Audiophilia: Know your ear's limits news

• Intermod Tests:
  
  
  
  • 30kHz tone + 33kHz tone (24 bit / 96kHz)
    [5 second WAV]
    [30 second FLAC]
  
  
  • 26kHz - 48kHz warbling tones (24 bit / 96kHz)
    [10 second WAV]
  
  
  • 26kHz - 96kHz warbling tones (24 bit / 192kHz)
    [10 second WAV]
  
  
  • Song clip shifted up by 24kHz (24 bit / 96kHz WAV)
    [10 second WAV]

    
    (original version of above clip) (16 bit / 44.1kHz WAV)

Assuming your system is actually capable of full 96kHz
playback [6], the above files should be
completely silent with no audible noises, tones, whistles,
clicks, or other sounds. If you hear anything, your system
has a nonlinearity causing audible intermodulation of the
ultrasonics. Be careful when increasing volume; running into
digital or analog clipping, even soft clipping, will suddenly
cause loud intermodulation tones.

In summary, it's not certain that intermodulation from
ultrasonics will be audible on a given system. The added
distortion could be insignificant or it could be noticable.
Either way, ultrasonic content is never a benefit, and on
plenty of systems it will audibly hurt fidelity. On the
systems it doesn't hurt, the cost and complexity of handling
ultrasonics could have been saved, or spent on improved audible range
performance instead.

16 bit vs 24 bit

OK, so 192kHz music files make no sense. Covered, done. What about
16 bit vs. 24 bit audio?

It's true that 16 bit linear PCM audio does not quite cover
the entire theoretical dynamic range of the human ear in
ideal conditions. Also, there are (and always will be)
reasons to use more than 16 bits in recording and
production.

None of that is relevant to playback; here 24 bit audio is
as useless as 192kHz sampling. The good news is that at
least 24 bit depth doesn't harm fidelity. It just doesn't
help, and also wastes space.

Revisiting your ears

We've discussed the frequency range of the ear, but what
about the dynamic range from the softest possible sound to
the loudest possible sound?

One way to define absolute dynamic range would be to look
again at the absolute threshold of hearing and threshold of
pain curves. The distance between the highest point on the
threshold of pain curve and the lowest point on the absolute
threshold of hearing curve is about 140 decibels for a
young, healthy listener. That wouldn't last long though;
+130dB is loud enough to damage hearing permanently in
seconds to minutes. For reference purposes, a jackhammer at
one meter is only about 100-110dB.

The absolute threshold of hearing increases with age and
hearing loss. Interestingly, the threshold of pain decreases
with age rather than increasing. The hair cells of the cochlea
themselves posses only a fraction of the ear's 140dB range;
musculature in the ear continuously adjust the amount of sound
reaching the cochlea by shifting the ossicles, much as the iris
regulates the amount of light entering the eye
[9]. This mechanism stiffens with age,
limiting the ear's dynamic range and reducing the effectiveness
of its protection mechanisms [10].

Environmental noise

Few people realize how quiet the absolute threshold of
hearing really is.

The very quietest perceptible sound is about -8dbSPL
[11]. Using an A-weighted scale, the
hum from a 100 watt incandescent light bulb one meter away
is about 10dBSPL, so about 18dB louder. The bulb will be
much louder on a dimmer.

20dBSPL (or 28dB louder than the quietest audible sound) is
often quoted for an empty broadcasting/recording studio or
sound isolation room. This is the baseline for an
exceptionally quiet environment, and one reason you've
probably never noticed hearing a light bulb.

The dynamic range of 16 bits

16 bit linear PCM has a dynamic range of 96dB according to
the most common definition, which calculates dynamic range
as (6*bits)dB. Many believe that 16 bit audio cannot
represent arbitrary sounds quieter than -96dB. This is
incorrect.

I have linked to two 16 bit audio files here; one contains
a 1kHz tone at 0 dB (where 0dB is the loudest possible tone)
and the other a 1kHz tone at -105dB.

