George wrote:
Dave wrote:

> I think 3 error needs to be below 2%, 5 error below 7%, 7 error below

> 10% and 11 error below 25%.

>

> My method of finding such things is clearly wrong.

>

> Can you do the calculations for the actual EDA's, or at least show

> the 11 error too? 275 and 2151-EDA's are definietely out.

I thought you knew about my consistency spreadsheet, but if not, then

enter the EDO# in the cyan cell to see all of the odds up to 51:

[Broken link replaced with:

Constncy.xlsx]

I haven't taken the trouble to adjust any of this for EDA's, but the

differences in the boundaries are very small. The apotome will change

by 7 times the 3-error, for 2460-ET <-> 233-EDA a shift of 0.02647c.

The half-apotome will shift by half that amount, or 0.01323c, and the

smaller minas by even less; e.g., in the 5C region the shift is ~0.005c

(about 1% of the width of a mina).

For EDO's that have a relative 3-error greater than that of 2460

(-0.8%), the relative shift will be somewhat more. But I don't think

that will be the case in whatever EDA we decide on for the tina.

> 576, 809 and 1105 are all very good. Is there no 31-limit consistent

> ET in this region? I keep thinking of the fact that Ben Johnston once

> composed in 31-limit.

That's a tough one. 20203-EDO (8539+11664, 1914-EDA) is 45-limit

consistent, with 0.3% 3-error, 0.9% 7-error, and 10.3% 11-error, but

its 5-error is 8.7% -- a little more than we would like. (Also, the

23-error, at 47.8%, though consistent, is rather excessive.)

I don't have any systematic way of looking for very many of these, so I

hope Gene will come up with some more suggestions.

>> One problem I have with 2151-EDA/22704-EDO is that 7 deviates by -18.6%

>> of 1deg22704. This indicates that a comma containing 7^3 will have a

>> cumulative error of -55.8% of a degree and probably won't be a

>> consistent number of tinas with respect to one containing a lower power

>> of 7.

>

> Not probably, certainly. I agree 2151-EDA is out.

>