Hi Dave,

>Now, I find this fascinating because it isn't the kind of approximation I

would have ever come up with. I suspect it is precisely *because* you don't

have a conventional math background that you came up with it

I think that�s fair� As well as [not having a conventional math background]

no excuse for erroneous data.

>It comes out with many N's and D's that are too high for my liking, but I

am curious to understand why it works at all, and what its limitations may

be.

Perhaps for mine too� Though I�ve yet to see a radically different

conversion method will both A) UNIFORMLY addresses _every_ interval of

_every_ (whole number) n-tET, _and_ B) CONSISTENTLY renders a closer

approximation in smaller ratios.

>What if we use 53-tET and get 31 * 22 / 53. This clearly doesn't work.

0

---- = 155/155.

53

1/1, 78/77, 157/153, 79/76, 159/151, 16/15, 161/149, 81/74, 163/147, 82/73,

33/29, 83/72, 167/143, 84/71, 169/141, 17/14, 171/139, 86/69, 173/137,

87/68, 35/27, 88/67, 177/133, 89/66, 179/131, 18/13, 181/129[i]�2/1

>How high does d have to go before this diverges from the original formula?

To be truthful I just (re)discovered this method this weekend (along with

about four or five other convoluted variations), and have not yet done any

of the tedious checks and double checks -- but I am pretty confident that

while the 'terraced overtones' will of course keep on increasing, and hence

become more and more �unsightly�� the net results should remain

appropriately analogous to the lower numbered divisions.

Dan