Sine Waves

Preface, brief definitions, the technology of music syntheisers.

Synthesis is one of the more misunderstood aspects of modern music technology. Reduced to its basics it usually involves the separation of sound into four components. Pitch, Harmonic structure, Amplitude & the interaction of these with Time. Could this form an acronym, PHAT?

Because these elements can be controlled independently, sounds become possible that are difficult to produce with traditional mechanical instruments. This demolishes some barriers to the creative process. The genre does not, by definition, necessarily require electronics. In fact the first musical instrument quoting synthesis in its patent was not electronic.

Currently however, electronic synthesis is usually implied & is the form discussed here.

Synthesis is broadly divided into two main categories, Additive & subtractive. This applies mainly to the Pitch & Harmonic elements. Other less common types exist.

A further feature will soon be added to this page. Any word in the text, highlighted in gold, will lead to a more complete explanation of that word or phrase.

Additive synthesis creates a harmonic structure by adding together individual Sine waves of differing pitches, usually harmonically related, to produce the required timbre. A Sine wave is the simplest of sounds, with no harmonics & no amplitude or frequency variations. All possible timbres can be created in this way.

One of the earliest and best known examples of this genre is the Hammond Organ although its performance control of amplitude is limited to harmonic percussion and a volume pedal. Not perceived as a synthesiser but has the required attribute of creating timbres by controlled addition of harmonically related sine waves.

The Hammond organ's predecessor was Thaddeus Cahill's Telharmonium, built early in the Twentieth Century, pioneering tone wheels & drawbars for harmonic addition. Unlike the Hammond it was touch sensitive. The word 'Synthesizing' was included in his 1896 patent.

Additive synthesis can be further modified by a Voltage Controlled Filter (VCF), allowing timbral sweep effects as in the subtractive genre. However full dynamic control of the addition process within the time domain can achieve all of this, and more without a filter.

Because of economic & design challenges comparatively few analogue additive synthesisers have been produced. Certain digital types may qualify, the DX7, for example, meets some of the requirements.

The effect of Harmonic Addition in creating Timbre have been known for a long time, predating the use of electronics. Some classical composers, particularly for the piano, wrote complex chord sequences to develop tone colours. Average performers of the day frequently had difficulty with such passages, today's classical players take them in their stride.

The technique was also used to good effect in many orchestral works.

A note on Harmonics. The Harmonic series includes every whole number multiple of the fundamental frequency, (commonly abbreviated to 'f'). Thus this series is f, 2f, 3f, & so on. The strict original definition does not call the fundamental a harmonic. So the first harmonic is 2f, the second harmonic is 3f etc..

We consider this to be weird, quaint & potentially confusing as do many others. So we adopt the more sensible, later American definition, which has its basis in arithmetical reality. Thus: The Second Harmonic is 2f, the Third Harmonic is 3f & so on. No confusion here, but what about the First Harmonic? Well, this is of course the Fundamental (f) in this series, so why not just call it that?

Forget the pedantic old-worlders, these are modern times, a new Century & all that.

N.B. Harmonics obtained by using higher notes in the scale are not strictly accurate if the interval is not a power of two. Due to the tempered scale, which determines that any other interval is slightly flat. This difference is noticeable, see the Harmonic Deviation page.

Subtractive synthesis works by taking a source that is rich in harmonics, such as a 'sawtooth', square or pulse wave and selectively attenuating or removing these harmonics to obtain the desired timbre.

In the case of an analogue instrument this is usually done with a Voltage Controlled Filter (VCF). Since the controlling Voltage can be changed during a note's duration very expressive sounds are possible.

One of the earliest and finest commercially successful examples is the Minimoog.

Certain 'preset' models use a number of fixed filters to control all or most of the various timbres. In some cases it is arguable whether these are more accurately described as organs. Two that come to mind are the Polymoog & Polymoog Keyboard.

More economical to design, Subtractive is by far the more numerous category.

More on Subtractive Synthesis

Synthesis is further divided into sub-categories relating to the technologies used. The main classifications are Analogue, Digital, Wavetable & FM. The latter three are mostly closely related, although in theory at least, FM synthesis can be applied to an analogue machine.

Some sites attempting to explain synthesis show a confusion between Subtractive & Analogue. This, although difficult to forgive when a site purports to be informative, is understandable. The majority of analogues are subtractive. Rather like saying 'Grass is green, so if it is green it must be grass'.

Analogue synthesis uses analogue (continuously variable) circuitry to construct sound. It is mostly subtractive, characterised by biting treble sounds, warm basses, with frequently a tendency to pitch drift. The Minimoog is of this type, as is the Yamaha CS-80, Sequential Prophet Five, ARP 2600 and very many others.

