What is sound?
Sound is a travelling wave which is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations. For humans, hearing is normally limited to frequencies between about 12 Hz and 20,000 Hz (20 kHz), although these limits are not definite. The upper limit generally decreases with age. Sound waves are characterized by the properties of waves, which are frequency, wavelength, period, amplitude, intensity, speed, and direction (sometimes speed and direction are combined as a velocity vector, or wavelength and direction are combined as a wave vector). Transverse waves, also known as shear waves, have an additional property of polarization. Our Atmosphere that surrounds us plays a big part in our perception of sound from moment to moment. If the atmospheric-pressure level around us remains steady or has little change, we hear silence. If atmospheric changes increase this pressure or other objects in your area are in motion, the results are anything from light audible noise to deafening thunder. To conclude all sounds that we know of are created through atmospheric changes or objects in motion vibrating the existing atmospheric pressure that surrounds us. A wild form of synthesis would be to change the barometric pressure inside a symphony hall while the orchestra was playing. Let me know if anybody can figure out how to make this happen.

a musical sound tone definition

All musical tones have a complex waveform, made up from loads of different frequencies. All sounds are formed using a combination of sine waves at varying frequencies and amplitudes. If we look at the frequencies of a complex waveform, then the lowest frequency is called the fundamental frequency. The fundamental frequency determines the pitch of the sound. The higher frequencies are called overtones. If the overtones are multiples of (x1, x2, x3 etc.) the fundamental frequency then they are called harmonics. The overtones or upper partials as some people like to refer to them as, must be multiples of the fundamental to be known as harmonics. These frequencies and their amplitudes determine the timbre of a sound.

If you have a waveform that has a fundamental frequency of 100 kHz, then the second harmonic will be 200 kHz and the third harmonic will be 300 kHz and so on……

If you think about the irregular waveform of noise then you will understand that it has no harmonics. Noise, as we discussed earlier, contains a wide band of frequencies and it is generally accepted that, at waveform level, there are no harmonics as the waveform is non-repeating.

Harmonics are essential when it comes to synthesis. In acoustics and telecommunication, a harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For example, if the fundamental frequency is f, the harmonics have frequencies f, 2f, 3f, 4f, etc. The harmonics have the property that they are all periodic at the fundamental frequency; therefore the sum of harmonics is also periodic at that frequency. Harmonic frequencies are equally spaced by the width of the fundamental frequency and can be found by repeatedly adding that frequency. For example, if the fundamental frequency is 25 Hz, the frequencies of the harmonics are: 25 Hz, 50 Hz, 75 Hz, 100 Hz, etc. If we use a simple metaphor like a singing quartet, the lead vocalist would be the fundamental frequency, while the other three vocalists are the harmonics, harmonizing with the lead vocalist.

How to make a sound

One of the most significant developments in the design of analog and digital sound synthesis techniques was the concept of unit generators (UGs). UGs are signal processing modules like oscillators filters and amplifiers, which can be interconnected to form synthesis instruments or patched together by wire in order to generate sound signals in a circuit type scheme.


The Oscillator

An oscillator creates a single periodic waveform at a certain frequency. In other words, the Oscillator is an electronic device used to generate a tone. In analogue synthesis, the Osc generates a sound or waveform, usually, a sine, saw, triangle, squar or pulse wave. The Osc generates this waveform continuously. The rate at which it generates one cycle is what we regard as pitch and this is measured in Hz. On analogue synthesizers the Oscs are referred to as VCO, Voltage Controlled Oscillator, on modern synthesizers that incorporate digital processing, DCO, Digitally Controlled Oscillator, on samplers they can be referred to as samples, voices, & waveforms.

Filter

A filter allows the cutoff frequency and Q factor of a soundwave to be continuously varied. Usually the filter gives a lowpass response, but may also be switchable to allow highpass, bandpass or even notch responses. The filter may offer a switchable slope which determines how intensely signals outside the pass band become attenuated, usually 12dB/octave (a '2 pole' filter) or 24dB/octave (a '4 pole' filter).

In analog synthesizers, which are commonly used to make electronic music, VCFs are commonly positioned after the oscillator(s). The oscillator generates an audio waveform, which (except for noise waveforms) includes a fundamental pitch and a series of harmonic overtones. By varying the cutoff frequency (the maximum frequency passed by the filter), the synth operator can add or remove some of the overtones to create more interesting and textured sounds.

