TOP Beep (4&5 7-limit)

Beep is the 7-limit version of bug temperament (4&5), with a wedgie of <<2, 3, 1, 0, -4, 6]]. The TOP tuning of beep has been given as P = 1194.642673, G = 254.8994697. But beep is another one of those temperaments with a TOP comma having only two prime components: [0, 3, -2, 0>. This is just the bug comma, so one valid tuning for beep is the same as 5-limit bug: P = 1200.0, G = 260.256797. But the tuning of prime 7 can be improved by widening the octave even more. The optimal tuning seems to be around P = 1206.049627, 266.306424, with TOP error of 6.049627 for both 2 and 7.

It looks like any temperament with a 0 in the wedgie somewhere is going to have issues like this for TOP tuning.

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> Beep is the 7-limit version of bug temperament (4&5), with a wedgie
of
> <<2, 3, 1, 0, -4, 6]]. The TOP tuning of beep has been given as P =
> 1194.642673, G = 254.8994697.

Yeesh, that is pretty far out there.

But beep is another one of those
> temperaments with a TOP comma having only two prime components: [0,
3,
> -2, 0>. This is just the bug comma, so one valid tuning for beep is
the
> same as 5-limit bug: P = 1200.0, G = 260.256797.

Which seems like a good choice.

> It looks like any temperament with a 0 in the wedgie somewhere is
going
> to have issues like this for TOP tuning.

So it has always been, but it looks like the default tuning could use
some improvement here.