MUMT 307 FM

MUMT 307

Outline

Theremin played by Leon Theremin
Theremin
Modular Synth with MML
JKnobMan

Examples:

http://bji.yukihotaru.com/knob.html
Search for "Knobman" in Google Images

Reverb downloads?
Wavetable and Additive Synthesis
Wavetable ann Additive Synthesis (lab)
Amplitude Modulations
Frequency Modulations

MUMT 307

Reverb 1 (lab)

Find and download Impulse Response files from different sites
Try this one first: http://www.voxengo.com/impulses/
Check out the Modeler
You will be assigned one of these to download and test: http://rhythminmind.net/STN/?page_id=4188
Here are some more:

http://www.resoundsound.com/4-impulse-response-reverb-packs/
Isophonics (96kHz)
These ones are in SoundDesigner II file format: http://fokkie.home.xs4all.nl/IR.htm

Note that you should be using these IR files for the next assignment (#4)

MUMT 307

Reverb 2 (lab)

Test the downloaded IR files with the Reverb demo
Use anechoic chamber recordings from University of York

MUMT 307

Wavetable and Additive Synthesis

Additive Synthesis (KAWAI K5)
`y(t)=sum_(k=1)^oo[a_kcos(2pifkt)-b_ksin(2pifkt)]`
Web Audio API: PeriodicWave (fromerly known as WaveTable)

PeriodicWave demo
PeriodicWave demo 2: http://www.g200kg.com/waorgan/

MUMT 307

Wavetable and Additive Synthesis (lab)

Using the PeriodicWave demo, create a sawtooth wavetable and a triangular wavetable with the following Fourier series with the fundamental frequency, `f`:

Square: `4/pisum_(k=0)^oo 1/k sin(2pifkt) text{ for } k=1,3,5,...`

Sawtooth: `1/2 - 1/pisum_(k=0)^oo 1/k sin(2pifkt) text{ for } k=1,2,3,...`

Triangle: `8/pi^2sum_(k=0)^oo (-1)^{(k-1)//2}/k^2 sin(2pifkt) text{ for } k=1,3,5,...`

MUMT 307

Why we do not use table lookups for sine wave generation

Machine cycles: cos(): on Intel 486: ~300 cycles compared to ~10 cycles for a table lookup
Also multiply was a lot longer than add (the shift trick)
Motorola 68030 (Atari, Mac II, PowerBook 180) cycles: FCOS 394; FADD: 56; FMUL: 76;

AT 33MHz; 60 cycles ~= 0.5MFLOPS; 400 cycles ~= 0.08MFLOPS

Spreadsheet showing history of CPU speeds (local file)
FLOPS
Using the GPU as FPU
Orders of magnitude

MUMT 307

Speed test your CPU (lab)

Speed test of your CPU

Download: speedtest.tar.gz
If you don't have gcc on your machine, upload (sftp) to a subdirectory of your music.mcgill.ca account
Uncompress speedtest.tar.gz (double-click on OSX or "tar -xf speedtest.tar.gz")
make c_speedtest
Reboot your machine
./c_speedtest -nsize 1000000 -niters 1000

Add a vectorCosine() test

MUMT 307

JavaScript speed tests (lab)

MUMT 307

Amplitude Modulation (AM) Syntheis

MUMT 307

Amplitude Modulation (AM) Math

Carrier: `c(t) = A*sin(omega_ct), omega_c = 2pif`

Modualtor: `m(t) = M*cos(omega_mt), omega_m = 2pif`

Amplitude Modulation: `y(t) = [1 + m(t)]*c(t)`

`= [1 + M*cos(omega_mt)]*A*sin(omega_ct)`

`= A*sin(omega_ct) + A*M*cos(omega_mt)*sin(omega_ct)`

`= A*sin(omega_ct) + A*M//2[sin(omega_ct+omega_mt)+sin(omega_ct-omega_mt)]`

since: `cos(b)sin(a) = 1//2[sin(a+b)+sin(a-b)]`

MUMT 307

Ring Modulation

Carrier: `c(t) = A*sin(omega_ct), omega_c = 2pif`

Modualtor: `m(t) = M*cos(omega_mt), omega_m = 2pif`

Ring Modulation: `y(t) = m(t)*c(t)`

`= M*cos(omega_mt)*A*sin(omega_ct)`

`= A*M*cos(omega_mt)*sin(omega_ct)`

`= A*M//2[sin(omega_ct+omega_mt)+sin(omega_ct-omega_mt)]`

since: `cos(b)sin(a) = 1//2[sin(a+b)+sin(a-b)]`

RM demo; AM demo; Tremolo demo

MUMT 307

Frequency Modulation (FM) Syntheis

Tutorial by Gaëtan Renaudeau
Theory (by Gary Scavone)
A simple FM synth
A demo inspired by Yamaha DX7 (iOS)
Yamaha DX7
What are the most popular synthesizers of all time?

Frequency Modulation (FM) Syntheis (Lab)

Make this work in Firefox: http://www.g200kg.com/shotit
Make this work in Firefox: http://dl.dropboxusercontent.com/u/695740/webaudiofmsynth/index.html
Make this work in Firefox: http://www.taktech.org/takm/WebFMSynth/