In electronic music, "filter sweeps" have become a common effect. These sweeps are created by varying the cutoff frequency of the VCF (sometimes very slowly) to reveal or conceal the oscillator's overtones. Controlling the cutoff by means of an envelope generator, especially with relatively fast attack settings, simulates the attack transients of natural or acoustic instruments.

A VCF is an example of an active non-linear filter: however, if its control voltage is kept constant, it will behave as a linear filter.


Envelope Generator (ADSR stands for Attack,Decay,Sustain & Release)

adsr

The main purpose of the envelope generator is to control the attack of the tone, it's decay from the high point of the initial attack, the sustain of the note as it decays and last the final fading out  or release of the note. The envelope generator gives the generated tone character and molds the tone into a more musically usable note.
 
Synthesizers usually have 2 or more envelope generators. One will control the VCF and the other the VCA. When used with the VCA, the EG is used to vary the volume of a sound to create the natural dynamic movement of a sound. When used with the VCF, it can change the timbre of a sound over time by controlling the cut-off frequency of the VCF.


Amplifier

A voltage-controlled amplifier is an electronic amplifier that varies its gain depending on a control voltage (often abbreviated CV).

VCAs have many applications, including audio level compression, synthesizers, and amplitude modulation.

A crude example is a typical inverting op-amp configuration with a light-dependent resistor (LDR) in the feedback loop. The gain of the amplifier then depends on the light falling on the LDR, which can be provided by an LED (an optocouple). The gain of the amplifier is then controllable by the current through the LED. This is similar to the circuits used in optical audio compressors.

A voltage-controlled amplifier can be realised by first creating a voltage-controlled resistor (VCR), which is used to set the amplifier gain. The VCR is one of the numerous interesting circuit elements that can be produced by using a JFET (junction field-effect transistor) with simple biasing. VCRs manufactured in this way can be obtained as discrete devices.

In audio applications logarithmic gain control is used to emulate how the ear hears loudness. David E. Blackmer's dbx 202 VCA was among the first successful implimentations of a logarithmic VCA.


The Father of Modern Synthesis

Max Vernon Mathews born November 13, 1926, in Columbus, is a pioneer in the world of computer music & synthesis. He studied electrical engineering at the California Institute of Technology and the Massachusetts Institute of Technology, receiving a Sc.D. in 1954. Working at Bell Labs, Mathews wrote MUSIC, the first widely-used program for sound generation, in 1957. In my opinion he is the father of modern day synthesis and it's practice through the use of electrical and digital devices. After the public presentation of his initial developments, dozens of synthesizing techniques are developed and manipulated both commercially and in performance.

To start this online work of synthesis and not get too caught up in the historical, lets start by understanding sound and the most current & valid approaches to sound synthesis through the manipulation of electronic devices and computers. As stated there are many forms of sound synthesis and not all of them electrical or related to music. My life has been consumed with computer technologys, electrical components and of course, music. I am going to skip delving into the works of Max Mathews and take a more current approach to the practice of modern synthesis and it's applicable use in my own creative musical process.


The Development of Different Types of Synthesis

The first synthesis approach to make use of these unit generator concepts was the MUSIC III program by Max Mathews and Joan Miller in 1960. By passing a sound signal through a series of various UGs a large number of synthesis algorithms were developed and implemented. I have never found an actual document clarifying what algorithms were derived at during the first executions of the MUSIC III program, so I will have to skip ahead and start with a more current collection of concepts that make up our current modern methods of synthesis.

Methods of Synthesis Used by Me

Of the forms of synthesis that are practiced in audio & music, you will find the rest of this page of mine is dedicated to the types of synthesis that can be found in the equipment I use and in the music I compose. There are many forms of audio synthesis and with the introduction of VSTs and soft synths, many new forms or enhanced forms of older synthesis practices are being currently developed. Creative electronic musicians will undoubtably favor one form or another methods of synthesiss and continue to develope exciting new forms of audio. As for me well I am a hardware musician and rely on a hands on approach to making my music. While composing, performing or recording I prefer to be in direct contact with my equipment, rather than tweeking a software application.
 

Synthesis Techniques (BASIC) Description
  
Subtractive Synthesis
 
Frequency Modulation or FM

Wavetable Synthesis
  
Wave Sequencing

                
Vector Synthesis 

Filtering of complex sounds to shape harmonic spectrum.

