Frequency Modulation (FM) Synthesis in Music: A Detailed Report

This report provides a detailed exploration of Frequency Modulation (FM) synthesis, a crucial technique in the audio and music industry. It begins with an introduction to FM synthesis and its encoding of information in a carrier wave, differentiating it from amplitude modulation. The report delves into various synthesis methods, including subtractive, additive (and resynthesis), physical modeling, wavetable, vector, LA (Linear Arithmetic), and phase distortion synthesis. It discusses the spectrum generated by FM synthesis, emphasizing the basics of each synthesis form. Furthermore, the report explores music synthesis techniques and the evolution of musical instruments, such as the Reactable, Audio Cubes, Kaossilator, Eigenharp, Xth-Sense, and AlphaSphere. The report also touches upon additive synthesis, square waves, and their applications in sound creation and manipulation. It highlights the increasing power and decreasing cost of electronic sound generation, including the use of MIDI and Open Sound Control languages, and the role of musical controllers and synthesizers. Overall, the report offers a comprehensive overview of FM synthesis and its diverse applications in the field of music production and electronic music.

FREQUENCY MODULATION
CCS

Abstract
In the audio and music industry, FM synthesis is a form of audio synthesis where the
resonance of a simple waveform (such as a square, triangle, or sawtooth) is altered
by assuaging its frequency to a modulator frequency that is also present in the audio range.

1.0 Introduction.
1In telecommunications and the processing of signal, frequency modulation (FM) is the
encoding of information in a carrier wave by changing the direct frequency of the wave. This
alteration with amplitude modulation, in which the amplitude of the carrier wave varies while
the frequency remains constant.
2As Chowning puts it in his original paper on FM synthesis: Music and mathematics are both
deeply expressive languages whose mysteries are made open through pattern and serendipity.
The composer John Chowning, whose work is the focus of this article, says that music is a
symbolic art. A painter gets the sensory feedback immediately unlike the musicians, who are
already inclined with writing things on paper and hearing them later. So they have to deal
immensely with symbols, things that are some distance away from their actual place at the
sensory level.3 This may be the reason why music was the first of the arts to make so much
artistic use of technology. There is more to the connection, however, as the nature of sound
and human hearing lend themselves to mathematical investigation. We'll consider how our ears
can perceive sound and how mathematics gives a powerful way to comprehend the sound and
then create and manipulate it.
1 Communication Systems" 4th Ed (Simon Haykin, 2001) p. 81
2 David B. Rutledge, The Electronics of Radio, 1st edn (Cambridge University Press., 1999), p. 310. ISBN 978-0-521-
64645-1.
3 H. P. Westman, ed., Reference Data for Radio Engineers (Fifth ed.). (Howard W. Sams & Co., 1970) p. 21-11.

The spectrum generated by FM synthesis with one modulator is given as follows:
For modulation signal , the carrier signal is
FM and additive synthesis
Many of those who use synthesizers within the today's technological world aren't well versed in
the basics of specific forms of synthesis. With the benefit of laptop-established synthesis, any
synthesis program can also be opened and fiddled around with by way of hearing until
something “cool” comes out. To interrupt the mold in the use of synthesizers within the today's
tune world, you have to be proficient or lucky. This is exactly why it’s more foremost now than
ever before to realize the basics of exceptional synthesis ways.
Subtractive Synthesis
This is a very simple signal chain of an oscillator (sound supply) running via a filter curve (EQ
curve) which is then sent to an amplifier to acquire staging and ADSR management. This
process could be very effortless to achieve in each analog and digital realms and can be utilized
to create countless (almost certainly endless) instruments, effects, and sounds.
The most important precept in the back of Subtractive Synthesis is that any harmonic
personality can also be developed via an oscillator or the blend of multiple oscillators. Then,
using strolling these oscillators using quite a lot of filters, and controlling the envelope
response, the harmonics gift within the oscillators tones can also be whittled into harmonic
buildings that reflect those of genuine devices.

