BSc Report on musical instrument physical modelling,

This report examines the effectiveness of current software synthesis processes. By research into various synthesis algorithms and software applications, a music composition will be produced containing a diversity of modelled acoustic and electric instrument sources.

Research showed that for software synthesis to be beneficial, a wider variation of musical instrument sources needs to be implemented within a single software application. The authenticity of many of the existing algorithms also needs to be improved and refined, and new methods of controlling the many parameters need to be developed.

Declaration: All the information in this report is the work of the author. Any other work or information used has been fully referenced to the persons responsible. This report adheres to the guidelines set out in BS4821: British Standard Recommendations for the Presentation of Theses and Dissertations as closely as possible.

Computers have played a significant role in music composition for almost two decades. Typically this role has been to control other sound producing devices such as drum machines or external synthesisers. More recently with the development of sampling and hard disk recording, it has become an established procedure to employ the computer as both recording medium and editing tool

Both these processes however rely on additional devices such as musical instruments or synthesisers to produce the sound. The computer is merely used for editing of audio or MIDI information. It is not typically applied in the process of sound creation. By utilising a selection of software based synthesis processes however, a computer can be used to produce sound and music

As a musician, it would be wonderful to have access to a much wider range of the many musical instrument sounds available. Considering the substantial cost and learning curve involved it is unfortunately not realistic to own a diverse selection.

Once skills of harmony and rhythm have been learnt, they can effectively be transferred to other musical instruments. The hardest element being the process of learning to interact with the vastly different physical properties of say a piano to that of an upright bass. If a technique existed where one could accurately model other types of musical instrument, the musical possibilities would be immeasurable.

By concentrating on various software synthesis techniques, my aim for this project is to produce a music composition using sounds created within a computer.

By investigation of current shareware, specialist academic and commercial synthesis applications my objectives are to present a balanced opinion on the current capabilities of software synthesis.

Although it is currently possible to achieve this by digital sampling, this is not a tangible solution. The static nature of sampling produces dull lifeless music. (Roads, 1996)

To compare the different processes and resulting sounds, a second music arrangement will be produced using authentic instrument sound sources.

Both music compositions and other relevant audio examples are supplied on the accompanying CD.

Due to time constraints, research has been limited to a Windows based PC platform. Although it is acknowledged that relevant software exists on other platforms.

A number of synthesis methods and software applications have been excluded due to financial cost, and space restrictions made upon this report.

The report is split into four chapters, chapter one outlines what is meant by synthesis, and examines some of its potential advantages. By looking at the background to computer synthesis, a number of processes are selected for further study.

Chapter two compares a number of available synthesis processes. A selection of algorithms are made using a criteria of quality of results and relevancy of proposed use, i.e. Does it claim to emulate a traditional musical instrument or produce its own singular sound. Although the concepts of physical modelling acoustic and electronic instruments are similar in technique, the resulting sounds are typically different. Therefore they are discussed as two separate entities.

Like a traditional musical instrument, the ability to interact with the musician is an important factor. Chapter three considers various ways of controlling sound parameters within a software synthesiser. Real time and offline rendering methods are compared. A brief outline of computer requirements is considered.

Chapter four compares the different software applications and processes applied to produce the music. Suggestions are made to overcome the current lack of specific instrument sounds. Problems incurred whilst producing the music are examined.

This addition describes the production of the second music arrangement using authentic instrument sources. It has been included to allow the different processes and resulting sounds to be compared.

Table of figures comparing the processes involved in producing both arrangements.

Although not actively applied within the music arrangement, it is recognised that important development work has been achieved in Csound. This addition outlines its capabilities and working methods.

"Theoretically, (Mathews, 1963) a computer may generate any sound. It is able to do this because the waveform corresponding to the sound may be described by a piece of music".

Sound synthesis can be defined as the generation of sound by electronic or mechanical processes. In its simplest form the action of beating a drum or blowing a simple bamboo reed may be deemed as synthesis, and thus its history dates as far back as that of humankind. (Russ, 1993a)

The realisation of music making and recording within a computer environment has many economic and creative implications. Computers have the capacity to play fast or complex music passages with far more precision than a musician. (Pierce, 1992a) Random order or chance can be combined into a composition. Producing new generative music forms that sound different in rhythm, harmony or even tonally on each successive play back. Sound producing capabilities potentially far exceed those of a traditional musical instrument. Not only does synthesis allow creation of sounds that we are familiar with, such as those that we associate with a traditional instrument like a piano, or violin, but new sounds can also be produced different in timbre.

This technology asks us to question and redefine the term "musical instrument". The skills of a musician are still an essential ingredient, and if musically pleasing results are to be obtained, the usual laws of harmony and melody have to be adhered to. However most synthesis processes demand a lot more knowledge than musical arrangement skills, and most require a least a basic understanding of the relevant synthesis method. Others call for a comprehension of computer based programming languages such as C++.

A software-based synthesiser has a number of possible advantages over its hardware counterpart. For example, its ability to display data graphically. A particularly complex synthesis architecture or waveform can be understood and controlled more easily if a descriptive graphical image is used. (Wiffen, 1998)

Synthesis can be divided into two areas. Algorithms such as physical modelling were developed with the principle aim of emulating other musical instrument sounds. Others such as Granular attempt to produce distinct unique sounds

Many synthesis processes were initially developed on analogue platforms. In the 1960`s Robert Moog`s experimentation with voltage control, provided the first reliable process for controlling the various electronic sound generating techniques that were currently available. The MiniMoog was capable of producing sounds unrealisable with a traditional instrument. "It is (Lord, 1997) not fully appreciated what the impact was of instruments which could produce sounds which had never before been heard by the human ear".