Modulating a carrier wave with one or more operators (FM)

Variating speed playback of recorded digitized waveforms.

Linear combinations of severtal small segments to create a new sounds.

Technique for fading between any number of different sound sources.

Synthesis Techniques (ADVANCED) Description

Granular Synthesis
 
Pulsar Synthesis
  
Filter Synthesis
 
Physical Modelling
 
Digital Waveguide Synthesis
 
Waveset Distortion 

Combining of several small sound segments into a new sound


Based on the generation of trains of sonic particles

Emu z plane filter

Mathematical equations of acoustic characteristics of sound

Waves guided by Algorithms and formulas

Irreversibly altering wavesets in sound through harmoic distortions


Synthesis Techniques (OTHER) Description

Sampling  



Composite Synthesis 



Phase Distortion 



Waveshaping 


Resynthesis  


Direct Digital Synthesis
  

Using recorded sounds as sound sources subject to modification

Using artificial and sampled sounds to establish resultant "new" sound

Altering speed of waveforms stored in wavetables during playback

Intentional distortion of a signal to produce a modified result

Modification of digitally sampled sounds before playback

Computer modification of generated waveforms (software synthesis)


There are many other forms of synthesis going on around us & in nature. The synthesis concepts stated here are those that apply to sound & audio in the application of music. If your interest is deeper than this I suggest a reading research into the various forms of synthesis being applied to human and animal vocal patterns, even further is the research being done in enviromental and astronomical sound waves.

Synthesis Techniques (BASIC)

Subtractive Synthesis 

This process involves the generating of complex waveforms and then filtering the frequencies so that you are then left with the sound you want. You take away the frequencies. Obviously the filters are crucial in subtractive synthesis and the better the filters and the wider the choice of filters available, the better the end result will be.

The basic components(UGs) needed for subtractive synthesis are as follows; oscillator or audio wave source, filter, envelope generator & amplifier. Lets take a moment to understand and break these components down.

In subtractive synthesis we use an oscillator that creates a tone, run it through a filter to remove the frequencies we want to remove and then adjust the volume of the sound over a period of time using the amplifier (shape).  I don’t want to get into the electronics of the signal path of an analogue synthesizer or how a synthesizer works. Just remember that when synthesizers were invented they worked off a voltage path and the voltage was controlled throughout the components. Tone is sent to the filter & in most patched schemes the envelope shapes the filter. If the tone is sent directly sent to the amplifier, the ADSR shapes the volume. The hard wiring and circuits of these synthesizers are made so that one EG went to the filter, which was controlled by voltage of course, and the second was sent to the amplifier, which was controlled by voltage as well. By using the CV input of the filter the voltage is controlled at the input stage. The same CV input is used as well on the amplifier. By varying the voltages at any of these input stages meant we altered the shape or filter characteristics of the sound. Today most synthesizers use digital signal processing to simplfy subtractive synthesis for the musician.

Check out the Analog Modular Synthesizer that I have been building.

My Modular Synthesizer

Frequency Modulation (FM)

The output of one oscillator (modulator) is used to modulate the frequency of another oscillator (carrier). These oscillators are called operators. FM synthesizers usually have 4 or 6 operators. Algorithms are predetermined combinations of routings of modulators and carriers. To really explain this we need to go into harmonics, sidebands, non-coincident and coincident series and the relationships between modulators and carriers.

John M. Chowning is known for having discovered the FM synthesis algorithm in 1967. In FM (frequency modulation) synthesis, both the carrier frequency and the modulation frequency are within the audio band. In essence, the amplitude and frequency of one waveform modulates the frequency of another waveform producing a resultant waveform that can be periodic or non-periodic depending upon the ratio of the two frequencies.

Chowning's breakthrough allowed for simple yet rich sounding timbres, which synthesized 'metal striking' or 'bell like' sounds, and which seemed incredibly similar to real percussion. He spent six years turning his breakthrough into a system of musical importance and eventually was able to simulate a large number of musical sounds, including the singing voice. In 1973 Stanford University licensed Chowning's discovery to Yamaha in Japan, with whom Chowning worked in developing a family of synthesizers and electronic organs.

