A constant
timbre
In music, timbre ( ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or tone. Timbre distinguishes different types of sound production, such as choir voices and musica ...
at a constant pitch is characterized by a
spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors ...
.
Along a piece of music, the spectrum measured within a narrow time window varies with the melody and the possible effects of instruments.
Therefore, it may seem paradoxical that a constant spectrum can be perceived as a melody rather than a stamp.
The paradox
[A. Chaigne (1988), “Psychoacoustique”, ENST, 114 pages.] is that the ear is not an abstract
spectrograph: it "calculates" the
Fourier transform of the
audio signal in a narrow time window, but the slower variations are seen as temporal evolution and not as pitch.
However, the example of paradoxical melody above contains no infrasound (i.e. pure tone of period slower than the time window).
The second paradox is that when two pitches are very close, they create a
beat
Beat, beats or beating may refer to:
Common uses
* Patrol, or beat, a group of personnel assigned to monitor a specific area
** Beat (police), the territory that a police officer patrols
** Gay beat, an area frequented by gay men
* Battery (c ...
. If the period of this beat is longer than the integration window, it is seen as a sinusoidal variation in the average rating: sin(2π(f+ε)t) + sin(2π(f-ε)t) = sin(2πft)cos(2πεt), where 1/ε is the slow period.
The present spectrum is made of multiple frequencies beating together, resulting in a superimposition of various pitches fading in and out at different moments and pace, thus forming the melody.
MATLAB/Scilab/Octave code
Here is the program used to generate the paradoxical melody:
n=10; length=20; harmon=10; df=0.1;
t=(1:length*44100)/44100;
y=0;
for i = 0:n,
for j = 1:harmon,
y=y+sin(2*3.1415927*(55+i*df)*j*t);
end;
end;
sound(y/(n*harmon),44100);
References
See also
*
Shepard-Risset tone, forever increasing pitch
* : forever accelerating beat
*
Spectral music
Spectral music uses the acoustic properties of sound – or sound spectra – as a basis for composition.
Definition
Defined in technical language, spectral music is an acoustic musical practice where compositional decisions are often inform ...
*
Auditory illusion
*
Musical acoustics Musical acoustics or music acoustics is a multidisciplinary field that combines knowledge from physics, psychophysics, organology (classification of the instruments), physiology, music theory, ethnomusicology, signal processing and instrument build ...
{{Auditory illusions
Perception
Sound
Melody