Topic: Converting percentages to decibel measurements?

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Anyone have a decent way to convert percentages of two sources used when mixed to relative db value adjustments?

For example. If I'm looking to use 40% of one wav track and 60% of another to get 100%, how can I map that to + or - decibel adjustment for each track? Any information is appreciated. Thanks.

[notlance]

Here is how I see it.  You want the sources to be in the ratio of 60% to 40% which is 0.60 / 0.40 = 1.5

1 dB = 10^0.1  Therefore, this is your equation:

(10^0.1)^x = 1.5

xlog(10^0.1) = log(1.5)

x = log(1.5) / log(10^0.1)

x = 0.176 / 0.1

x = 1.76 dB

Therefore, your track you want to be at 60% of the mix should be at a level 1.76 dB higher than the 40% track.

[easy jim]

IMO, use your ears and forget about percentages.  They're really kind of meaningless, and I doubt any real sound/recording engineer would consider it to be a useful consideration aside from a basic approximation.  Labelling a mix with a calculation of percentages between the sources doesn't convey much.  I think it serves more as an advertising point for the unaware to 'sell' the quality of a recording on a torrent site..."mine is better because is has 60% SBD/40% AUD instead of a 50/50 mix...

The percentages are relative to what, anyhow? The average RMS level of the tracks?  The maximum peak levels of the tracks?  It's not unusual to have SBD tracks with higher peak levels, but lower average RMS levels, than a complimentary AUD source.  Do you calculate the percentages based on the peak levels, then, or the RMS levels?

I'd question the accuracy of any assessment of percentages using the maximum peak levels as a baseline, rather than average RMS levels, since maximum peak levels do not necessarily reflect the average loudness of the sources (which is much more relevant IMO).  But, again, what's the relevance?  It's either a good mix or not, and the sources have either been utilized as optimally as possible within the mixer's skill set or they have not.   

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IMO, use your ears and forget about percentages.  They're really kind of meaningless, and I doubt any real sound/recording engineer would consider it to be a useful consideration aside from a basic approximation.  Labelling a mix with a calculation of percentages between the sources doesn't convey much.  I think it serves more as an advertising point for the unaware to 'sell' the quality of a recording on a torrent site..."mine is better because is has 60% SBD/40% AUD instead of a 50/50 mix...

The percentages are relative to what, anyhow? The average RMS level of the tracks?  The maximum peak levels of the tracks?  It's not unusual to have SBD tracks with higher peak levels, but lower average RMS levels, than a complimentary AUD source.  Do you calculate the percentages based on the peak levels, then, or the RMS levels?

I'd question the accuracy of any assessment of percentages using the maximum peak levels as a baseline, rather than average RMS levels, since maximum peak levels do not necessarily reflect the average loudness of the sources (which is much more relevant IMO).  But, again, what's the relevance?  It's either a good mix or not, and the sources have either been utilized as optimally as possible within the mixer's skill set or they have not.   

Yeah, I thought about that, one of the reasons I'd go to the trouble of the math was for that Phish ambisonic sample that was posted if I were going to derive the surround sound aspect. While sonically the LF and RF tracks may not be the best sound that could be created, they represent what was going on at that angle to the listener to build the appropriate (and hopefully realistic) soundstage.

Otherwise I agree with out that the percentages are generally meaningless except for purely academic information purposes.

[Todd R]

I've never seen that formula lance uses, and I don't think it is right.

For sound, db = 20 * log (ratio)

A sound that is twice as loud as another is ~6db louder -- 20 * log(2) = 6.02db.  Similarly, a sound that is half as loud is half as loud is 6db lower -- 20 * log(0.5) = -6.02db

For the original poster, a 60/40 mix would be 20 * log (60/40) = 3.52db higher for the 60% side.  Or alternatively, 20 * log(40/60) = -3.52db, so the 40% side would need to be 3.5db lower.

Personally, I can't think in terms of percentages at all.  When I see them posted by someone, I need to translate them into db for them to have any meaning at all to me.  I'm generally with easyjim with what he says, though it helps me to have an idea on where to start with the board recording vs the aud, or the board vs the onstage mics (or mic pair A vs mic pair B).  I listen to each source to figure out what I want out of it, then make some guesses on where I should start with the mixing based on db relative to one another.  For this, I do it compared to each source's RMS level, not it's max level.

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I've never seen that formula lance uses, and I don't think it is right.

For sound, db = 20 * log (ratio)

A sound that is twice as loud as another is ~6db louder -- 20 * log(2) = 6.02db.  Similarly, a sound that is half as loud is half as loud is 6db lower -- 20 * log(0.5) = -6.02db

For the original poster, a 60/40 mix would be 20 * log (60/40) = 3.52db higher for the 60% side.  Or alternatively, 20 * log(40/60) = -3.52db, so the 40% side would need to be 3.5db lower.

Thanks, I'll give it a shot. Eyeballing/listening to it, that seems more like it as I notice the biggest differences come after about a 4db swing.

Personally, I can't think in terms of percentages at all.  When I see them posted by someone, I need to translate them into db for them to have any meaning at all to me. 

Same here, the problem is for the values I have to derive patterns from the figure 8/omni merge, all of my general reference points are in percentages (per the Josephson C700 manual). If they had given me decible relationships, it would have been moot.

For reference in case someone at a later date comes across this thread, what I'm speaking about is:

For these formulas, consider the output as a combination of W (omni) and D (figure 8) signals where w+d=1.
Some common ratios are

Omni: all W
Subcardioid/hypocardioid/wide cardioid: 0.66W+0.33D
Cardioid: 0.5W+0.5D
Hypercardioid: 0.33W+0.66D
Supercardioid: 0.25W+0.75D
Figure-8: all D

http://www.josephson.com/pdf/srs7ug.pdf
page 8

[notlance]

I've never seen that formula lance uses, and I don't think it is right.