The pitch sources are Voltage Controlled Oscillators or VCOs.

Many later models use hybrid technology to improve tuning stability. Use is often made of programmable dividers for the pitch source, these are somewhat inaccurately called Digitally Controlled Oscillators or DCOs. Typical examples include the Roland Juno-106 & Korg Poly-61. Mostly a quartz crystal provides the master clock, giving high stability,

A few, such as the Oberheim Matrix Six, use Coil/Capacitor (L/C) oscillators.

Synthesis

Digital synthesis converts analogue values into numbers, as in sampling, or creates new values, manipulates these numbers mathematically and converts back to analogue. It has the potential for creating sounds beyond the scope of most analogue instruments and when it comes of age will probably do so.

Currently most examples attempt to copy their predecessors (analogue modeling), which never quite comes off, but they will eventually grow up. Some combine sampled sounds, arithmetical manipulation and digital filtering. An early, successful, example of this type is the Roland D-50. This model includes some aspects of the next category.

Wavetable synthesis use digital tables of sounds, frequently sampled, to provide the initial source, usually for subtractive synthesis. Many use hybrid circuitry, with filtering and amplitude control in the analogue domain. Good examples include the PPG Wave and Sequential VS (Vector).

Some instruments allow players to construct wavetables from the control panel, in various ways, giving greater versatility.

Synthesis

FM (Frequency Modulation) synthesis, usually the least understood type, simply turns 'conventional' amplitude synthesis on its head. If a sine wave is varied in amplitude the result can be seen as momentary variations in frequency or additional frequencies.

In AM radio these are termed 'sidebands', as they spread on both sides of the original, carrier, frequency, spaced from it by the frequency of modulation.

It follows that if these momentary frequency variations are added to a simple sine wave the amplitude variations will be created (the law of reciprocallity). In practice, with complex waveforms, the mathematics are very involved.

Simplifying the calculations to enable them to be performed in 'real time' creates inaccuracies, resulting in the characteristic sound of FM synthesis. The best known and most successful example is the Yamaha DX7.

A bit more explanation. Take a complex repetitive waveform, such as the output of an un-modulated oscillator. This can be shown to consist of a fundamental sine wave, plus a number of harmonic multiples.

It can also be considered as a single sine wave, who's frequency is being constantly changed (modulated), during the span of each cycle. This may be difficult to visualise, but think about it.

Alternatively it can be thought of as a single sine wave, with its amplitude varied during a cycle. This is probably no easier to visulalise than the frequency approach, the maths to prove either can be a bit hairy.

The important point is the correlation between frequency & amplitude. This is why FM Synthesis works.

It is the inaccuracies or imperfections of most musical instruments which gives character, making them interesting and recognisable. At the end of the day a synthesiser is no more artificial than a grand piano or pan pipes. All are examples of music technology, as are sequencers and samplers.

It can be argued that training the human voice to comply with the tempered tonic scale developed for mechanical instruments makes us artificial. However it can also be said that anything we are capable of doing is as a result of our nature, therefore it is natural. With this view all technology is simply a natural result of our creativity.

Post Script. There are other categories of synthesis possible, apart from Additive or Subtractive. This will be the subject of a future chapter.

Further chapters will expand on each of the categories listed here. Each technology will be covered comprehensively. In addition individual models will be described in detail. Some information is on the Classic Instruments page, which includes what to look for when buying. Chapters on the maintenance of classic & modern instruments are planned.

Chapters on MIDI will be added as this site develops. Contributors with original material, viewpoints or questions will be welcome.

Anyone wishing to contribute can E-Mail us. Your experiences with particular instruments or when needing them serviced. Reviews on new or old instruments with good & bad points etc. Our main requirements are relevance to our cause & nothing defamatory.

Not all synthesisers are classics or elderly. The genre is alive & well. A number of builders are keeping the Analogue flag flying, Big Briar, Robert Moog's company has introduced Voyager, a new version of the venerated Minimoog.

Digital on the other hand has yet, in my view, to show its true potential. It must get out of the imitation groove.

Subtractive Synthesis

For analogue subtractive synthesis a number of elements are required.
As a minimum:

1 Oscillator, the Pitch source.
1 Filter, the subtractive element, controls the Harmonic content.
1 Variable Amplifier, controls the Amplitude over Time.

The traditional monophonic form has:

One or more Voltage Controlled Oscillators (VCOs). The most common form of tone (pitch) source. This usually provides simple repetitive waveforms rich in harmonics. The Control Voltage is usually supplied by a keyboard with a resistor chain or an external input. Modern types may use a Digital to Analogue Converter (DAC) driven by a MIDI system. MIDI will be discussed later.

