be sure you satisfied the criteria listed above.
• Submit your Max patch in Canvas.