If 3db is twice as loud...

[punkedrock]

How much does this split the difference if it's less than 3db increments?
Like say I increase it by 1.5db, what am I doing here.
And how do I get a slightly louder terminology down here for myself to think with? (Increasing by less than 3db, surely there's a fraction here and I mean I'm curious how db's are measured.)

 

[WoodyLuvr]

Decibels are measured on a logarithmic scale.

 

[castleofargh]

It's usually said that +10dB is twice as loud, not 3. And even that can depend on frequency and what not(see equal loudness contour).
If we take +10dB as reference, then another +10dB will again double your perception of loudness relative to the last value, so that would make +20dB 2*2=about 4 times as loud. And so on. +3dB would be about 1.23 times louder according to the graph below. Already it starts to not be all that helpful subjectively, I get that's what you asked for, but it's a subjective thing, and we aligned with a logarithmic scale like dB only because of how nonlinear our hearing is, it's not a perfect match, just something closer.

To get a sense of what a given value means to you, I can only suggest that you take some player(I use Foobar) with a volume level shown in dB, and play with that. Then you get some perhaps useful reference, like how for me at normal listening level, going down by -30dB is already very quiet. It's not much, but you start to get a feeling that when people talk about the improved sound for something done better at -120dB, they're probably full of crap.

The super generic visual you didn't care about, for future readers who wondered but didn't know about Wikipedia or google:

 

[punkedrock]

It's usually said that +10dB is twice as loud, not 3. And even that can depend on frequency and what not(see equal loudness contour).
If we take +10dB as reference, then another +10dB will again double your perception of loudness relative to the last value, so that would make +20dB 2*2=about 4 times as loud. And so on. +3dB would be about 1.23 times louder according to the graph below. Already it starts to not be all that helpful subjectively, I get that's what you asked for, but it's a subjective thing, and we aligned with a logarithmic scale like dB only because of how nonlinear our hearing is, it's not a perfect match, just something closer.

To get a sense of what a given value means to you, I can only suggest that you take some player(I use Foobar) with a volume level shown in dB, and play with that. Then you get some perhaps useful reference, like how for me at normal listening level, going down by -30dB is already very quiet. It's not much, but you start to get a feeling that when people talk about the improved sound for something done better at -120dB, they're probably full of crap.

The super generic visual you didn't care about, for future readers who wondered but didn't know about Wikipedia or google:

Thanks!

 

[VNandor]

I'll try to answer your question first. a 3dB increase usually corresponds to a doubling of power in Watts. The formula to calculate the power ratio is Power ratio=10^(dB/10). So 10^(3/10)=1.99 which is twice the power. An 1.5dB increase would be 10^(1.5/10) which is 1.41 times the power. Notice that this is a ratio. Going from 5W to 10W is 3dB difference but going from 10W to 15W is not 3dB.

The formula to calculate the power in dB is dB=10*log(W/W0), where dB is the power in dB, W is the power, and W0 is the reference. So from the previous example, going from 10W to 15W is 10*log(15/10)=1.76 so the increase in power is 1.76dB.

Now with that out of the way, let me tell you that your question is wrong, sorry!
castle already pointed out that it's usually said that 10dB increase in power is roughly perceived twice as loud. To bring one of the most used quantity when talking about sound, the sound pressure level (SPL): a 20dB increase in SPL corresponds to 10 times pressure level, 100 times acoustic power and roughly 4 times louder sound. SPL is based on a ratio between pressure levels measured in Pascals.

Loudness isn't a physical quantity, it's entirely perception based. As such it can not be measured simply by a microphone or a multimeter. You need someone that can perceive and "quantify" loudness for you The first unit that tried quantify loudness was the phon. Phon is a unit of measurement for loudness. Nowadays, we tend to use something conveniently called the "Loudness Unit" when talking about loudness differences. It's a way more modern and refined unit for quantifying loudness compared to the phon.

 

[punkedrock]

I'll try to answer your question first. a 3dB increase usually corresponds to a doubling of power in Watts. The formula to calculate the power ratio is Power ratio=10^(dB/10). So 10^(3/10)=1.99 which is twice the power. An 1.5dB increase would be 10^(1.5/10) which is 1.41 times the power. Notice that this is a ratio. Going from 5W to 10W is 3dB difference but going from 10W to 15W is not 3dB.

