help with maths question "please"

decibel madness -

PREAMBLE - having read the posts in the 64 v 32 bit mixing post, i decided to run the output from my Audigy NX1 USB soundcard to a scope to view the “actual” audio output - and i must congratulate Soundblaster for the quality of the sound both visually and aurally they produce - the audio source was a 1khz sinewave recorded at 0db - as i say the output was perfect even ot 0db not a hint of cliping, so next i cloned the track and played back to check for any phasing errors there was none - i did this at 32bit and 64bit mixing levels and could neither see or hear any improvement using 64bits - BUT here is the question -

what is the answer to this equasion “0db plus 0db equals ?” -

I.E. i add 1 (mono) track at 0bd to another (mono) track at 0db what is the combined (added) decibel output ? -

according to two websites (links below) the answer is +3db but N shows +6db ? -

one website shows that the SPL of 0db plus 0db is +3db - and that the SPL of 0db plus 0db is +6db - but there is a difference between the “SPLs” one that generates +3db refers to Signal Power Levels, the one that gives +6db refere to Sound Pressure Levels, IE the presure (level) of sound that is generated by an audio emiting evice (a speaker) not the level of a waveform before it has been sent to a speaker -

so if the answer is +3db then the mixing levels produced by N are "TECHNICALLY IINCORRECT - then if the answer is +6db then all is well -

over to you -

Dr J

links to decibel calculators

I don’t think you should be concerned with SPL. I would think the meters are dsiplaying dBu or dBv. Most likely dBu RMS or P to P as determined by the signal interpreted by the AD/DA converters.

Where’s LearJeff when you need him?


PS Certainly the soundcard output should be measured using dBu or dBV. dBu is the amplitude RMS referenced to 0.775V. dBV is referenced to 1V. We’re talking electrical properties here not acoustic properties.

shouldn’t the question be, "what happens when you divide by 0db?

“what happens when you divide by 0db?” - please explain how when mixing two items into 1, division is involved ?

Dr J


I have no idea. I’m sure that encounter could create a time paradox, the result of which could cause a chain reaction that would unravel the very fabric of the space-time continuum and destroy the entire universe. Granted, that’s worst-case scenario. The destruction might in fact be very localized, limited to merely our own galaxy.

Plus, it would probobly sound like crap.

I think Fish was joking Dr J :D

But, Diogenes has got it.

Doubling of power is an increase of 3dB, doubling of voltage or current is 6dB (assuming constant impedance of course). That’s because power is related to V squared or I squared, and a square logarithmically becomes ‘twice’.

And speaking acoustically, we have the same thing; sound intensity, (sound power) is double at +3dB.

But, SPL (sound pressure level) measures pressure, not intensity (it’s the acoustic equivalent of voltage, sort of) so twice the SPL is +6dB, i.e., 4 times the power.

Anyway, answering the joke, :D dividing by 0dB is no problem, just think in terms of logarithms.

0dB as a ratio is 1:1, so multiplying or dividing by it is just the same as multiplying or dividing by 1, i.e, no change. :p

PS, I’ve realized I haven’t actually answered your question Dr J.

So, I don’t know how n-track or other digital measuring/estimating circuits work, but in the real analogue world with linear circuits:…

If you add two unrelated signals together, but with the same average power, then the sum will be around +3dB, i.e. twice the power.

However, if the two signals are truly identical, and in phase, then the voltage peaks will sum, giving +6dB, i.e., 4 times the power. (And of course, if they’re 180 out of phase, you’ll get nothing, and if they’re somewhere between in-phase and 180 out of phase, you’ll get a vector sum between -inf and +6, depending.)

yes looks like its voltage (+6db) as Sonar LE shows same as N, interestingly though Magix music editor shows tracks as 0db and shows master output as 0db - individual tracks are shown on output meter as -6db -

Dr J

Some applications, including n-Tracks when the function is turned on, will lower output blindly based on the number of tracks.

n-Tracks, as far as I know is doing the right thing when that function is off (I’d expect +6db when two tracks are identical).

It’s VERY confusing…OH YEAH! :D

I didn’t read the page you posted. Here are the facts. BTW, it has nothing to do with what dB scale you’re using, or voltage, etc.

When adding uncorrelated two audio tracks at the same level, the increase is 3dB.

A track is 100% correlated to itself. The result of doubling a track is a 6dB increase, or double the amplitude, just as you found out.