Most forms of synthesis have now successively been ported onto the computer. Due in part to the immense advances in computing power that has evolved over the last number of years. This "number crunching" power has been essential to cope with the many calculations that are required to produce complex sounds in software. Thus the advancement of software synthesis has followed a parallel tangent to that of the computer.

The first computer based music arrangement was produced in 1957 at the Bell Telephone laboratories. This 17-second composition written by Newman Guttman was composed using Music 1, a software application written by Max Matthews. (Track1.CD)

Computers had actually been applied to produce musical sounds before this date. Typically by controlling mechanical devices such as printers. "Max Mathews compiler was (Pierce, 1992b) however the first deliberate step toward using a computer to produce complex sounds for musical purposes".

Four years later, John Kelly developed one of the first implementations of a physical model. By analysing human speech, a computer was programmed to vocalise words. A composition entitled "Bicycle built for two" was produced using Music IV a Fortran based software application. (Track2.CD)

In 1968 Richard Moore and Max Mathews developed the GROOVE system. This was the first computer capable of real time performance.

The beginning of the 1970`s saw the release of the Synclavier synthesiser, the first all digital real time synthesiser.

The release of the Commodore 64 in 1982 introduced the first polyphonic sounds to mass market computer users. Aside from being limited to producing just three sounds simultaneously, the specially designed sound chip (SID) was in effect a complete digital synthesiser "As such it (Trask, 1999) represented a major development in the sonic capabilities of personal computers".

The Development by Creative Labs of the SoundBlaster range of sound cards in 1992 provided the first CD quality sounds for computer users, with over 44 million units sold. The capabilities of this card encouraged many musicians to participate in computer music. (Henrick, 1998)

Rebirth released in 1997 contributed hugely towards mass-market acceptance of software synthesis. Developed jointly by the Propellorheads and Steinberg. Rebirth emulated a number of classic hardware synthesisers, namely the Roland 303 Bass line and 808 Drum machine. Due to the cost and rarity of the original synthesisers on which they were based, and the popularity of analogue type sounds at the time, Rebirth was a huge success.

Synthesis applications are continually advancing in popularity, capabilities and refinement, In the time since this project was conceived, as many as five new software synthesisers have been released. Possibly due to current dance music fashions, most applications attempt to model analogue synthesisers. Only a small percentage strives to emulate acoustic instruments.

There are many methods to synthesise a sound. These range from the simple fusion of waveforms, to complex algorithms that imitate a musical instrument’s physical properties mathematically.

Based on concepts introduced by the seventeenth century mathematician Joseph Fourier. Additive is one of the oldest synthesis techniques. By summing together simple sine waves of different frequencies, it is possible to produce sounds with more tonally complex timbres. To accurately recreate a complex waveform would require an immeasurable number of sine waves. Useful results however can be obtained by replicating the most dominant waveforms. (Track3.CD)

It is possible to create expressive and dynamic sound textures by altering the relative volume and frequency of the sine waves over time. However many control parameters are needed. Each oscillator requires its own amplitude, pitch, and velocity control. Considering that one note may consist of twenty or more oscillators, the number of required parameters to adjust could be up to a hundred or more.

An instrument such as the Bagpipes is a simple form of mechanical additive synthesis. The output sound from this instrument is made up of a number of notes at different pitch intervals, not just a single note.

Many sine waves are required for additive synthesis, to imitate a guitar note for instance may require up to a hundred, due to the rich harmonic content. (Russ, 1996b)

Initially derived from electronic hardware based equipment. The term subtractive describes the principles on which it performs. In its simplest form, subtractive synthesis begins with the production of a harmonically complex waveform. By applying a filter to the output of the source, it is possible to modify the tonal properties of the sound.

Applying a filter to the output of the source modifies the tonal characteristics of the sound. (Track4.CD)

The production of subtractive synthesis typically utilises a modular layout. Independent components are patched or wired into each other to produce a synthesiser. Typical layouts of the basic components are discussed below.

The initial selection of the source waveform determines the tone or timbre of the sound. This sound is produced using an oscillator. Overall pitch is set by the frequency of the oscillator. A single waveform may be used, or multiple waves may be summed together to produce more complex tones.

Low pass filters are generally used in subtractive synthesis. A filter is in essence a passive tone control that allows specific frequencies to pass through, whilst attenuating others. A low pass for example, permits lower frequencies through and discards the higher harmonic frequencies.

An amplifier together with an envelope is used to control the volume of the waveform over time. In its simplest form the envelope can be seen as an automated volume control with two parameters. The attack is the period from initial silence to full volume. A slow attack time for example, would produce a note that would slowly increase or swell in volume after the initial key press. When a key is released, the note may end instantly, or decay slowly. The release control determines this element. Most envelopes have more parameters than this simple AR (attack release) controller, the most common being the ADSR, or attack, decay, sustain, release. (Russ, 1996c)

Both Additive and subtractive synthesis methods have been imitated on the computer. Whereas an electronic synthesiser uses control voltages to produce waveforms, a computer produces binary numbers to represent the waveform. Some hardware-based synthesisers have utilised digital oscillators for many years, so the transition onto a standalone computer has been straightforward.

