This is a little waveform synthesis tutorial.

Most synthesizers on the market today have many similarities. I wanted to bore down to the basics, because a lot of the tutorials out there seem to make things overly complex in the way of explanation. This is a way for me to research and learn about waveform synthesis. I’ll preface this with the fact that I’m not an expert on this subject, and this tutorial is more for me than for everybody else. If you spot an error, please comment and correct me.

A sound wave is nothing more than a burst of pressure in the air over a given time. It core part is a wave that starts at nothing, then rises, falls, then returns to nothing. This cycle is called a Hertz. The loudness of this cycle is called Amplitude. This cycle repeats hundreds of times per second in order to produce sound.

There are many types of waves (which will be detailed later) but the four basic shapes are: Sine, Triangle, Saw (or Sawtooth), and Square.

Pitch

The more cycles in a second of sound will produce a higher pitch, less cycles will produce a lower pitch.

Hitting an “A” note in the middle of the piano (A4) will produce a series of wave cycles 440 times in one second. This frequency is expressed as 440Hz (Hertz). All the notes in the western scale of music can be expressed by frequency using some simple math. Dividing 440Hz in half will produce a lower pitched “A” (or A3) an octave lower at 220Hz. Multiplying 440Hz by two will produce a higher pitched “A” (or A5) octave higher at 880Hz. So, to jump to the next octave in any note, simply either multiply or divide it’s frequency. To jump half steps through the notes, just multiply the base frequency by 2^n/12.

Here is a Frequency/Note chart to get you started:

Note/Octave	0	1	2	3	4	5	6	7	8
C	16.35	32.70	65.41	130.81	261.63	523.25	1046.50	2093.00	4186.01
C#	17.32	34.65	69.30	138.59	277.18	554.37	1108.73	2217.46	4434.92
D	18.35	36.71	73.42	146.83	293.66	587.33	1174.66	2349.32	4698.64
D#	19.45	38.89	77.78	155.56	311.13	622.25	1244.51	2489.02	4978.03
E	20.60	41.20	82.41	164.81	329.63	659.26	1318.51	2637.02	5274.04
F	21.83	43.65	87.31	174.61	349.23	698.46	1396.91	2793.83	5587.65
F#	23.12	46.25	92.50	185.00	369.99	739.99	1479.98	2959.96	5919.91
G	24.50	49.00	98.00	196.00	392.00	783.99	1567.98	3135.96	6271.93
G#	25.96	51.91	103.83	207.65	415.30	830.61	1661.22	3322.44	6644.88
A	27.50	55.00	110.00	220.00	440.00	880.00	1760.00	3520.00	7040.00
A#	29.14	58.27	116.54	233.08	466.16	932.33	1864.66	3729.31	7458.62
B	30.87	61.74	123.47	246.94	493.88	987.77	1975.53	3951.07	7902.13

*Note: Piano rolls on DAWs will express A4 as A3 (Middle C, or C4, is usually denoted on piano rolls as C3). I have no idea why this is.

Frequency Analysis

Another way of looking at sound is with a frequency spectrum graph. A saw wave in C (523.25 Hz), will produce the following image:

Now bear with me on this, because I’m not entirely sure I have this right. The note played is the highest most prominent peak, called the Fundamental Frequency. The smaller peaks are the harmonics, in-harmonics, and overtones called partials. There is some math that goes into this that I won’t get into here, but the main thing is how to read this.

Oscillators

Most synths have one or more oscillators. This is where you set the initial waveform and pitch. This is usually the start of the path for a synth. The pitch (or tuning) comes in handy when using two or more oscillators, which will be discussed later. Most synths will have knobs for Octave, Semi, and Tune. Octave will jump through Octaves, naturally. Semi will adjust the half steps through 12. And Tune (or Fine, Detune, or Cent) will adjust the half-steps through cents.

Some synths feature a Pulse Width Modulation knob, PWM for short. This is another type of waveform, usually associated with the square waveform. PWM allows for squeezing the trough and crest of a wave cycle, this can be usually be modulated by other waveforms or have it’s own modulation control, creating a pulsing sound.

Other controls in the Oscillator include a FM control, which allows you to modulate the frequency with another carrier wave. Keyboard Tracking culls the amount of pitch up to one note. This is useful for making a sound that needs only one pitch, such as a drum hit – or to disable a waveform from the keyboard to be used as a modulator for other oscillators.

Filters

The next stop for the sound path is a filter (or filters). The filter shapes the waveform by cutting out specified frequencies. Filters generally come in these flavors:

• Low Pass – where the higher frequencies are cut, letting the lower frequencies through.
• High Pass – where the lower frequencies are cut, letting the higher frequencies through.
• Band – where both the lower and higher are cut.
• Notch – where the middle frequencies are cut, or “scooped”.

These flavors are usually denoted with “12dB” or “24dB”, which means how severe the slope in which the cut takes place. A LP 24db is sharper slope than an LP 12db, so the effect of the filter is more severe.

The Cutoff knob (also labeled Frequency) is where the cut off takes place among the frequency spectrum. The Resonance (or Q) knob is how the frequency acts jump before the cut.

Amp

This is usually the last stop before the sound leaves the synth. It’s presence is often just a volume knob. Sometimes it will also house a Pan (left and right, if the synth handles stereo) control and possibly some keyboard velocity (how hard you strike a key with affect the loudness of the sound).

End of Part One

In the next part, we will go over Envelopes, Modulation, LFO, Routing, and Effects.

This entry was posted on Tuesday, August 4th, 2009 at 8:50 pm and is filed under Rock God. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.