I recently put a 130mm 52t SuginoSR ring on my bike.
I didn't have an EAI cog with 18 teeth, so I put a cog made by another manufacturer on the hub.
As I spun the pedals with my bike on the workstand, I could see the chain loosening and tightening as everything went round and round.
I thought I might have somehow put the chainring on the spider off center, and so I tried Sheldon Brown's method of centering the chainring.
I spent half an hour trying to center the chainring and didn't get much improvement.
Anyway, I rode with this combination for about two weeks, listened to the chain noise which came and went rhythmically, and eventually decided I had an out-of-round chainring.
Today I decided I had sufficiently habituated to the 75.9 gear inches that 52t X 18t X 23mm provided and I might find it interesting to play around with 80.5 gear inches.
I rummaged through my parts box, found a 17t EAI cog and put it on my hub.
As I spun the pedals my chain did not go up and down.
As I rode my bike with the EAI cog, I could hear nothing from the chain.
All along I had had an out-of-round cog, and not an out-of-round chainring.
I won't name the manufacturer of the out-of-round cog.
Suffice it to say that EAI has made at least one very round 17t cog.
I have found that with SuginoSR chainrings from Sheldon Brown on the outer position of the spider, if I use an EAI cog with the flange against the hub, I have a perfect, silent chainline with no loose or tight spots in the spin.
With this bike, a 2005 Pista, I have decided to buy and use only EAI cogs.
i'm trying to get used to around 80 gear inches and it's a bit much for me right now. i had a nice training ride the other day, all pretty flat, but commuting-especially in any kind of headwind- is a little bit of a grunt. i've got 48x16 (81 in.) right now, but i just ordered a 44t ring to put me at 74.2 in. which should be about perfect.
let me hear how over 80 inches treats you.
consider me to be (at least) the fourth user who wants to know the cog manufacturer.
also, ken, when you say "rhythmically" i assume you are referring to a "periodic" chain noise. i'm thinking you could tie it to either the chainring or the cog based on the period, relative to turning the cranks. if the noise (or loosening-tightening) is "rhythmically" synchronized with turning the cranks, then it really has to be related to the chainring, don't you think? alternatively, if the period is synchronous with the wheel rotation, then yes it pretty much has to be the cog. if it isn't really in sync with either, though, then the problem is likely with both the ring and the cog. at least that's what i think.