The process of modelling a synthesiser is broken down into individual components such as oscillator or filter. Each element is replaced with a software engine. Utilising virtual wires or connectors, components are wired together to produce a circuit or synthesiser. There are numerous potential advantages of computer modelling over its analogue counterparts. Traditional oscillators (VCO) are notorious for their tuning problems, whereas a digital oscillator (DCO) remains in perfect tune. (Wiffen, 1998)

Many hardware synthesisers were limited to monophonic output, computer based modelling has no such limitations. The number of simultaneous voices is determined purely by the power of the host processor or CPU.

Developed in the early 1970s by Dr John Chowning of Stanford University. FM applies a process where the output of one oscillator is used to modulate the pitch of another. (Track5.CD)

To produce simple FM, just two oscillators are necessary. The primary oscillator, known as the modulator is fed into the second, or carrier. Each of the oscillators is referred to as an operator, and the last operator in a chain is always a carrier. The pitch of the carrier fluctuates in sync with the output of the modulator. The frequency of the modulator thus defines the dominant pitch of the output sound.

If for example a sine wave were used to modulate an oscillator, a vibrato effect would occur. Increasing the modulator output would increase the depth of the vibrato, increase its speed and the vibrato accelerates. Past a certain threshold, the vibrato effect appears to fade and a smoother sound is produced. (Russ, 1996d)

Implementing FM digitally is far more efficient than previous electronic methods. FM benefits from the stability of digital oscillators. Practically all budget computer soundcards utilise FM. This technique allows manufacturers to produce complex sounds from simple, cheap components.

One of the newest synthesis processes, physical modelling is the terminology used to describe a variety of synthesis methods. Although slightly different in technique, they all share one common concept. By manipulation of mathematical equations and formulas to describe acoustic behaviour, it is claimed to be possible to authentically imitate any sound source. (Track6.CD)

All sound originates from the results of a mechanical action. The sound produced by plucking a string for instance can be described as a mechanical energy surge transferred from the musician’s plectrum to the string. Due to the highly resonant nature of a string under tension it continues to vibrate as the energy is dispersed. Mechanical behaviour such as this can be described using physics. (Russ, 1996e)

"The structure (Russ, 1996f) of a physically modelled instrument will closely follow that of its original counterpart". Consequently the instrument behaves like the real thing. Musical expression and realistic transitions between notes are achieved. A brass instrument for instance would exhibit all the subtle nuances and accidents found within a real performance such as breath noise and rasps. A stringed instrument would produce realistic timbre changes. Vibrato and bends for example would alter the tonal characteristics of the sound not just the pitch.

In order for successful models to be created, the designer needs to understand the mechanical and acoustic properties of the instrument extensively. This information then has to be converted from mathematical equations into software.

The process of modelling an instrument can be reduced into two basic components the Exciter and the Resonator. The initial energy burst required to produce the sound is different for all instruments, for example the air blown through a reed on a flute, or hammer striking a piano string. This initial excitation is called the exciter or driver. The resonator determines the tonal characteristics of an instrument. For example the energy of a vibrating string on an acoustic guitar would be passed via the bridge to the instrument body through which the sound is modified by amplification and resonance.

As the structure of most musical instruments does not change, it can be understood that the resonator is a fairly consistent factor that defines the instruments sound. The exciter on the other hand is constantly fluid. A bowed instrument such as a violin exhibits this clearly with the amount of expression that can be achieved simply by changing the velocity and pressure of the bow. (Roads, 1996a)

On some instruments such as a clarinet, the column of air emitted through the reed can be fed back through the bore to the reed. Consequently this will have an effect on the reed vibrations and sound character. In some situations therefore, the resonator has an effect on the behaviour of the exciter. (Russ, 1996g)

When a string is plucked two waves are produced. They travel from the point of impact to the ends of the string, The bridges absorb some of this energy. The remaining energy is reflected back through the string towards the centre. The two waves interact at this point, producing interference and resonance. This two-direction movement of energy continues until the sound decays. (Roads, 1995b)

Using a series of delay lines it is possible to replicate this sound path of air motion. Because acoustic sound waves decay over a period of time, a time delay is used to replicate this decay. The Delay line is injected with an excitation wave, this travels through the delay line until it hits the scattering junction. The Scattering junction reproduces acoustic connections in the sound path, such as a finger pressing on a string, and it emulates this by dispersing some energy back to the exciter, and some to the output junction.

A plucked string, for example initially produces a bright tone, rich in harmonics. As the sound decays, the character of the sound dulls due to friction and energy dispersion. Using a low pass filter before the output stage of a waveguide imitates this high frequency energy loss.

Possibly the most enticing aspect of physical modelling is the ability to produce sounds that can not be created in a real environment. Conventional instruments are limited in construction by mechanical and structural laws. Modelling allows these rules to be abandoned. "A Musician (Roads, 1995c) could construct a virtual guitar for instance whose strings are as long and thick as suspension cables".