• Sample 1: 1kHz tone at 0 dB (16 bit / 48kHz WAV)


• Sample 2: 1kHz tone at -105 dB (16 bit / 48kHz WAV)

How is it possible to encode this signal, encode it with no
distortion, and encode it well above the noise floor, when
its peak amplitude is one third of a bit?

Part of this puzzle is solved by proper dither, which
renders quantization noise independent of the input signal.
By implication, this means that dithered quantization
introduces no distortion, just uncorrelated noise. That in
turn implies that we can encode signals of arbitrary depth,
even those with peak amplitudes much smaller than one bit
[12]. However, dither doesn't change
the fact that once a signal sinks below the noise floor, it
should effectively disappear. How is the -105dB tone
still clearly audible above a -96dB noise floor?

The answer: Our -96dB noise floor figure is effectively
wrong; we're using an inappropriate definition of dynamic
range. (6*bits)dB gives us the RMS noise of the entire
broadband signal, but each hair cell in the ear is sensitive
to only a narrow fraction of the total bandwidth. As each
hair cell hears only a fraction of the total noise floor
energy, the noise floor at that hair cell will be much lower
than the broadband figure of -96dB.

Thus, 16 bit audio can go considerably deeper than 96dB.
With use of shaped dither, which moves quantization noise
energy into frequencies where it's harder to hear, the
effective dynamic range of 16 bit audio reaches 120dB in
practice [13], more than fifteen times
deeper than the 96dB claim.

120dB is greater than the difference between a mosquito
somewhere in the same room and a jackhammer a foot
away.... or the difference between a deserted 'soundproof'
room and a sound loud enough to cause hearing damage in
seconds.

16 bits is enough to store all we can hear, and will
be enough forever.

Signal-to-noise ratio

It's worth mentioning briefly that the ear's S/N ratio is
smaller than its absolute dynamic range. Within a given
critical band, typical S/N is estimated to only be about 30dB.
Relative S/N does not reach the full dynamic range even when
considering widely spaced bands. This assures that linear
16 bit PCM offers higher resolution than is actually
required.

It is also worth mentioning that increasing the bit depth
of the audio representation from 16 to 24 bits does not
increase the perceptible resolution or 'fineness' of the
audio. It only increases the dynamic range, the range
between the softest possible and the loudest possible sound,
by lowering the noise floor. However, a 16-bit noise floor is
already below what we can hear.

When does 24 bit matter?

Professionals use 24 bit samples in recording and
production [14] for headroom, noise
floor, and convenience reasons.

16 bits is enough to span the real hearing range with room
to spare. It does not span the entire possible signal range
of audio equipment. The primary reason to use 24 bits when
recording is to prevent mistakes; rather than being careful
to center 16 bit recording-- risking clipping if you guess
too high and adding noise if you guess too low-- 24 bits
allows an operator to set an approximate level and not worry
too much about it. Missing the optimal gain setting by a
few bits has no consequences, and effects that dynamically
compress the recorded range have a deep floor to work
with.

An engineer also requires more than 16 bits during mixing
and mastering. Modern work flows may involve literally
thousands of effects and operations. The quantization noise
and noise floor of a 16 bit sample may be undetectable
during playback, but multiplying that noise by a few
thousand times eventually becomes noticeable. 24 bits keeps
the accumulated noise at a very low level. Once the music
is ready to distribute, there's no reason to keep more than
16 bits.

Listening tests

Understanding is where theory and reality meet. A matter is
settled only when the two agree.

Empirical evidence from listening tests backs up the
assertion that 44.1kHz/16 bit provides highest-possible
fidelity playback. There are numerous controlled tests
confirming this, but I'll plug a recent paper,
Audibility
of a CD-Standard A/D/A Loop Inserted into High-Resolution
Audio Playback, done by local folks here at the
Boston Audio
Society.