The analog subtractive synthesizer was designed in the beginning for this purpose–as an
alternative to hiring musicians to play on recordings, however, it rapidly morphed into its own
instrument, creating various sounds in no way earlier than made by way of any acoustic
instrument.
Additive Synthesis (and Resynthesis)
Additive Synthesis is making an attempt to reap the identical outcomes as Subtractive
Synthesis, but techniques the process from an optimistic philosophy, as a substitute than
carving. Instead than supplying a wall of harmonics and carving out the harmonic constitution
desired, in additive synthesis, the multiple sine waves of varying levels and frequencies are
collectively combined to build the harmonic constitution desired. Readily put, rather than
starting with the whole lot you want and throwing away what you don’t want, you start with
nothing and construct harmonic buildings from scratch.
The very related procedure of Resynthesis is particularly linked to Additive Synthesis. In
essence, Resynthesis entails inspecting the harmonic constitution of a sampled sound and
looking to recreate that structure. Additive Synthesis is virtually Resynthesis, aside from the
truth that Resynthesis is the activity of a targeted present sound, now, not a common
instrument tone. Given this hyperlink, additive synthesis is quite more often than not used in
Resynthesis processes.

Aspect (physical) Modeling Synthesis
Bodily Modeling Synthesis is mathematical and makes use of set algorithms to define the
harmonic and acoustic characteristics of the sound that is being generated. This approach is
used for developing real-sounding instruments, as it is programmed to make characteristic
distinctions between the few elements of instrument that are being created. For example, the
materials that make up the instrument, the dimensions, the stiffness of a membrane, the
quantity of a reverberant object (with a view to reproducing its resonant frequency), and many
different great important points are factored into the algorithm that generates every sound’s
one of a kind features using quite a lot of varieties of synthesis (stylish upon company).
Wavetable Synthesis
Wavetable Synthesis employs using a desk with quite a lot of switchable frequencies performed
in specific orders (wavetables). As a secret is pressed, the sound strikes in order through the
wavetable, no longer spontaneously altering the waveform, but easily altering its shape into the
quite a lot of waves in the desk.
This process produces sounds that can evolve fairly rapidly and smoothly. The method was once
intended to create digital sounding noises, so it isn't used for instrument replication very

probably, but is a potent technique to create pads or harsh-sounding tones like bells or digital
sounds.
Vector Synthesis
Vector Synthesis is just about exactly the identical as Wavetable Synthesis, most effective it
employs a two-dimensional grid, through which wavetables can also be made even smoother
and works with sequences as good as wavetables.
LA (Linear Arithmetic) Synthesis
LA Synthesis used to be created via Roland as an attempt to make use of Wavetable Synthesis
to create actual-sounding instrument patches. They carried out this by reducing the waves on
the wavetables in 1/2 and mixing the problematic attack (first 1/2) wave patterns with easy
liberate (2d 1/2) wave patterns, as a consequence emulating more of an acoustic atmosphere.
Section Distortion Synthesis
Segment distortion synthesizers are subtractive synthesizers with one difference – they appoint
the waveform flexibility of wavetable synthesis within the oscillator. So, instead of having set

waves to decide upon from at the oscillator, you're given full manage over the shape of the
waveform between all set shapes – in different words, variable waveform control.
Additive synthesis and analysis
4It is possible to break down the frequency components of a recorded sound producing a "sum
of sinusoids" demonstration. This illustration can be re-synthesized using additive synthesis.
One method of breaking down a sound into a time varying sinusoidal partials is short-time
Fourier transform (STFT)-based Analysis.
By altering the sum of sinusoids demonstration, timbral alterations can be made before
resynthesis. For example, a harmonic sound could be simplified to sound inharmonic, and vice
versa. Sound hybridization or "morphing" has been implemented by additive resynthesis.
Music synthesis techniques
The increasing power and the inversely decreasing cost of electronics generating sound
(especially of the personal computer), in conjunction with the regulation of the MIDI and Open
Sound Control musical performance description languages, and has smoothed the separation of
musical instruments into music controllers and synthesizers.
By far the most common musical controller is the musical keyboard. Other controllers include
the radio drum, Akai's EWI, the guitar-likeSynthAxe, the Buchla Thunder, the BodySynth,
the Roland Octapad, the Continuum Fingerboard, various isomorphic keyboards which include
the I-CubeX, and Kaossilator Pro, and kits like the Thummer.
4 B. P. Lathi, Communication Systems (John Wiley and Sons 2003) 1968ISBN 0-471-51832-8, p, 214–217