Contrary to most other digital synthesis methods, Granular does not attempt to re produce any particular musical instrument, yet it is capable of complex, sound textures. Granular synthesis, like digital audio sampling, takes advantage of the inadequacies of the human ear which cannot distinguish between sounds played repeatedly over very short time scales. Many short bursts of audio are combined linearly. Each burst or sound grain is slightly different in character, resulting in a sound that is perceived as one continuous evolving tone. (Ekman, 1998) The sound grains are typically 10-20ms long. Minute crossfades are required to produce zero amplitude crossing points between each consecutive grain. This prevents clicks or discontinuities in amplitude level. The initial audio source may be a sample, or even a short piece of music. Typical parameters are pitch, length and density of sound grains. Granular requires a significant amount of processing power due to real time linking of the many sound grains. (Russ, 1996h)(Track7.CD)

Synthesis applications are separated into two regions, the control interface and synthesis engine. Parameter adjustments in the control interface determine the resulting sound output from the synthesis engine.

To successfully control all the variables of a traditional musical instrument, the number of parameters required can be immense. The approach and playing style of a jazz player for instance would produce guitar tones very much different to that of a rock guitarist playing the identical instrument. Characteristic musical changes such as these define musical style and creativity.

A competent saxophone player for example would use expressions such as lip pressure and breath attack within a performance. Playing experience will have made these actions natural to the player with no conscious effort been required. Using synthesis forces us to examine in detail these playing techniques, and study why a particular musical arrangement has a particular feel or vibe.

A software synthesiser does not necessarily have to be controlled via a mouse or ASCII keyboard. Most tend to comply with the MIDI protocol. This allows control to be implemented using external hardware. Ideally a physical modelled instrument should be controlled with an interface similar to its real counterpart. For instance it is not particularly effective to play a drum kit or cello via a piano keyboard. (Roads, 1995g)

The most common controller tends to be a piano type keyboard. One or more data wheels may be available, for control of pitch bend, modulation etc. "The keyboard (Russ, 1996i) is good for producing complex polyphonic performances based on notes and dynamics, but not so good when expression is required".

Essentially designed to control wind instruments such as flute or saxophone. In its simplest form a breath controller converts air pressure to volume, and finger presses to note pitch. Breath controllers are typically limited to producing monophonic or single note passages.

Various methods exist to control a synthesiser with a guitar interface. The most common approach however is to use a hexaphonic pickup. The pitch of each string is converted to MIDI data. Parameters such as pitch bend and velocity range usually have to be predefined to aid the conversion to MIDI. Early incarnations tended to be fairly inaccurate and unresponsive to bends and polyphonic playing. The recently released Parker MIDI-Fly guitar however seems to have improved many of these inaccuracy problems, and is considered to have "excellent (Walden, 1999) MIDI control".

Virtual interfaces are used within most software packages. Visual representations of hardware such as switches and sliders are used to control the synthesis process. Clicking or dragging with a mouse alters these parameters. Although a virtual or MIDI slider may appear to function just like a genuine one. A hardware potentiometer works in a linear manner, with an infinite number of settings between minimum and maximum value. A virtual slider however, works in stepped increments. In particular if it is controlled via MIDI, the maximum number of potential settings is fixed at 127.

Certain synthesis applications request a certain amount of rendering time to produce a sound output. Typical procedure is to determine the tonal attributes of the sound using either numerical or virtual slider based inputs. By clicking a render or synthesise button, all the variables and parameters are calculated. Several seconds (or sometimes minutes) later, The sound is rendered to a WAV file and can be monitored.

Some software applications such as Csound, require that both the sound attributes, and description of note sequence be entered in a numerical form. Similar in fashion to a traditional score, note duration, tempo and pitch are described. The principal distinction being that the timbre or tonal qualities of the sound are also described.

Utilising the advance in computer power, more recent software applications tend to produce the sound in real time. Similar to a traditional musical instrument, the user presses a key on the control interface and the resulting sound is calculated immediately.

However, due to increased computational demands, a small time delay exists between pressing a key and hearing the resulting sound. The duration of this time lag is dependent on many factors, such as CPU speed, sound card driver and efficiency of the synthesis implementation. Latencies vary between applications from about 10ms which is unnoticeable, to 500ms. Anything above 50ms produces an instrument that feels sluggish and unresponsive.

Most synthesis applications simply produce sounds. If anything more is desired, for instance the ability to use the sounds as part of a musical arrangement, a Sequencer is required. This is a software package for recording, processing and playing multiple sound or MIDI sources. The process typically involves running the sequencer and synthesis application simultaneously.

Essentially similar in purpose, both standards provide a low-level connection between synthesiser and sequencer. Providing sample accurate synchronisation, superior control possibilities and lower latencies. VST instruments utilise a plug-in format, and thus can only be accessed via the host Sequencer. Rewire applications on the other hand, can also be used as stand alone or independent applications. (Walker, 1999)

Due to the fact that "computers (Guttman, 1995) deal with numbers and the human ear responds to sound waves", it is important to point out that some equipment is essential to monitor the results of synthesis on a computer. Thus a soundcard is used. Utilising a digital to analogue converter a soundcard converts the numerical data into sound waves.

All digital synthesis methods require copious amounts of computing power. The quantity of available power determines many things, such as complexity of synthesiser structure, polyphony, number of oscillators etc. When using a sequencer and software synthesiser simultaneously the processing demands can increase significantly.

Through experimentation, it was realised that no single software application was able to model all the instruments required to produce a music arrangement. Thus various software packages were applied. The resulting sounds were arranged and mixed within a music sequencer. An overview of the software used is discussed below.

Research into software revealed that very few attempted to model acoustic drums. A number of physically modelled percussion instruments were available such as bongos, although snares and cymbals were unobtainable.