The first product to incorporate the FM algorithm was Yamaha's GS1, a large piano sized digital synthesizer that first shipped in 1981. Some thought it too expensive at the time, Chowning included. Soon after, Yamaha made their first commercially successful digital FM synthesizers, the DX series. Along this line, it is my personal opinion the Chowning had more to do with the DX1series, than the commercially modified DX5, and the even more modified DX7. These modifications resulted in a less hands on synth, like the DX1, in favor of a complicated programming approach found on the DX7.

Chowning FM Theory uses the basic sine wave as both the carrier and modulating waveform. One of the strengths of FM is the ability to do alot with two very simple waves. Chowning FM modulations are linear, whereby the carrier is pushed an equal number of cycles per second above and below its center frequency. Exponential FM, where the carrier is pushed up and down on an equal musical interval (therefore more Hz up than down) drifting upward in its pitch axis as the modulation depth is increased . Linear FM allows the strength of modulation to be increased without the perceived center frequency rising.

The Yamaha DX series of synthesizers was built around Chownings Principles of Audio-rate Frequency Modulation and his calculations based on the CM Ratio.The CM Ratio is defined as the carrier frequency (Cƒ) plus and minus all the integer multiples of the modulating frequency (Mƒ). This approach opened up areas of synthesis where many things could be done to create very complex spectra with FM. The DX-7 was built around the idea of double-carrier FM, in which a single modulator controls two carriers, tuned differently. This allows the creation of formant (see formant synthesis below) areas not possible with single FM. Also, stacks of modulators, where a modulator was itself modulated, could either produce wildly complex spectra if tuned inharmonically or produce weighted spectra, which could create a more realist bass. This helped with one of FM's greatest drawbacks--the strength of the upper and lower sidebands are equal, but our human hearing requirings more energy in the lower frequencies to be considered as equally loud as the higher frequencies. Therefore, single FM always seemed weighted to the treble,. Another interesting idea is to modulate the modulation index itself, providing a rapid timbral shift. or to low-frequency modulate the modulator or carrier, changing the C:M ratio and therefore the frequencies of the sidebands for some very nice effects.


Wavetable Synthesis - Morphing the soundwave & the Palm Productions GmbH (PPG).

This form of synthesis incorporates the use of pre recorded digitized audio waveforms of real or synthetic instruments. The waveforms are then stored in memory and played back at varying speeds for the corresponding notes played. These waveforms usually have a looped segment which allows for a sustained note to be played. Using envelopes and modulators, these waveforms can be processed and layered to form complex sounds that can often be lush and interesting. The processes are algorithmic and memory is crucial to house the waveforms. Linear crossfading sequentially, quasi-periodic and sine functions are used in this type of synthesis.

The PPG system was the first of the wavetable synthesizers, where related single-cycle waveforms were stored in a group of 32. The user could pick a starting waveform and then use an envelope or LFO to move around in the wavetable, causing timbral changes as the waveform being read out changed. Differences between adjoining waveforms were fairly slight, so the degree of timbral change was determined by how far and how fast the readout moved from the original starting point.

Wave Sequencing - Morphing the soundwave part 2 & the Sequential Circuits Prophet VS.

The transition from waveform to waveform in Sequential's Vector Synthesis, first seen on the Prophet VS, was a simple crossfade, and although two of these crossfades could be controlled or programmed by the joystick which was so integral to the Vector Sythesis system, the maximum number of waveforms which could be involved in a single sound was four. However, Sequential Circuit's next development, called Wave Sequencing -- allowed up to 255 different waves to be involved. This innovation was introduced on the Korg Wavestation, which still featured joystick-controlled Vector Synthesis, but added the much greater potential for transitional synthesis than what wave sequencing gives.

Prophet VS 

The Prophet VS used four digital wavetable oscillators based on those in the PPG Wave as its four sound sources. The limitations, particularly the digital aliasing, of this design, coupled with its use of Curtis analogue filter ICs to process the mixed sound, gave the Prophet VS its distinctive sound.

In the case of wave sequencing, coming 10 years after wavetable synthesis, there was much less economic restriction on memory for storing waveforms. As a result, instead of access being limited to 32 single-cycle waveforms, full PCM samples were available, and up to 255 could be 'on-line' for use by an oscillator in a sound. Each stage in the wave sequence could be occupied by a PCM sound radically different from the one before or after it in the sequence. The potential for striking sonic change is therefore much greater in wave sequencing, especially since the PCM waveforms can be deliberately moved around by the user to contrast as much as possible with the other PCM waveforms.

