Septimals and TU

Hmm. Not sure what's going on here...

BL :
> Why hit only near a 7:6 or a 9:7 when you can hit
> directly on one of them?

Why indeed? Well, because:

> because those (2/7 comma) 3rds aren't pure, they're (arguably) more
attractive
> just by virtue of being livelier, not sitting there dead-on.

Clear? Slightly tempered thirds are (Brad clearly wants to say) more
attractive, but pure septimals are more desirable. But -

> Every listener might of course have a different opinion about that.

Every listener might even change his or her opinion within five
minutes about whether slightly tempered intervals were preferable to
pure ones.

But that's not so important. The point, without getting too far into
the details of exactly which intervals are better pure and which are
better slightly tempered, is that without doing anything irregular we
can create a large number of only slightly tempered - that is,
recognisably near-pure - intervals, at the cost of only doing violence
to 3/2.

In the regime near 1/4 or 2/9 comma or 31EDO we get the pure 7:5 and
7:4 as aug4 and aug6. If we go to the 'other side' of 1/4-comma, near
2/7-comma or 50EDO, the 7:5 gets rather flat, but we get a good 7:6
instead and a tolerable 9:7. It depends what one is keener on, out of
tritones, aug 6's, aug 2's (alias subminor) and dim 4's (alias
supermajor). Some time ago I tuned my best shot at 2/7 comma - not
something that can be done very systematically by ear - and the purity
of 7:6 was immediately obvious. Regular tuning that aims for the least
error of 5-limit thirds has the bonus of doing very well by the
7-limit thirds.

Not that keyboard music of the relevant period will be using the
distant thirds (Bb-Db, F#-A#) very much, or even at all - but the
septimal aug2 and dim4 can turn up relatively often in the role of
dissonances.

Here's a relevant calculation that TU are particularly messy at
dealing with, if they can even be used at all:
What is the temperament of the fifth in a regular meantone such that
F-G# is a pure 7:6?

Answers in any comprehensible form.
~~~T~~~

> Some time ago I tuned my best shot at 2/7 comma - not
> something that can be done very systematically by ear -

Hi Tom-

Are you familiar with

/tuning/topicId_59873.html#59873

?

-Carl