To overcome this, an application titled Stomper was used. This application utilises simple narrow band oscillators to produce sound. The output of each oscillator can be pitch shifted anywhere from a low thud to a high pitched click.

By dividing the sound of a snare drum, for example into its basic fundamental components, different sounds can be used to model the sequence of events occurring.

The initial attack as the drumstick hits the skin produces a bright click. Using a sine wave pitch shifted to around 2000Hz provided a similar sound. By applying a short burst of narrow band noise at 8000Hz, a sound akin to the vibration of the snare wires was created. The resonating thump of the drum walls vibrating was simulated by a third sine wave. The frequency or pitch of this oscillator was set to drop linearly over the period of the sound. This gives the drum tone its characteristic "thwack" sound, and adds body to the overall timbre. By mixing multiple oscillator outputs it was possible to produce quite effective implementations of a bass drum, multiple snares a ride and crash cymbal. (Anderson, 1998)(Track8.CD)

The bass line was produced using Steinberg`s Virtual Bass, a physical modelling program. The VB-1 employs the VST instruments architecture, and once loaded into the instrument "rack" is accessible via standard MIDI commands. Because the bass is modelled in real time, there is a small delay between pressing a key and hearing the resultant sound. Although relatively short (about 250ms), experimentation showed that playing the bass in real time using a keyboard, is impracticable. Thus to write a bass line with VB-1 involves using the key edit facilities in a sequencer. The approach is therefore similar to producing a standard MIDI file.

VB-1 has a number of parameters to provide control similar to a real instrument. Plectrum or playing position can be altered. Moving the plectrum towards the bridge produces brighter timbres, adjustments towards the fingerboard or neck produce duller sounds with more bass presence. A damper function attempts to emulate basses fitted with a string mute. Essentially, higher settings result in less sustain. Different driver sources can be selected. From synthesised bass tones, to more traditional strung basses.

Virtual Waves has a number of different synthesis processes available. To produce the Harpsichord, The Karplus-Strong physical modelling algorithm was applied. By using delay line processes, this algorithm attempts to model plucked strings.

The software follows the modular approach and single elements are interconnected to produce a virtual circuit. The Karplus-Strong module allows controls over note pitch, length and amplitude.

It is not possible to use Virtual Waves in real time, and most sounds require a short rendering time. Depending of the complexity and number of modules used, this can be up to five minutes. Virtual Waves has only rudimentary MIDI control. This is limited to basic note on/off information, it does not recognise velocity, which is essential for adding realism and dynamics. Thus it is not possible to sync Virtual Waves to a master device such as a sequencer.

To control or trigger the harpsichord involved preparing three notes at different pitches or frequencies. Using layered sampling techniques, the notes were assigned to their respective keys to cover three octaves. The harpsichord could then be played in real time.

Native Instruments Reaktor: Hi hats, Clap, Strings, FM piano, Square/Sine wave

Although a number of software applications were available that attempted subtractive and FM synthesis, experimentation indicated that Reaktor was the most suitable, mainly due to its well implemented MIDI control.

Reaktor takes the modular approach, although where other applications allow pre-programmed modules to be wired together, this software allows you to build your own modules. It can almost be perceived as a virtual collection of electronic components. Standard modules include a selection of oscillators, filters and dynamic processes. Each has its own relative panel, with parameter adjustment in the shape of virtual sliders and control knobs. Any parameter can be assigned and adjusted using MIDI.

Reaktor works almost in real time, the latency being around 10ms. These benefits constitute an instrument that can be played with a keyboard.

To produce and record the respective synthesisers involved inter-connecting the appropriate modules to create a circuit or structure. For example, connecting an envelope, oscillator and high pass filter respectively produced the square wave synthesiser. Utilising Reaktors own virtual MIDI port, pitch and parameter information can be controlled by the host sequencer.

Some problems were incurred running Reaktor and a sequencer simultaneously. Due to the amount processing power required, screen redraws when switching between applications were very slow (30secs). Random crashes were also occasionally experienced.

Contrary to its traditional analogue counterparts, Reaktor is multitimbral. Dependent on CPU power, numerous separate synthesis structures can be built each with independent control.

Exploration of a number of applications indicated that Reality was the only software that currently attempted real time physical modelling of traditional instruments. Reality utilises a number of synthesis processes, including subtractive and FM. Of particular interest, are its physical model implementations of Waveguide and Modal (resonating filters) synthesis. The former based on research by Sonidus and Stanford.

The number of instruments modelled is limited to around twenty, but these cover a varied selection of stringed, reed, and percussive instruments. Selective models such as tonal and modal are capable of a varied range of sounds from wood blocks and pipe organs to bell like sounds. Others such as the nylon-strung guitar are fixed models.

Parameter control of most models tends to be basic envelope and volume adjustment. Characteristic adjustments that may be expected with a physical modelling program are not catered for. For example none of the model types allow selection of instrument construction material, or physical size of instrument. Exceptions to this are the distorted guitar and bowed bass. The former allows speaker to microphone distance to be altered. The bowed bass allows adjustment of bow position, pressure and length.

The pluck algorithm is particularly interesting. This allows different driver or exciter sources to be combined. So, for example a slap-bass excitation could be mixed with that of an electric piano. (Track9.CD)

Reality has its own virtual MIDI connection, which allows the models to be controlled using a sequencer. Due to the relatively high CPU usage involved, the preferred option was to use its built in sequencer. The tracks were thus composed in a sequencer and exported into Reality as MIDI files. The files could then be rendered to audio using the capture facility.