For sound, db = 20 * log (ratio)

A sound that is twice as loud as another is ~6db louder -- 20 * log(2) = 6.02db.  Similarly, a sound that is half as loud is half as loud is 6db lower -- 20 * log(0.5) = -6.02db

For the original poster, a 60/40 mix would be 20 * log (60/40) = 3.52db higher for the 60% side.  Or alternatively, 20 * log(40/60) = -3.52db, so the 40% side would need to be 3.5db lower.

Well, this all gets rather confusing.  If you are measuring pressure or voltage, the equation is dB = 20log(ratio).  If your are measuring power or intensity, the equation is 10log(ratio).  The different equation arise because intensity = pressure² and power = voltage².  Note that here and in my original post I never used the word "loud" or "loudness"; those are psycho-acoustic concepts.  It is generally accepted that for a sound to be perceived as "twice as loud" as another sound, the louder sound must be 10 dB more intense than the softer, not 6 dB

Here are a couple of links that probably explain it better than I can:
http://www2.sfu.ca/sonic-studio/handbook/Decibel.html
http://www.phys.unsw.edu.au/jw/dB.html

The original post asked for the dB difference between two tracks mixed in a ratio of 1.5.  To achieve that, one track needs to be about 1.76dB more intense than the other.

Now I agree that doing such a calculation usually does not make any sense on several levels when mixing tracks; if it sounds good, it is good.  This is also true when mixing mic signals to achieve a particular polar pattern.  For example, if a Cardioid is 0.5W+0.5D, what pattern would you get if the mix was 0.49W+0.51D?  It's still a Cardioid, but just a little different pattern.  Maybe it will sound better, maybe it will sound worse, maybe it will just sound different, maybe you won't be able to tell the difference.

[notlance]

This is interesting because now after having looked into the Josephson C700, I know exactly what you are trying to do.  You see, I have a pair of Sennheiser MKH800 Twin mics which achieve the same effect as the C700 by a slightly different means.  Do you have the C700A or the C700S?  The C700S is able to do what is commonly called a Double MS (DMS) configuration.  Schoeps has published some info on the technique.  See these links:
http://www.schoeps.de/E-2004/double-ms.html
http://www.schoeps.de/E-2004/PDFs/Schoeps_DoubleMS_Paper.pdf

I often set up my two Twins in a DMS and adjust the patterns in post.  However, I do it by ear rather than by calculating dB level differences.  The biggest problem I have is the technique gives me so much flexibility that I have a hard time deciding when good is good enough.

[page]

This is interesting because now after having looked into the Josephson C700, I know exactly what you are trying to do.  You see, I have a pair of Sennheiser MKH800 Twin mics which achieve the same effect as the C700 by a slightly different means.  Do you have the C700A or the C700S?  The C700S is able to do what is commonly called a Double MS (DMS) configuration.  Schoeps has published some info on the technique.  See these links:
http://www.schoeps.de/E-2004/double-ms.html
http://www.schoeps.de/E-2004/PDFs/Schoeps_DoubleMS_Paper.pdf

I often set up my two Twins in a DMS and adjust the patterns in post.  However, I do it by ear rather than by calculating dB level differences.  The biggest problem I have is the technique gives me so much flexibility that I have a hard time deciding when good is good enough.

I did a similar function using two busman mics (1 stereo and 1 single) in the same setup as the 700S during the last night at Phish's reunion in Hampton this March. So I have 2 8s and an omni which *by ear* I've decoded to 2 track stereo. Since you can derrive 5.1 out of the setup in post, thats really what sparked this objective as the surround sound setup to be an accurate representation of how it went down, would benefit from "pointing" each channel at the respective angle that the user would (ideally) be listening at to make it as realistic as possible.

The theory is, 3 hypers for the front channels with the two sides being at an angle of maybe 110/120ish, and the rear being cards at 90. I can probably figure out the angle easily enough, but the pattern could use a little work.

raw sample of the recording:
http://taperssection.com/index.php/topic,119469.msg1596014.html

[Todd R]

Thanks notlance and mshilarious for your inputs and those articles.  Looks like I've got some more reading and homework to do. I thought I was understanding db's, but apparently not quite.  I think dbu (voltage) and db SPL (pressure) I'm getting, but I'm not sure how those end up relating to dbFS.

[DSatz]

Arrgh. No, the decibel was not "used for two different measures"--it is always a power ratio. But when power is developed in a given (fixed) impedance, the current is proportional to the voltage. The power is then proportional to the square of the voltage--so you can predict the change in signal power that will result from a given change in signal voltage.

The formula given by notlance assumed that the "60/40 mix" was expressed in terms of signal power. There would be good theoretical justification for such an approach, BUT in modern practice it is almost never what anyone means when they use percentages like that (e.g. in Adobe Audition where the M/S matrixing controls are set in terms of percentages). Instead, they are nearly always talking about signal voltages feeding a high impedance.

If you're historically-minded, this may come across as a perversion of what decibels were originally about back when 600 Ohm loads and impedance matching were the norm for audio. Those who are aware of the distinction and proud of it--or who are versed primarily in physics rather than modern audio practice, will generally say flat out that they're dealing with signal and/or noise power as such.

But that is only likely to happen in an academic discussion or a research paper. Otherwise, people nearly always mean voltage when they use percentages like this. So I think that the relevant formula is the one which Todd R gave, and his answer is the same as I would have given: a 3.5 dB difference in gain.

--best regards