Unfortunately, downloading the full paper requires an AES
membership. However it's been discussed widely in articles
and on forums, with the authors joining in. Here's a few
links:

• The Emperor's New Sampling Rate


• Hydrogen Audio forum discussion thread


• Supplemental information page at the Boston Audio Society, including the equipment and sample lists

This paper presented listeners with a choice between
high-rate DVD-A/SACD content, chosen by high-definition
audio advocates to show off high-def's superiority, and that
same content resampled on the spot down to 16-bit / 44.1kHz
Compact Disc rate. The listeners were challenged to
identify any difference whatsoever between the two using an
ABX methodology. BAS conducted the test using high-end
professional equipment in noise-isolated studio listening
environments with both amateur and trained professional
listeners.

In 554 trials, listeners chose correctly 49.8% of the
time. In other words, they were guessing. Not one listener
throughout the entire test was able to identify which was
16/44.1 and which was high rate [15],
and the 16-bit signal wasn't even dithered!

Another recent study [16] investigated
the possibility that ultrasonics were audible, as earlier studies had
suggested. The test was constructed to maximize the possibility of
detection by placing the intermodulation products where they'd be most
audible. It found that the ultrasonic tones were not audible... but
the intermodulation distortion products introduced by the loudspeakers
could be.

This paper inspired a great deal of further research, much
of it with mixed results. Some of the ambiguity is
explained by finding that ultrasonics can induce more
intermodulation distortion than expected in power amplifiers
as well. For
example, David
Griesinger reproduced this experiment
[17] and found that his loudspeaker
setup did not introduce audible intermodulation distortion
from ultrasonics, but his stereo amplifier did.

Caveat Lector

It's important not to cherry-pick individual papers or
'expert commentary' out of context or from self-interested
sources. Not all papers agree completely with these results
(and a few disagree in large part), so it's easy to find
minority opinions that appear to vindicate every imaginable
conclusion.
Regardless, the papers and links above are
representative of the vast weight and breadth of the
experimental record. No peer-reviewed paper that has
stood the test of time disagrees substantially with these
results. Controversy exists only within the consumer and
enthusiast audiophile communities.

If anything, the number of ambiguous, inconclusive, and
outright invalid experimental results available through
Google highlights how tricky it is to construct an accurate,
objective test. The differences researchers look for are
minute; they require rigorous statistical analysis to spot
subconscious choices that escape test subjects' awareness.
That we're likely trying to 'prove' something that doesn't
exist makes it even more difficult. Proving a null
hypothesis is akin to proving the halting problem; you
can't. You can only collect evidence that lends overwhelming
weight.

Despite this, papers that confirm the null hypothesis are
especially strong evidence; confirming inaudibility is far
more experimentally difficult than disputing
it. Undiscovered mistakes in test methodologies and
equipment nearly always produce false positive results (by
accidentally introducing audible differences) rather than
false negatives.

If professional researchers have such a hard time properly
testing for minute, isolated audible differences, you can
imagine how hard it is for amateurs.

How to [inadvertently] screw up a listening comparison

The number one comment I heard from believers in super high
rate audio was [paraphrasing]: "I've listened to high
rate audio myself and the improvement is obvious. Are you
seriously telling me not to trust my own ears?"

Of course you can trust your ears. It's brains that are
gullible. I don't mean that flippantly; as human beings,
we're all wired that way.

Confirmation bias, the placebo effect, and double-blind

In any test where a listener can tell two choices apart via
any means apart from listening, the results will usually be
what the listener expected in advance; this is
called
confirmation bias and it's similar to
the placebo
effect. It means people 'hear' differences because of
subconscious cues and preferences that have nothing to do
with the audio, like preferring a more expensive (or more
attractive) amplifier over a cheaper option.

The human brain is designed to notice patterns and
differences, even where none exist. This tendency can't just
be turned off when a person is asked to make objective
decisions; it's completely subconscious. Nor can a bias be
defeated by mere skepticism. Controlled experimentation
shows that awareness of confirmation bias can increase
rather than decreases the effect! A test that doesn't
carefully eliminate confirmation bias is worthless
[18].

