• WANTED: Happy members who like to discuss audio and other topics related to our interest. Desire to learn and share knowledge of science required. There are many reviews of audio hardware and expert members to help answer your questions. Click here to have your audio equipment measured for free!

100% guaranteed no audible [signal] distortion

mike7877

Addicted to Fun and Learning
Joined
Aug 5, 2021
Messages
744
Likes
158
I'm wondering something, but to pose the question, I first need to set the stage:

Say that your best case hearing threshold is 0dB. Iin case anyone's wondering, 0dB isn't zero energy, it's sound at 1/10th the power of the ultra-quiet level of 10dB.

Now say that you're listening to some music that peaks at 80dB

If THD+n / IMD in the source signal is lower than -80dB, with its peaks at 0dB (the same difference as between your hearing threshold and the loudest reproduced sound),
in the very best case (your hearing is juuust able discern a 0dB pin drop 40m away during the 80dB peak, and all noise and harmonics and intermodulation distortion is at -1dB (sound level, not signal level) or lower,

your ears are now the limit, no question about it: all distortion coming through is below your ability to hear it.

Correct?

Obviously I'm not counting room interactions, wave propagation, and coloration from loudspeaker frequency response variations in this, or anything else. Imagine everything else is perfect for this hypothetical
 
No question your ears are the limit. Various tests have shown that even the best ears only hear maybe to -70dBc. Most aren't that good.
 
No question your ears are the limit. Various tests have shown that even the best ears only hear maybe to -70dBc. Most aren't that good.

Specifically I'm asking if the way I did the math is right with the sound level peaking at 80dB.

Consider cassette tapes as another example - using a quality (Type II/IV) tape that's been properly recorded from a good source and played back on a good deck: they sound as good as CDs (with just 60dB SNR!)
That is, until you turn the volume up high enough. Usually with cassettes it's noise that becomes apparent first, but distortion can be the more obvious problem. Specifically some snares of electronic drum kits can be problematic.
 
Various tests done way back indicate that on music or speech (not test signals), Harmonic distortion under 1% (i.e. -40dB) in imperceptible provided that it has a normal distribution of harmonics, i.e. they decay in amplitude with increasing frequency. That resulted in the generally held view amongst audio engineers that an amplifier with 0.1% distortion at all frequencies and powers under clipping was transparent as far as distortion went, under all circumstances.

I have seen nothing written since that suggests that this criterion is inadequate. That amplifiers today can manage 0.01% (-80dB) routinely, and some even 0.001% (-100dB) doesn't make them audibly any better.

S
 
Various tests done way back indicate that on music or speech (not test signals), Harmonic distortion under 1% (i.e. -40dB) in imperceptible provided that it has a normal distribution of harmonics, i.e. they decay in amplitude with increasing frequency. That resulted in the generally held view amongst audio engineers that an amplifier with 0.1% distortion at all frequencies and powers under clipping was transparent as far as distortion went, under all circumstances.

I have seen nothing written since that suggests that this criterion is inadequate. That amplifiers today can manage 0.01% (-80dB) routinely, and some even 0.001% (-100dB) doesn't make them audibly any better.

S

It should be impossible to hear if it was below 0dB, correct?
I get there's a difference between hearing a harmonic and a completely different sound, but this is supposed to be 100% of the time, in the best of circumstances (trained ear, woke up on the right side of the bed and put best foot forward etc etc)
Or, for the sake of discussion, pretend that it's audible below 0.1%
Follow the logic of my hypothetical in the OP.
It's correct?
 
Specifically I'm asking if the way I did the math is right with the sound level peaking at 80dB.

Consider cassette tapes as another example - using a quality (Type II/IV) tape that's been properly recorded from a good source and played back on a good deck: they sound as good as CDs (with just 60dB SNR!)
That is, until you turn the volume up high enough. Usually with cassettes it's noise that becomes apparent first, but distortion can be the more obvious problem. Specifically some snares of electronic drum kits can be problematic.
It isn't that straightforward. There are masking effects when real music is playing (see sergeauckland post above). Your analysis might work for a single tone, but most people don't listen to those.
 
