back to list

Alhalis temperament

🔗Gene Ward Smith <gwsmith@svpal.org>

1/24/2006 11:15:07 PM

In the 7-limit, this is the 41-et relative of hemififths temperament,
with wedgie <2 -16 13 -30 15 75|; it can also be described as 41&65.
It has a neutral third slightly flatter than hemififths; 79/270 is a
good generator. It tempers out 245/243 and 32805/32768.

If you now add 385/384 to the commas, you get 11-limit alhalis. This
has wedgie <2 -16 13 5 -30 15 1 75 67 -31|. 79/270 is still a poptimal
generator, and it still can be described in terms of rounded vals or
whatever we are calling them this week as 41&65. If we skip the 5 part
of the mapping, we get a nice no-fives temperament.

Here's a mapping to primes:

[<1 1 7 -1 2|, <0 2 -16 13 5|]

🔗Gene Ward Smith <gwsmith@svpal.org>

1/25/2006 12:05:33 AM

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> Here's a mapping to primes:
>
> [<1 1 7 -1 2|, <0 2 -16 13 5|]

The main trouble with this temperament is that the competition from
hemififths is too stiff; for the 11 limit you can call that 41&58
rather than 41&65. You can use 99-et for the 7-limit version, and it
also works fine (and in fact is poptimal) for the 11-limit.