Equal Temperament, history of, judgement of

Billbrpt@AOL.COM Billbrpt@AOL.COM
Mon, 25 Feb 2002 19:57:53 EST


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In a message dated 2/25/02 1:23:47 PM Central Standard Time, 
JD@Pianomaker.co.uk (John Delacour) writes:


> From what I've read here recently of what Jorgensen says, I think 
> I'll stick with authors that base their writings on historical fact 
> rather than opinion and conjecture.
> 
Jorgensen's book is full, page after page of documentation that supports his 
finding. I only wish I had the time to quote even a little of it.  Basically, 
what I see in the 18th and 19th Centuries is the same back and forth struggle 
which is occurring presently.  People seem to want from a 12 tone system 
something they cannot really have. At some point, the ultimate compromise is 
discovered or proposed, it sounds like a good idea and a lot of people "jump 
on the bandwagon" only to have some people revert to older practices after 
everyone thought all of the issues had been decided and settled.

The specifications provided in your recent post would not insure a good piano 
tuning by today's standards.  It might be possible but the likelihood that 
some kind of cumulative error would produce unintended and unrecognized 
effects is very high.  This goes for Braide White's instructions and for many 
others too.  WIthout the understanding of the 4:5 ratio of contiguous 3rds, 
ET is next to impossible to get exactly right every time.

The idea that errors in tuning other temperaments would be just as 
commonplace as when attempting ET and have the same unintended effects is not 
really true.  Ron Koval made some very interesting graphs which showed this.  
It is rather easy to turn ET into some kind of Meantone, Well-Temperament or 
as I have often lamented, Reverse Well but to make mistakes and have the 
temperament come out perfectly equal is among the remotest of possibilities.  
Errors made in the HT's merely produce variants of these while not changing 
the intended effects while errors in ET produce unintended effects which ruin 
the desired equality.

<<and, referring to equal temperament:

"...the pianoforte is doubtless a very useful instrument for making 
the acquaintance of musical literature, or for domestic amusement or 
for accompanying singers.  But for artistic purposes its importance 
is not such as to require its mechanism to be made the basis of the 
whole system of music.">>

Yet we do use the piano and other keyboards for just that:  the foundation of 
nearly all music composition.  When I tune a piano in the EBVT, I can really 
"hear" or imagine what the orchestra will sound like much easier than with ET.

<<...and a lot more besides in various places.  Helmholtz was a fervent 
advocate of JUST intonation and would probably commend your work 
highly as an attempt to relieve the unpleasantness of equal 
temperament which he felt most keenly.>>

Now, this is interesting because my impression of Helmholtz was that he was 
the King of the ET only mad scientists.  However, my EBVT has all tempered 
tonalities.  There is a sprinkling of just intonation, yes but any triad has 
a tempered 3rd or minor 3rd.  The Equal Beating effect does hide some of the 
tempering and in context, makes much early music sound as if it is being 
played on a far more restrictive temperament.  This leaves the remote keys 
within a range that even the most HT resistant ears usually find palatable.

If Helmholtz would have liked that, maybe he wasn't so bad after all.  But I 
must say that these "Just Intonation" tunings I've heard on the piano really 
turn my stomach.  I can't ever imagine that becoming popular.  Listen for 
yourself.  Try this link but don't be surprised if it makes you lose your 
dinner!

http://www.newmusicbox.com/32/audio/harrison1.ram

Bill Bremmer RPT
Madison, Wisconsin
 <A HREF="http://www.billbremmer.com/">Click here: -=w w w . b i l l b r e m m e r . c o m =-</A> 

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