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This is a series of articles titled the basis of synthesis. Read on:

The basics of synthesis

1) The harmonic series

Pitched musical instruments such as stringed, wind and keyboard  instruments, tuned to a particular tuning system, e.g. concert pitch create sound waves that resonate and decay in a mathematical relationship to the note first played.  It is the interaction with the surrounding air that creates audible sound waves that travel away from the instrument. The typical spacing of these resonances, results in frequencies that are usually integer multiples, or harmonics, of the lowest frequency. These multiples form the harmonic series.

But, enough of that boring stuff!  Put simply, a note played on say, a guitar will vibrate in such a way that it creates audible sound waves at a higher frequency until they fade to silence.  Still confused? Hit the middle C on a piano and as well as hearing the note you played - the C, you will also hear a note half a pitch above it and a quarter above it and a sixteenth above it and so on.  The note you play is called the fundamental as shown on the picture below, that illustrates all the other harmonics above that note.

A feature of this harmonic series is that each note above the fundamental will sound quieter until there is just silence and therefore the fundamental will appear to be the loudest note.  Also, we can perceive the pitch of the fundamental even if it is missing, but beware, the brain can also be fooled into perceiving the wrong fundamental pitch, but let's not go there yet.

Each of the harmonics are directly related to each other and sound harmonious, but depending on the structure of the instrument, particular harmonics may be emphasised, adding musical colour. For example, plucked instruments will decay faster than bowed instruments where the bow sustains the vibration.

Partials are really thought of as additional harmonics that occur between principle harmonics and the term Inharmonicity is the extent to which a partial deviates from the closest ideal harmonic, these deviations are measured in cents or one-hundredths for each partial. Wow, that's confusing isn't it, well lets just think of these partials as additional musical colour that distinguishes one musical instrument from another, and why people pay big money for a Martin acoustic guitar and don't just content themselves with a cheap Chinese import.

Some pitched instruments, particularly percussion instruments like a vibraphone, have non-harmonic partials, that make a rich sound to the ear.

Finally, overtones refer to any partial except the lowest and does not mean that the instrument is either harmonic nor inharmonicity in sound, it simply is a term that excludes the fundamental. Therefore the first overtone is the second partial.

If that is confusing, look at the following chart that shows the fundamental and harmonics of various instruments including the human voice.  This illustrates the huge amount of additional musical information the brain hears or body feels when a particular instrument is played. Note that the male voice has a potentially huge range and con be extended further by basso profundo and whistling, that can be found on YouTube, if you're curious.

Music Ranges https://www.independentrecording.net/irn/resources/freqchart/main_display.htm 

Electronic instruments, such as synthesizers, can play a pure frequency with no overtones.  At the same time, they can be used to create frequencies and sound characteristics to simulate other instruments, or combine various instrumental textures and random noises together to create a unique sound.

2) The harmonic content of a sine, triangle, square and sawtooth waveform

The graph below, illustrates the four periodic sound waves mentioned above. They are called periodic because they repeat the same waveform shape again and again.  These are the main wave forms used in synthesis.

A waveform consists of many different sine waves, and the slowest is the frequency of the note, with the slowest sine wave being the fundamental harmonic. Put another way, a basic sine wave has not harmonics and consists only of the fundamental.

 

A sine wave

 

All sounds are made up of sine waves and the harmonic content of a waveform, is a feature of frequencies of all the sine waves that are present within it  and how loud they are.

A triangle wave

 

A triangle wave, as the name suggests looks triangular and the wave falls slowly then rises slowly. Odd harmonics only, are present in the triangle wave and the higher harmonics are of low amplitude.

 

A square wave

 

The square wave only has odd harmonics with the first sine wave, the third, the fifth and so on. A square wave is similar to a ramp wave, (see below) but with every even numbered harmonic missing. This gives it sound hollow by comparison with the saw tooth or ramp wave shown below.

 

A sawtooth wave

 

So named because it looks like the teeth of a saw. There are actually two sorts of sawtooth wave that can be created: a ramp wave or rising sawtooth, that rises slowly then falls quickly, and this is the most common of the two, or a sawtooth wave that falls slowly. The rising sawtooth wave includes all harmonics, including the fundamental harmonic, and then a second sine wave, half as loud but twice as fast. The third one is a third as loud, but three times the speed. The ramp waveform has a rich timbre with plenty of harmonics.

