Unit 35 - Sound Creation and Manipulation - LO1 - Sam Hayes

Acoustic Theory and Fundamentals of Synthesis

In this article, I am going to discuss the basics of acoustic theory and the fundamentals of synthesis along with examples, to give you an insight into the world of creating sound and how that relates to acoustic theory.

The Basics of Acoustic Theory

The most basic sound wave is a sine wave.  A sine wave is one pure tone and the sound of this tone will be shown in the amplitude, wavelength and frequency of the sound.

The wavelength is how long it takes to make one whole cycle, with the frequency being how many there are of these cycles per second (this is measured in Hertz). The higher the frequency, the higher the pitch of the tone. The amplitude is the measure of how high the crest/ peak/displacement goes during the tone, AKA the volume or dynamics of the tone.

A basic sine wave is a 'pure tone', but for instruments and sounds to have their specific 'timbre', they will have harmonies and overtones that will sound at other frequencies to the fundamental frequency of the tone. These overtones will resonate with the fundamental frequency (which is the lowest frequency that is being played) and will be either integer or non-integer, which means that if it is an integer, than it will be a multiple of the fundamental frequency and will be a harmonic. Non-integer overtones will not be harmonic with the fundamental frequency, but still contribute to the sound created. For instance, if a fundamental frequency is 100Hz then the next harmonic will be 200Hz, but if the next frequency was 240Hz, then it would be a non-integer overtone.

Other wave types include saw, square, triangle and there are many others. These wave types are made of combinations of harmonics of the fundamental frequency. For instance, saw waves are made of every harmonic of the fundamental and square waves are made of every odd numbered harmonic e.g. 3, 5, 7... etc, along with the fundamental, with the volume decreasing for every added frequency. Triangle waves are created in the same way as square waves but every harmonic decreases in volume a lot quicker. These wave shapes can be created in an oscillator in a synthesizer. These wave types are useful for creating different sounds, e.g. triangle waves may be better for softer instruments such as flutes or pipes as triangle waves have a smoother, softer tone than other wave types and saw waves may be used more for string, bass or brass sounds due to its clear and bright sound. You could also use square waves for percussion, bass or reed instruments as it has a more hollow sound that can be made to be more percussive and punchy if it is combined with other sounds and waves.

The Fundamentals of Synthesis

One thing that you will probably use when creating sounds, is an enveloper. The main options used for an enveloper are attack, decay, sustain and release (ADSR). Attack refers to how long it takes for the played note to reach full volume. Decay is how long it takes for the sound to drop from its loudest peak  to the sustain level. The sustain level is the volume the note will keep after the decay until the played note is released. Release is how quickly the sound fades out after the played note is released.
You can relate this to acoustic theory as ADSR can manipulate the amplitude of a sound manually to acquire a desired tone, by controlling how long it takes to reach its loudest note, how much it drops from that loudest peak and so on.

Filters are another feature in subtractive synthesis that is important as they can be used to get rid of any frequencies that you don't want in your sound. There are different types of filter, such as the low pass filter that is used to cut out higher pitched frequencies, the high pass filter, which cuts out low frequencies and band pass filters which can be used to find specific frequencies in the middle of your wave formation and either cut them out or give them a boost. This is useful if there are any resonating frequencies in your sound that you don't want so you can get rid of them. You can add filter resonance to your tracks which essentially give a slight boost to the frequencies around the cut-off and give a resonating sound around the parts you have cut off.
LFOs are similar to normal oscillators but has a lower sub frequency that creates a pulse that can be used to modulate effects such as tremolo (if applied to volume), phase (if applied to a filter cutoff) or vibrato (if applied to pitch) on your created sounds.
This relates to acoustic theory, as filters are used to get rid of certain waves at different unwanted frequencies.

As an example, I created a sound using the ES2 Hybrid Synth in Logic Pro which gives the ability to change the shape of waves using built in oscillators, change filter cut-off, add filter resonance and give the ability to change effects such as pitch changes, tremolo and panning. On my sound, I have used three oscillators to create a combination of a sine wave, a square wave and a saw wave as I wanted a more buzzy, rough sound. I used a low-frequency oscillator, using a triangle wave, to edit the rate at which my sound oscillates. I did this by using a low-pass frequency via a bender to the LFO, essentially creating a low pass frequency oscillation and by using my second LFO on my second parallel filter cut-off. I used a triangle waves on my LFOs as it was different to the other wave types I used on the oscillators and I wanted to create a smoother, more even wavy noise that i couldn't have created if I used other wave types. If I had used a square wave or other wave types then it would have created a more uneven pulsating wave sound. The attack on my main ADSR is very short as I wanted the full volume of my sound to come out straight away, and had the decay take along time to happen as well as making my sustain last a long time as well so I don't lose much volume if I hold a note for a long time. I also made my release short as I want my note to realise as soon as I would want the note to finish as soon as I let go of it. This is so my sound is more controllable and accurate to what I want.

On my sound, I didn't edit the pitching of my sound too much so all the fundamental frequencies are the same as they would be for a simple sine wave. For instance, at C3, the standard fundamental frequency is 130Hz and this is the same for my sound as well at C3.
Here is a simple sine wave example and my example synth that I created in the ES2 synthesizer:

       Simple Sine Wave Example                                                     Example Synth

Other Synthesisers

As I was only able to use the default logic synthesizers, I wanted to look at other possible synths I could've used as logic synthesizers have limitations, so I found another digital software synthesizer called the LinPlug Spectral which has a lot more features than the ES2 Hybrid synth I was using to create the last sound. For one thing, the ES2 only has 3 oscillators whereas the Spectral has 4, all with their own filter and amp/filter envelope. The spectral also has 5 LFOs when the ES2 only has 2. The ES2 also has 10 modulation matrix slots when the Spectral has 15, as well as having 6 available effect slots that you can use any combination of 14 different effects on including; reverb, chorus, delay, phase and others, as well as a master EQ. It also has a 32-step arpeggiator which means you can create 8 bars of looping sounds and chord memory ability so you can save full chords to single notes on your keyboard.
Overall, it has a lot more features than the ES2 and has an easy to learn interface with a lot of usability. As it has a lot of features including the large amount of LFOs and oscillators, it is able to create a lot of interesting sounds, being even more editable due to the variety of effects and filtering abilities it has.