Korg Wavestation 

Vector Synthesis - Morphing the soundwave part 3
vector synth

The Korg Wavestation took the concepts of the Prophet VS & the Yamaha SY22 & went even further. The wavestation allowed each of the four sound sources to produce not just a static tone, but a complex wave sequence, by playing back or cross-fading one wave after another.

This method of synthesis incorporates the combining and processing of digital waveforms. Using PCM samples, effects and filtering this method of synthesis can create stunning sounds, from lush and evolving pads to strange stepped sequences. Korg made the famous Wavestation range of synthesizers and these were based around the Sequential Circuits Prohet VS. Working off a 2 dimensional envelope using an X and Y axis (joystick) and 4 voices, this synthesizer also had wave sequencing, playing a loopable sequence of PCM samples in a rhythmic and/or crossfaded fashion. The idea was to be able to crossfade 2 or more waveforms using the joystick.

There have been a number of different implementations of vector synthesis. These differ in what they use for the four sound sources, and what processing is done to the sound after the vector synthesis stage. The actual vector synthesis concept first developed by Sequential Circuits is identical.


Synthesis Techniques (Advanced)

Granular Synthesis



This is the method by which tiny events of sounds (grains or clouds) are manipulated to form new complex sounds. By using varying frequencies and amplitudes of the sonic components, and by processing varying sequences and durations of these grains, a new complex sound is formed.

Granular Synthesis is a method by which sounds are broken into tiny grains which are then redistributed and reorganised to form other sounds.

Granular synthesis is perceived as a relatively recent development in sound synthesis, but it can also be seen as a reflection of long-standing ideas about the nature of sound. Quantum physics has shown that sound can be atomically reduced to physical particles(Wiener 1964). This physical form of sound was first envisioned by the Dutch scientist Isaac Beeckman (Cohen 1984). He explained that sound travels through the air as globules of sonic data. It has only been through the use of modern computers that this form of synthesis could be practiced and it's results appreciated. Though this is one of the newer concepts in synthesis technology, the concept and principles are just about as old if not older than the concepts arrived at by Max Mathews.

Later works including those by Gabor (Gabor 1946) and more recently Xenakis (Xenakis 1971), Roads (Roads 1988), and Truax (Truax 1990) has evolved the particle theory of sound into a synthesis method whereby the natural sound particle is imitated and magnified, referred to as a grain. The grain is then layered with other grain, either cloned or extracted through a similar process as the original to create different sounds and sonic textures. The original intent of the process described by Gabor was to reduce the amount of data required to convery an audio human communication.

Gabor's research came into the hands of Xenakis, who recognised a musical application for this work (Xenakis 1971). Xenakis' first works involving granular synthesis were created with a reel to reel tape recorder. By splicing magnetic tape into tiny segments, rearranging the segments, and taping the new string of segments together. After attending a seminar conducted by Xenakis on this topic, Roads began experimenting with this idea on a computer. His first experiments were extremely time consuming, even when rendering just a one minute mono sound (we are not talking minutes here, nor hours, but days, usually weeks, depending on scheduling and transferring). After reading an article about granular synthesis written by Roads in 1978, Truax began developping a way to create granular synthesis in real-time, first realised in 1986. From this point on, granular synthesis has slowly become available to a growing number of musicians and sound artists.


These basic questions might help you understand granular synthesis

What is a grain?
A grain is a small piece of sonic data. In granular synthesis it will usually have a duration between 10 to 50 ms. The grain can be broken down into smaller components, the envelope and the contents. The envelope is used primarily so that there is no distortion and crunching noises at the beginning and end of the sample. The shape of the envelope though has a significant effect on the grain. The contents of the grain is audio. This can be derived from any source. Sine wave, square wave, audio sample, etc.

What is wavelet synthesis?
Wavelet synthesis is very closely related to granular synthesis except that it is more strict in its definition and construction. A granular synthesis grain can be set at any length arbitrarily, whereas a wavelet derives its "grain" length as determined by the pitch of the contents, using the wavelet transform. The wavelet is designed to start and end at 0 phase. Wavelet synthesis can be used for better pitch shifting and reproduction than granular synthesis, but it requires so much analysis that it is much slower to work with in a real-time environment.