It isn't that straightforward. There are masking effects when real music is playing (see sergeauckland post above). Your analysis might work for a single tone, but most people don't listen to those.
I get there's a difference between hearing a harmonic and a completely different sound, but this is supposed to be 100% of the time, in the best of circumstances (trained ear, woke up on the right side of the bed and put best foot forward etc etc)
 
I get there's a difference between hearing a harmonic and a completely different sound, but this is supposed to be 100% of the time, in the best of circumstances (trained ear, woke up on the right side of the bed and put best foot forward etc etc)
Higher harmonics stick out, but 2nd and to some extent 3rd can be tougher to hear. It's intermodulation that is probably the worst and most objectionable. It's a big subject, with a lot of studies. I don't think we can cover it all here.
 
I don't want to get into a huge disussion on the audibility of harmonics - that wasn't the purpose of the thread - just to ensure 100% inaudibility (not figure of speech, 100%)

I agree with both of you: harmonic distortion is hard to hear.
There are effects it has though, which aren't immediately apparent.

An important one is listening fatigue.
An amplifier with lower distortion will take longer to induce listening fatigue in the listener. Of course this varies by the song, how many songs, how loud they are, how well they're recorded. Even how well hydrated the listener is has an effect. But the point is: increased distortion increases listening fatigue. Severity isn't easily quantifyable.
 
I don't want to get into a huge disussion on the audibility of harmonics - that wasn't the purpose of the thread - just to ensure 100% inaudibility (not figure of speech, 100%)

I agree with both of you: harmonic distortion is hard to hear.
There are effects it has though, which aren't immediately apparent.

An important one is listening fatigue.
An amplifier with lower distortion will take longer to induce listening fatigue in the listener. Of course this varies by the song, how many songs, how loud they are, how well they're recorded. Even how well hydrated the listener is has an effect. But the point is: increased distortion increases listening fatigue. Severity isn't easily quantifyable.
The elephant in the room is a SET amp, with several percent of even-order distortion. Some people love them, and listen for long periods.
 
Think of my OP not being about distortion, but of another sound.
I guess I answered my own question by going through it.
The way to ensure 100% inaudibility is to follow my guidelines.
Distortion might have to be up by 20dB (from the 0dB in my example) for most to hear it, but
some will hear it up only 12dB
and some will hear it up just 8

But unchanged?
NOBODY will hear it.

Get what I mean?
 
The elephant in the room is a SET amp, with several percent of even-order distortion. Some people love them, and listen for long periods.

I forgot to say odd order
And I forgot to say mostly!
lol
 
Another elephant dancing around this room is your speakers. These days even most cheap amps have inaudible distortion. Speakers are orders of magnitude worse.
 
I'm wondering something, but to pose the question, I first need to set the stage:

Say that your best case hearing threshold is 0dB. Iin case anyone's wondering, 0dB isn't zero energy,
0dB SPL = 20 microPascal.

Humans do not hear dB SPL though but closer to dBA so while people with good hearing may well be able to hear a single tone @ 1kHz of 0dB and even below 0dB SPL around 3kHz we cannot possibly hear 0dB SPL at 50Hz.

Now say that you're listening to some music that peaks at 80dB
This is background level SPL of somewhere 60-70dB average.

If THD+n / IMD in the source signal is lower than -80dB, with its peaks at 0dB (the same difference as between your hearing threshold and the loudest reproduced sound),
in the very best case (your hearing is juuust able discern a 0dB pin drop 40m away during the 80dB peak, and all noise and harmonics and intermodulation distortion is at -1dB (sound level, not signal level) or lower,

A pin drop SPL depends on how far away that is and to be able to hear that would require that nothing is masking that sound (say music at 60dB average)

your ears are now the limit, no question about it: all distortion coming through is below your ability to hear it.
Ears and transducers are the practical limits. Usually the transducers are worse than the ears.
 