 

The waveforms above, are the periodic waveforms most often produced by the oscillators of synthesisers, however it is possible to synthesize virtually any shape of waveform when experimenting with synthesizers.  It is claimed that the human ear gets bored with harmonic as they become too predictable. Using lots of with variations such as quasi-periodic waveforms,

can overcome this boredom, however the instability of analogue circuitry is making a comeback.  long live analogue I say, but on the other hand, digital synthesizers are so user friendly, it is hard to resist them.

 

More info can be found on the link below, which also gives you the chance to hear the sounds these wave forms produce.

https://www.thedawstudio.com/Tips/Soundwaves.html

 

The ES2 synthesizer featured in Apple Logic Pro 9

        

 

The ES2 is laid out as follows:

 

The arrowed knobs below give a choice of three oscillator wave forms to use with a Logic channel strip and the triangle allows adjustment of how much of each waveform to use as a building block for the sound effect.

The Glide button at the bottom allows the transition of the pitch to be short or long and the analog button above it allows for different levels of deleting to take place when used with the Unison button also arrowed.

The Octaves can be tuned for each oscillator, from -32 to +32, also, the oscillator can produce more complex sounds by choosing the word sine from the oscillator button and dragging it up and down. This is the Digi facility, see below. This can also be controlled whilst recording, to give varied sound effects. This is called wave sequencing.

    

Various filters can be applied to the oscillator and there is a bank on the left and right side that can be switched on or off and blended in full, or say part left filters and part right filters to give a wide variety of sound options. The filters consist of high and low pass, band pass, peak, Band reject, together with various Db cuts including a fat button, these are all similar to Equalisation or (EQ).  There is also is FM (frequency modulation) and resonance buttons to turn up resonance at the cutoff point and a drive button (bottom left that can be used to over drive the filters and cause distortion. This is different to the distortion effect in the amplifier section. Hmm confusing isn't it?  Best way is to try out all the settings and check out the sounds they make and see what gives you the sound you like. Also, you can switch the filter off and see what it would sound without it.

 

A handy tip is to use an EQ plug in and use the analyse button to review the sound wave visually.

 

Now to the distortion effects, a larges range are available in this section, time based effects such as such as Flanger and phaser, together with various controls for intensity speed and tone.  The amount of distortion can be varied together with the intensity and volume of it.

Finally, polyphonic or layered notes can be selected or mono single notes.  Up to 32 voices can be used and in unison.

If you need more effects, echo and reverb can be added

 

And now for something different

 

Task list 1

1) Create a monophonic bass sound that uses a unison mode set to 16 voices, your patch should contain 3 sawtooth oscillators slightly detuned and at equal levels.

 

2) Create a monophonic lead sound based around a single triangle wave that makes use of glide/portamento between notes. Add reverb and delay via inserts.

 

3) Create a monophonic bass sound based around a single sawtooth oscillator that is thickened by the addition of the sub oscillator. Within the synthesiser engine add to it distortion and flanging. 

 

Task list 2

1) Create a pad sound using many sawtooths in unison. Modulate a high pass filter so that the  sound gradually thins out of time and then gradually fills out again back to its full thickness.

2) Take the patch you made in part 2 of task one and add to it pitch based vibrato

3) Take the patch you made in part 3 and add to it a tremolo effect that is tempo sync'd to an 1/8th note.

 

Task list 3 

1) create a pad where you can use the mod wheel on your keyboard to control the amount of vibrato.

2) create a pad with a bandpass filter and lowpass filter where the patch alternates between the two filters over time.

 

Envelopes and ADSR

 

This week I'm going to talk about envelopes and what Attack, Decay, Sustain, and Release are in Logic's ES2.

 

First let's go back to basics and remind ourselves what synthesizers such as the ES2 actually do. They are called subtractive because they remove something from the signal, with the most reduced signal being the sine wave that has had all the harmonics removed. The following diagram shows the flow of sound through a subtractive synthesizer such as the ES2. It consists of various signal generating and processing modules—and these are coupled with a number of modulation and control modules.

            The Oscillators Generate the basic signal, by way of a waveform that is rich in harmonics.  The ES2 has three oscillators.  These were covered in an earlier blog.





            The Filter section is used to change the basic signal by filtering out bits of the frequency spectrum. ES2 has two filters that can be applied discretely to the oscillator signals.  The Amplifier section is used to control the level of the signal over time and the amplifier uses a module known as an envelope.

