Fletcher
Munson Theory
This page is
important if you want to understand why the patches you've created
sound different to you when played at loud, normal or bedroom sound
level.
This all has to do
with the theory Fletcher Munson has givin us. Apart from that your
sound will be influenced by roomsize, playing level, reflections,
materials in the room etc... However it's good to understand why there's
a difference and general tips can be givin on how to adjust this.
You will see lots of
references to equal loudness curves or equal loudness contours. These
are based on the work of Fletcher and Munson at Bell labs in the 30s,
or perhaps refinements made more recently by Robinson and Dadson.
These were made by asking people to judge when pure tones of two different
frequencies were the same loudness. This is a very difficult judgement
to make, and the curves are the average results from many subjects,
so they should be considered general indicators rather than a prescription
as to what a single individual might hear.
What in the
world is a Fletcher-Munson equal loudness curve, and why should I
care?
Humans don't hear all frequencies of sound at the same level. That
is, our ears are more sensitive to some frequencies and less sensitive
to other frequencies. Additionally, the sensitivity changes with the
sound pressure level (SPL). Take a look at the chart below. You'll
notice it's marked horizontally with a scale denoting the frequency
of sound. Vertically it's marked in SPL.
On the chart are a
number of curved lines, each with a number (loudness level) marked.
First, notice the lowest solid line marked with a loudness level of
10 phons. (The loudness level in phons is a subjective sensation--this
is the level at which we perceive the sound to be.)
From about 500Hz to
roughly 1,500Hz the line is flat on the 10dB scale. This means that
for us to perceive the sound at a loudness level (LL) of 10 phons,
(the overall curved line), frequencies from 500Hz to 1,500 Hz must
be 10dB. Next, look further into the higher frequencies to 5,000Hz.
Notice the line dips
here--this indicates that we perceive 5,000Hz to be 10 phons when
the source is actually only 6dB. To perceive 10,000Hz at the same
level (10 phons), it would need to be about 20dB. From this we can
clearly see the ear is more sensitive in the 2,000Hz to 5,000Hz range,
yet not nearly as sensitive in the 6,000Hz and up range.
Look down at the lower frequencies to 100Hz. For us to perceive 100Hz
as loud as we do 1,000Hz (when the source is at 10dB), the 100Hz source
must be at 30dB–that's 20dB higher than the 1,000Hz signal! Looking
even farther down, a 20Hz signal must be nearly 75dB (65dB higher
than the 1,000Hz signal)! We can clearly see our ears are not very
sensitive to the lower frequencies, even more so at lower SPL levels.
Why is this? A simply physical explanation is that resonance in the
ear and ear canal amplifies frequencies typically between 2,500Hz
and 4,000Hz. Why can’t we hear every frequency at the same level?
One reason could be because most intelligibility is found in the 2,000Hz
to 5,000Hz range. Our ears are designed to be more sensitive here.
While our ears are capable of hearing the lower frequencies, our bodies
feel them more than we actually hear them.
This is the reason
why many people who are nearly or completely deaf can still enjoy
music--they can still feel the low frequency content in their bodies.
(This assumes the level is sufficient that they can feel it. Often
such people will actually sit on a speaker so they're in direct contact
with it and the vibrations of the speaker are conducted right into
their body.)
Notice how as the overall loudness level increases that the low frequency
curved lines flatten out. This is because at higher SPL's we are more
sensitive to those lower frequencies. Also notice that as the SPL
increases, our sensitivity decreases to the frequencies above 6,000Hz.
This explains why soft music seems to sound less rich and full than
louder music--the louder the music is, the more we perceive the lower
frequencies, thus it sounds more full and rich. This is why many stereo
systems have a loudness switch--when you're listening to the stereo
at low volumes, you activate this switch that boosts the low and some
of the high frequencies of the sound.