Another elephant dancing around this room is your speakers. These days even most cheap amps have inaudible distortion. Speakers are orders of magnitude worse.

In the best case
lol.
It's hypothetical!

My speakers... tweeter THD in its passband is never more than -70dB above 2kHz at 96dB. And usually it's much lower than that (between 90 and 100)

Woofer? No test but same designers specifically designed it for low HD

- underhung (ooooh yeah!)
- 3" voice coil
- >200oz magnet
- thickest cast basket I've ever seen
- ATC's famous (very low HD) dome midrange attached to the 3" voice coil which also drives a cone shaped like the midrange waveguide which is quite small - just under 5".
- the suspension is equally reactive to force from either the + or - direction (a technique to minimize 2nd order distortion)

Also, I made its cabinet dead as a stone. Almost.

I'm sure I forgot other stuff. I could talk about the tweeter which is balanced the same way, has a double suspension, fully saturated >2T magnetic gap (either 1.5mm or 2.0mm with 1.0mm VC)

I have VERY low distortion speakers.
They also sound amazing - you should listen if there's a dealer in your area

They're called:
ATC SCM20 Pro PSL Mk2
Low low LOW distortion!

Sidenote: someone sent an extremely aged previous version here for review called the SCM20.
Tweeter, woofer, cabinet, crossover (slope and point) are all different.
The woofer looks the same, and actually has the same 3" dome in the centre, but otherwise, completely different
 
0dB SPL = 20 microPascal.

Humans do not hear dB SPL though but closer to dBA so while people with good hearing may well be able to hear a single tone @ 1kHz of 0dB and even below 0dB SPL around 3kHz we cannot possibly hear 0dB SPL at 50Hz.


This is background level SPL of somewhere 60-70dB average.



A pin drop SPL depends on how far away that is and to be able to hear that would require that nothing is masking that sound (say music at 60dB average)


Ears and transducers are the practical limits. Usually the transducers are worse than the ears.

I went with 60dB for the music (-40 left 20)

Good point with the frequency, I wasn't even considering the ear's extremes (low and high sensitivity ranges). Actually, I was. I was counting on the harmonic being in the 2-5kHz range.

I know there's masking and a whole lot of other things that make it unlikely for a relatively quiet sound to be heard during music.

I realised one of the things I wanted was to have a level I could turn to with a known distortion level and have the knowledge that IMD / HD weren't going to be contributors to listening fatigue
 
I don't want to get into a huge disussion on the audibility of harmonics - that wasn't the purpose of the thread - just to ensure 100% inaudibility (not figure of speech, 100%)

I agree with both of you: harmonic distortion is hard to hear.
There are effects it has though, which aren't immediately apparent.

An important one is listening fatigue.
An amplifier with lower distortion will take longer to induce listening fatigue in the listener. Of course this varies by the song, how many songs, how loud they are, how well they're recorded. Even how well hydrated the listener is has an effect. But the point is: increased distortion increases listening fatigue. Severity isn't easily quantifyable.
Not necessarily. SET amplifier lovers will say the opposite. They can listen to their highly distorting amplifiers for hours, whereas they would turn off something 'clean' as being dull and boring.

If you want to be sure not to hear any distortion, in the presence of music, then the criterion I mentioned above, i.e. no more than 0.1% distortion (-60dB) will ensure that.

If you are listening to single tones, especially where the harmonics don't naturally decay, but have been artificially created to enhance higher harmonics, like 5th and 7th, then what level of distortion is audible will depend on the actual case, what frequency tone, what harmonic structure. I don't know of ANY electronics where the harmonics don't decay naturally, so you would never have the case where a 5th or 7th harmonic was higher than the third, so the 0.1% criterion applies.

As mentioned above, intermodulation distortion is more upsetting than pure harmonic distortion as it creates distortion products that are not harmonically related, but as both harmonic distortion and intermodulation are created by the same process, that of non-linearity, an amplifier with low harmonic distortion will also have low intermodulation distortion.