If anyone remembers their physics and calc, the 3dB increase corresponds exactly to the sqrt(2) increase you get when adding two noise sources (e.g., when calculating probable errors). But I’ll spare you the math.

Try it: generate two white noise waves, set them to 0dB, and mix: you get 3dB higher (on average!).

BTW, correlation is very important when considering the result of adding two tracks. Two music tracks in the same song are only “mostly” uncorrelated. (Fortunately, they’re less correlated than you might think – otherwise we’d have even more ‘rogue peaks’.) And if you add a signal that’s “anti-correlated” (180 degrees out of phase), the result is -infinity dB (silence). So, be careful about understanding the difference between talking about arbitrary, uncorrelated tracks, and special cases like the same track or the same track inverted.


Rules of thumb:

3dB - noticeably louder, the result of adding two uncorrelated tracks, twice the power
6dB - twice the amplitude, 4 times the power
10dB - twice as loud, 10 times the power

Moral: if anyone tells you “look, this amp is 150 watts, so it should be way louder than that 100 watt amp”, don’t believe it. The difference here is in the weeds, and depends far more on the overall quality and which is more conservatively rated. If the two amps were in the same series of a given manufacturer, the 150W would be barely louder than the 100W one. (Less than 2dB, IIRC – can you really tell that difference? Well, sort of. I think I can detect a 1.5 dB change, but not out of context.)

Oh, after looking at one of the pages: we’re talking about the equivalent of sound pressure level, not sound power level. Ignore sound power level for our purposes, it just adds to the confusion.


Here are the facts. BTW, it has nothing to do with what dB scale you’re using, or voltage, etc.

In Doc’s case it does have something to do with it. He is looking at the output of the card with an O’scope. He should use dBu or dBV for his mathematical noodlings yes?


PS Well… I guess for this exercise it probably doesn’t really matter. It would prove interesting to me though to have the Soundcard’s specs, properly load the output and THEN observe the correlation between actual “power” versus displayed “power” by the softies Vu meters…

Hi All:
I can remember working at the Musicstop and servicing Yamaha P-2200 power amps… The “Magic” numbers after powering up one of those amps was when The output of one of those amps could generate 48 volts P-P into an 8 ohm resistive load. Equal to 200 watts into an 8-Ohm load… The signal generator developed 1khz. at ~1.414 volts If the scope saw the 1 khz. wave form with no distortion for maybe 5 minutes, I would call the repair O.K. I would allow the amp to idle for one hour and then adjust the bias idling current with no signal applied and repeat the signal at some frequency other than 1 khz. and that would be IT for the the amp… if the offset voltage was lower than 10 mv. D.C. at the speaker terminals and the amp idled at room temperature…

A power amp that develops 20 volts AC. into an 8-ohm resistive load is generally rated at 100 watts…

A power amp that is twice that power or double that in rating is considered to have to be a 400 watt rated amp into an 8-ohm load… Or square root scale… or would have to generate 80 volts AC. into an 8-ohm load… Equal to 3 db. or Log. scale…

I stand corrected… as to how those numbers are expressed…


the ideas behind it are pretty well explained here. I was just going to add that I’m pretty sure if you pan a track from left or right to center that it increases by 6 db. So I’ve always correlated cloning a track to that… don’t know if this will be use to anyone lol

OK so far, i thank everyone for their help with decibels, when the topic switched from the inside world the DAW to the outside world “the amplifier” something was missed out, “the soundcard” and this opens up another problem - a soundcard is not strictly speaking an amplifier it is a line level device - i was testing it straight into the scopes 1 meg ohm inputs which may not have been the correct loading, i really should have made a breakout cable so that i could observe the signal when loading the soundcard with powered speakers or when signal is going to the line in of a poweramp -

two points - (as said beforre) Magix software shows 0db on track meters and -6db down on the output meter, using Ns reduce levels on added tracks does reduce the levels of added tracks but leaves the first track unaltered, to obtain a better balance it would be better if N reduced the level of the first track as well -

clicking just above the fader knob on track and master meters increases fader level by 1 tenth of a decibel clicking below the fader knob decreases level by same amount, precision fading or what -

Dr J


using Ns reduce levels on added tracks does reduce the levels of added tracks but leaves the first track unaltered, to obtain a better balance it would be better if N reduced the level of the first track as well

Yes. Not reducing all tracks the same amount would be a bug.

