I had an idea. Why not space gears on a bike the same as musical notes? For example, in music, if you start on a certain note (let's say C3), you need to go up 12 more half steps (notes) to get to C4, an octave above C3. The frequency of C4 vs. C3 is exactly double. The notes are spaced with intervals of 2 ^ (1/12) which is about 1.06. So for a 12 speed bike, you would have 12 closely spaced gears which you could shift individually if you need close ratio or in pairs if you want more normal 12% spacing. When you run thru all those gears you could then flick a doubler gear (maybe located in the bottom bracket) that then doubles all the ratios and then you repeat all of those 12 gears again in order. There would also be a doubler gear in the hub. So for example, in the low mode, you can have gears 0.50 to 0.94 Engage one doubler (either one) and you get 1.00 to 1.92, engage both doublers and you get 2.00 to 3.84. Notice there is no overlap in the gears. you will basically have a progressive 36 speed with the option to shift 2 gears at a time (skipping gears) if you want 12% between gears and thus making it a progressive 18 speed. More likely is you would pick a range (low, med, or high) and use it as a close ratio 12 speed. You could even use it as a super wide range (4:1) 3 speed. Just pick a middle cog for example with the halving gear enabled, spin that out then disable it, thus doubling your gear. After spinning that out actuate the doubler gear and you can go fast.

You can control the overall range by changing the single front sprocket. For example, 36T could start you out at 0.50 in the low gear but maxes out at 3.84. If you prefer taller you could run a 45T so you start out at 0.625:1 and top out at 5.00:1. (135 gear inches on a 27" diameter tire).

Also since the gear changes between the 3 ranges are from one end of the shifter (12) to the other (1), you can just twist the shifter quickly, eliminating the need for a precision shift like in a 3x9 progressive shift attempt where you have to "bounce" between chainrings and cogs.

So here is my 1st attempt at getting close to 6% between gears using cogs:

36, 34, 32, 30, 29, 27, 25, 24, 23, 21, 20, 19.

I know for me, I would spend a lot of time in the middle range (1.00 to 1.92) and would love to have the close ratios for when I get a headwind. What sometimes happens is I would shift from a 16T cog to an 18T but what I really needed is a 17T. Well my new gearing system would handle that cuz you can shift from a 32T to 34T which is same as going from 16T to 17T as far as gear ratio.

So is this a good enough idea for someone to build this bike? What would be the drawbacks of it? Might the efficiency go down significantly with the triple gear setup or should it be ok? Note that on motorcycles, only about 85% of the power of the engine makes it to the rear wheel so I would think if a bike is 85% or better that is acceptable with 90+% being a target.

Correction: one will be a halving gear and the other would be a doubling gear. With both disabled (bypassed), the bike would be in the midrange gears (1.00 to 1.92 for example). Front sprocket would be size 36T to get midrange to start out at 1.00 (36/36) but of course roadies can adjust larger such as 45T and mountain bikers can adjust lower such as 32T or even 30T.

Extreme hill climbers that want a 7.5" gear (27" diameter tires) would need a 0.278:1 low gear which can be had by replacing the 36T front sprocket with a 20T. Even with that ultra low first gear, shifting to the highest gear would give about 60 gear inches which is good enough for cruising around.

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    This is 8 questions on gearing in 4 days. Same question as bicycles.stackexchange.com/questions/36684/… Yes voting to close. – paparazzo Jan 24 '16 at 9:38
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    @David you ask a lot of questions but you never actually do anything with any answers you're given except ask more questions. – Móż Jan 24 '16 at 21:15
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    @David Oh, excuse me, music space makes it totally different? An octave is double. So you purchased an inner tube - what does that have to do with gearing? You have a strange sense of logic. I will try not to be rude but I will vote to close any of your strange questions. To me this is spam. – paparazzo Jan 24 '16 at 22:54
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    I'm starting to agree with @Frisbee here: but for a slightly different reason. What is the question you are asking @David? It seems like you just want to start a discussion about gearing - which is fine and could result in a brilliant new breakthrough - but I think the idea of StackExchange forums is to be Question/Answer format so that people can get questions answered, and search for old answers to similar questions. Your open-ended discussion doesn't really fit that pattern. A simple test is: could someone actually provide an answer to your question that would resolve it? – brendan Jan 25 '16 at 4:37
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    @brendan apparently not, he's now asked 13 questions in 3 days. He's accepted none of the answers and hasn't reported that he has tried to implement any of them. – Móż Jan 25 '16 at 11:19

I think it is a good idea since it gives the rider a choice between close ratio and skipping gears. Perhaps a special shifter that has 2 rings, one shifts every gear and the other shifts to every other gear (such as cogs 1,3,5,7...). Then the rider can start in a desired low gear and perhaps quickly go up thru the gears 2 at a time until the midrange gears at which point there will be some fine tuning based on load (wind, slight hill...) so then use the close ratio gears of about 5.9% spacing.

A more practical setup might be a 2x7 using chainrings and cogs but with a doubler/halver gear either in the rear hub or BB. That would be 28 progressive gears but can be shifted in 2s (like a progressive 14 speed).

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