<sigh>
I know what you're saying, but the working lingo dictates that 18:1 is a lower gear ratio than a 4:1. No ands ifs or buts. Yes, it may not seem to make sense to you, but it is the working language.
If you're looking at a new truck with a 3:07 rear gear, and you want to tow a trialer, the salesman will suggest you buy a lower set of gears and have them installed. He'll not suggest a 2:41, he'll suggest a 3:42 or 3:73
If you call grover and ask for their tuners with the lowest gear ratio, they'll send you their 18:1 tuners, not their 14:1
Argue all you want about quotient and other stuff, the working language is what it is. Accept it. You're not going to change how to world speaks gear ratios.
Guage works backwards, too, and so many people don't understand it. I overheard a fella bragging of his new boat once, and he was describing the differences between it and a competitor's boat that he was looking at. He said he bas4ed his purchase decision on the fact that the one he bought was made of 16 gauge aluminum and the competitor's was 14 gauge. He was so proud of his smart decision to buy the stronger one that I didn't have the heart to tell him that his 16 gauge was much lighter and thinner than the other's 14 gauge.
Same happens here. Folks often buy the wrong something or other because they don't know, or refuse to believe, that higher numerical numbers in gears mean lower gears. A lot of folks have too much pride when on the phone ordering stuff, and they won't ask; they'll look at the catalog, make their decision and call and place the order like they know what they're talking of. A good example would be if you hear me say to someone that the Grover Sta-Tites with the lower ratio are the better ones, you might run out and order them up, asking for their 14:1 instead of their 18:1. Wrong....
In the case of our truck, you may tell the salesman to knock a few hundred off the price and you'll take care of the gears. He accepts, you buy the truck, then ask him what gear set he recommends. He just simply says that the next set down will be perfect for you. So, you run to the hot rod shop, and look in the catalog, and see that the next one down is 2.71:1, and you have them install the gears. Truck sucks the big one, and can't pull your trailer. The reason? The next gear set down was a 3.42:1, not the 2.71:1 You refused to accept the working language, and it bit you. You can sit there for hours, telling the salesman that you are totally ticked off at his for telling you you needed lower gears when in your mind, you needed higher gears, but he'll just shrug and repeat what I'm saying: lower numerical ratios are higher gears, higher numerical ratios are lower gears.
Period.
s in automotive usage, a 3.14 final drive is a 1:3.14
NO!!!
A "1:3.14" ratio is an overdrive(input turns one revolution, output would turns 3.14 times)
In our world, we have a 3.14:1 ratio, where the input(the driveshaft) turns 3.14 times while the output(wheel axle) turns once.Mario38494.5817361111
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) supporting a resergence of popularity for the instrument? I don't mean to be slamming the instrument but there is a reason why they (and lutes too, for that matter) lost favor to the guitar.
) but if this guy can make a living doing this (he kind of looks full-timeish to me) maybe I should give it a try. I think I'll start building high-end tin whistles! 
