Gold: a temperament with phi as a generator

Here is what the world has undoubtedly been waiting for--a temperament
for which (1+sqrt(5))/2 is an excellent choice for generator. I give
the 19-limit mapping below:

[<1 12 -31 16 -25 28 27 -2|, <0 -15 48 -19 41 -35 -33 9|]

Here is how the generator phi fairs, using the above mapping:

3: 3.002931
5: 5.005839
7: 7.009948
11: 11.034264
13: 13.009855
17: 17.030122
19: 19.003289

It's got Graham complexity 83, which is a trifle high, of course. The
MOS go 7, 10, 13, 23, 36, 49, 85, 121, 167, 278 ...

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> Here is what the world has undoubtedly been waiting for--a temperament
> for which (1+sqrt(5))/2 is an excellent choice for generator. I give
> the 19-limit mapping below:
>
> [<1 12 -31 16 -25 28 27 -2|, <0 -15 48 -19 41 -35 -33 9|]

Unsurprisingly, ratios of Fibonacci numbers give the generator.
From 13, 21, 34 we get 21/13 as approximately phi, and 34/21 as
closer. This makes (34/21)/(21/13) = 442/441 a comma; also two
generators in a row are (21/13)*(34/21) = 34/13.

This suggests we could look for a less complex and accurate temperament
where 13/8 and 21/13 were generators, and 169/168 was a comma, and a
more complex and accurate temperament with (34/21)/(55/34) = 1156/1155
as a comma.