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FM Synthesis I, global and simple

acoustic vibrations

In the traditional acoustic musical instruments, sound is generated by 
means of a vibrating mechanism. Overall we can distinguish two 

diferent ways.

Firstly resonators, such as strings, stretched sheets and rods, which 
spontaneously get into a damped oscillation when we hit them with an 

energy boost. The hammer striking a piano string is one example.

On the other hand, we fnd complex composite systems as in string 
and wind instruments. Under certain conditions these systems become 

to vibrate, to oscillate. Each musician knows from experience that it 
spends time and efort to realize these conditions by doing and 

discovering.

oscillator

In the electronic musical instruments, a periodic vibration is generated 

by means of an electronic circuit. That vibration is fnally converted by 
the speaker back into an acoustic signal. Such an electronic circuit that 

serves as the basic tone generation is called an oscillator.

operator

In the frst FM synthesizers from Yamaha, as with the well-known 

DX7

sound generation was completely formed in the digital domain in what 
was called in Yamaha speak, the operator.

FM Synthesis I, global and simple, © Ernst Bonis 1985/1993/2013

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Summary of Contents for FM Synthesis

Page 1: ...tions these systems become to vibrate to oscillate Each musician knows from experience that it spends time and efort to realize these conditions by doing and discovering oscillator In the electronic musical instruments a periodic vibration is generated by means of an electronic circuit That vibration is fnally converted by the speaker back into an acoustic signal Such an electronic circuit that se...

Page 2: ...ch operator acts as a carrier wave which is connected via an amplifer to the speaker This carrier frequency is controlled by the modulator wave This cyclic variation of the carrier frequency takes place at audio rate It is so fast that we experience this a new hearing sensation a change of timbre 1 1 many In this simple FM model the two operators generate pure tones sine waves without overtones Ac...

Page 3: ...her frequencies are called overtones or harmonics One such pair of operators with sinusoidal waveforms the carrier and the modulator is in the electronic and computer music language is called simple FM timbre the frequency ratio between carrier and modulator determines which overtones can be obtained In musical terms the pitch interval between the modulator and carrier controls which harmonics or ...

Page 4: ...ore operators that serve as a modulator These diferent ways of linking together can be seen as an imprint on the DX7 synthesizer These are numbered confgurations of rectangular blocks The bottom blocks represent the carriers the modulators are indicated by the blocks above There is always a connection represented by a line From top to bottom between the blocks standing one above the other This sym...

Page 5: ...ruments for each operator we may choose a sine wave and 15 additional complex waveforms The previously mentioned 4 operator instruments TX81Z etc provide a sine wave operator and 7 complex waveforms feedback In the diagrams of algorithms we see always one operator from wich it s output is connected back to it s modulation input see for instance alg 32 operator 6 This is called self modulation or f...

Page 6: ...started when pressing and end when you release a key indicates a possible variation in time We thus obtain a better understanding of how the amplitude of the modulator and carrier oscillation changes with time and thus directly connected how the resulting sound itself develops over time Such a variable in time called an envelope and is formed by the so called envelope generator EG volume and timbr...

Page 7: ...d instruments literally breath gives expressive life to the sound breathing and muscle actions The player actions on an acoustic instrument can be considered as a low frequency modulating control of the carrier oscillation the tone the sound of the instrument external fne structure modulation The subtle low frequency tone variations obtained in this way are of utmost importance for the vitality an...

Page 8: ...foot swell pedals In almost all Yamaha FM sythesizers we fnd an additional very powerful way to infuence the tone forming the use of a breath controller This instrument records the breath pressure of the player By means of varying the breath the modulator and carrier output levels can be afected This provides opportunities for a very expressive way of playing Also there is the possibility to conne...

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