Panning makes a difference, too. Some higher end analog mixers go to great lengths to keep an even volume-as-heard level when a channel is panned. I think that means it’s -3db when it’s dead centered when compared to hard panned to either side. I don’t think I’ve ever seen anything in the digital world do that, but I’m sure some must.

Comes from…_mixing and is related to Zynewave Podium, but it still gets at some stuff discussed here…


Technical Note On 64-Bit Mixing

If your music production mainly concentrates on using softsynths and encoding the final master to MP3 files, then don’t bother with 64-bit mixing as you won’t be able to hear any improvements in audio quality.

If however you are producing music recorded in pristine studio conditions and aimed for reproduction on high end audio equipment, 64-bit mixing will offer better precision and larger dynamic range.

The 64-bit mixing will be utilized when the mixer engine is processing and routing audio internally. The audio will be converted down to 32-bit when routed through plugins that only support 32-bit processing. Support for 64-bit processing was introduced with the VST 2.4 plugin protocol.

When describing floating point numbers, the 32 and 64 bits refer to the amount of memory that is required to store the floats. The bits are split into two parts that store the precision and the exponent for the ‘floating point’. 32-bit floats offers 25 bit precision and 64-bit floats offers 54 bit precision.

The advantage of 64-bit mixing is evident when an audio signal is gain scaled or when two or more audio signals are summed in the mixer engine.

Gain scaling occurs when the track gain or pan settings are affecting the audio signal. The scaling involves multiplying the floating point audio signal with a floating point scale value. These multiplications will result in values that use more precision bits than the original audio signal, causing the least significant bits of the result to be discarded.

To illustrate the effect of summing, let’s assume that you have two 25 bit precision audio sources that you want to mix together. These sources could be wave files or the 32-bit floating point output of VST plugins. If you mix these sources together without changing the gain of the tracks, the output will fit within 32-bit floats, provided that the summed output does not clip. If you change the gain of one of the tracks, then the 25 bit precision of that track is displaced up or down in relation to the other track. A gain change of 6 dB will result in approximately one bit displacement. When summing the two tracks the combined precision interval has thus been extended beyond the 25 bits that can be stored in 32-bit floats, so the least significant bits are truncated and you loose some of the precision in the audio sources.

This is where 64-bit mixing will offer an advantage over 32-bit mixing, as it can use 54 bit precision to store the results of gain scaling and summing, and thereby reduce the artifacts of the floating point truncations.

So what’s the point of the higher precision if the master output is being bounced to a 24-bit or 16-bit wave file? For every audio track that you add to a mix, you add noise as a result of the truncation of the lower bits of the signal. The accumulation of these rounding errors can result in a slightly degraded output that can be present even when rendering to 16-bit wave files.

Despite these apparent mathematical benefits, 64-bit mixing will only yield a minimal quality improvement. 32-bit mixing is still fully sufficient for professional grade productions.

good read - now have that link stored in my favourites section -

Question - how does PODIUM compare to N ?

Dr J

Hi Gents:
I’d like to reply to this thread with some ideas that I have questioned over the years with this pan topic…

I’ve serviced some of the top-end mixing desks that were available in the world over the years that I serviced recording equipment…They ranged from Nieve/MCI/SSL SoundCraft and down to Mackie/Peavey…

The panning on the Top-End Desks had designs that had multi-ganged pots that controlled the attenuation of the channel levels as the pan was adjusted… The lower-end mixers had pan pots that took the L-or-R channels to earth/ground as the pan pot was adjusted… That adjustment allows for ~ +3db gain change to the channel that the signal is being panned… to… Depending upon the value of the pot in the circuit design…

That circuit design is acceptable if you are not concerned with “Levels-and-Frequency” compensations…

As well, the lower-end circuit designs do not address the pan circuit’s “Loading” of the signal’s through-put… And… it’s not even called a T-Pad attenuator…

The Hi-End designs compensate for Levels and Loading as the pan is adjusted… The attenuator’s circuit addresses the “Loading” and the “Frequency” of the signal’s path by using a multi-ganged pot in it’s design… As well, the Hi-End desks have inter-stage Buffer/Unity-Gain circuits that isolate/buffer every circuit stage from each-other, on the “Strip”…

I’m sure that there is “Maths” that can be coded to address this in the “Digital Domain”…

This … in my opinion would be “Tilling” NEW Ground for any Multi-Track Editor Programmer, interested in presenting this design to the Digital Audio Community…