Small temperament octave

Billbrpt@AOL.COM Billbrpt@AOL.COM
Wed, 17 Jan 2001 14:17:15 EST


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In a message dated 1/17/01 12:55:07 PM Central Standard Time, 
cneuman@phy.duke.edu (Charles Neuman) writes:


> Wow, that's interesting. I never thought about that: you can choose to
> keep the 5ths pure and still have ET if you let the temperament octave be
> stretched. Now, how about ET with pure 4ths? That would involve scrunching
> (there must be a technical term for the opposite of stretching) the
> temperament octave. I would imagine it would sound horrible, but I'm
> curious if anyone has tried it.
> 
> 

Thanks for your question.  Yes, here in Madison, WI, we call it the "New York 
Stretch".  I've also heard it called "New York style ET" and "Steinway style 
ET" because Steinway technicians tend to favor a pure or nearly pure 5th.  A 
New York technician named Lucas Mason wrote a whole book about it in 1985 (I 
think) called, "The New Tuning".

Some people like the idea but it has been controversial.  Jim Coleman, Sr. 
RPT wrote an article about it in the PTG Journal to which there were many 
responses, including one from me.  One of the big problems with it is that it 
is easy to make a mistake and end up with the kind of backwards version of a 
Well-Tempered Tuning that I call, "Reverse Well".  Also, tuning a true 
Pythagorean Tuning which has all pure 5ths except the one which cannot be 
reconciled will produce uneven 3rds which are fast and slow in a reverse 
pattern from that of a Well-Tempered Tuning.

The ET with pure 5ths is most recommended for a large concert grand with high 
inharmonicity such as a Steinway B or D and in a setting such as a concert 
hall where maximum projection and clarity are desired.  I wouldn't recommend 
it for a small vertical piano or for a small, intimate setting.  It can make 
all of the harmony sound strained.

Your other idea of pure 4ths would occur if you made your octave narrow 
enough and your 5ths tempered enough.  It's a worthwhile exercise to see 
which kinds of effects you can produce. It is well known that the Equal 
Beating major triads in second inversion cannot occur in ET but I have 
theorized that with an octave that is narrowed just the right amount might 
produce that effect.  I just have never got around to experimenting with it.

I believe the technical term for "scrunching" would simply be "narrow" or 
"narrowing" or "contracting" such as "ET with a contracted (or narrowed) 
octave".

Bill Bremmer RPT
Madison, Wisconsin

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