The Reactables
The Reactable is a translucent table, round with a backlit communicating display. By engaging
and influencing blocks called tangibles on the surface of the table while communicating with
the visual display via gestures of the finger, a virtual modular synthesizer is operated, creating
music or sound effects.
Percussa Audio Cubes
AudioCubes are those series of autonomous wireless cubes powered by an internal
rechargeable battery and computer system. They have got internal RGB lighting and are
proficient at detecting each other's location, orientation, and distance. The cubes are also
capable of detecting distances to the user's hands and fingers. Through interaction with the
cubes, a variety of music and sound software can be obtained. AudioCubes can be applied in
various niches like sound design, music production, DJing and live performance.
Kaossilator
The Kaossilator and its advanced version—the Kaossilator Pro, are compact musical instruments
where the position of a finger on the touchpad controls dual note-characteristics; usually, the
pitch of the note is changed with a motion from left-right and the tonal property, filter or other
parameter changes with a motion from up-down. The touchpad can be set to diverse musical
tones and keys. The instrument can record an iterating loop of modifiable length, set to any
tempo, and new loops of sound can be coated on top of existing ones. This phenomenon lends
itself to electronic dance music but is more limited for a well-ordered series of notes, as the pad
is bland on a regular Kaossilator.

Eigenharp
The Eigenharp is a large musical instrument similar to a bassoon, which can be operated
through touch-sensitive buttons, a mouthpiece, and a drum sequencer. The sound processing is
carried out on a separate computer.
The Xth-Sense
The Xth-Sense is a wearable musical instrument that uses muscle sounds from the human body
(also known as mechanomyogram) to make sound effects and music. As a performer moves,
the body produces muscle sounds that are caught by a chip microphone worn on the leg or
arm. The muscle sounds are then live-sampled using a library of modular audio effects and a
dedicated software program. The performer regulates the live-sampling parameters by
weighing the force, speed and articulation of the movement.
AlphaSphere
The AlphaSphere is a spherical musical instrument that consists of forty-eight tactile pads which
respond to touch as well as pressure. Custom software lets the pads be indefinitely
programmed individually or by groups regarding pressure parameters, function, and note
among many other settings. The principal concept of the AlphaSphere is to upsurge the level of
expression at the disposal of electronic musicians, by allowing for the playing style of most
musical instruments.
The additive kind of synthesis builds up sounds from sums of sinusoids with given frequencies
and amplitudes that may vary over time. One advantage of the additive synthesis is that any
sound can be represented perfectly. By carrying out a Fourier analysis of short windows of the

sound produced, you get a sequence of time frames of the band at that moment. From this
representation, you would usually pick the strongest spectral points and synthesize the sound
from a sum of its sinusoids. This technique is referred to as the tracking phase vocoder. A
popular extension is Spectral Modelling Synthesis, which incorporates noise.
i. Square wave:
A square wave is naturally a non-sinusoidal periodic waveform (which can be represented as an
infinite sum of the individual sinusoidal waves), in which the amplitude alternates at a
steady frequency rate between a fixed minimum and the maximum values, with the same
duration expended at both the minimum and maximum levels. The transition from minimum to
maximum is instant for an ideal square wave; this is not attainable in most physical systems.
Square waves are usually encountered in electronics and signal processing. Its stochastic
matching part is a two-state route. A similar but not symmetrical wave, with random durations
at the minimum and maximum levels, is referred to as a pulse wave (of which the square wave
is one special case).
In mathematics, the square wave has many definitions, which are comparable:
It can be defined as simply the sign function of a periodic function, an example being a sinusoid:

ii. Sawtooth Wave:
The sawtooth wave is a non-sinusoidal waveform. It is so named based on its similarity to the
cutting teeth of a saw.
The conventional representation is that a sawtooth wave rises upward and then drops sharply.
However, in a "reverse (or in an inverse case) sawtooth wave", the wave slopes downward and
then rises sharply. It can also be considered the exciting case of a lopsided triangle wave.