1. CS 591 S1 – Computational Audio -- Spring, 2017
Wayne Snyder Computer Science Department Boston University
Lecture 9 (Tuesday)
Conclusions on Karplus-Strong
Conclusions on Music Synthesis
Questions on Midterm
Demo of Software Synthesizer (Ebrahim)
Midterm One on Thursday 3/2! 1

2. Physical Modeling Synthesis: Karplus-Strong
Karplus-Strong String Synthesis
This process is modeled by a Ring Buffer Queue (remember those, CS 112 folks??). The algorithm is actually very simple: to create a signal of length M samples, fill the queue with random values, and then rotate the queue, but inserting the average of two values times a decay factor:
(Actually this diagram is reversed left-to-right compared with the Python code.) 2

3. Physical Modeling Synthesis: Karplus-Strong
Now of course, you can try different variations, varying the frequency and the decay; here is low and slow:
KarplusStrong(1000,44100*5,0.99) /1000 = 44.1 Hz 3

4. Physical Modeling Synthesis: Karplus-Strong
Now of course, you can try different variations, varying the frequency and the decay; here is high and short:
KarplusStrong(20,10000,0.9) /20 = 2205 Hz 4

5. Physical Modeling Synthesis: Karplus-Strong
Or, you can start tweeking the various components of the algorithm:
Load it with non-random values to start, maybe a square wave or a sample;
Use a different smoothing algorithm, e.g., weighted average, average of 3, or average of two values separated by k samples, etc. etc.
Here I have taken the average of
4 samples:
two samples, skipping 2:
Here is a weighted average (0.75a b)
Here I have loaded the queue with a square wave
at Hz:
Here I have loaded the queue with the
first 200 samples of the SteelString.wav file:
Original: 5

6. Physical Modeling Synthesis: Karplus-Strong
Some other variations that have been explored include probabilistically inverting the value inserted into the queue (reminiscent of Ring Modulation, perhaps):
For p = ½ this simulates a drum sound:
For other values of p, we can mix the string and drum sounds:

7. Physical Modeling Synthesis: Karplus-Strong
Or we can load the queue with an appropriate non-random signal:
here is a square wave at 220 Hz:
And one at 44.1 Hz:
Here is the clarinet sound at 220 Hz:
And a Bell sound at 1000 Hz:
Or we can change the length of the queue to simulate glissando and other pitch-specific effects:
The possibilities seem endless… Any ideas?

8. Granular Synthesis
There are many other approaches that have been taken to sound synthesis, and we will not have time to cover all of them. One of the most interesting is called Granular Synthesis, and consists in taking very short samples, say 0.2 seconds or shorter, and combining these in groups of clouds of sound; as we have seen with previous methods, when individual units are combined at higher than 20 Hz, the result is a new timbre instead of a recognizable sequence of sounds….

9. Putting it all together: Music Synthesis
We have focussed on creating realistic (and not so realistic) timbres of sound, and creating individual notes such as might be created by a musician. In the end, these sounds must be combined into an extended piece of music or as a soundtrack to a film, video games, etc.
Fundamentally, we must create a process by which a score, which records which notes are played when, is played by some entity, either human or machine.

10. Putting it all together: Music Synthesis
The result we may call Music Synthesis as opposed to simply Sound Synthesis. Here is a (very simple) example of such a process:

11. Putting it all together: Music Synthesis
Here is another that I use quite frequently, embedded into an editor for guitar tablature notation, called Guitar Pro:

12. Putting it all together: Music Synthesis
A very popular framework for Music Synthesis is called Midi, which allows for the specification of a sound file in terms of individual notes, and for the connection of physical devices, such as keyboards, with synthetic sounds:

13. Putting it all together: Music Synthesis
[Software Synth Demo by Ebrahim]