RE: circumference / diameter = 3

James Jeude wrote,

>Yes, this posting is a hoax. Also a hoax is the rumour that Indiana at
>one time attempted to legislate the same thing.

The latter is not a hoax. Please refer to Petr Beckmann's "A History of
Pi" for a detailed discussion of the bill in question. The Indiana bill
did not actually prescribe the number 3 but in fact was full of
contorted geometrical wordings which can be interpreted to yield values
of pi as high as 9! Also included was a rational value for the square
root of two.

On Tue, 28 Apr 1998, Daniel Wolf wrote:
> Thanks to Paul Hahn for his table. Too bad that Yamaha didn't put the TX81Z
> into 612ET!

You're welcome. I should dig out my program and run it a little ways
past 1200, just to make sure there isn't some awesome ET out there that
would get us a lot more accuracy/consistency for not too much more
resolution. For example, I found this line in my consist2.txt table:

1848| 46 5 5 5 4 . .

1848 has higher consistency at the 11-limit, where 612 stops, is also
consistent at the 13- and 15-limits, and is divisible by 12 to boot!

--pH http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
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NOTE: dehyphenate node to remove spamblock. <*>

Jessie Gay wrote:

'Several books I have read say that one of the largest reasons for the
popularity of Equal Temperament in western music is that the most
prominent piano manufacturers all decided to make pianos in ET, and that
constructing a JI piano creates some serious mechanical difficulties.
However, the books have never mentioned what these mechanical difficultie=
s
are. Does anyone have any input on this question?'

I may be entirely wrong about this, but I think
that the generally heavier construction of the piano
(esp. the tuning block and frame) made the instrument
simply better able to hold a tuning over a longer
period of time and thus shifted the responsibility
for the tuning from the performer or instrument owner
to professional piano tuners. While most musicians
can learn to set a meantone or well temperament and
learn quickly to correct a tuning before and during
a rehearsal or performance, approximating an equal
temperament is a specialist activity and cannot be
done on the fly. Douglas Leedy speaks about
'invention being the mother of necessity' in this
case: because the piano was able to hold a tuning in
ET, it became necessary to tune it in ET.

There are arguments about ET and the piano based upon
the stretched intonation of the partials of the
rigid piano wire. I have great trouble in supporting
these arguments historically, however, because the
early pianos were wired at a much lower tension
than modern instruments and were considerably less
stretched. (La Monte Young's _Well Tuned Piano_ =

deliberately uses a lower tension to reduce, but not
eliminate the stretching. The actual tuning he uses
deviates considerably from just intonation when =

measured but is instead a subjectively convincing
approximation.)

Daniel Wolf
rankfurt =

On Tue, 28 Apr 1998, it was written:
> I should dig out my program and run it a little ways
> past 1200, just to make sure there isn't some awesome ET out there that
> would get us a lot more accuracy/consistency for not too much more
> resolution.

I've now generated that table and it is available at

http://library.wustl.edu/~manynote/consist4.txt

It covers ETs from 1200 upt 2400. I haven't had a chance to scan it for
more candidates yet.

--pH http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>