One problem incurred was that the duration of a rendered audio file was significantly longer than its original MIDI file. Although only around half a second over a period of a minute, was enough to throw tracks out of sync. This was overcome by rendering each track in short, single bar lengths.

Before undertaking this project, it was assumed that there would be many physical modelling applications to research, This was an oversight on my behalf. Research revealed that the quantity of software packages to employ modelling techniques is limited in number.

The latencies inherent in computer synthesis are in my opinion an important issue. For instance, the Virtual Bass by Steinberg had a delay of nearly a quarter of a second. This makes it impossible to use it as a real time instrument. Although with the current rate of advancement in processing power, I doubt these latencies will be a valid limitation for much longer.

Although offline synthesis processes certainly have their uses and are capable of producing sounds similar in quality to real time methods. In my opinion they lacked the satisfaction and enjoyment of real time synthesis. Having to wait to hear the resulting sound is not beneficial to the creative process of music making.

More processing power is needed to fully implement real time physical modelling. Current computers can only cope with running two or three modelled instruments simultaneously. Random crashes were constantly experienced with nearly all software packages used.

The advancement of physical modelling acoustic instruments has been relatively slow. Currently only a few instruments have been modelled. Investigation revealed that it is potentially easier to successfully model some instrument types than others. Various software applications for example produced an implementation of an acoustic guitar. None however attempted a grand piano.

There are not presently enough software physical modelled algorithms available to fulfil the notion of producing music entirely within a computer. For instance, no acoustic piano or drum kits could be found. Though research did uncover hardware equivalents where some of these instruments had been successfully modelled. Thus other algorithms do exist, but they have yet to be implemented on a computer.

Authenticity of results varied widely between software applications and algorithms. The flute and harpsichord for example were unconvincing. Although both contained tonal elements of realism, the harpsichord was harsh and brittle sounding, the flute lacked the breath tones and sibilance of its real counterpart. Other instruments such as the nylon strung acoustic guitar were very credible and responded to pitch bend and velocity in a convincing manner. Although the dissonance produced by a real stringed instrument between certain musical intervals was non existent.

Compared to other synthesis processes, physical modelling provides the musician with unprecedented control over sound characteristics of a musical instrument. The problem lies in how to implement this control so that it can be applied in a creative and intermediate manner. Although its beneficial to have access to parameters such as lip pressure and bridge attenuation, most musicians have no idea of the relationship between these and the physical properties of a real instrument. Having to physically work out detailed nuances that occur naturally when playing a real instrument is a huge restriction.

The authenticity of sounds produced by analogue modelling was excellent in all software applications examined. Reaktor for instance produced timbres that in my opinion are almost identical to the real equivalent. Modelling analogue synthesisers suffers from many of the control problems as modelling real instruments, but to not such a degree. A switch is just a switch whether virtual or real. Dragging a mouse however will never be as effective and spontaneous as playing a real synthesiser. Because of the many potential parameters involved, searching through lots of virtual pages for the right slider removes the fun and instant gratification experienced when playing a real synthesiser. Although using an external controller may be helpful, these suffer from the limitations of MIDI.

To summarise, my research and experimentation showed that for physical modelling to be beneficial, a wider variation of musical instrument sources needs to be implemented within a single software application. The authenticity of many of the existing algorithms also needs to be improved and refined. New methods of control that are not restricted to the constraints of MIDI need to be developed.

Anderson, H (1998) Stomper: The Manual. [Internet] p1. Available from: <http://www. master-zap.com/>

Comajuncosas, J (1999) The JM Csound Repository. Available from: <http://members.tripod.com/csound/>

Ekman, R (1998) Granulab: Documentation. [Internet] p1. Available from : <http:www. Hem.passagen.se/rasmuse>

Heckroth, J (1995) Tutorial on MIDI and music synthesis. p1-23. La Habra CA, The MIDI Manufacturers Association.

Henrick, H (1998) Future music: Ooh you’re a card . Vol.65, p52-64. Bath, Future Publishing

Hind, N (1999) Additive Synthesis. [Internet] Available from: <http://ccrma-www.stanford.edu/CCRMA/

Lord, N (1997) Future Music: What the hell is analogue synthesis.Vol.63, p93-97. Bath, Future Publishing

Mathews, M. Guttman, N (1962) The Historical CD of Digital Sound Synthesis: Musical Sounds from Digital Computers. p35. Germany, Wergo

Miller, M (1998) Sound Synthesis on a Computer. [Internet] Available from: <http://www.sospubs.co.uk/>

Pierce, J (1992a) The Historical CD of Digital Sound Synthesis: Recollections. p11. Germany, Wergo

Pierce, J (1992b) The Historical CD of Digital Sound Synthesis: Recollections. p9. Germany, Wergo

Roads,C (1995) The Computer Music Tutorial: Sampling synthesis. Ch.2, p117-134. Cambridge, The MIT Press

Roads,C (1995a) The Computer Music Tutorial: Physical modelling. Ch.2, p268. Cambridge, The MIT Press

Roads,C (1995b) The Computer Music Tutorial: Waveguide Synthesis. Ch.2, p282. Cambridge, The MIT Press

