The Science of Synthesis - Part 1

Today's recording techniques would have been regarded as science fiction forty years ago.

Today's dance . and club-based music relies just as heavily on the technology as it does on the musicality; therefore, to be proficient at creating this genre of music it is first necessary to fully comprehend the technology behind its creation. Indeed, before we can even begin to look at how to produce to music, thorough understanding of both the science and the technology behind the music is paramount. You wouldn't attempt to repair a car without some knowledge of what you were tweaking, and the same applies for dance - and club - based music.

Therefore, we should start at the very beginning and where better to start than the instrument that encapsulated the genre - the analogue synthesizer. Without a doubt, the analogue synthesizers are becoming increasing difficult to source today, nearly all synthesizers in production, whether hardware or software, follow the same path laid down by their predecessors. However to make sense of the various knobs and buttons that adorn a typical synthesizer and observe the effects that each has on a sound, we need to start by examining some basic acoustic science.

Acoustic Science

When an object vibrates, air molecules surrounding it begin to vibrate sympathetically in all directions creating a series of sound waves. These sound waves then create vibrations in the ear drum that the brain perceives as sound.

The movement of sound waves is analogous to the way that waves spread when a stone is thrown into a pool of water. The moment the stone hits the water, the reaction is immediately visible as a series of small waves spread outwards in every direction. This is almost identical to the way in which sound behaves with each wave of water being similar to the vibrations of air particles.

Difference between low and high frequencies

For instance, when a tuning fork is struck, the forks first move towards one another compressing the air molecules before moving in the opposite direction. In this movement from 'compression' to 'rarefaction' there is a moment where there are less air molecules filling the space between the forks. When this occurs, the surrounding air molecules crowd into this space and are then compressed when the forks return on their next cycle. As the fork continues to vibrate, the previously compressed air molecules are pushed further outwards by the next cycle of the fork and a series of alternating compressions and rarefactions pass through the air.

The number of rarefactions and compressions or 'cycles', that are completed every second is referred to as the operating frequency and is measured in Hertz (Hz). Any vibrating object that completes, say, 300 cycles/s has a frequency of 300Hz while an object that completes 3000 cycles/s has a frequency of 3kHz.

The frequency of a vibrating object determines its perceived pitch, with faster frequencies producing sounds at a higher pitch than slower frequencies. From this we can determine that the faster an object vibrates, or 'oscillates' , the shorter the cycle between compression and rarefaction. An example of this is shown in the previous picture.

Any object that vibrates must repeatedly pass through the same position as it moves back and forth through its cycle. Any particular point during this movement is referred to as the 'phase' of the cycle and is measured in degrees, similar to the measurement of a geometric circle. As shown in Figure 1.2, each cycle starts at position zero, passes back through this position, known as the 'zero crossing', and returns to zero.

The zero crossing of a waveform

Consequently, if two objects vibrate at different speeds and the resulting waveforms are mixed together, both waveforms will start at the same zero point but the higher frequency waveform will overtake the phase of the lower frequency. Provided that these waveforms continue to oscillate, they will eventually catch up with one other and then repeat the process all over again. This produces an effect known as 'beating'.

The speed at which waveforms 'beat' together depends on the difference in the frequency between them. It's important to note that if two waves have the same frequency and are 180º out of phase with one another, one waveform reaches its peak while the second is at its through, and no sound is produced.

This effect, where two waves cancel one another out and nos sound is produced, is known as 'phase cancellation' and will be shown in the next picture.

As long as waveforms are not 180º out of phase with one another, the interference between the two can be used to created more complex waveforms than the simple sine wave. In fact, every waveform is made up of a series of sine waves, each slightly out of phase with one another. The more complex the waveform this produces the more complex the resulting sound. This is because as an increasing number of waves are combined a greater number of harmonics are introduced. This can be better understood by examining how an everyday piano produces its sound.

The strings in a piano are adjusted so that each oscillates at an exact frequency. When a key is struck, a hammer strikes the corresponding string forcing it to oscillate. This produces the fundamental pitch of the note and also, if the vibrations from this string are the same as any of the other strings natural vibrations rates, sets these into motion too. These are called 'sympathetic vibrations' and are important to understand because most musical instruments are based around this principle. The piano is turned so that the strings that vibrate sympathetically with the originally struck string create a series of waves that are slightly out of phase with one another producing a complex sound.

Two waves out of phase

Any frequencies that are an integer multiple of the lowest frequency (i.e. the fundamental) will in harmony with one another, a phenomenon that was first realized by Pythagoras, from which he derived the following three rules.

• If a note's frequency is multiplied or divided by two, the same note is created but in a different octave.
• If a note's frequency is multiplied or divided by three, the strongest harmonic relation is created. This is the basis of the western musical scale. If we look at the first rule, the ration 2:3 is known as a perfect fifth and is used as the basis of the scale.
• If a note's frequency is multiplied or divided by five, this also creates a strong harmonic relation. Again, if we look at the first rule, the ration 5:4 gives the same harmonic relation but this interval is known as the major third.

Here concludes the second part of this post, if you want to know more about acoustic science please read Rick Snowman's Dance Music Manual (Second Edition) Tools, Toys and Techniques.