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Is there a particular reason why neck pickups on guitars are often placed exactly where an open string harmonic is found ? Years ago I suffered from 'lost harmonics' till I realised that the one directly over the neck pickup won't sound if only that pickup is on. It was trying to pick up the part of the string that was NOT vibrating !Switch another pickup on, and the same harmonic can be heard.

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Yes, pickups are places to take advantage of string harmonics. In addition to additional harmonics, there are harmonic deadspots that you would want to avoid as well.

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2  
This is one reason why 22-fret guitars sound different than 24-fret guitars. With a 21 or 22-fret neck, it's possible to position the neck pickup in the "sweet spot" for certain harmonics on the open strings. With a 24-fret neck, the pickup has to be positioned away from the position where those harmonics are the richest. – user1044 Jan 11 '13 at 4:07
    
thanks for the input, but if they're placed where the harmonic happens, surely they won't pick it up. My point entirely. – Tim Jan 12 '13 at 17:51

A "harmonic" on a guitar is a note played by gently touching a vibrating string at the node point of some overtone, and doing this mutes all the overtones you'd hear from the full length string that don't share this node. So you're asking if there's a reason why neck pickups seem to be placed under the node point of an overtone for an open string, or really, are neck pickups placed under the node for a low-order overtone?

This is a good question, because if so the chosen location mutes one of the overtones most responsible for the definitive timbre for six of the most commonly played notes on a guitar. The short answer is yes because there is no location for a neck pickup--especially a single coil--that is not under a node, or so close to a node that it may as well be under a node.

Here's a graphic from the Wikipedia Guitar_harmonics page illustrating node locations for harmonics of increasing order (the nodes are where the lines cross):

Basic and harmonic oscillations of a string

and here's another graphic from the same source showing where these nodes fall relative to the fretboard (touchdown points are nodes, peaks are anti-nodes):

enter image description here

From the second illustration you can see that the amplitude/volume of the various anti-nodes (where an overtone is loudest) varies the most at 1/2 and 1/4 the length of the fretboard, and varies the least as you get closer to the bridge or the nut. In other words, the overtones are going to be highly uniform over the bridge pickup, and heavily colored around the neck pickup, emphasizing some overtones at the expense of others. Anywhere you locate it, there will be a tradeoff.

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Thanks. My point is that at any node, theoretically, the vibration of an open string will be less, if not at all. So why would the location for a pup be exactly under a node rather than between two, which from the graphics is entirely possible. – Tim Jan 19 at 20:52
    
You can select a point that is technically not exactly under a node for orders 2, 3, or 4, yes but the vertical distance between the curves at any point represents an audible imbalance. At the bridge pickup--your point of reference--the curves are all very close together, so in comparison the neck pickup is always going to have one or more overtones that are so dwarfed, they may as well be a node. – Jay Huggins Jan 19 at 21:47

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