Fundamentals of Music
Technology
Juan P. Bello
•  Office: 409, 4th floor, 383 LaFayette Street (ext. 85736)
•  Office Hours: Wednesdays 2-5pm
•  Email: jpbello@nyu.edu
•  URL: http://homepages.nyu.edu/~jb2843/
•  Course-info: Tuesdays 4.55-6.35pm (Studio F)
E85.1801: Fundamentals of Music Technology
Course materials at:
http://www.nyu.edu/classes/bello/FMT.html
Lectures tentative schedule
•
•
•
•
•
•
•
•
•
•
•
•
Weeks 1-2 What is sound?
Weeks 2-3 Hearing
Week 4 Microphones
Week 5 Loudspeakers
Weeks 6-8 Mixers
Week 7 Mid-term exam (30%) – October 20
Weeks 8-9 Cabling and Interconnection
Weeks 10-11 Basics of digital systems
Week 12 Communication\MIDI
Week 13 MIDI code
Week 14 MIDI sound control/synthesis
Week 15 Final exam (30%) – December 15
Demonstrations schedule
•  Teaching Assistant: Langdon Crawford (demonstrations,
assignments + teaching in week 8)
•  Thursdays 4.55-6.10pm, Studio F
•
•
•
•
•
•
Week
Week
Week
Week
Week
Week
3: Wave propagation
5: Transducers
6: Mixers and signal flow
10: Building your own studio
12: Sampling and Quantization
14: MIDI and Synthesis
•  8 Assignments (weeks 1, 3, 5, 6, 8, 10, 11 and 12). Due a week
later.
Evaluation and Resources
•
•
•
•
Mid-term exam = 30%
Final exam = 30%
Assignments = 40%
Attendance and class participation
•
All relevant information is (or will be published) on the class website Please read it carefully and keep checking for updates.
Assignments will be announced with sufficient time and published online
Penalties will apply to delays
•
•
•
Book: Francis Rumsey and Tim McCormick (2002). “Sound and Recording:
An Introduction”, Focal Press.
•
•
Further reading will be recommended as the course progresses.
USE THE OFFICE HOURS (Wednesdays 2-5pm)
What is sound?
Juan P Bello
Sound
•  Sound is produced by a vibrating source that causes the matter
around it to move.
•  No sound is produced in a vacuum - Matter (air, water, earth)
must be present!
Air particles
•  The vibration of the source causes it to push/pull its neighboring
particles, which in turn push/pull its neighbors and so on.
•  Pushes increase the air pressure (compression) while pulls
decrease the air pressure (rarefaction)
•  The vibration sends a wave of pressure fluctuation through the air
Waves
•  Waves can be longitudinal (the particles move in the same
direction of the wave) or transversal (the particles’ movement is
perpendicular to the wave’s direction)
Longitudinal
Transversal
Sound waves (1)
•  In sound wave motion air particles do not travel, they oscillate
around a point in space.
•  The rate of this oscillation is known as the frequency of the sound
wave and is denoted in cycles per second (cps) or hertz (Hz).
•  The amount of compression/rarefaction of the air is the amplitude
of the sound wave.
•  The distance between consecutive peaks of compression or
rarefaction is the wavelength of the sound wave (denoted by λ)
•  A fast traveling wave results on a greater λ
Sound waves (2)
•  If the frequency of oscillation is fixed, then the sound wave is
periodic (with period t, and frequency 1/t)
•  The simplest periodic wave is a sinusoid
t
Compressions
Rarefactions
•  Because of the inverse relationship, the higher the frequency, the
shorter the time between oscillations.
•  Humans frequency range: 20-20kHz (20,000 Hz)
Sound waves (3)
•  The speed of a wave (c), depends on the density and elasticity of
the medium (and thus in its temperature).
•  In air, at 70 °F (21 °C), c = 769 mph (344 meters/s). This is slow
when compared to most solids.
•  If the speed c and the oscillation frequency f are known, the
wavelength can be calculated as: λ = c/f
wavelength
Frequency and wavelength
•  There is then an inverse relationship between wavelength and
frequency
•  E.g. for f = 20 Hz, λ = 56.4 ft, and for f = 20kHz, λ = 0.67 in
•  Frequency range is behind size differences in, e.g. musical
instruments and loudspeakers
Different types of sounds
•  Sinusoids are only one possible type of sound
•  They correspond to the simplest mode of vibration, producing
energy at only one frequency
•  They are often called pure tones and are extremely rare in real life
(e.g. a recorder produces an almost pure tone)
•  However most sounds are not so simple resulting in complex
waveforms
•  The more complex, the noisier the sound is - when the pattern of
vibration is random, the sound is said to be noise
•  Demo: ftm_demo1
Periodicity (1)
•  If a waveform pattern is repeated at
regular intervals, then the sound wave is
periodic and has definitive pitch
•  We can use Fourier Analysis to break down
the waveform into a series of frequency
components known as harmonics
•  These components can be seen in an
amplitude vs frequency graph of the sound
known as frequency spectrum
•  Consider a sinusoid: it has a simple
pattern that repeats at its oscillating - or
fundamental - frequency (f0)
Jean Baptiste Joseph
Fourier (1768-1830):
French mathematician
and physicist
Fourier Analysis
f0
Periodicity (2)
•  For more complex patterns, more complex configurations of
spectral lines will appear (see ftm_demo1)
•  The underlying assumption in Fourier Analysis is that any sound
can be made out of the combination of (many) simple sinusoids
with different amplitudes
+
•  Note that a sound wave is periodic (and pitched) no matter how
complex the repeated pattern is
•  Pitch perception occurs as long as the repetition rate is within the
human audio frequency range (see ftm_demo2)
Spectral Analysis (1)
•  What are these complex spectral configurations and what
waveforms do they produce?