In single-blind testing, a listener knows nothing
in advance about the test choices, and receives no feedback
during the course of the test. Single-blind testing is
better than casual comparison, but it does not eliminate
the
experimenter's bias. The test administrator can easily
inadvertently influence the test or transfer his own
subconscious bias to the listener through inadvertent cues
(eg, "Are you sure that's what you're hearing?", body
language indicating a 'wrong' choice, hesitating
inadvertently, etc). An experimenter's bias has also been
experimentally proven to influence a test subject's
results.

Double-blind listening tests are the gold
standard; in these tests neither the test administrator nor
the testee have any knowledge of the test contents or
ongoing results. Computer-run ABX tests are the most famous
example, and there are freely available tools for performing
ABX tests on your own computer[19].
ABX is considered a minimum bar for a listening test to be
meaningful; reputable audio forums such
as Hydrogen
Audio
often do
not even allow discussion of listening results unless they
meet this minimum objectivity requirement
[20].

I personally don't do any quality comparison tests during
development, no matter how casual, without an ABX
tool. Science is science, no slacking.

Loudness tricks

The human ear can consciously discriminate amplitude
differences of about 1dB, and experiments show subconscious
awareness of amplitude differences under .2dB. Humans
almost universally consider louder audio to sound better,
and .2dB is enough to establish this preference. Any
comparison that fails to carefully amplitude-match the
choices will see the louder choice preferred, even if the
amplitude difference is too small to consciously notice.
Stereo salemen have known this trick for a long time.

The professional testing standard is to match sources to
within .1dB or better. This often requires use of an
oscilloscope or signal analyzer. Guessing by turning the
knobs until two sources sound about the same is not good
enough.

Clipping

Clipping is another easy mistake, sometimes obvious only in
retrospect. Even a few clipped samples or their aftereffects
are easy to hear compared to an unclipped signal.

The danger of clipping is especially pernicious in tests
that create, resample, or otherwise manipulate digital signals
on the fly. Suppose we want to compare the fidelity of 48kHz
sampling to a 192kHz source sample. A typical way is to
downsample from 192kHz to 48kHz, upsample it back to 192kHz,
and then compare it to the original 192kHz sample in an ABX
test [21]. This arrangement allows us
to eliminate any possibility of equipment variation or sample
switching influencing the results; we can use the same DAC to
play both samples and switch between without any hardware mode
changes.

Unfortunately, most samples are mastered to use the full
digital range. Naive resampling can and often will clip
occasionally. It is necessary to either monitor for clipping
(and discard clipped audio) or avoid clipping via some other
means such as attenuation.

Different media, different master

I've run across a few articles and blog posts that declare
the virtues of 24 bit or 96/192kHz by comparing a CD to an
audio DVD (or SACD) of the 'same' recording. This comparison
is invalid; the masters are usually different.

Inadvertent cues

Inadvertant audible cues are almost inescapable in older
analog and hybrid digital/analog testing setups. Purely
digital testing setups can completely eliminate the problem in
some forms of testing, but also multiply the potential of
complex software bugs. Such limitations and bugs have a long
history of causing false-positive results in testing
[22].

The
Digital Challenge - More on ABX Testing, tells a
fascinating story of a specific listening test conducted in
1984 to rebut audiophile authorities of the time who asserted
that CDs were inherently inferior to vinyl. The article is
not concerned so much with the results of the test (which I
suspect you'll be able to guess), but the processes and
real-world messiness involved in conducting such a test. For
example, an error on the part of the testers inadvertantly
revealed that an invited audiophile expert had not been making
choices based on audio fidelity, but rather by listening to
the slightly different clicks produced by the ABX switch's
analog relays!

Anecdotes do not replace data, but this story is
instructive of the ease with which undiscovered flaws can bias
listening tests. Some of the audiophile beliefs discussed
within are also highly entertaining; one hopes that some
modern examples are considered just as silly 20 years from
now.