Talk about buzz... lots of good observations buried in here, amidst quite a bit of confusion. I was hoping to wait until I actually have my own Alembic (should be a matter of weeks at this point), but can't bear to remain on the sidelines any longer, so let me take a stab at focusing the discussion a bit.
The original question had to do with how to achieve the lowest possible action, and so far we've covered construction, setup, string selection, playing style, and of course physics - which is probably the right set of topics.
Construction: Mica sort of said as much, but to be clear I think it's fair to say Alembic is not going to build a bass differently depending on whether you prefer high or low action. They'll set it up specially if you ask, but there's no need for a fundamentally different design.
You need a strong, uniform neck (all frets exactly the same height, no weird twist or anything), securely attached to the body, but you'll get this on any Alembic. On a lesser instrument, the frets may not be even, or more likely you'll get some bumps or dips in the neck itself, particularly with higher tension strings (and more truss rod), which will give you buzz in some particular locations before others, so you won't be able to get the overall action as low.
If you want to push the limits of low action, you'll have less tolerance for environmentally-induced shifts of the neck, so you would probably benefit a little - but only in the sense of having to adjust it less often - from a neck-through design and having some laminates in the neck.
Frankly, you can meet these basic requirements for a lot less money than an Alembic will cost you, if you know what to look for and have enough patience. But Mica is absolutely right, that if you just walk into a guitar shop and try things, most of them aren't going to be set up very well, and even if they are it will probably be with a more medium action, so that it's easier to play for an average customer.
(Mikey's case of having the bridge as low as it will go sounds a bit extreme - I suspect something is wrong here, not that the bass wasn't built to support low action.)
Setup: Joey is absolutely right, you'll never be happy until you learn to do your own setups (unless maybe you have a dedicated guitar tech who understands and can mimic your playing style perfectly...). It's *not* that hard, just takes a little time to learn, and is definitely worthwile. And like he says, settling on a set of strings is a big help. Once you get things to your liking, about all you should need to do is adjust the truss rods a little for seasonal (or traveling) changes, whereas switching to a completely different set of strings is probably going to cost you several hours, over the course of a few days, by the time you get everything tweaked just right again (bridge height, intonation, pickup height, in addition to neck relief).
Let's try to clear up any remaining confusion about neck radius vs. relief. When you sight up the neck, radius is the curve you see perpendicular to the length of the neck, i.e. in the usual case the middle strings stick up higher than the outer strings, and the neck radius (and bridge and nut) generally follow this curve. Classical guitars, and Trip's bass, are flat in this respect and may be said to have zero, or perhaps infinite radius (sorry Mica, I'm not sure 180 degrees is an appropriate term here).
Unless you have a very unusual playing style, you almost certainly want a more typical radius of 12 to 15 inches (12 is the Alembic standard, which seems just fine for most people). Neck radius is absolutely *not* related to action, assuming everything else is properly constructed and adjusted.
Relief is the term used to describe the concave bow you see sighting up the length of the neck. A neck which is setup perfectly straight is said to have zero relief - you could lay a straightedge across the frets and every one would just barely touch.
You normally want a *tiny* bit of relief (even perfectly straight Joey says you let just enough relief back in...). One way of measuring this is to hold down a string at the 1st and 24th frets, and then measure the gap between the string and the 7th fret (not quite the middle - normally you'll get a little more bow up towards the end of the neck, which is where you want it anyway).
Buy a cheap capo to hold down the strings at the first fret, use one hand to hold down a string at the 24th, and then try slipping a playing card between the string and 7th fret, without displacing the string. Personally, I'm happiest with just a touch more relief than one card, but definitely not two (my deck of 52 measures 15mm, so my card is not quite .012 inches). You should check both outer strings, and they should be close (though if necessary, favor more on the fat strings because they're going to move more).
Note that by holding down the string at both ends, we've eliminated nut and bridge height as factors. Other than putting on the strings you want to use, the first step is always to adjust the truss rod tension to get the relief pretty close to right, and then you can start working on the other stuff. I'm not going to get into that, just wanted to give you some idea that this really isn't very hard - by all means pick up a book and give it a try. I never even considered letting someone else set up my basses or guitars for over 25 years.