What is grainlet synthesis?
It is actually another name for wavelet synthesis. It is the more commonly used term when referring to compositions created using the wavelet transform, whereas wavelet synthesis is the more commonly used term when referring to the analysis and reconstruction of audio. I personally prefer to use the term wavelet synthesis for all outcomes using the wavelet transform.

What is Glisson Synthesis?
A derivative of granular synthesis whereby the contents of each grain are modified with a glissando, the gliding from one pitch to another..

Key to all granular techniques is the grain envelope. For sampled sound, a short linear attack and decay prevent clicks being added to the sound. Changing the slope of the grain envelope, in classic microsound practice, changes the resulting spectrum, sharper attacks producing broader bandwidths, just as with very short grain durations.

granular synthesis

The diagrams above show a grain stream of equal duration grains, producing Amplitude Modulation with grain durations less than 50 ms. The bottom diagram shows 3 grain streams with variable delay time between grains, the sum of which resembles asynchronous granular synthesis.

Types of granular synthesis

Quasi-synchronous granular synthesis


granular synthesis

A grain stream of equal duration grains, producing Amplitude Modulation with grain durations less than 50 ms. The bottom diagram shows 3 grain streams with variable delay time between grains, the sum of which resembles asynchronous granular synthesis.


Asynchronous granular synthesis

granular synthesis

Grains are distributed stochastically with no quasi regularity
.

Pitch-synchronous granular synthesis:

granular synthesis

Overlapping grain envelopes designed to be synchronous with the frequency of the grain waveform, thereby producing fewer audio artifacts.


What is most remarkable about the technique is the relation between the triviality of the grain (heard alone it is the merest click or 'point' of sound) and the richness of the layered granular texture that results from their superimposition. The grain is an example of British physicist Dennis Gabor's idea (proposed in 1947) of the quantum of sound, an indivisible unit of information from the psychoacoustic point of view, on the basis of which all macro-level phenomena are based. In another analogy to quantum physics, time is reversible at the quantum level in that the quantum grain of sound is reversible with no change in perceptual quality. That is, if a granular synthesis texture is played backwards it will sound the same, just as if the direction of the individual grain is reversed (even if it is derived from natural sound), it sounds the same. This time invariance also permits a time shifting of sampled environmental sound, allowing it to be slowed down with no change in pitch. This technique is usually called granulation.


Pulsar Synthesis


A form of particle synthesis whereby each grain is created as a pulsar, generated by an impulse generator. I found very little that really demonstrates Pulsar Synthesis. A new field of studyboth sonicly and visually. The youtube vide was selected out of only three that I have come across. Though this video's audio may work or maynot. The video functions perfectly on the youtube website. Double click on the video and it will take you to youtube.

Pulsar synthesis is a method of electronic music synthesis based on the generation of trains of sonic particles. PS can produce either rhythms or tones as it criss-crosses perceptual time spans. The basic method generates sounds similar to vintage electronic music sonorities, with several interesting enhancements. This video performance method combines multiple pulsar trains with sampled sounds. Pulsar synthesis to me is a new type of clock or metronome that could be used in a Pure Data structure or MaxMSP, the results should be very interesting and complex.

Filter Synthesis

The Z-plane synthesis concept developed by Emu Systems is an element of transitional synthesis. However, the transition does not happen between different oscillator waveforms but in the filter section of the synth. Z-plane synthesis was first implemented in the wittily-named Morpheus (the name has nothing to do with the figure from Greek mythology but refers to 'morphing', a term which means to change from one thing to another), and its use of interpolation between two filter shapes is very reminiscent of how the Fairlight 'merged' from one waveform to another. Extremely complex filter shapes are created through the use of up to eight filter components, each of which is comparable to the traditional low-pass, band-pass or high-pass filters or parametric equaliser bands (see Figure 2 for one configuration example). The resulting sculpting of the sound is far more precise and subtle than in any previous type of synthesis. In addition to the basic function of the filter, starting by removing the high and/or low end, peaks and notches can be placed at will anywhere across the entire audible frequency range. The Z-plane filter is found only in some commercially available products;emu's Morpheus, emu's ultra proteus & emu samplers with the EOS operating system installed, all have the Z-plane filter.

