• • -Transverse

Particles move Perpendicular to the direction of the wave. The Particles do not move along with the wave, they just oscillate up and down around an equilibrium position. These are the types of waves formed by water.

 

• • -Longitudinal

Particles move parallel to the direction of the wave. The particles do not move along with the wave, they just oscillate back and forth around an equilibrium position. This is type of wave that sound travels as.

 

Introducing.. The Sine Wave

All complex sounds are made up of combinations of sine waves of verifying amplitude and frequency.

 

• Parts and Properties of a Wave

 

 

 

Parts of a wave that you need to know:-

 

• -Cycles (One complete revolution of the wave)

-Frequency (Measured in Hz, Frequency is the number of times a wave cycles in a second. This Figure determines the pitch of the sound.)

-Amplitude (Measured in db, the amplitude of the waveform determines how loudly it will be heard.)

 

These Sine waves can exist at any frequency, but are only audible between 20Hz and 20 kHz, as this is the range of human hearing.

 

 

Harmonics and Fourier Plots

The sine waves that make up a complex sound can be split up into various categories.

 

• • -Partials – Any of the sine waves that are contained within a sound.

-Fundamental – The single sine wave that determines the pitch the sound is heard as. It is usually the lowest and most dominant wave.

-Overtones – All of the sine waves that are contained within a sound excluding the fundamental.

-Harmonics – All of the sine waves contained in a sound that are whole number multiples of the fundamental. These waves are musically related to the fundamental, and the fundamental is part of this set.

-Enharmonics – All of the overtones that aren’t included in the harmonic set. These waves are usually non-musical to the fundamental.

 

This picture shows the fundamental wave at the top, and then the 6 following harmonics. They are 2x the frequency, then 3x, then 4x the fundamental etc..

 

 

We can then describe a sound by using “Fourier Plots,” that graph the harmonics contained in a sound. The first bar is the fundamental, or the first harmonic, then the following harmonics are shown by the blue bar. I have plotted the four most common waveforms contained on any synthesizer.

 

Sine waves contains only the fundamental

 

 

Square waves contains only odd harmonics

 

 

Saw waves contains all the harmonics

 

 

Triangle Waves containing only odd harmonics, but not as many as a square waves.

 

And here is a diagram showing the different shapes of these waveforms.

 

Subtractive Synthesis

 

Subtractive synthesis is the most basic kind of synthesis. The idea is that you start with a harmonically rich sound, such as a saw wave, and shape your sound by subtract harmonics from it by way of filtering.

The main components in a subtractive synthesizer are:-

 

• Oscillators.

An oscillator is the device on a synthesizer that actually generates the sound. They will oscillate between 20Hz and 20KHz. Most synthesizers contain multiple oscillators. There are many different waveforms that an oscillator can generate, but the four most common are:-

• Sine Wave – Is a pure tone. Sounds very simple & soft. Creates great bass.
• Triangle – Quite similar to a sine wave, but sounds slightly brighter.
• Square – Sounds slightly hollow, but also rich and bright.
• Saw – Sounds very rich and can be a bit harsh.

 

There can be many different parameters associated with oscillators depending on the synthesizer, but the most common ones are:-

 

-Octave (Raises or lowers the pitch of the waveform in Octave steps)

-Semitone (Raises and lowers the pitch of the waveform in semitone steps. There are 12 semitones in an octave)

-Detune or Cent (Raises and lowers the pitch of the waveform in cent steps. There are 100 cents in a semitone)

• -Level – Controls the level of the Oscillator.

 

• Filters

 

A filter is the primary device used to shape the harmonic content of a sound. The two main parameters used by filters.

o      Cutoff Frequency – Sets frequency at which the signal will begin to be filtered.

o      Resonance – Adds a boost in the signal at the cutoff frequency, which helps to “Highlight” the cutoff. Great for filter sweeps.

 

The four main types of filters are:-

o      LPF (Low Pass Filter) – Allows the frequencies below the cutoff to pass through unaffected, while cutting the frequencies above the cutoff.

o      HPF (High Pass Filter) – Allows the frequencies above the cutoff to pass through unaffected while cutting the frequencies below it.

o      BPF (Band Pass Filter) – Allows a band of frequencies around the cutoff to pass through unaffected, while cutting frequencies below and above it.

o      Notch Filter – Cuts a band of frequencies around the cutoff, while allowing the frequencies below and above it to pass through unaffected.

 

The final point in filters is the steepness or sharpness that the filter cuts its frequencies outside of the cutoff.

The most common is 12db per Octave or a “2 pole filter”, which means the filtered portion of the signal is cut by 12db per octave outside of the cutoff. Another common one is 24db per Octave or a “4 pole filter.” Essentially, the lager the number, the steeper the roll off created by the filter.