The formula to calculate the power in dB is dB=10*log(W/W0), where dB is the power in dB, W is the power, and W0 is the reference. So from the previous example, going from 10W to 15W is 10*log(15/10)=1.76 so the increase in power is 1.76dB.

Now with that out of the way, let me tell you that your question is wrong, sorry!
castle already pointed out that it's usually said that 10dB increase in power is roughly perceived twice as loud. To bring one of the most used quantity when talking about sound, the sound pressure level (SPL): a 20dB increase in SPL corresponds to 10 times pressure level, 100 times acoustic power and roughly 16 times louder sound. SPL is based on a ratio between pressure levels measured in Pascals.

Loudness isn't a physical quantity, it's entirely perception based. As such it can not be measured simply by a microphone or a multimeter. You need someone that can perceive and "quantify" loudness for you The first unit that tried quantify loudness was the phon. Phon is a unit of measurement for loudness. Nowadays, we tend to use something conveniently called the "Loudness Unit" when talking about loudness differences. It's a way more modern and refined unit for quantifying loudness compared to the phon.

I picked up +3db being twice as loud from car audio. Still, it does seem to make my bass subjectively twice as loud when I tried it.
Anyways, I appreciate all of the info.

 

[gregorio]

I picked up +3db being twice as loud from car audio. Still, it does seem to make my bass subjectively twice as loud when I tried it.
Anyways, I appreciate all of the info.

Unfortunately, it’s somewhat complicated or rather, a lot more complicated than you seem to be trying to make it. The decibel scale provides a logarithmic ratio relative to a given reference. There are actually over 50 decibel scales, some measure entirely different things, others measure related things and others measure the same thing under different conditions, all of which depends on the given reference. So, some dB scales are directly equivalent/convertible, others cannot be converted and some are convertible but only with confounding variable/s. That’s your problem in this case, you are confusing different dB scales which are not directly convertible or, are you even comparing dB scales? Is it just +3 on your volume knob or is it specifically +3dB and if it is specifically +3dB, +3dB what? Is it +3dBW (dB Watts, the power being consumed by your amp) or +3dBu (dB volts, unloaded), possibly even +3dBVU if it’s an old or retro amp or maybe it’s the dBFS (the scale used for digital audio) and you just mean you added 3dB of level rather than an actual setting of +3dBFS (which isn’t possible)? But even if your volume knob is actually a dB scale and we knew which scale, still it wouldn’t help because as already mentioned by others, the human perception of loudness does not directly correlate with any of these scales.

You might be wondering; if there’s no direct relationship, then how come the table that castleofargh posted exists? The answer is that the dB scales for sound pressure and sound intensity obviously have different references but both were set to the threshold of human hearing, so 0dB on both scales is equivalent to the point at which a sound could become audible under certain conditions. However, that’s only at 0dB, at higher levels the relationship is more convoluted and also varies depending on conditions. So, +10dB sound pressure level and +10dB sound intensity only roughly equates to a doubling of loudness with a sine wave at 1kHz in a free field (anechoic chamber). You on the other hand are talking about bass rather than a 1kHz signal and car audio rather than an anechoic chamber. Obviously these are completely different conditions and therefore the stated relationship doesn’t apply. It maybe that the +3 or +3dB setting does indeed result in a perception of double the loudness, there’s no way to know without measuring your system in your car and using the actual dB loudness scale (dB LUFS, decibels in Loudness Units as stated by VNandor).

In other words, you are trying to correlate a dB scale (or possibly just an arbitrary volume scale with no relation to a dB scale) with the human perception of loudness, which don’t correlate (unless you’re specifically using the dB LUFS scale). Not sure I’ve helped rather than just confused you more but if you are confused more, then you’re on the right track because it is confusing and there’s no easily calculated correct answer given your conditions.

G

 

[71 dB]

I picked up +3db being twice as loud from car audio. Still, it does seem to make my bass subjectively twice as loud when I tried it.
Anyways, I appreciate all of the info.

