Basics Tutorial 5: A Review of Fundamentals
Exercises in the fundamentals of MSP
In this chapter, we suggest some tasks for you to program that will test your understanding of the fundamentals of MSP presented in the tutorials so far. A few hints are included to get you started. Try these three progressive exercises on your own first, in new file of your own. Then check the example patch to see a possible solution, and read on in this chapter for an explanation of the solution patch.
Write a patch that plays the note E above middle C for one second, ten times in a row, with an electric guitar-like timbre. Make it so that all you have to do is click once to turn audio on, and once to play the ten notes.
Here are a few hints:
- The frequency of E above middle C is 329.627557 Hz.
- For an ‘electric guitar-like timbre’ you can use the AIFF file gtr512.aiff that was used in Basics Tutorial 3. You'll need to read that file into a buffer~ object, and access the buffer~ with a cycle~ object.
- Your sound will also need an amplitude envelope that is characteristic of a guitar: very fast attack, fast decay, and fairly steady (only slightly diminishing) sustain. Try using a list of line segments (target values and transition times) to a line~ object, and using the output of line~ to scale the amplitude of the cycle~.
- To play the note ten times in a row, you'll need to trigger the amplitude envelope repeatedly at a steady rate. The Max metro object is well suited for that task. To stop after ten notes, your patch should either count the notes or wait a specific amount of time, then turn the metro off.
Modify your first patch so that, over the course of the ten repeated notes, the electric guitar sound crossfades with a sinusoidal tone a perfect 12th higher. Use a linear crossfade, with the amplitude of one sound going from 1 to 0, while the other sound goes from 0 to 1. (We discuss other ways of crossfading in a future chapter.) Send the guitar tone to the left audio output channel, and the sine tone to the right channel.
- You will need a second cycle~ object to produce the tone a 12th higher.
- To obtain the frequency that's a (just-tuned) perfect 12th above E, simply multiply 329.627557 times 3. The frequency that's an equal tempered perfect 12th above E is 987.7666 Hz. Use whichever tuning you prefer.
- In addition to the amplitude envelope for each note, you will need to change the over-all amplitude of each tone over the course of the ten seconds. This can be achieved using an additional *~ object to scale the amplitude of each tone, slowly changing the scaling factor from 1 to 0 for one tone, and from 0 to 1 for the other.
Modify your second patch so that, over the course of the ten repeated notes, the two crossfading tones also perform an over-all diminuendo, diminishing to 1/32 their original amplitude (i.e., by 30 dB).
- This will require yet another amplitude scaling factor (presumably another *~ object) to reduce the amplitude gradually by a factor of .03125.
- Note that if you scale the amplitude linearly from 1 to .03125 in ten seconds, the diminuendo will seem to start slowly and accelerate toward the end. That's because the linear distance between 1 and .5 (a reduction in half) is much greater than the linear distance between .0625 and .03125 (also a reduction in half). The first 6 dB of diminuendo will therefore occur in the first 5.16 seconds, but the last 6 dB reduction will occur in the last .32 seconds. So, if you want the diminuendo to be perceived as linear, you will have to adjust accordingly.
Solution to Exercise 1
To make an oscillator with a guitar-like waveform, you need to read the audio file gtr512.aiff (or some similar waveform) into a buffer~, and then refer to that buffer~ with a cycle~. (See Basics Tutorial 3.)
Note that there is a limit to the precision with which Max can represent decimal numbers. When you save your patch, Max may changevalues slightly. In this case, you won't hear the difference.
If you want the audio file to be read into the buffer~ immediately when the patch is loaded, you can type the filename in as a second argument in the buffer~ object, or you can use a loadbang object to trigger a message to buffer~. In our solution we also chose to provide the frequency from a number box - which allows you to play other pitches - rather than as an argument to cycle~, so we also send cycle~ an initial frequency value with loadbang.
Now that we have an oscillator producing the desired tone, we need to provide an amplitude envelope to shape a note.
We chose the envelope shown below, composed of straight line segments. (See Basics Tutorial 3.)
This amplitude envelope is imposed on the output of cycle~ with a combination of line~ and *~. A metro is used to trigger the envelope once per second, and the metro gets turned off after a 10-second delay.
Solution to Exercise 2
For the right output channel we want a sinusoidal tone at three times the frequency (the third harmonic of the fundamental tone), with the same amplitude envelope. To crossfade between the two tones, the amplitude of the first tone must go from 1 to 0 while the amplitude of the second tone goes from 0 to 1. This can again be achieved with the combination of line~ and *~ for each tone. We used a little trick to economize. Rather than use a separate line~ object to fade the second tone from 0 to 1, we just subtract 1 from the output of the existing line~, which gives us a ramp from 0 to -1. Perceptually this will have the same effect.
This crossfade is triggered (via s and r objects) by the same button that triggers the metro, so the crossfade starts at the same time as the ten individual notes do.
Solution to Exercise 3
Finally, we need to use one more amplitude envelope to create a global diminuendo. The two tones go to yet another *~ object, controlled by another line~. As noted earlier, a straight line decrease in amplitude will not give the perception of constant diminuendo in loudness.
Therefore, we used five line segments to simulate a curve that decreases by half every two seconds. (The curve~ object will do this automatically.)
This global amplitude envelope is inserted in the signal network to scale both tones down smoothly by a factor of .03125 over 10 seconds.