Roads,C (1995c) The Computer Music Tutorial: Physical modelled Synthesis. Ch.2, p266. Cambridge, The MIT Press

Roads,C (1995d) The Computer Music Tutorial: Musical Input Devices. Ch.2, p641. Cambridge, The MIT Press

Russ, R (1996a) Sound Synthesis and Sampling: Background. Ch 1, p9. Oxford, Focal Press

Russ, R (1996b) Sound Synthesis and Sampling: Additive Synthesis. Ch.2, p104-110 Oxford, Focal Press

Russ, R (1996c) Sound Synthesis and Sampling: Analogue Synthesis. Ch.2, p66-103. Oxford, Focal Press

Russ, R (1996d) Sound Synthesis and Sampling: FM. Ch 5, p218-226. Oxford, Focal Press

Russ, R (1996e) Sound Synthesis and Sampling: Physical modelling. Ch.5, p243-251. Oxford, Focal Press

Russ, R (1996f) Sound Synthesis and Sampling: Physical modelling. Ch.5, p247. Oxford, Focal Press

Russ, R (1996g) Sound Synthesis and Sampling: Interaction Emulation. Ch.5, p245. Oxford, Focal Press

Russ, R (1996h) Sound Synthesis and Sampling: Granular Synthesis. Ch.5, p243-251. Oxford, Focal Press

Russ, R (1996i) Sound Synthesis and Sampling: Controllers. Ch., p328-336. Oxford, Focal Press

Punch, B (1999) Computer Music Composition. [Internet] Available from: <http://garage.cse.msu.edu/>

Physical Modelling Theory (1999) A Light Treatment for Musicians. [Internet] Available from: <http://web800.com/music/>

Smith, J (1999) Basics of Digital Waveguide Modelling. [Internet] Available from: <http://ccrma-www.stanford.edu>

Trask, S (1999) Sound on Sound: Elsid. Vol.15, p188-194. Cambridge, SOS Publications

Tveraas, J (1999) Reviewed: Reaktor by Native Instruments. [Internet] Available from: <http://www.harmony-central.com/>

Walden, J (1999) Sound on Sound: Parker Fly. Vol.15, p202. Cambridge, SOS Publications

Walker, M (1999) Sound on Sound: Rewired for Sound. Vol.15, p70. Cambridge, SOS Publications

Walker, M (1999) Reality Software Synthesiser. [Internet] Available from: <http://www.sospubs.co.uk/>

Wiffen, P (1999) Modelling Strings and Wind Instruments. [Internet] Available from: <http://www.sospubs.co.uk/>

Wiffen, P (1998) The Imitation of Analogue. [Internet] p1-7. Available from : <http:www. sospubs.co.uk/>

Whittle, R (1999) Robin Whitles Csound page. [Internet] Available from: <http://www.firstpr.com.au/csound>

Yahaya, T (1999) Subtractive Synthesis. [Internet] Available from: <http://www.freeyellow.com/members2>

It was important to ascertain that any physically modelled instruments used could be replicated. I wanted to compare software synthesis to real and sampled instruments so selections of both were used.

Like most musical instruments the process of successfully sampling a drum can be involved. A competent percussionist is able to produce many sounds with subtle changes in nuance and pitch from the simple act of striking a single drum. To reproduce this authentically would require hundreds samples to be layered and triggered correctly. Typically, sampling compromises by using one sound per drum and this was the method applied. The drums were triggered using the same MIDI files as the modelled versions, because of slightly different relative volumes however the levels between the individual drum sounds had to be adjusted using velocity.

Many instruments such as harpsichord were recorded by using a MIDI keyboard as a control device. Most sequencers allow the tempo of an arrangement to be slowed down so that parts can be recorded easier. If as in my case limited keyboard skills restrict the performance this can help considerably. Once recorded, the tempo can be returned back to its original setting. Samples were layered using soundcard-based facilities. To effectively produce sampled pitched instruments typically involves multi-sampling. For instance the lowest C note on a piano would sound unrealistic if pitch shifted to represent the highest C. (Roads, 1995) Typically one note is used to cover an octave As many of the parts were within a limited pitch range, only three or four samples were generally required.

The Acoustic guitar and electric bass sections were recorded using standard microphone techniques. By utilising the computers hard disc recording capabilities, the parts were recorded in a linear manner similar to the approach of a tape-based system. Using the cut, copy and paste functions within a sequencer it is possible to move parts in the arrangement. Thus, mistakes or bad takes were removed and replaced. The various acoustic guitar parts were looped and moved to various sections of the arrangement. Due to the fact that the bass line evolved throughout the song, the modelled version was imported into the arrangement and monitored through headphones whilst recording. The electric guitar was produced in a similar fashion except that the microphone was replaced with a direct box.

To gain a balanced opinion between the modelled synthesisers and the sampled versions, both were coloured through the same filters (modifier). To achieve this Reaktor was used. By replacing the oscillator in a structure with an audio input, it is possible to use Reaktor`s dynamic processing facilities on external audio sources. For example to produce the sampled square wave, the relevant modelled version was opened. By substituting the oscillator with an audio input, the structure is accessible as an insert effect within the sequencer. Because all the parameter movements such as cutoff had previously been recorded in to a MIDI file, it was a simple procedure to apply the same processes to the sampled versions.

Some software synthesisers such as Reality also allow instruments to be created using conventional sample playback methods. The electric piano was a sampled patch supplied with the software. Reality includes a basic sequencer and audio rendering facility. This was used to capture the piano to audio.