+3 dB can be said to be twice as powerful: Going from 100 W to 200 W amp power means +3 dB for example, but the perceived loudness isn't doubled. We need to go from 100 W to about 1000 W (+10 dB) to double the perceived loudness, but even that is frequency dependent. Due to the shape of equal loudness curves, at low bass frequencies going from 100 W to 316 W (+5 dB) is more or less perceived as doubled loudness. Perceived loudness is subjective. I don't even like much myself concepts like "twice as loud." Does doubling the amoung of pepper in food make it taste "twice as spicy?" Maybe for some people. What makes more sense for me is that 0.5 dB increase in sound pressure level is the amount just about everyone can notice.

 

[SilverEars]

+3 dB can be said to be twice as powerful: Going from 100 W to 200 W amp power means +3 dB for example, but the perceived loudness isn't doubled. We need to go from 100 W to about 1000 W (+10 dB) to double the perceived loudness, but even that is frequency dependent. Due to the shape of equal loudness curves, at low bass frequencies going from 100 W to 316 W (+5 dB) is more or less perceived as doubled loudness. Perceived loudness is subjective. I don't even like much myself concepts like "twice as loud." Does doubling the amoung of pepper in food make it taste "twice as spicy?" Maybe for some people. What makes more sense for me is that 0.5 dB increase in sound pressure level is the amount just about everyone can notice.

Our hearing is not perceived linearly

 

[71 dB]

Our hearing is not perceived linearly

Where did I claim it is?

 

[2leftears]

Our hearing is not perceived linearly

Where did I claim it is?

You didn't; I was wondering the same. But I think @SilverEars' comment was maybe just an added observation.

A number of human senses are non-linear and often a logarithmic scale (like the dB) seems to correspond well to our perception over a range of 'normal' conditions.

• Loudness is perceived approximately on a logarithmic scale (we use decibels, a log₁₀ scale)
• Sound frequency is perceived approximately on a logarithmic scale (use of octaves in music, a log₂ scale)
• Brightness (of light) is perceived approximately on a logarithmic scale (use of exposure stops in photography, a log₂ scale)

But I agree with @71 dB; for me the concept of 'twice as loud' doesn't really mean a whole lot perceptually, but it may well do to others. Nor does e.g. a 2kHz tone 'feel' twice as high as a 1kHz tone to me. It feels "right" to me as in feeling like "the next one up" but honestly I can't say it feels "twice" as high.

 

[71 dB]

You didn't; I was wondering the same. But I think @SilverEars' comment was maybe just an added observation.

A number of human senses are non-linear and often a logarithmic scale (like the dB) seems to correspond well to our perception over a range of 'normal' conditions.

• Loudness is perceived approximately on a logarithmic scale (we use decibels, a log₁₀ scale)
• Sound frequency is perceived approximately on a logarithmic scale (use of octaves in music, a log₂ scale)
• Brightness (of light) is perceived approximately on a logarithmic scale (use of exposure stops in photography, a log₂ scale)

But I agree with @71 dB; for me the concept of 'twice as loud' doesn't really mean a whole lot perceptually, but it may well do to others. Nor does e.g. a 2kHz tone 'feel' twice as high as a 1kHz tone to me. It feels "right" to me as in feeling like "the next one up" but honestly I can't say it feels "twice" as high.

Senses kind of have to be logarithmic, because physical strength of the sensory stimulus worth sensing can vary several orders of magnitude, but our brain can only process information in a much smaller "cognitive dynamic range." At around 1 kHz for example the physical air pressure of a 120 dB SPL sound (pain threshold) is 1000 000 times bigger than for a 0 dB SPL sound (threshold of hearing). However, if each 10 dB increase in the sound pressure level translates into "twice as loud" sound, the 120 dB SPL sound causes 2¹² = 4 096 times bigger stimulus in the brain than 0 dB SPL sound and these are more or less the extremes. The range of stimulus level has dropped 2.4 orders of magnitude thanks to logarithmic perceived loudness.

2 kHz tone is "twice" as high as a 1 kHz tone in music sense, because of the perfect consonance these two tones form together. In general, our hearing analyses the frequency band at critical bands which goes between 1/3 octave and whole tone bands above about 400 Hz and became constant (about 100 Hz below 400 Hz). This explains why close notes at lower octaves in music become "muddy." Above G3 (196 Hz at 440 Hz tuning) close notes don't cause muddiness (but musical dissonance is to be expected!) while below G3 the muddiness problem becomes worse and worse fast the lower the notes are.