           

            An Envelope is a time signal and there are 3 available in ES2: Env 1, 2 and 3.  The envelope allows the signal to be broken down into several elements that will provide level control for the beginning, middle, and end portions of the signal. The Envelope controls amplitude, the rise and fall of the filter cutoff frequency and modulation sources.  The Envelope has been likened to a “remote control” for a given parameter.

With the ES2, we are attempting to copy the Attack, Delay, Release and Sustain that would be characteristic of a real musical instrument, such as a snare drum that has a fast peak level with no sustain and the sound decaying rapidly, compared with say that of a violin where the sound slowly builds up to a peak as the bow is drawn across the strings and is sustained for a while as the bow pressure on the string reduces, then stops when the bow is lifted.  A piano keyboard could have a fast attack and decay and sustain, but holding down the key and using a pedal will prolong the sustain.  As you can see, these three sounds have very different characteristics over time, and whilst you may not want your sound to mimic a snare drum or grand piano, it is necessary to have a concept of the sound you would like to produce and how to create its qualities using these ES2 settings.

 

To summarise, the attack, decay, sustain and release (ADSR) are as follows:

 

Attack: Is the time taken from zero amplitude to 100%, full amplitude. Low attack will make the sound plucky, whilst a long attack may sound like a glide, handy though for a gradually rising and falling sound effect.

Decay: Is the time it takes to fall from 100% amplitude to the sustain level.

Sustain: Is the steady amplitude level produced when a key is held down.

Release: Is the time taken for the sound to decay from the sustain level to zero amplitude when the key is released.

A sustain level of zero would be similar to a piano played without holding the key down and without a pedal;  percussive with no continuous steady level, even when a key is held. With pianos and plucked string instruments, high notes decay quicker than low notes.

 

ENV 1 can be used with Attack time and Decay time parameter.  Clicking on the D will change the parameter from Decay to Release.

ENV 1 can be used to simulate an early analog polysynths similar to Moog Polymoog, Yamaha SK20, and Korg Poly-800. The Poly mode will give a fast attack and decay whereas mono or retrigger give a slower attack and decay.

ENV 2 and ENV 3 are velocity sensitive, so no point in setting via to Velo in the modulation routing; just leave via off. ENV 3's task is to define the dynamic stage of each note.

 

The bottom half of the ES2 features LFOs and Envelopes.

 

LFO is an abbreviation for low frequency oscillator. As the name suggests, this is an oscillator, but different to the three oscillators in the top section of the ES2:

            The LFO generates signals below the audio frequency range, between 0.1 and 20 Hz, but sometimes as high as 50 Hz. as it cannot be heard, it serves simply as a modulation source for periodic, cyclic modulation effects and does not form part of the actual audio signal.

      

            LFO 1 is polyphonic and can work on multiple voices and is key-synced, so each time a key is played, the modulation starts from zero.

 

            The LFO 2 is monophonic, so the modulation is identical for all voices and when a chord is played on the keyboard, the pitch of all voices in the chord will rise and fall synchronously.

          

            To further explain the LFO 1, The EG slider arrowed above is used to control the time taken for the LFO modulation to fade in and out.  The Rate slider to the right, controls the frequency in hertz of the LFO 1 modulation. The value is displayed in Hertz (Hz) beneath the slider.

The Wave buttons arrowed are used to select the desired waveform for LFO 1.

            LFO 2, The Rate slider arrowed is the parameter that specifies the frequency in hertz or speed or speed e.g 1/64th of the LFO 2 modulation.

LFO 2 rhythmic modulation effects will retain perfect synchronicity, even when the project tempo changes.

 

Working with Modulation

            The following areas have been arrowed above as they play an important role in modeling different sounds and effects:

 

            The Modulation Router does what it says, routes things you want to effect via the object you want to effect it with. The router links modulation sources like the envelope, to the modulation targets such as the oscillators and filters. There are 10 modulation routing columns.

            The Modulation sources include the LFOs and envelopes.

            The Vector Envelope is a sophisticated, loop-capable, multipoint envelope that can control the Planar Pad and Triangle (i.e. the oscillator mix options). The Vector Envelope shapes the sound and can be viewed by clicking the Vector Envelope button to the right of the router.

Planar Pad: The Planar Pad is a controller that enables the simultaneous manipulation of two, freely assignable, parameters and is available as viasources as well, enabling you to control modulation intensities with them. It can be controlled with the Vector Envelope.

Modulation Target can be connected to any Modulation Source, rather like a studio patch bay.

