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On sound pressure level and decibel usefulness

felipeviegas

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Hello people,

Out of nowhere I stumbled upon the KZ scandal again today and learned that Delta Fyre kind of retracted himself. He was the first person to mention that nothing was done by the additional drivers on KX ZEX Pro (aka, Crinacle's tuning), besides the DD. Here some context, if you really missed this novel last year.

The puzzle part for me is that he cites some properties of decibel to justify that measurements could be deceiving (this is on his facebook post, not on headphonesty site). From Wikipedia (my highlight):
The decibel is useful for representing large ratios and for simplifying representation of multiplicative effects, such as attenuation from multiple sources along a signal chain. Its application in systems with additive effects is less intuitive, such as in the combined sound pressure level of two machines operating together. Care is also necessary with decibels directly in fractions and with the units of multiplicative operations.
I will be grateful to hear all of you with knowledge of the math side of this, @amirm himself. Should FR graphs be interpreted with this amount of caution?! No change in FR response, but with audible differences in treble quality ("subtle crispiness" as mentioned by Delta Fyre)?

As I am kind of new over here, please there is no need to bring your stones. I am asking this because I really do want to understand the math behind it and the implications for psychoacoustics. For me, sticking with the "subtle crispiness" is not enough! But if the (decibel) math is right, it would be interesting to discuss other ways of measuring these phenomena.

Thanks and cheers!
 

fpitas

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No change in FR response, but with audible differences in treble quality ("subtle crispiness" as mentioned by Delta Fyre)?

How does that work with a headphone? That sounds suspiciously like, "There are things science can't measure!", which is common in selling useless but expensive stuff.

dB has been used for a hundred years now to measure sound levels. I'm not aware that the situation has changed.
 
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felipeviegas

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No change in FR response, but with audible differences in treble quality ("subtle crispiness" as mentioned by Delta Fyre)?

How does that work with a headphone? That sounds suspiciously like, "There are things science can't measure!"which is common in selling useless but expensive stuff.

dB has been used for a hundred years now to measure sound levels. I'm not aware that the situation has changed.
I agree! Still, I cannot tell what "large ratios" mean. That is the main doubt to me.
 

fpitas

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I agree! Still, I cannot tell what "large ratios" mean. That is the main doubt to me.
The fact is, our hearing is logarithmic, like seeing. You need large ratios to perceive differences.
 

notsodeadlizard

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There was no scandal, just something about these innumerable pseudo-brands became clear, the logarithmic scale has nothing to do with it
 

Curvature

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The dB can be used to represent both vanishingly small and extremely large quantities because it is a ratio. It is useful because it's a decent approximation for our sense of loudness and frequency resolution, which follow a logorithmic trend. To go up and down the scale you have to use very different quantities and the actual pressure differences (as in SPL) at play are immense. We can hear, without taking into account equal loudness, from roughly from -9dB SPL (yes, that's a negative number) to 120-130dB SPL, the latter representing the threshold of pain. In general the way hearing works is that there is a certain atmospheric pressure on Earth, which equals 1 bar or roughly 100k pascal, and all sound is any disturbance which is superimposed on that pressure. -9dB SPL is a 7 micropascal disturbance (0.000007 p), 130dB SPL is 63 pascal. And then the air itself loses its normal acoustic properties with a disturbance of 194dB SPL, equal to the magnitude of normal atmospheric pressure, again 1 bar or 100k pascal. The dB allows simpler comparison of these very different quantities. Otherwise a resonance of 10dB from 80dB to 90dB on an FR chart would be 200k vs 633k micropascal, while 100dB SPL would be 2m micropascal. It would be unreadable.

The dB also allows, again because it is a ratio, proportional comparison of different processes once a reference is established. The digital volume scale of a music signal (look up how bits work), the voltage and power coming out of your amp, the pressure produced by speakers/IEMs.

If I remember correctly the contribution of certain redundant drivers in that IEM was too low to affect frequency response. If true then that's the end of the discussion. There is no sense in which dB SPL could not be used to compare the output, no matter how large or small.

Edit: Typos.
 
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felipeviegas

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The dB can be used to represent both vanishingly small and extremely large quantities because it is a ratio. It is useful because it's a decent approximation for our sense of loudness and frequency resolution, which follow a logorithmic trend. To go up and down the scale you have to very different quantities and the actual pressure differences (as in SPL) at play are immense. We can hear, without taking into account equal loudness, from roughly from -9dB SPL (yes, that's a negative number) to 120-130dB SPL, the latter representing the threshold of pain. In general the way hearing works is that there is a certain atmospheric pressure on Earth, which equals 1 bar or roughly 100k pascal, and all sound is any disturbance which is superimposed on that pressure. -9dB SPL is a 7 micropascal disturbance (0.000007 p), 130dB SPL is 63 pascal. And then the air itself loses its normal acoustic properties with a disturbance of 194dB SPL, which represents a disturbance equal to normal atmospheric pressure, again 1 bar or 100k pascal. The dB allows simpler comparison of these very different quantities. Otherwise a resonance of 10dB from 80dB to 90dB on an FR chart would be 200k vs 633k micropascal, while 100dB SPL would be 2m micropascal. It would be unreadable.

