Time to break up all this Burlesque talk with something a little different. What's going on here, then?
Intonation. It's a bug-bear for some. We could talk about equal temperament concerns and mathematical subdivisions of scale-length and whatnot, but it would get dull quickly. Suffice it to say, tuning on any fretted instrument is always a little bit of a compromise.
In order to try get the damn thing to sound as closely in tune as possible, we 'intonate' each string to compensate its length so it sounds right when fretted. On most electric guitars, we do this by adjusting the string's saddle—moving it backwards or forwards to slightly lengthen or shorten the string's sounding length. Easy-peasy (unless it's a Floyd Rose-type bridge in which case it's more annoying than being repeatedly kicked in the shin by a crying child in a restaurant).
Acoustic guitars offer a bit more of a challenge than most electrics though.
An acoustic guitar generally has a fixed saddle (of bone or whatever). The fact that the saddle is installed at a slight angle (increasing string length from 1st to 6th) string is a nod towards some string compensation. The pre-shaped, compensated saddles that many guitars have these days is another step in the right direction.
For most people (and most guitars and strings) these get close enough that tuning issues aren't glaringly awful.
Sometimes, and for some people (depending on playing style and the curse of having a good ear), it's not enough.
Intonation depends on precisely seventeen million variables. Well, give or take—there are a lot of factors that all interact to determine the best setting. Tweaking setup and string choice can help if there are problems but sometimes that's not an option or isn't sufficient.
What's going on in the images above is that I've used little chunks of rosewood to individually intonate each string on this acoustic guitar. The saddle has been removed and the rosewood is acting like an individual saddle for each string. I poke it back and forward to find where each string properly intonates.
StewMac actually offers a doohickey that does this without fiddling with bits of wood. I've been threatening to get one for a while but I'm forgetful and tight.
Popping a piece of cellophane over the bridge lets me mark the location of each intonation point and the actual saddle location itself. This gives me an indication of where each string should sit on the saddle to sound best. It's easy to transfer this to a new saddle blank.
This guitar, its setup and strings, actually indicates a complication: As you can see in the image in the right, some of the optimum intonation points sit outside the actual saddle.
This happens sometimes. On an older guitar, it's not unusual to have a saddle actually misplaced. This can necessitate filling the slot and actually re-routing it in a new position. That doesn't tend to happen so much these days but, depending on other factors, it's possible that one or more intonation points might be in front of, or behind, the saddle. Of course, making a much wider saddle is an option but that adds expense and entails modifying the bridge to accommodate that wider saddle.
The other option is compromise (we're back to that word again). In this case, carving a new saddle with intonation points as close as possible to those measured will improve things considerably. Four of six strings will be pretty much perfect and the remaining two will be a lot closer to perfect than they originally were. Overall, it sounds much more in tune than it did without the need to irreversibly modify the bridge to accommodate a wide saddle.
So, we end up with a slightly odd looking saddle that sounds a lot better and the original is safe in the case in case it's ever needed. Not too shabby.
It's worth remembering that this is probably overkill for the majority of people. Most guitars and guitarists are generally ok with the regular or pre-compensated saddle. Failing that, a good setup or a change of string-gauge will probably get you close enough that you'll be happy. If you're still hearing problems though, a custom-compensated saddle might be an option.