It's fairly obvious that when I'm on the smallest chainring and the lowest gear on the derailleur, I'm in "first" gear, and on the biggest chainring and the highest derailleur gear I'm in "24th" gear - but what about all those gears in between? Say I'm in the middle chainring and the third derailleur gear - am I in 6th gear? What does that make the first chainring and 6th derailleur gear? Is there some esoteric, arcane mathematical formula, or is this something we just don't talk about?

The answer is, it depends.

Depending on the size of your chainrings and the cogs in your cassette, there can be any number shifting patterns to get through the gears, and there are likely redundant ratios. In other words, if you have 3 chainrings and 9 cogs, you may think you have 27 gears, but in fact you have less than that because of duplicate ratios. Also, you should avoid the two ratios that cause the chain to cross over at an extreme angle, i.e. big/big and small/small. So, in practical terms, a 27 speed transmission really has 27 minus 2 minus 'all the redundant ratios' speeds. How many is that? It depends.

Here's a calculator to help figure it out for your setup:
Sheldon Brown's Gear Calculator

To get through the gears in order, you may have to do double shifts, i.e. move both the front and rear shifters. This is an occult art.

I avoid the entire arcane mess by using a NuVinci infinitely variable transmission. Since there are an uncountably infinite number of 'gears' I don't bother with counting, I just ride the d*mn trike. Cuz, ya know, some things just ain't worth doing.

Well, I'm certainly not going to lose any sleep over it, I was mostly just curious. Like the old saying goes, ...er, I forgot how the old saying goes. Oh well, I'll just find the gear I can pedal comfortably in and never mind what number it is.

As I recall, back in the OLDEN days, even before spandex, and 10-speeds were the creme de la creme of road bikes...

Bear with me now, many gallons of delicious cerveza have passed through this ol' body since then...

We used to talk about the gear we were in terms of the chainring number, a comma, and then the cassette number.

So, on my Schwinn 10-speed Suburban, when I had the chain on the largest ring (number "2") and the cassette in the middle gear (number "3") I would say I was in "2,3".

Does anybody know if they even use that nomenclature anymore?

I think too many people don't even know what the word "nomenclature" means...

>I think too many people don't even know what the word "nomenclature" means...<

Isn't that a new kind of clipless pedal made of unobtanium and meteorite shavings?

"nomenclature"

no - men - clay - ture;

nom - encla - y - ture;

nomen - clay - ture;

I figured it out, it means "follow the women riders because you will turn into clay"!

That's better than turning into a pillar of salt, I suppose...