However, not satisfied with being able to tailor the most precise filter responses ever, Z-plane synthesis is then able to interpolate smoothly between two of them. This not only allows the user access to a myriad of additional filter responses, if the filter is held static in any of the transition positions, but as the interpolation can be carried out in real time, radical changes in the filter response can be made in the course of a sound being played back, with the 'Morph' parameter enabling the user to change backwards and forwards at will between the starting and ending filter shapes. With Emu's long-established modulation matrix providing a host of possible controllers for this Morph parameter, these timbral changes can be controlled by anything from velocity, envelopes or wheels, through to custom Function Generators. Whilst this is all similar in concept to controlling the cutoff frequency of a conventional filter using an envelope or LFO, the actual results produced are far more striking to the ear.

Once you've managed to get your head round this, brace yourself, because we still haven't scratched the surface of Z-plane synthesis. In fact, the basic Morph parameter on its own might be thought of as X-axis synthesis. Another parameter, Frequency Tracking, introduces the equivalent of a Y-axis into the equation. This is the closest parameter to the conventional filter cutoff, in that it moves the complex Morph filter up and down the frequency range.

In combination with the Morph parameter, Frequency Tracking gives two-dimensional control over the filter shape. Unlike a conventional filter cutoff, though, the Frequency Tracking parameter cannot be moved in real time, but must be set at Note On (presumably because there has to be some limit on the processing power required). This makes it suitable for hooking to parameters like keyboard tracking and velocity, but unavailable for controlling from aftertouch or envelopes. However, the real-time Morph parameter allows much more radical effects than filter cutoff movement, and thus more than makes up for the fact that you have to fix the Frequency Tracking at Note On.

The observant amongst you will have spotted that I've still not mentioned the 'Z' axis that completes Z-plane synthesis: a third parameter, Transform 2. The function of this varies from Z-plane filter to Z-plane filter, but one example of what it can do is increase the size of the peaks and notches in the filter contour (similar to the individual peak which is increased in a conventional filter by the resonance control).

The Transform 2 parameter, like the Frequency Tracking parameter, is also fixed at Note On, but this actually gives you more flexibility than most traditional filtering, where there is rarely any automatic control of resonance at all and you have to make do with the fixed setting whatever the note played or its velocity. Not all of the 197 filter types in the original Morpheus feature this third Transform 2 parameter, but about half do (so technically there are around 100 Z-plane filter configurations in Morpheus). All the filter configurations are individually described in the manual, complete with comments and suggestions for specific uses, so there's no danger that you'll be left to yourself to try and work out where to use them (although I find that random assignment leads to some of the most exciting results.

You really can make some major timbral alterations to your source waveform, changing it almost beyond recognition. In fact, the sheer range of filter types and the way they can be altered in performance, the technology used to create and modify the filter contours on an individual basis, and the resulting sonic variations in the sound, make Z-plane synthesis a real precursor to  physical modelling (also known as virtual synthesis or acoustic modelling). This uses shedloads of DSP power to modify source waveforms in the same way that the physical modifiers of the real instrument (shape and size of resonating case or vibration column, for example) affect the input sound. Many of the Z-plane filters available in the emu Morpheus synth are described in these terms -- for example, F097 ("designed to make possible a set of piano presets that sound like they were recorded with the sustain pedal down"), or F105 ("designed to emulate some of the resonant characteristics of an acoustic guitar body"). As such, the Morpheus probably represents the missing link between instruments which just use DSP to add some effects sparkle, and
those which create the entire sound through raw DSP, as in physical modelling instruments such as the Yamaha VL series or the Korg Prophecy or Z1.


Physical Modelling (PM or PHM)

This form of synthesis simulates the physical properties of natural instruments, or any sound, by using complex mathematical equations in real-time. This requires huge processing power. You are not actually creating the sound but, you are creating and controlling the process that produces that sound. Waveguides and algorithms come into this process heavily.

All the other methods of synthesis I have described have parameters involved with each type of synthesis that don't change depending on the type of sound you're trying to get. There's a filter attack parameter on an S&S (Sample & Synthesis) synth whether you're trying to produce a piano, strings, or a synth bass. There are harmonic levels on an additive synth whether you're making a brass sound or a harpsichord. The wave sequencing parameters on a Wavestation are always there, whether you use them or not!

