Someone on the Linux Audio Users list asked how they could analyse a load of FLAC files to work out if it was true for their music collection, that bass frequencies below about 150 Hz (say) tended to be centre-panned. Here's my answer.
First of all, coincidentally I know that Pedro Pestana published a nice analysis of exactly this phenomenon, at the AES 53rd conference recently. He actually looked at hundreds of number-one singles to determine the relationship between panning and frequency in the habits of producers/engineers for popular tracks. The paper isn't open access unfortunately but there you go.
So anyway here's a Python script I just wrote: script to analyse your audio files and plot the distribution of panning per frequency. And here's how it looks when I analyse the excellent Rumour Cubes album:
(Just to stress, this is a simple analysis. It simply looks at the spectral representation of the complete mix, it doesn't infer anything clever about the component parts of the mix.)
See any patterns? The pattern I was looking for is a bit subtle, but it's right down at the bottom below 100 Hz (i.e. 0.1 kHz on the scale): the bass tends to "pinch in" and not get panned around so much as the other stuff.
This analysis of Lotus Flower by Radiohead (by Daniel Jones) shows the effect more clearly.
This is what's generally observed, and widely known in mixing engineer "folklore": pan your bass to the centre, do what you like with the rest. Not everyone agrees on the reasons: some people say it's because the bass can cause the needle to skip out of vinyl records if it's off-centre, some people say it's because we can't really perceive the spatialisation very well at low frequencies, some people say it's just to maximise the energy in the mix. I have no comment on what the reasons might be, but it's certainly folk wisdom for various audio people, and empirically you can test it for yourself by analysing some of your music collection.
NOTE: Code and image updated 2014-02-08, thanks to Daniel Jones (see comments below) for spotting an issue.