•  Harmonics (or Overtones or Partials) are frequency components
that occur at integer multiples of the fundamental frequency
•  Their amplitude variations determine the timbre of the sound
Amplitude
Amplitude
T = 1/f
time
Frequency
f
Amplitude
Amplitude
T = 1/f
time
f
2f 3f 4f 5f 6f
Fundamental Harmonics
frequency Overtones
(first harmonic) Partials
Frequency
Spectral Analysis (2)
•  Example: Square wave - only odd harmonics (even are missing).
Amplitude of the nth harmonic = 1/n
Harmonic modes
•  Most sources are capable of vibrating in several harmonic modes
at the same time
•  Examples: a guitar string, this room
1st harmonic
2nd harmonic
nodes
antinodes
3rd harmonic
4th harmonic
Complex sounds
•  Most pitched instrumental sounds also present overtones which
are not integer multiples of the fundamental.
•  These are known as inharmonic partials
Harmonic
Inharmonic
Non-periodic sounds
time
Amplitude
Amplitude
•  Non-periodic sounds have no pitch and tend to have continuous
spectra, e.g. a short pulse (narrow in time, wide in frequency)
Frequency
Amplitude
Amplitude
•  The most complex sound is white noise (completely random)
time
Frequency
Phase (1)
•  In phase: cycles coincide exactly (sum duplicates amplitude)
Amplitude
1
2
-1
1
+
-1
0
-2
time
•  Out of phase: half cycles are exactly opposed (sum cancels them)
Amplitude
1
2
-1
1
+
-1
0
-2
time
Phase (2)
•  There is a range of partial additions and cancellations in between
those extremes (ftm_demo3)
•  What causes phase difference?
delay
t1
Amplitude
t2
time
0
t1
t2
•  The phase difference depends on the delay time and the wave’s
frequency
Phase (3)
•  Phase is commonly measured in terms of degrees of the
oscillating cycle of a periodic wave
90°
180°
0°
0°
90° 180°
270°
0°
90° 180° 270°
270°
•  The frequency defines the number of cycles per second, thus the
delay x frequency x 360° returns the (unwrapped) angular phase
difference
Sound power and intensity
•  A source (e.g. bell) vibrates when a force (e.g. striking hammer)
is applied to it.
•  The force applied and the resulting movement characterize the
work performed by the source (W = F x Δs)
•  Power (P = W/t) is the rate at which work is performed and is
measured in watts.
•  An omnidirectional sound source produces a 3-D longitudinal
wave. The resulting wavefront is defined by the surface of a
sphere (S = 4πr2), where r is the distance from the source.
Wavefront
r
Sound source
The original power is distributed
on the surface of the wavefront.
As r increases, the power per
unit area (intensity) decreases:
I = P/S
Intensity and SPL
•  The effect of sound power on its surroundings can be measured in
sound pressure levels (SPL) - much as temperature in a room
relates to the energy produced by a heater.
•  Both intensity (Watts/area) and sound pressure (Newtons/area)
are usually represented using decibels (dB)
•  dB are based on the logarithm of the ratio between two powers,
thus describing how they compare (dB = 10log10(P1/P2)).
•  This can be applied to other measures (intensity, SPL, voltage), as
long as their relationship to power is taken into account.
•  In the case of intensity and SPL, the denominator of the ratio is a
reference value, defined according to the quietest sound
perceivable by the average person.
•  Thus by convention, 0 dB corresponds to SPL = 2x10-5 N/m2 or I
= 10-12 watt/m2
Acoustic fields
•  The previous model of sound energy distribution only applies to
omnidirectional sources and free fields (acoustic areas with no
reflections)
•  Free fields are extremely rare as there are always reflections
(from the ground and nearby surfaces)
•  In rooms there is both direct and reflected sound
•  Where reflected sound energy is predominant the field is said to
be reverberant (or diffuse)
•  The near field is close to the source, where direct energy is much
higher than reflected
•  The distance from the source at which reverberant energy
becomes predominant depends on the room’s volume and
absorption.
Useful References
•
•
Francis Rumsey and Tim McCormick (2002). “Sound and Recording: An Introduction”, Focal
Press.
–  Chapter 1: What is sound?
Dave Benson (2002). “Mathematics and Music”. http://www.math.uga.edu/~djb/index.html
–  Chapter 1: Waves and harmonics