 

• Envelopes

 

Envelopes are used to create a change over time in various parameters. The most common parameter being assigned to an envelope is level, or volume, although it is also very common for a filters cutoff frequency to be controlled by an envelope too.

 

The common settings on envelopes are:-

 

• -Attack – Time taken for sound to reach its peak level. This phase of the envelope is triggered by a note being played on the keyboard.

• -Decay – Time taken for sound to decay down to its sustain level from the peak.

• -Sustain – Unlike the other parameters on an envelope, this setting controls the level of sound, rather that time. It sets the level of the sound held until the note is released

• • -Release – Time taken for sound to go from the sustain level to silence once the note is released.
  
  

 

• Modulation

 

At this point, the sound generated using the previous devices will be relatively static and lifeless. In order to create an interesting sound that’s natural, inspiring and exciting, we need to create movement within the sound. For this we can use modulation. There are many different types of modulation.

 

LFO (Low Frequency Oscillator)

This is a device that, much like an audio oscillator, generates waves, but unlike and audio oscillator, its output is never sent to any audio output. Further more, the rate it oscillates at is much slower, typically between 0Hz and 20Hz, so is not used to generate sound. This device is used to control various parameters, such as filter cutoff, or oscillator pitch or level to name a few. The term Tremolo (Modulations in Level) or vibrato (Modulations on Pitch) maybe be familiar terms for musicians and can be recreated in synthesizers using LFO’s. The common parameters you will find in an LFO are

 

o      Waveform – Much like an Audio oscillator, you can choose the wave that it generates, and usually uses much similar waves too.

o      Rate – Measure in either Hz or beats, this parameter dictates how fast the modulation occurs at. If its synced to the beat, its rate will be affected by the BPM (Beats Per Minutes) of the track you writing and will oscillate in time with your music.

o      Amount – This is usually measure on %. It will determine how much the chosen parameter is affected by the LFO

 

Velocity

Velocity is used to mimic the force to which a note is struck. When you program notes into you arrangement, you can set the velocity of each note.

Velocity can then be assigned to various parameters to control how the sound reacts to high or low velocity notes. The most common use for velocity is to control level and filter cutoff, so that a soft note is quieter and dull, and a hard note is loud and brighter.

 

PWM (Pulse Width Modulation)

PWM is typically used in square waves, but has been adapted to many other waveforms. The pulse length is the time a wave spends at its top position. In the diagram you can see three settings. The 50% wave is the common square wave that we use, but you can change the width of its pulse to create very nice movements in sound.

 

 

Oscillator Sync

Oscillator Sync is where you use two oscillators, one selected as the master, one as the slave. The slave oscillator is forced to reset its cycle every time the master does. If the two oscillators are running at the same frequency, it will have no effect, but if they are tuned differentially, the salve oscillator will be forced to run at the same frequency by distorting its shape.

In this Diagram, you can see the top saw wave is the master. The lower saw wave, is running at a faster frequency, but is forced to restart its cycle as the top does. It results in a different shaped wave that is now at the same frequency. By modulating the pitch of the slaved oscillator you can achieve very attractive results.

 

 

Additive Synthesis

Additive is the other type of synthesis I would like to cover. It is the opposite to subtractive synthesis. Instead of starting with a rich sound and subtracting harmonics from it, you start with a simpler sound, and add harmonics to it by way of modulation. There are two main types of additive synthesis.

 

AM (Amplitude Modulation)

In AM synthesis, you add harmonics by taking an Audio Oscillator, and instead of feeding its output to an audio mixer, you use its wave to modulate the amplitude of another audio oscillator. Much like using an LFO, except the rate of modulation is much faster (Between 20Hz and 20Khz). Instead of creating a tremolo effect, it results in added harmonics and a change in sound.

 

FM (Frequency Modulation)

FM synthesis is much the same as AM, except instead of modulating the amplitude, you use an audio speed oscillator to modulate the frequency of another audio oscillator. Instead of sounding like vibrato, it results in added harmonics and a change in sound.

When using an envelope to control the amplitude of the modulating oscillator, you can create very nice tones and changes in sound over time.

 

A Final Note

 

I realise that this is a lot of information to begin with. Essentially, I wanted to introduce you to all these concepts of sound and synthesis. In the following weeks we will explore Ableton Live, and these ideas, and use them to achieve desired results. You will become more and more familiar with them as time goes by, as we use these this knowledge week after week. This document will be a great reference for your all. Thanx.

 

-Andy

 

P.S. the .PDF is available for download HERE