Beat Rates in music

[Billbrpt@AOL.COM]

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In a message dated 8/7/02 8:09:24 AM Central Daylight Time, 
Richard.Brekne@grieg.uib.no (Richard Brekne) writes:


> Hi Bill, and thanks for the reply:
> 
> Billbrpt@AOL.COM wrote:
> 
> > I have a general preference for octave stretch, yes, and
> > that is for triple octaves across the piano to match
> > perfectly.  This means that single and double octaves are
> > slightly expanded and minimizes the tempering in the 5ths.
> > This sounds a lot like what you have been doing.  This
> > will generally give you the best sound for a large concert
> > grand in a large room.
> > 
> 
> I wonder if you could describe what you mean by << triple
> octaves to match perfectly >>
> in terms of octave types. Do you mean that you have 4:2:1
> pure for example ?? or if not just how would you word this ?
> 
> >
> > There are other circumstances, other kinds of pianos,
> > different kinds of music and the personal taste of some
> > very discriminating artists.  I use both temperament and
> > octave size as a kind of "throttle" to give the piano a
> > sound which is appropriate to the circumstances......
> 
> Interesting comments, and exactly the kind of thing I was
> asking about. Thank you Bill.
> 
"Triple octaves matching perfectly" means that the fundamental of the upper 
note is beatless with the corresponding partial of the lower note (8th 
partial, I think).  The way I do this is all described in my website in the 
article called "How to tune Tempered Octaves".


In a nutshell, however, what I do to expand from the temperament sequence 
octave (F3-F4) upwards is to compare the 4th, 5th and octave.  I favor the 
5th over the other two but am careful not to let any interval beat 
excessively.  Once 2 octaves have been completed, I compare the double octave 
and the octave and 5th, making an Equal Beating compromise between the two.  
Once into the 5th octave, 4ths don't seem to matter much any more but I still 
listen to 5ths way unto the 6th octave.

This will result in triple octaves being in tune once 3 octaves have been 
tuned.  It is then possible to listen to triple octaves and make them 
beatless by ear.  It is also easy to do this with the Accu-Tuner and enter 
the exact values into a program which can be repeated quickly and precisely 
thereafter.

I do a mirror image of this going the other way into the bass.  It may seem 
like I am describing an ET tuning here which as I have often said, I never 
do.  I have been creating my octaves this way for a very long time, about 20 
years, longer than I have been tuning nonequal temperaments.  This kind of 
octave stretching is suitable for ET, of course but also for any kind of mild 
nonequal temperament.  It will also serve to even out any unintended errors 
in a tuning which is meant to be ET.

In a mild Well Tempered Tuning, there are usually some pure 5ths or at least 
some 5ths which are purer than ET 5ths should be and some which are more 
tempered.  When the pure 5th and octave (or their extensions) are compared, 
it is easy to find a point where both intervals sound good and "pure" 
sounding.  When there is a tempered 5th, the compromise is a little more 
difficult but there will always be a point at which all of the intervals will 
sound acceptable.

As you may see, this is a very good way of sorting out what some people have 
called a "sloppy" temperament.  I deliberately never make my temperament 
completely equal even though I know thoroughly the techniques for doing so.  
The closest I come is a Quasi Equal Temperament ("quasi" means "almost") 
where all of my 4ths & 5ths sound about like most technician's ET 4ths & 5ths 
would sound but I still make my 3rds agree with the cycle of 5ths, thereby 
giving the piano some slight tonal color.

In my experience, there is always a threshold where even very experienced and 
discriminating musicians who are used to ET and who do not like the sound of 
typical HT's will still like the sound of a Quasi ET better than strict ET 
because the piano is more expressive.  Sometimes, holding off on what I would 
consider to be the ideal amount of stretch is what I have to do in order to 
please such an individual, particularly those who play highly complex, 
heavily Romantic era music from the 19th and early 20th Centuries, written in 
many sharps or flats.

Quite obviously, the greater the amount of stretch put in the octaves, 
regardless of temperament, the greater the amount of tension there will be in 
the music.  There can easily be a fine line between where this tension is 
titillating and pleasing and just plain "sour" sounding.  That fine line can 
vary from individual to individual.

Lastly, the speed at which the rapidly beating intervals beat constitute a 
particular and controllable resonance which constitutes a kind of "vibrato" 
which the piano produces when music is played.  A strict ET with conservative 
octaves produces a very regular and homogenous kind of sound.  Stretching 
this out increases the intensity.  Varying the temperament produces different 
levels of intensity depending on what key one is playing in, very much the 
way a musician playing another kind of instrument will vary the intensity of 
vibrato while performing.  Some very perceptive performers do use the speed 
of this vibrato like sound to influence the tempo at which they play.

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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