Basics Tutorial 2: Adjustable Oscillator

Introduction

In this tutorial we'll look at how to control the amplitude of signals we work with in MSP. In addition, we'll look at an object that helps us generate signal ramps from Max messages that we can use to smoothly control the parameters of MSP objects.

Amplifier: *~

As we saw in our last tutorial, the dac~ object represents the final output of our audio signal network; anything you want to come out of your speakers (or into your headphones) needs to eventually find its way to a dac~ object. Now, any signal you want to listen to - a signal you send to dac~ - must be in the amplitude range from -1.0 to +1.0. Any values exceeding those bounds will be clipped by the dac~ (i.e. sharply limited to 1 or -1). This will cause (in most cases pretty objectionable) distortion of the sound. Most MSP objects that generate sound do so in the range of -1.0 to 1.0:

The default output of cycle~ has amplitude of 1

As a result, learning to adjust signal amplitude is important so that we have control over the volume that we're sending to the output.

To control the level of a signal you simply multiply each sample by a scaling factor. For example, to halve the amplitude of a signal you simply multiply it by 0.5. (Although it would be mathematically equivalent to divide the amplitude of the signal by 2, multiplication is a more efficient computation procedure than division.)

Amplitude adjusted by multiplication

The *~ object in MSP multiplies the signal in its left inlet by whatever comes into the right. This can be a constant number or a signal. If we wish to change the amplitude of a signal continuously over time, we can supply a changing signal in the right inlet of *~. By continuously changing the value in the right inlet of *~, we can fade the sound in or out, create a crescendo or diminuendo effect, etc.

• In the tutorial patcher, start the audio by clicking the message box labeled start. You won't hear anything yet, because the *~ objects in the patch are multiplying their input by 0, resulting in silence. In the patcher area labeled 1, type the number 300 into the floating-point number box labeled Frequency. In the number box labeled Amplitude, type 0.2. You should hear a 300 Hz sine wave playing softly out of your audio device. Click in the Amplitude number box to the right of the decimal point and drag the value up and down. You should hear the sine wave fade in and out in volume, just as it did in the last tutorial when we manipulated the gain~ slider. However, you may hear something less pleasant as you change the volume, namely a series of clicks in the sound. This is called zipper noise, and results from sudden drastic changes in amplitude which cause discontinuities in the signal:

Instantaneous change of amplitude causes a noisy distortion of the signal

Before we address that problem, set the volume in the number box to a comfortable amplitude, and drag in the number box labeled Frequency. As you hear the oscillator's pitch rise and fall, you may also hear a form of zipper noise do to the sudden changes in frequency. If we're going to be continuously controlling either of these parameters (the frequency of the cycle~ object or the amplitude output by the *~ object), we may want to modify those parameters using a signal instead of sending Max messages.

Line segment generator: line~

Take a look at the right-hand piece of patcher logic in the tutorial (labeled 2). If, instead of an instantaneous change of amplitude (which can cause an objectionable distortion of the signal), we supply a signal in the right inlet of the *~ object that changes over the course of 500 milliseconds, we interpolate between the starting amplitude and the target amplitude with each sample, creating a smooth amplitude change.

The line~ object functions similarly to the Max object line. In its left inlet it receives a target value and a time (in ms) to reach that target. The line~ object calculates the proper intermediate value for each sample in order to change in a straight line from its current value to the target value.

• Turn down the volume on the left-hand audio circuit in the tutorial patcher by typing 0 into the Amplitude number box. In the right-hand part of the tutorial patcher, set the Frequency of the cycle~ object to 300. Then, clicking in the number box labeled Amplitude, set the volume to 0.3. Rather than the sound immediately coming on as before, you should hear the sine wave fade in over half a second. If you drag within the number box, you should feel that the volume is chasing your actions, smoothly interpolating between values as if you were slowly manipulating a volume knob on an amplifier.

The second value of the value/time pair we send to the line~ object determines the smoothness of the transition. If we feel that the volume control isn't quite responsive enough, it's easily changed by playing with the transition value.

• Unlock the patcher and change the message box connected to the line~ object controlling the Amplitude. If you'd like a quicker fade, try changing it to read $1 50. When you lock the patch and manipulate the number box again, you should feel that the volume is changing much more responsively to your commands.

Technical detail: Any change in the over-all amplitude of a signal introduces some amount of distortion during the time when the amplitude is changing. (The shape of the waveform is actually changed during that time, compared with the original signal.) Whether this distortion is objectionable depends on how sudden the change is, how great the change in amplitude is, and how complex the original signal is. A small amount of such distortion introduced into an already complex signal may go largely unnoticed by the listener. Conversely, even a slight distortion of a very pure original signal will add partials to the tone, thus changing its timbre.

Adjustable oscillator

The patcher logic on the right uses a combination of *~ and line~ to make an adjustable amplifier for scaling the amplitude of the oscillator. However, the line~ object can output signals that can be used to control a lot of things... not just volume.

• With the volume on the right-hand patcher logic raised, adjust the number box labeled Frequency. Try typing in a value distant from the current one, e.g. make the frequency jump from 300 to 1000 Hz. Notice that, unlike in the left-hand example, the frequency smoothly transitions over 500 milliseconds.

As with the amplitude control, the line~ object is sending a signal that smoothly transitions based on value/time commands sent to it by Max messages. By controlling the frequency of the oscillator in this way, we've created a gliding effect referred to in synthesizer design (and instrument performance) as portamento. If you think the transition is too slow for your tastes, unlock the patcher and change the message box so that you have a shorter transition time. See how short you can make it so that the portamento disappears but you still avoid hearing any clicks in during a frequency change.

Summary

Multiplying each sample of an audio signal by some number other than 1 changes its amplitude; therefore the *~ object is effectively an amplifier. A sudden drastic change of amplitude can cause a click, so a more gradual fade of amplitude - by controlling the amplitude with another signal - is usually advisable. The segment signal generator line~ is comparable to the Max object line and is appropriate for providing a linearly changing value to the signal network. The combination of line~ and *~ can be used to make an envelope for controlling the over-all amplitude of a signal. In addition, a line~ object can be used to smoothly control the parameters of nearly any MSP object, such as the frequency of a cycle~ oscillator.

Name	Description
cycle~	Sinusoidal oscillator
dac~	Audio output and on/off
line~	Linear ramp generator