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Volume and logarithm


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1 "Bel" is a logarithmic representation of the ratio of measureable loudness to our perception of loudness. 2 Bels is perceived to be "twice as loud" as 1 Bel.

 

1 Bel is equal to 10 decibels, or 10dB. 20dB is said to be twice as loud as 10dB.

 

1dB is widely accepted as the minimum change in loudness that can be perceived by the human ear, no matter if the starting ("reference") point is 65dB or 120dB. (Although at higher SPLs natural compression takes place in our hearing patterns that may make it difficult to detect 1dB changes.)

 

A change of +3dB is equal to twice the power (watts). A change of +6dB is equal to twice the voltage.

 

In system metering, a dB is a dB. For example, if you increase the mixer's level so its meter shows an increase from -6dB to 0dB, the mixer's voltage output has doubled once, but the amplifier power has doubled twice. And (ideally) the entire system is putting out 6dB more than it was at the previous setting.

 

The formula for determing any dB ratio for wattage is

 

10log(P1/P2)

 

Use the little Windows Calculator. In the menu, change the View from Standard to Scientific. If you wanted to determine the increase to a 200 from a 100 watt amp, type:

 

200/100 = 2. Click the Log button. Multiply that by ten = 3.01dB. (Rounded to 3)

 

It also works in reverse:

100/200 = .5. Click the Log button. Multiply that by ten = -3.01dB.

 

As for percentage, it's also a ratio equation. Because it's tied to wattage, we can use the same formula: What is 25% of the output of a 300-watt amp? We know that 300 watts is equal to 100%.

 

10log(25/100) = -6dB.

 

For the actual output wattage, simply multiply the total available wattage by the percentage: 300 * .25 = 75 watts.

 

Oh, yeah ... to answer your question: The increase in the loudness from a 100 watt amp to a 200 watt amp can be expressed as a percentage of the decibel relationships. We know that doubling amp power results in an increase of 3dB. But we also have to have something to relate it to in order to derive a percentage increase. We know that an increase of 10dB is perceived by most to be "twice as loud." Therefore, an increase of 3dB should result in the output being 3/10, or 30% louder.

 

It seems logical in theory, but it is never expressed that way in the real world. Getting two people to agree on a percentage of loudness increase is simply not possible.

 

That's why the original phone companies developed the Bel in the first place. (Indeed, it is named after Alexander Graham himself.)

 

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Originally posted by Audiopile


Would double the perceived loudness be considered a 50% increase or a 100% increase. A 100% increase would be appropriate if you started with nothing and now have something.

 

 

You can certainly start with something and still have a 100% increase. A price that doubles from $1 to $2 increases by 100%. So if a 10dB increase is twice as loud (a perceived "doubling" of loudness) it is equal to a 100% increase. A 3dB increase is 3 tenths, or 30%. In theory, that is. This theory applies to any doubling of loudness, which is always +10dB: Increase the SPL from 110dB to 120dB. The audience hears it as twice as loud -- a 100% increase.

 

 


... would 1dB equal 1.25% if the change is on the verge of not being detectable?

 

 

It's still 1 tenth, or 10% of "twice as loud." That's because our constant reference is +10db = "twice as loud." Again ... in theory.

 

 

 


Hummm.... I guess this could keep me awake all night.

 

It's not worth it. Percentages are rarely if ever used to represent changes of loudness in our line of work. It is interesting, though, that arguably one of the best mastering apps for the PC (Sound Forge) defaults to percentages rather than decibels in certain functions.

---

I searched the 'net for minimum perceived loudness change in decibels and found a bunch of sites. They were about equally divided between 1dB and 3dB.

 

To my ears (poor as they are after 30+ years of performing and mixing), I couldn't detect a 1dB increase unless my ears knew that my fingers had moved the fader and my eyes saw the meter. 3dB is it.

 

But to "virgin" ears, 1dB carries a lot more weight. At least if they are listening at a reasonable SPL.

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I've always followed the 3db, Yamaha approach as well. But, at the end of the day, it's really hard to argue over perceived anything. That's why I like the ole imperical scientific stuff! If the bar owner says turn it down a bit...I go for at least 3db. If they say it's still too loud, another 3db whose to argue with perception.

 

I found myself arguing the other day over a cartoon my 12 year old was watching on TV. I told him to "turn off that Pokemon crap and get to his chores" (insert the Flintstones and it was my dad all over again...scarey!). He very insistently replied, "that's not Pokemon, it's Ruruni Kenshin" (another Japanese anime thing that all look like bad speed racer rip-offs to me). I claimed "they all look the same to me" and he argued that they didn't look the same, as though his limited 12 year old "cool" depended on it. I guess his anime cartoon perception was/is more acute than mine. I also think he would rather argue the relative merits of Anime cartoons than do his chores... I guess he won that one. Later I reflected back on my wiser father. You see, he never argued that the Flintstones looked like the Jetsons....even though they kinda did. He just said "turn that crap off and do your chores"....no argument.

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By Audiopile

You know, if kids have such great hearing, why don't they seem to hear when you tell them to clean up their room?

 

 

Hate to get off subject but..........There's something about the word clean that does not compute with kids. I try to ask nicely but around the 4th time...........my voice is usually around 3 db higher. Sometimes the louder volume works & sometimes it don't. When it don't, I have to take more drastic measures like no TV for the day. That usually will get his attention. Having said that......... If you ever need advice, ask a 5 yo. They know EVERYTHING. LOL. I got into an argument with my 5 yo. about weather Tom from Tom & Jerry actually speaks. I say that he yells when his tail gets stuck in something but I don't ever recall an actual word that ever came from his mouth. My 5 yo will argue that one to the death. I'm tellin you........the kid is going to be a lawyer or a used car salesman and either way, he'll be a millionaire.

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