This question is an exact duplicate of:
This question is not the same as the 36 gear post which used a combination of internal hub gears, cogs, and chainrings. This one is much simpler and much lower cost.
Part of the problem of something like a 1x15 (which doesn't exist) is chain misalignment. However what about something like this to get 15 progressive gears with good chain alignment? You have 5 cogs in the back, spanning a 1.75:1 range (28, 24, 21, 18, 16 for example). However, instead of the typical triple front, have the fronts so they are 2x of the next smaller chainring. For example, imagine something like 14, 28, and 56 front. This would be most practical on something like a roadbike. The 3 front chainrings would be aligned with the innermost, the middle, and the outmost cog. Crosschaining would be moderate at most so nothing to worry about. The idea here is you can start with the granny chainring, shift all 5 cogs, then go to the middle chainring and repeat all 5 cogs, then shift to largest chainring and shift all 5 cogs again. That would give you 15 progressive gears without having to do any fancy interleaved shifting. There is no way to get duplicate gear ratios here and the change between adjacent gear ratios is a reasonable 15%. The range (spread) between lowest and highest gear would be 7 which is quite generous (lowest is 14/28 = 0.5 and highest is 56/16 = 3.5). If someone wanted this biased more towards taller gearing that could easily be done.
So my question is why don't we see gearing like this on bikes when it makes good sense? Even a child can grasp the simple concept of shifting thru all 5 cogs then go to the next larger chainring and repeat.
This concept can be tweaked to 3x4 for someone who wants wider gaps between gears and fewer gear ratios and to 3x6 for someone who wants narrower gear spacing and more gears (18 vs 15 vs 12 gears total).
If a 56 tooth front chainring is too large, we can go with 13, 26, and 52 instead and adjust the rear cogs to 26, 23, 20, 17, 15.
I think it would be fun to make a bike like this but I think the problem is the FD wont be able to handle that much difference in tooth ranges but if that is the only limiting factor, then perhaps a 2x5 or even a 2x6 with this same concept. That would have a spread of about 4 which is good enough for a roadbike.
I actually checked this technique with my bike and if I change my granny chainring to 22 and keep my 42 large, it will work fine cuz when I shift from small/small, I don't then go to large/large cuz of the MegaRange gear I may eventually have. I am actually temped to try it. It would give me 13 progressive gears which beats a 1x11 in several ways. 1x11 has its advantages but well chosen sprockets in a 2x7 setup can beat it in other ways. Changing my $100 bike to a 2x7 is much more cost effective than going to a 1x11 and I will have more range too. Actually there is $0 cost if I just shift over the middle chainring (skipping it entirely but just using it as a "ramp" between the smallest and largest chainrings.