--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> The one tuning that really stands
> out on the chart that I haven't played with is Amity, which never
really
> sounded like it would be all that useful, but should be better than
Orwell
> according to the chart (its predicted error and Tenney Complexity
are both
> lower). I've had some "interesting" results with Orwell, although
that was
> a long time ago, and it takes some time to feel your way around an
> unfamiliar tuning.

Herman, I need to clarify something.

[-21 3 7] = 2109375/2097152 is a comma (actually, it's called
the 'semicomma', due to Fokker).

'Orwell', on the other hand, is Gene's term for any 'linear
temperament' with a generator of about 19/84 octave and a period of 1
octave. Gene usually thinks of it in terms of higher limits than 5.

If you temper the semicomma out from the 5-limit lattice, you indeed
get a linear temperament that fits the 'Orwell' description. However,
if you temper it out from the 7-limit lattice, you get a 'planar
temperament'; temper it out from the 11-limit lattice, a 'spacial
temperament'. In these cases, the information on my charts remains
valid.

However, in order to get 7-limit Orwell, which is a 'linear
temperament', you need to temper out an additional comma from the 7-
limit lattice. Alternatively, you could start over and use the two
commas 225/224 and 1728/1715. Since these are a lot simpler than
2109375/2097152, it's a pretty good guess that you're dealing with a
simpler temperament here. To get 11-limit Orwell, you need to temper
out three commas -- you could use two of the above and one more, or
you could use 99/98, 121/120, and 176/175. Note that these are all
very simple, and all superparticular (thus being the smallest size
possible for their complexity)!

I foresaw this confusion which is why, on the big list of commas
and 'linear temperaments' on Monz's ET page, you'll see that the
entry for orwell actually says "orwell (5-limit)".

For a different sort of example, note the appearance of [-19 12 0] =
531441/524288 on my charts. This is the famous Pythagorean comma.
Tempering it out is usually associated with 12-equal -- in fact, in
my Top scheme, it leads to an equal division of a 1200.61705-cent
octave into 12 equal parts, or 12ED2.00071297. But as is well known,
the 5-limit errors of 12-equal are much larger than the 5-limit
errors of meantone, and yet on the graph, the Pythagorean comma is
lower, meaning it has lower errors, than the syntonic comma. Why?
Because tempering out the Pythagorean comma from the *5-limit*
lattice does not lead to 12-equal, instead it leads to an infinite
number of parallel 12-equal systems at a ratio of 5:1 apart from one
another (the Pythagorean comma doesn't touch the 5-axis, as you can
see from the third entry in its monzo being 0). This is a 'linear
temperament' with a period of about 100 cents and a generator of
about 15 cents; it was the subject of my second or third post ever to
the tuning list in 1996; and we now call it 'aristoxenean'. A true 5-
limit use of 12-equal involves tempering out *two* commas, not one,
and so can't be evaluated from my charts. My charts *will* read
correctly whether you are considering the effect of tempering out the
Pythagorean comma in the 3-limit, 5-limit, or any higher limit -- as
long as you aren't employing a hidden assumption about other commas
being tempered out.