Typically people become uncomfortable with levels above 100dB. You
will notice 100dB is needed to perceive a loudness level of 100 phons
at 1,000Hz--only 90dB is required to give a percieved loudness level
of 100 phons at 4,000Hz. Again, about 104dB is required to produce
a percieved loudness level of 100 phons at 100Hz.
Why is all of this so important?
Simply put, it helps
us understand why many subwoofers are required to produce a loudness
level equal to those attained at higher frequencies. It shows us how
much more sensitive our ears are to the higher frequencies which can
become very piercing if too loud.
Many times it helps to use an equalizer to cut some of the frequencies
around 2,000Hz to 5,000Hz a little if music is being played loudly.
This action keeps the sound crisp sounding, but not distorted and
piercing at higher SPL levels.
A decibel meter (or SPL meter) measures the amplitude of sound. Inexpensive
meters react to all frequencies equally, resulting in what's called
"flat response". More expensive SPL meters allow measurements
to be taken with both "C-weighting" and "A-weighting".
A-weighting is more
close to resembling the frequency response of our ears (the low end
of the measurement device is rolled off, downward to simulate our
lesser sensitivity to the low frequencies).
C-weighting takes more
of the low frequencies into account, even though our ears don't hear
them at the same level.
Thus, it's best to
make measurements with an A-weighting setting to know how our ears
are responding to the sound. At the same time, it's interesting to
flip the switch to look at the C-weighted response as well--During
heavy rock music or a Fourth-of-July fireworks celebration, the difference
between the A-weighted measurements and C-weighted can be 10dB or
more!
Fig 2. Equal loudness contours or Fletcher-Munson
curves.
The numbers on each curve identify it in terms of phons, a unit of
loudness that compensates for frequency effects. To find the phon
value of an intensity measurement, find the db reading and frequency
on the graph, then see which curve it lands on.
The interesting aspects
of these curves are that it is difficult to hear low frequency of
soft sounds, and that the ear is extra sensitive between 1 and 6 kilohertz.
Phon Explained
A unit used to describe
the loudness levelof a given sound or noise. The system is based on
Equal Loudness Countours, where 0 phons at 1,000 Hz is set at 0 decibels,
the threshold of hearing at that frequency (see graph). The hearing
threshold of 0 phons then lies along the lowest equal loudness contour.
If the intensity level at 1,000 Hz is raised to 20 dB, the second
curve is followed.
It will be noted, therefore,
that the relationship between the decibel and phon scale at 1,000
Hz is exact, but because of the way the ear discriminates against
or in favour of sounds of varying frequencies, the phon curve varies
considerably. For instance, a very low 30 Hz rumble at 110 decibels
is perceived as being only 90 phons (see graph);
Compare: Sound level,
Volume.
It is important to
realize that the phon is used only to describe sounds that are equally
loud. It cannot be used to measure relationships between sounds of
differing loudness. For instance, 40 phons is not twice as loud as
20 phons. In fact, an increase of 10 phons is sufficient to produce
the impression that a sine tone is twice as loud.
For the purpose of
measuring sounds of different loudness, the Sone scale of subjective
loudness was invented. One sone is arbitrarily taken to be 40 phons
at any frequency, i.e. at any point along the 40 phon curve on the
graph. Two sones are twice as loud, e.g. 40 + 10 phons = 50 phons.
Four sones are twice as loud again, e.g. 50 + 10 phons = 60 phons.
The relationship between phons and sones is shown in the chart, and
is expressed by the equation:
Phon = 40 + 10 log2
(Sone)
Equal loudness contours for pure tones and normal threshold of hearing
for persons aged 18-25 years, using free-field hearing (from ISO recommendation
R226).
If you wanna
know more on this matter read this
A combination of table and formula is given
in
D.W. Robinson and R.S. Dadson,
'A re-determination of the equal-loudness relations for pure tones',
British Journal of Applied Physics, 7, 1956, 166-181
These data are generally regarded as being more
accurate than those of
Fletcher and Munson. Of course both sources apply only to pure tones
in
otherwise silent free-field conditions, with a frontal plane wave
etc
etc.
