311 equal comma basis

In case someone finds something interesting to do with it, I'm giving
a basis for the commas of 311-et in the 41 limit:

1025/1023, 595/594, 2695/2691, 703/702, 714/713, 820/819, 900/899,
1955/1953, 1000/999, 1036/1035, 1887/1886, 2665/2664

I didn't try TM reducing; this is weighted LLL reduction, which gives
reasonably good results.

Here's the TM basis for 13-limit 270-et, which I think I've given before:

676/675, 1001/1000, 1716/1715, 3025/3024, 4096/4095

Both 270 and 311 could be made the basis of a notation.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> In case someone finds something interesting to do with it, I'm
giving
> a basis for the commas of 311-et in the 41 limit:
>
> 1025/1023, 595/594, 2695/2691, 703/702, 714/713, 820/819, 900/899,
> 1955/1953, 1000/999, 1036/1035, 1887/1886, 2665/2664
>
> I didn't try TM reducing; this is weighted LLL reduction, which
gives
> reasonably good results.
>
> Here's the TM basis for 13-limit 270-et, which I think I've given
before:
>
> 676/675, 1001/1000, 1716/1715, 3025/3024, 4096/4095
>
> Both 270 and 311 could be made the basis of a notation.

Hmmm, it's too bad that the difference between:
(81/80)^2 and 40/39
nor that between:
(81/80)^3 and 27/26
(in each case amounting to ~0.8 cents)
does not vanish in 311, so the same symbol can't be used for these
two dieses.

Also, it's too bad that the difference between:
(5120/5103) and 289/288
nor that between:
(1408/1377) and 45/44
(~0.2 and ~0.4 cents, respectively)
does not vanish in 270.

In the course of the Sagittal notation project, examples such as
these revealed that 217 and 494 are better choices.

BTW, 388 suffers from the difference of:
352/351 and 5120/5103
(difference of ~0.8 cents)
not vanishing.

Anyway, as it turned out, we ended up *not* basing the notation on
any particular ET.

--George