As both instruments produce both pitched and percussive sounds, either the key or drum editor could have been applied to arrange the parts. The preferred option was to use the key editor. The notes were thus inputted via a mouse.

All sampled sources were rendered or recorded as audio files so that dynamic processing could be applied. Both compositions were fed through identical auxiliary and insert effects. This was achieved by saving the individual effects parameters as banks in the modelled arrangement, and importing them into the new arrangement. To Mix the relative volumes between both compositions involved mastering the modelled track onto tape. This was then referred to whilst mixing. Although it would have been possible to feed both arrangements through the same mixer settings, the amount of processing power required to access both tracks simultaneously was unrealisable.

Instrument type	Original source	modelled	FX processes
square wave	Sample	Reaktor Subtractive	HP filter /delay
guitar feedback	Guitar	Reality PM	Compression EQ Delay
damp guitar	Guitar	Reality delta strings	Compression Delay EQ Reverb
Harpsichord	Sample	Virtual Waves Karplus-Strong	Compression EQ Reverb
Rhodes Electric Piano	Sample	Reaktor FM	Tape saturation EQ
Drawbar Organ	Sample	Reality PM tonal	EQ Compression
Nylon guitar	Guitar	Reality PM	EQ Compression Reverb
Flute	Sample	Reality PM	Reverb
Big verb Percussion	Sample	Reality Percussion	Big Reverb Flanger
Synth strings	Sample	Reaktor PWM strings subtractive	VST Chopper Reverb Delay
Saw tooth	Sample	Reaktor PM oscillator	VST Chopper
Bass	Bass	VST Virtual Instrument PM	Compression EQ
Vibraphone	Sample	Reality Vibes	Reverb Compression
Marimba	Sample	Reality Marimba PM	Reverb Compression

MIDI number	Original	Modelled
36 Bass drum	Sample	Mixed narrow band oscillators (Stomper)
37 Side stick	Sample	Physical model (reality)
38 Snare drum	Sample	Mixed narrow band oscillators (Stomper)
39 Hand clap	Sample	White noise, input delay low band and high pass filters (Reaktor)
40 Snare Drum	Sample	Mixed narrow band oscillators (Stomper)
41 Reverb Snare	Sample	White noise (Reaktor) mixed with initial transient of physical model percussion (Reality)
42 Closed Hi-hat	Sample	White noise through low and band pass filters (Reaktor)
44 Stick Hi-hat	Sample	White noise through low and band pass filters (Reaktor)
46 Open Hi-hat	Sample	White noise through low and band pass filters (Reaktor)
49 Crash Cymbal	Sample	Time stretched Ride cymbal with EQ
51 Ride Cymbal	Sample	Mixed narrow band oscillators (Stomper)
54 Tambourine	Sample	Mixed narrow band oscillators (Stomper)
56 Cowbell	Sample	Physical model (Reality)
60 Hi Bongo	Sample	Physical model (Reality)
61 Low Bongo	Sample	Physical model (Reality)

Csound is a cross platform public domain application. Based on Music 4, a program written by Max Mathews at Bell Telephone Laboratories in the 1960`s.

Barry Vercue of MIT developed csound to its present incarnation, yet, its architecture allows development by any third party with the required technical knowledge. Its sound generation capabilities include additive subtractive, fm, granular, sample playback and physical modelling, all of which can be used simultaneously, allowing for unlimited sound creation possibilities.

" It is (Whittle, 1999) a powerful but unforgiving programming language" with a huge learning curve for the uninitiated, and, thus tends to be used in the field of academia and research. Csound differs from most current software synthesis applications in that it is a command, or text based programming language, with no graphical interface, although, some utility programs and interfaces do exist to make working with the language easier.

Opcodes, or unit generators, as they are known to csound are wired together, within a software environment, these modules may be sound generators, dynamic processing tools such as a reverb, or signal analysis tools. There are currently more than 400 modules available. The Sound output can be rendered to an audio file, which can be at any sample rate. This output is a standard Microsoft wave file, which can be accessed and previewed, in any audio editor. All Csound internal calculations are in 32 bit floating point format so it is 256 times more accurate than CD quality 16-bit audio.

It is possible to control sounds in real time via MIDI input, but this has to be implemented in code within the score file. Use of the more advanced opcodes requires rendering time, which may be anything up to several hours.

Working with Csound requires the creation of two text-based files, the orchestra and the score. These files work independently of each other.

The orchestra file denotes information about the "instruments" or sounds used within a composition. All instruments have a unique identification name, and the number of instruments an orchestra file can contain are virtually unlimited. Under the header section of the orchestra file, parameters for the sound output are defined, such as sample rate, control rate and the proposed number of audio channels. Below the header section, the instrument definitions are stated. Each module is chosen by specifying its particular name, and is separated by the INSIR and ENDIN statements. Modules may be wired and interconnected to create one, or a number of independent instruments.

The score, as its name implies, plays the orchestras instruments. In its simplest form it can be compared to MIDI, thus it informs the orchestra file at what specific point in time to play each note, how long the note should be and its pitch. Two or more notes may share the same start and end times allowing for polyphonic instruments to be created The list of controllable parameters, unlike MIDI is unlimited, and can be redefined independently for each note. These parameters are usually unique for each chosen module. (Whittle, 1999)