One Voltage Controlled Filter (VCF), some models use more than one. This is the main subtractive element, reducing or eliminating harmonics selectively to leave the desired timbre. Most common is a multi stage low pass type, a DC Control Voltage sets cutoff frequency & often also feedback or resonance. Usually its effect can be controlled in the Time domain.

One Voltage Controlled Amplifier (VCA), this controls the Amplitude over Time to create the required envelope shape. Sometimes additional VCAs are used for overall volume control, amplitude modulation etc.

One or more Envelope Generators (EGs), sometime called Contour Generators. Providing the Control Voltages, varying with Time, required by the other elements. Usually the VCF & VCA are controlled by these, for Pitch bend effects the VCO(s) may also be controlled.

One Low Frequency Oscillator (LFO), sometimes more, to provide Modulation Voltage. This can give Vibrato when supplied to the VCO(s), Tremolo via the VCA or VCF. The width of the VCO(s) pulse output may also be controlled giving Chorus type effects. The LFO may itself be controlled by the keyboard, E.G. or external input.

Apart from the E.G. & LFO a number of control elements are commonly used:

A keyboard, usually providing a Control Voltage increasing in steps, towards the right (treble). The most common scale was standardised by Moog, one Volt per Octave. Each key supplies one twelfth of a Volt more than the one below. The VCOs respond in an anti-logarithmic way to this, giving a nearly six percent increase in pitch for each step (the Tempered Scale).

Some models have a Volts per C/S (Volts per Hz) response, typically those from Korg or Yamaha are of this type. With this less common standard the relationship with pitch is linear, doubling the Voltage doubles the pitch.

This type does not require a thermally sensitive anti-log converter. So it is typically more stable at higher frequencies (greater CV). There is a limit to the highest Voltage that can be used, so the low end uses very small Voltages. Inherent offset drifts in circuitry make low pitches less stable. Another problem is that interfacing is more difficult. See note at end of section.

Two hand controlled wheels or levers. These 'performance controls' are usually for 'Pitch Bend' & 'Modulation'. The first gives another CV, usually directed to VCOs or the VCF to raise & lower overall frequency. The second usually controls the output of an LFO to whatever destination is selected.

Synchronising (Sync) of one VCO (Slave) by another (Master) is often provided:

'Soft Sync' controls just the 'flyback' of the ramp generator commonly used, the ramp is then free to restart if the end of its cycle has not been reached. This results in a Slave's pitch which is that of the Master but a timbre governed by its natural pitch and its relationship to the Master.

If just the Slave is varied in natural pitch by, for example, a pitch wheel, E.G. or LFO a timbral variation, often complex, is obtained with no change in output pitch. Variation of the Master only causes timbre (waveshape) to change with pitch. Varying both together will not change the timbre, although this may be complex.

'Hard Sync' is similiar except that ramp restarting is also controlled. This less common type produces a different timbral response.

Other elements are less commonly used, these include:

Ring modulator, this uses one tone source to control the amplitude of another. It can create fairly complex timbral effects, such as bell sounds etc. In combination with CVs etc. various sound effects can be produced.

Sample and Hold (S/H). This uses a timing element such as an LFO or Keyboard Gate. This in turn controls an electronic switch to read the instantaneous value (Sample) of a varying Voltage such as another LFO, a VCO or Noise Generator. The Voltage obtained is stored (Held) by a capacitor until the next sample.

The output is a more or less arbitrary Voltage stepping in value at the rate of the LFO or Gate etc. This can be used as a CV to control VCOs or a VCF. The result is stepped pitch or timbral variations. A possible sophistication is to 'quantise' these variations to exact notes in the musical scale. Not so popular now as in the sixties and seventies.

Note: When a number of VCOs are used, as in a polyphonic instrument, an alternative to simple linear or anti-log response is possible. This uses Linear Control Voltages & oscillators. The necessary anti-log response is provided by a single converter, shared between all VCOs, using multiplexing (time sharing) or similiar trickery.

The main advantage of this technique is that thermal drift in the converter is equal for all VCOs. keeping them together. An example is the Korg Poly-Six, this keeps all VCOs reasonably well together despite having no 'auto-tune', a neat trick from a once innovative marque.

Polyphonic instruments evolved later & generally follow a similiar format to monophonic types. Digital circuitry is usually employed, with the Control Voltages obtained via a DAC (Digital to Analogue Converter). Most use a microprocessor or microcontroller system (MPU or MCU).