S.
 
The real answer is that we have fairly good general approximations which are repeated in this forum a lot and which everyone interested in audio can use as excellent guidance for navigating the current gear landscape.

We do not gave final conclusive evidence or a comprehensive model for the psychoacoustic effects of nonlinearity. This isn't to say we should be taken in by what manufacturers allow themselves to say to increase sales or the unfounded speculations even experts allow themselves. We should be accurate about what we know, what we don't and where we're guessing.
 
Not necessarily. SET amplifier lovers will say the opposite. They can listen to their highly distorting amplifiers for hours, whereas they would turn off something 'clean' as being dull and boring.

If you want to be sure not to hear any distortion, in the presence of music, then the criterion I mentioned above, i.e. no more than 0.1% distortion (-60dB) will ensure that.

If you are listening to single tones, especially where the harmonics don't naturally decay, but have been artificially created to enhance higher harmonics, like 5th and 7th, then what level of distortion is audible will depend on the actual case, what frequency tone, what harmonic structure. I don't know of ANY electronics where the harmonics don't decay naturally, so you would never have the case where a 5th or 7th harmonic was higher than the third, so the 0.1% criterion applies.

As mentioned above, intermodulation distortion is more upsetting than pure harmonic distortion as it creates distortion products that are not harmonically related, but as both harmonic distortion and intermodulation are created by the same process, that of non-linearity, an amplifier with low harmonic distortion will also have low intermodulation distortion.

S.

Yes, those SET amps especially sound good with music mixed analog. And stuff like quality reel-to-reel recordings. And most things at least sound good through them. Their character sound ( richer bass and sometimes a bit foreward sounding ) is conventient, since they're typically low powered. We all know of the Loudness switch on vintage gear - restores balance to sound during quieter listening. SET imaging, especially in the midrange, is mysteriously magical.
They're not all perfect though.
Sharper, heavy hitting, treble heavy sounds, where phase is important, is top of the AHHH list. Electric drum kit: snare comes to mind as possible enemies. Not always - some well designed tubes get away with it, but from what I gather, for the ability, they lose some of their magic. Using tubes on the input stage with well designed solid state output is better. More accurate and more powerful, too.

I started with an analogy of vision and monitors and it got pretty long. We all know the limits of hearing are hard to get exact, and like anything, preferences vary. Lots varies. Too much!

When I talk about THD+n at one frequency, internally, in my mind, I'm extrapolating that to IMD as well. Basically, while THD+n at -60 might be fine for one tone, consider 10-15, and that the harmonics from the upper midbass to midrange have harmonics in the extremely sensitive 1-5kHz zone, where the natural harmonics from instruments which give them their character and contain enough information that one can determine whether the instrument is real or synthesized is.

Is your -60dB figure from average power, like where the VU meter would be, not the peak meter?

If so, it's pretty close to what I usually have planned around.
Of equipment, I've required -90dB THD+n.
-105 allows for digital attenuation with very little repercussion
 
The real answer is that we have fairly good general approximations which are repeated in this forum a lot and which everyone interested in audio can use as excellent guidance for navigating the current gear landscape.

We do not gave final conclusive evidence or a comprehensive model for the psychoacoustic effects of nonlinearity. This isn't to say we should be taken in by what manufacturers allow themselves to say to increase sales or the unfounded speculations even experts allow themselves. We should be accurate about what we know, what we don't and where we're guessing.

You missed the point of the thread.
It wasn't:
"At what level is distortion free"
It was:
"If this is the dynamic range of one's hearing, and harmonic distortion is discernable from music, during music, then up to how loud can music be played with 0% chance of harmonic distortion being audible, if peak distortion is at -xx dB"

Purely theoretical. The logic tracked. We had an interesting conversation otherwise though

(I switched things around a bit for your explanation, but only because it's a lot longer to summarize exactly what I wrote, and this means the same thing [+ I'm explaining what you didn't read in the first sentences of the OP]
 
Back
Top Bottom