The same is not true of a current multi-model synthesizer such as the Korg Prophecy/Z1 or a Yamaha VL-series synth. Look for the same parameters you used to make a flute sound when using the Bowed String model and you'll be out of luck: the parameters change depending on the model you have selected. This is why the time it takes to change patches on a modelling synth is often perceptible, because so many different parameters need to be broken down and re-configured. Quite often when you change models, you are quite literally changing synths. This can make physical modelling as a method of synthesis quite challenging to define, which is why the DSP effects analogy is quite useful. We expect the parameters to change when we switch a multi-effects unit from reverb to flanging or distortion; the multi-modelling synth is the same -- only more so. Think of changing from a tenor sax to a soprano as akin to changing from a hall reverb to a room; changing to a violin is like selecting a phaser effect instead. The only real difference is one of scale: the amount of DSP power is greater in a modelling synth by at least a power of 10 or two.


The physical model attempts to work out what happens in the real world, and then uses mathematical calculations to attempt to recreate this in software. The degree of realism achieved depends on two things: how
accurate is the analysis or 'model' of what happens in the real world, and how closely the DSP algorithms used reproduce this analysis. If a  sound designer misunders how the sound is produced in the real world, then -- however good his DSP code is -- it's unlikely that he'll make a very realistic-sounding reverb or plucked string instrument (although he may create some great new effect or sound which can't be produced in the real world). On the other hand, however great the understanding of the processes involved, if the sound designer doesn't have the necessary DSP horsepower to hand he may get into the right ballpark, but he isn't going to fool anyone that this is a real hall or a real guitar. Physical modelling approach to synthesis is an all out attempt to recreate that which is naturally heard through a mathematical algorithmic process.



Digital Waveguide Synthesis

Digital waveguide synthesis is the synthesis of audio using a digital waveguide. Digital waveguides are efficient computational models for physical media through which acoustic waves propagate. For this reason, digital waveguides constitute a major part of most modern physical modeling synthesizers.

A lossless digital waveguide realizes the discrete form of d'Alembert's solution of the one-dimensional wave equation as the superposition of a right-going wave and a left-going wave,

y(m,n) = y + (m − n) + y − (m + n)

where y + is the right-going wave and y − is the left-going wave. It can be seen from this representation that sampling the function y at a given point m and time n merely involves summing two delayed copies of its traveling waves. These traveling waves will reflect at boundaries such as the suspension points of vibrating strings or the open or closed ends of tubes. Hence the waves travel along closed loops.

Digital waveguide models therefore comprise digital delay lines to represent the geometry of the waveguide which are closed by recursion, digital filters to represent the frequency-dependent losses and mild dispersion in the medium, and often non-linear elements. Losses incurred throughout the medium are generally consolidated so that they can be calculated once at the termination of a delay line, rather than many times throughout.

Waveguides such as acoustic tubes may be thought of as three-dimensional, but because their lengths are often much greater than their cross-sectional area, it is reasonable and computationally efficient to model them as one dimensional waveguides. Membranes, as used in drums, may be modeled using two-dimensional waveguide meshes, and reverberation in three dimensional spaces may be modeled using three-dimensional meshes. Vibraphone bars, bells, singing bowls and other sounding solids (also called idiophones) can be modeled by a related method called banded waveguides where multiple band-limited digital waveguide elements are used to model the strongly dispersive behavior of waves in solids.

The term "Digital Waveguide Synthesis" was coined by Julius O. Smith III who helped develop it and eventually filed the patent. It represents an extension of the Karplus-Strong algorithm. Stanford University owns the patent rights for digital waveguide synthesis and signed an agreement in 1989 to develop the technology with Yamaha.

An extension to DWG synthesis of strings made by Smith is commuted synthesis, wherein the excitation to the digital waveguide contains both string excitation and the body response of the instrument. This is possible because the digital waveguide is linear and makes it unnecessary to model the instrument body's resonances after synthesizing the string output, greatly reducing the number of computations required for a convincing resynthesis.



Waveset Distortion


Generally refers to any process which irreversibly alters the wavesets in a sound, waveset inversion, omission, reversal, shaking, shuffling, substitution, averaging and harmonic distortion. Specifically used to refer to power-distortion, raising each sample of the sound to a power (e.g. squaring, cubing, taking the square root.). Simply put, to exponentially increase a single parameter of a sound, thus distorting one of it's features. A simple process that can be accomplished in a number of ways through both analog and digital means, but the process does yeild an entirely new wave form.


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