Modulation Intensity is set with a slider and affects the extent to which the target is influenced by the source. Once a value other than off has been selected for a Via, the Intensity slider which is divided into two halves, becomes available, with the lower half defining the minimum modulation intensity and the upper half defining the maximum modulation intensity. The area between the two slider arrows is the modulation range of the via controller.  The O in the centre of the vertical router is the zero intensity point. Finally, the via effect can be inverted by clicking on the invert area.

Ten modulation routings are available for source, via and target and these can operate simultaneously. Any of the ten modulation routings can be used and it is possible to select the same target, sources and controllers in multiple modulation routings.

A common sound setting is to use the modulation wheel on a keyboard to control the modulation intensity.  Setting the router as below with target = pitch 123, Via = ModWhl, Source = LFO1

            The Modulation intensity slider position can be played with to get the desired amount of modulation and the LFO 1 settings to modulate the frequency or pitch of the three oscillators (Pitch 123).  This gives a vibrato effect, the depth of which can be further controlled with the mod wheel on the keyboard.

 

The Vector Envelope

The Vector Envelope allows for real-time control of the square icon movements in the Triangle and the Planar Pad. Whilst the Vector Envelope shares the same space occupied by the modulation router, it can be viewed by clicking the Vector Envelope button to the right of the router.

 

 

The Vector Envelope button when switched on, allows the user to specify the target to be controlled: the Planar Pad and/or the Triangle.  If switched off, control of these parameters can still be carried out manually.

If Mix is selected, the Triangle, is controlled but not the Planar Pad.

If XYis selected, the Planar Pad is controlled but not the Triangle.

If Mix+XY is selected, both the Planar Pad and the Triangle are controlled.

 

 

A maximum of 16 points can be displayed on the time axis  and each point can control both the square icon positions of the Triangle and the Planar Pad. Shift/click between two existing points to add additional points.

There are a minimum of three points, with Point 1 as the start point, point 2 as the Sustain point, and point three as the end point.

Any point can be declared the Sustain point by Clicking in the turquoise strip above the desired point.

Any point can be declared the Loop point by Clicking in the turquoise strip below the desired point.

The following Loop modes can be selected: Off, Forward, Backward, and Alternate.

 

            In Off mode, the Envelope runs from start to end.

            In Forward, the Envelope runs from the start to the Sustain point, then repeat that in a forward direction.

            In Backward, the Envelope runs from the start of  the Sustain point, then repeat that section in a backward direction.

            In Alternate, the Envelope runs from the start to the Sustain point, switches to the Loop point, then back again to the Sustain point, alternating between backward and forward directions.

 

The cycle speed of the loop speed can be set and also synchronized with the project tempo.

SAMPLE 1

1) Go to the oscillator section and set Osc 1 to a sawtooth, Osc to a square wave and Osc 3 to a sine wave.

2) Go to the mixer and balance all three oscillators so that they are approximately equal in volume.

3) Route the oscillators through just Filter 2 so that Filter 1 isn't heard and set the resonance to 12 o'clock.

4) In the modulation matrix route LFO1 to change the pitch of all three oscillators. Set the amount of modulation to a tasteful amount of vibrato. Set the LFO rate to 5.5Hz

5) Using the amplifier envelope set it so that each note fades up to full volume over 500 ms and once you release the note it fades out over 1 sec.

6) Route Envelope 2 to the Cutoff of Filter 2  and set it so that once a note is play the filter cutoff goes from zero to its full amount in approximately 700ms.

 

SAMPLE 2

1) choose the usual init patch

2) turn off all the cells in the modulation matrix

3) Go to the oscillator section set Osc 1 to - saw and the coarse pitch to +24, set Osc 2 to triangle and the coarse pitch to +7, set Osc 3 to sine and leave the pitch at its default value of 0

4) In the Vector set it to the MIX setting leaving the XY unselected.

5) In the Vector make sure there are four points 

6) Set point one so that you hear just Osc 1, point 2 so that you hear just Osc 2, point 3 so that you hear just Osc 3 and point four to a mix of all three.

7) set the Vector loop mode to forward and the Loop Rate to a 1/4 note.

8) Lastly add chorus and a small amount of the ES2's soft distortion effect.

SAMPLE 3

1) choose the usual init patch

2) turn off all the cells in the modulation matrix

3) go to the oscillator 1 and choose a square wave

4) turn the Unison mode on, make the patch Monophonic and then set the

voices box to 6

5) Go to the Filter section and set it so that only Filter one is heard.

