ramblin' (tunign by pure 5ths)

[Frank Weston]

Jim wrote:
> 
> Hi Richard:
> 
> One little thing caught my eye in your last reply where you said that
> a pure 4th and a pure 5th could be tuned within a pure octave. Well, for
> one pair that is true, but you can't have both continuing in a
> temperament.
> As you spread the octave in order to fit in the pure 5ths, the 4ths
> actually get faster. Now I'm learning that they will always be faster than
> the stretch octaves. Sometimes more than twice the speed of the octave.
> 
> I hope this clue helps those who are actually trying to set a scale with
> pure 5ths. Doing it with the SAT was so easy, that almost all the pianos
> I tune now are tuned this way. But doing it aurally is quite another
> matter.  I am working out a foolproof method now for doing it aurally.
> It should be on the list in just the next few days.  I would like to
> actually do it a few more times before I publish.
> 
> Jim Coleman, Sr.

Of course you can't have pure 5ths and pure 4ths in the same
temperament!  There are two immutable laws of the Universe which should
concern persons attempting to tune a keyboard instrument.

1.  You never get something for nothing.
2.  n*log2(3/2)  will never be equal to n for any value of n except
zero.

The history of temperament is the history of attempts to reconcile these
two laws.  The tradeoff has always been more pure intervals vs. more
freedom to modulate.  When a new system of tuning is proposed, the
question must be asked, "What does it give us?"  Does the new system
provide intervals which are more pure?  Does the new system result in
more freedom to modulate?  Does the new system have some historical
significance to the music that will be played?  If the answer to these
questions is no or mostly no, then what is the benefit of the new
system?  We must bear in mind that the purpose of a tuning system or
temperament is ultimately to make music, NOT to be convenient to the
person doing the tuning or to the device used to do the tuning.

So, the question:  What does tuning by pure 5ths give us except for
convenience?  More musical intervals?  No.  Perfect fifths are traded
for less than perfect octaves, thirds and sixths.  More freedom to
modulate?  No.  Modern equal temperament is the ultimate in this
regard.  Historical significance to music of a particular era? 
Possibly.  According to Jorgensen, some English  harpsicord tuners in
the early 18th century claimed to tune 5ths perfect with good results.  
Now ask yourself, what English harpsicord music from the 1720’s would
you like to reproduce?

For me, the ultimate temperament will always be a well temperament, and
Vallotti is my favorite.  Why?  Because the musical intervals are
relatively more pure (or at least more interesting) than equal or
attempts at equal, and they are well suited to the characteristics of
the piano.  Because there is key-coloration.  And finally because I am a
big fan of Baroque and Classical Music.   Actually a good
well-temperament is usually suitable for most music except for modern
art-music and competently played jazz.

My two cents worth.

Frank Weston