The dB also allows, again because it is a ratio, proportional comparison of different processes once a reference is established. The digital volume scale of a music signal (look up how bits work), the voltage and power coming out of your amp, the pressure produced by speakers/IEMs.

If I remember correctly the contribution of certain redundant drivers in that IEM was too low to affect frequency response. If true then that's the end of the discussion. There is no sense in which dB SPL could not be used to compare the output, no matter how large or small.
That's a helpful answer, @Curvature. Thanks!
But if I may be a pain in... therefore the description of the decibel properties in Wikipedia would be just wrong, that is, it would not be useful just for large ratios, correct?
 

Curvature

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That's a helpful answer, @Curvature. Thanks!
But if I may be a pain in... therefore the description of the decibel properties in Wikipedia would be just wrong, that is, it would not be useful just for large ratios, correct?
The Wikipedia entry is incomplete, and a little misleading without having the background knowledge, but not wrong.

Attached is a better explanation IMO
 

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  • decibel_scale_eele417.pdf
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DVDdoug

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I don't think it says it's not useful for small ratios. But for example, the noise spec for ACX audiobooks is -60dB or better. That's 1/1000th of full scale or (a "large ratio"). And the peaks are specified as -3dB (or lower) and that's about 70% of full scale (a "small ratio"). These are amplitude ratios for digital levels or voltage. The power (Wattage) ratios are higher. (The dB sound level difference is the same but there are different calculations depending on if you are measuring amplitude or power.

It can also be useful to think in percentages. A 2:1 ratio is 6dB (amplitude again). So double the voltage (or digital level) is +6dB and half the voltage is -6dB.

Switching to power... When you double the power that's +3dB so if you go from 1W to 2W that's a small but noticeable +3dB loudness change. But a 1W change from 100W to 101W is an unnoticeable 0.04dB increase (the same wattage change but a smaller percentage).


-----------------------------------------
Note that our ear's frequency response is not flat. It's most sensitive to mid-frequencies (around 1-2kHz). SPL meters are usually A-weighted to (approximately) compensate for the ear's sensitivity at different frequencies. But electrical measurements are flat and of course we want our equipment to be flat to properly reproduce the sound. And, our ear's frequency response is not linear... When you turn-won the volume it sounds like you've turned-down the bass even more. (Equal Loudness Curves)

Also, note that the dB SPL reference of 0dB is close to the quietest sound that can be heard so dBSPL measurements are positive. For digital audio the reference of 0dBFS (0 decibels full scale) is the "digital maximum" so digital dB levels are usually negative. For 16 or 24-bit integer formats 0dB is literally the highest you can "count to" with a given number of bits (with one bit for the +/- sign). For electrical audio the dB levels are also usually negative.

There is no standard calibration between digital and acoustic levels but there is a direct correlation... If you reduce the digital level by 3dB (3dB more negative) the SPL level also drops by 3dB. (That's assuming everything is linear so the amplifier isn't clipping/distorting and assuming you don't move or change the volume control, etc.)
 

sarumbear

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Hello people,

Out of nowhere I stumbled upon the KZ scandal again today and learned that Delta Fyre kind of retracted himself. He was the first person to mention that nothing was done by the additional drivers on KX ZEX Pro (aka, Crinacle's tuning), besides the DD. Here some context, if you really missed this novel last year.

The puzzle part for me is that he cites some properties of decibel to justify that measurements could be deceiving (this is on his facebook post, not on headphonesty site). From Wikipedia (my highlight):

I will be grateful to hear all of you with knowledge of the math side of this, @amirm himself. Should FR graphs be interpreted with this amount of caution?! No change in FR response, but with audible differences in treble quality ("subtle crispiness" as mentioned by Delta Fyre)?

As I am kind of new over here, please there is no need to bring your stones. I am asking this because I really do want to understand the math behind it and the implications for psychoacoustics. For me, sticking with the "subtle crispiness" is not enough! But if the (decibel) math is right, it would be interesting to discuss other ways of measuring these phenomena.

Thanks and cheers!
The wiki article is badly written but not wrong. You cannot simply add a 80dBSPL sound at 100Hz with another at 1000Hz and get 86dBSPL. Signal addition is linear only if two signals are at the same frequency and are in phase at the measuring point. That’s what the article is trying to say but making a mess of it.
 
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