Is there a way to merge to mono without boosting the center component?

Question

Normally, if you merge stereo to mono, the center component gets a +3dB boost because it is doubled. Is there a way to merge stereo to mono while keeping the balance between the center and sides?

Answer 1

If you want to control the relative levels of mid versus side information, a clear way to go is first run the stereo signal through a mid/side processor, then run that output through whatever process is collapsing to mono. If the mono collapse seems to change the balance of mid vs. side, you can compensate by adjusting the levels in the mid-side processor.

Answer 2

What is the question about?

When one mixes down a stereo recording to mono, the tracks which were originally closer to the center sound louder than the ones originally mixed on the sides, in comparison to the sound of the original stereo recording played on stereo speakers.

Why does it happen?

Let us imagine three different audio tracks e.g. three recordings of three vocal lines. For simplicity, let us assume they have the same average amplitude and loudness, and letters A, B and C represent the waveforms of these tracks.

Let us mix a stereo track in a way that the track B is in the center, track A is hard-panned to the left, and track C is hard-panned to the right. Let's do it without touching the mixer levels, and without pan-law compensation. The resulting waveforms of the left and right channels are:

L = A + B , (1)

R = B + C . (2)

Let us play this on stereo speakers. What will be the relative volumes of the three tracks A, B and C? A and C are played by a single speaker each, so they will have the same volume.

Track B is played by both speakers, with the same amplitude, so it will sound louder. By how much? The signal is 100% correlated in both speakers, which may result in a boost of up to 6 dB. However, sound coming from two displaced speakers and also possible reflections will result in a pattern of constructive and destructive interference in the listening space. For now, let us assume the track B sounds 3 dB louder than the tracks A and C, though let's keep in mind that the exact value may depend on the speaker placement, and acoustic properties of the listening space. Let us also note that this is not the boost mentioned by the OP.

What happens in mono mixdown?

Mixing down to mono involves adding two channels of the stereo track together, and dividing the result by 2 to avoid clipping:

mono = (L + R)/2 = A/2 + B + C/2 . (3)

What are the relative levels of track A, B and C now? A still has the same loudness as C. B has now twice larger amplitude than A and C, which corresponds to 6dB difference. In stereo the difference was 3dB. Therefore, the relative level difference between the track B and the tracks A and C increased by another 3dB in comparison to listening in stereo. This is the 3dB boost mentioned by the OP. Please also note that this value is approximate, just as the difference between levels in stereo we assumed is approximate too.

Why the pan law is not a solution?

Because it is irrelevant in the context of a single stereo track.

Pan law allows to automatically reduce the levels of tracks panned in center. The mixing engineer could have used it in the example above to reduce the level of the track B to prevent it from sounding louder than the tracks A and C in stereo. That would be equivalent to adding an additional factor (e.g. 1/sqrt(2) for 3dB attenuation) in front of the component B in the Eqs. (1) and (2) when producing the stereo mix.

However, pan law is not applicable to the subsequent process of summing the stereo signal to mono. It doesn't have any effect on the additional relative boost introduced in Eq. (3).

Why mid/side processing is not a solution?

...or at least it is not a solution in its simplest form

Let's start with explaining how mid/side processing works. Stereo left/right signal can be converted to mid/side channels, as follows:

M = (L + R)/2 = A/2 + C/2 + B, (4)

S = (L – R)/2 = A/2 – C/2 . (5)

one can then perform some processing on these channels, resulting in modified waveforms M' and S'. Then, we can convert the signals back to left/right:

L' = M' + S' , (6)

R' = M' – S' . (7)

Let us mix this down to mono:

mono' = (L' + R')/2 = M' . (8)

One might be tempted to boost the S channel, in order to compensate for the boost of the tracks in the center during mono mixdown. However, as shown in equation (8), side channel does not contribute to the mono mixdown. Therefore, any kind of processing of the side channel has no impact on the mono mixdown, and in particular, cannot compensate for the boost.

How can shifting phase help?

Mixing a signal with its copy with phases rotated by 90° results in sqrt(2) increase in amplitude, that is 3dB boost. Let's rotate the right channel from Eq. (2) by 90°. We get:

R'' = B'' + C'' , (9)

where R'', B'' and C'' are signals R, B and C transformed with the 90° phase shift. Let us mix it down to mono

mono'' = (L + R'')/2 = A/2 + C''/2 + (B+B'')/2 = A/2 + C''/2 + sqrt(2)·B/2 . (10)

What happened with amplitudes? Shifting phase of C'' does not (or should not) affect its sound. Thus, A and C still have the same amplitude. The amplitude of B is now sqrt(2) times larger than A and C, or 3dB more. This is the same difference as it was in stereo. Therefore the phase shift trick helped to compensate for the mono mixdown boost. A phase shift different than 90° will result in a different level of compensation.

Answer 3

You could put a Hilbert transform on one side signal before the addition. I would suspect that you might get more useful responses in the DSP stackexchange or possibly the Sound Design Stackexchange.

Answer 4

Folding down to mono by summing Left and Right doesn't merely double the Mid† component, it discards the Side component entirely:

The transform from Mid-Side to Left-Right encoding is as follows:

L = (M + S) / 2

R = (M- S) / 2

When folding down to mono by summing, we get:

mono = L + R

which is:

mono = [(M + S) / 2] + [(M - S) / 2] = M

...in other words, just the Mid component.

This is why testing for mono compatibility of a mix is important.

Even if you don't fold down to mono electronically (or digitally), the result is essentially the same when listening to a binaural recording when the distance from you to the speakers is substantially greater than the distance between them.

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† I am using the more common "Mid" term instead of "Center".