If you were trying to characterize the action you prefer, I think the most useful measurements would be the amount of neck relief, and the gaps between the outermost strings at the 24th fret, and possibly the strings you use. (Nut height mostly affects only notes at the first few frets, so it's somewhat less critical assuming it's not grossly off.)
Just to throw out some numbers, I'm using Thomastik jazz flatwounds, relief is about .013-.015, and string height averages about 3/32 at the 24th fret (mine happens to be fretless Carvin). I play fingerstyle with a fairly light touch, and consider this to be moderately, but not extremely, low action. (Mica - would you share with us the specs for your standard medium height setup?)
String tension: is determined *solely* by scale length, pitch, and the design of the string. Nothing else matters. In fact, the only thing that matters about the string itself is the mass. There's a good discussion of the math involved at
http://www.mcdonaldstrings.com/String_tensions.pdf (The problem with doing the calculations yourself is that you really need to know the mass of the string, but if the manufacturer publishes the tensions you can work backwards to calculate that. I did this myself when trying to figure out how much more tension I'd see by putting a 34 scale set on a 35 instrument.)
Note that what counts about the string is the mass, not necessarily the gauge. There's enough variation in materials and design, even between different types of sets from the same manufacturer, that two strings of the same gauge may result in different tensions (a flat wound will typically have more mass than a roundwound of the same gauge, because it's filled in with metal).
Anyway, assuming the same style of string from some particular manufacturer, putting the same set on a longer scale instrument (with the same tuning) will increase the string tension, as will using heavier gauges of the same strings, either of which will allow for slightly lower action because the string excursion will be less (for identical plucking, etc.).
Note that this does *not* imply that a 32 scale instrument is going to have less tension or higher action than a 34 - you'd most likely use a set of strings which were designed for that scale length, and they'll probably be smaller gauge or otherwise constructed somewhat differently to have less mass.
String tension is simple physics. Assuming the same scale length and tuning, a given set of strings will have exactly the same tension no matter who builds the bass or how it's constructed (assuming you don't make the neck out of rubber or something).
Playing style: it seems everyone understands that if you play hard, you'll need more neck relief and/or higher action and/or more string tension to avoid buzz, and that if you want low action, you're going to have to be gentle with it. But there are some slightly off-topic comments in here worth elaborating on.
Michael W. mentions he's noticed that the whole length of the string has different harmonics depending on where you pluck it, which is an excellent observation. In fact, the distribution of harmonics you get also depends on *how* you pluck it - if you pluck it in the same position, you'll get a wider or richer set of harmonics by using the broad side of your thumb (a wide plectrum) as compared to the sharp edge of a pick, because it excites the string differently.
Now, Bryan mentions that he likes to play over the bridge pickup, and wonders about moving it to a place where he prefers the tension of the string, and whether that would affect the sound. Yes, moving the pickup would affect the sound, but we need to consider that as a completely separate issue from where the string is plucked. It's really not at all like putting your mouth closer to the microphone, for example.
Where and how you pluck determines the relative strengths of the different harmonics which are set in motion. Pickup position determines which of those harmonics are heard, and at what relative strength. If you put a pickup under the 12th fret and played an open string, it would not pick up the 2nd harmonic at all, because the 2nd harmonic has a node (a place where the string doesn't move) right there in the middle of the string. (You know this, of course, because you can play the harmonic and actually leave your finger on the string as it continues to sound, right?)
So generally what you want to do is position the pickups at positions which are a good compromise for picking up a wide mix of harmonics. And it's always a compromise, because if you did the best you could for an open string, it would be quite a bit different as you fretted notes higher up the neck, and the harmonic nodes start getting more bunched up.
There's some interesting stuff on pickup placement and harmonic sensitivity at
http://www.till.com/articles/PickupResponse/ - you can skip the math and just look at the pictures, and get a pretty good idea of what's going on here.
For anyone who wants to get really deep into how strings vibrate (among other things), a classic reference is Fundamentals of Musical Acoustics by Arthur Benade. Unfortunately it barely mentions electric guitars (and not solid bodies at all), but many of the principles of pianos and violins are relevant to some degree. (Caution: it's a pretty serious book - I've read it twice now, and still haven't grasped everything in there...).
I know this has been an outrageously long post. I hope it's helpful, but if you feel I've wasted your time or space, go ahead and let me have it.
-Bob