6) Set Filter One to a bandpass filter.

7) Modulate the filter cutoff of Filter 1 with envelope 2 so that it is initially at its maximum value and then over a period of 1 second the filter cutoff drops to approx. 50%

8) Go to the Glide control and set it to 200ms

And now something different

Starting off by loading the Analogue Saw Init patch and then clear each cell in the modulation matrix so that each Target, Via and Source section is empty.

Now create the following patch

 

1) Make the patch monophonic.

2) Turn the Unison function on and set the ES2 so that it layers 16 voices in unison. 

3) Set all 3 of the ES2's oscillators to sawtooth waveforms, ensure that you do not use the oscillator sync waveforms.

4) Make sure that all three oscillators are mixed at equal volume.

5) Detune the oscillators so that the patch is thickened but the patch does not stray from concert pitch.

6) Set the ES2's sub oscillator labeled Sine Level to 12 o'clock to thicken the patch and strengthen the fundamental pitch.

7) Add a small amount of subtle distortion from the output stage of the synth.

8) Pass the oscillators through only a high pass filter with the resonance set to the mid point. Make sure you set the filter section correctly so that only the output of the high pass filter is heard and that no other filtering takes place.

9)  Modulate the Cutoff of the high pass filter so that when a note is held down on your keyboard the filter cutoff of the high pass filter rises from a minimum value to a maximum value over 200ms and falls back to the original minimum value after 2400ms. This should all happen whilst a note is being held down.

10) Add a small amount of pitch vibrato using an LFO set to a triangle wave. The vibrato should be a tasteful amount similar to that of the amount a violinist would add. Ensure that the vibrato is on permanently and cannot be varied by other control sources.

11) Set the patch so that the volume of each note increases to maximum amplitude over approximately 100ms and then once the note is released if fades out to nothing over approximately 980ms.

12) Lastly add a small amount of the ES2's inbuilt phaser effect to further thicken the sound.

 

Within an envelope the parameters attack, decay, sustain and release are defined as:

 

Attack: Is the time taken from zero amplitude to 100%, full amplitude. Low attack will make the sound plucky, whilst a long attack may sound like a glide, handy though for a gradually rising and falling sound effect.

Decay: Is the time it takes to fall from 100% amplitude to the sustain level.

Sustain: Is the steady amplitude level produced when a key is held down.

Release: Is the time taken for the sound to decay from the sustain level to zero amplitude when the key is released.

 

With the ES2, we are attempting to copy the Attack, Delay, Release and Sustain that would be characteristic of a real musical instrument, such as a snare drum that has a fast peak level with no sustain and the sound decaying rapidly, compared with say that of a violin where the sound slowly builds up to a peak as the bow is drawn across the strings and is sustained for a while as the bow pressure on the string reduces, then stops when the bow is lifted.  A piano keyboard could have a fast attack and decay and sustain, but holding down the key and using a pedal will prolong the sustain.  As you can see, these three sounds have very different characteristics over time, and whilst you may not want your sound to mimic a snare drum or grand piano, it is necessary to have a concept of the sound you would like to produce and how to create its qualities using these ES2 settings.

 

A sustain level of zero would be similar to a piano played without holding the key down and without a pedal;  percussive with no continuous steady level, even when a key is held. With pianos and plucked string instruments, high notes decay quicker than low notes.

 

The most significant difference between envelope 3 and envelope 2 in the ES2 is that ENV 3 is hard wired to the amplitude, whereas the ENV2 is assignable to anything. Both are velocity sensitive.

The differences between Filter 1 and Filter 2 in the ES2 are that Filter 1 can operate as a lowpass, highpass, bandpass, band reject, or peak filter.

Filter 2 is a lowpass filter that offers variable slopes (measured in dB/octave).

Filter 2 offers three different slopes:  12 dB, 18 dB, and 24 dB per octave. The steeper the slope, the more severely the level of signals below the cutoff frequency are affected in each octave.

The Fat setting also provides 24 dB per octave of rejection but features a built-in compensation circuit that retains the “bottom end” of the sound. The standard 24 dB setting tends to make lower end sounds somewhat “thin.”

 

Most filters do not completely suppress the portion of the signal that falls outside the frequency range defined by the Cutoff parameter. The slope, or curve, chosen for Filter 2 expresses the amount of rejection below the cutoff frequency in decibels per octave.