Alternative Temperaments

[Richard Moody]

> Hi list.
> 
> Paul Erlich wrote me this and asked me to pass it on to all
interested.
> It is in reply to Richard Moodys last post.
> 
> Richard Brekne
 
Posted on Aug 27

Moody (>>)said....
>> from the 14thcentury to the 19th the theory of tuning and the
>>practice of tuning
>> probably had little in common.

Paul Erlich replied... 
> I would say they had much in common, 
>..... are close enough that one can meaningfully
> distinguish between different tuning systems used in different
>periods of time, in both theory and practice:


........................................................... 
> >2/7 comma (Zarlano) doesn't tell you
> >much of anything.  It gives a Third of LESS than pure, but
>>what is the objective??
..................................................
> 
> The objective is to optimize the tuning of both the major
>third and the minor third. In Zarlino's tuning both are only 1/7 comma
>(about 3 cents) off just.
.........................................................

	This is an example of the difference between theorists and
tuners.(practice)  The tuner would need to know the meaning  "Optimize the
tuning of both the major third and minor third"  Then figure out 
which way from just.   The theorists can propose 3 cents from just or "temper fifths
by 2/7 comma", "leading to thirds 1/7 off just" but it is the tuner who must
establish what that sounds like, and  hopefully the rest of music world will be
pleased.  Now how close this comes out to what the theorist had in mind, is best
determined by "cent" only known since 1880. The intended results of the theorist and
the actual results of the tuner should have something in
common, but the two get there by completely different ways. 
	Now enter the historians from Mersenne to Jorgensen who give tuning schemes as
circles of fifths never including thirds or fourths as part of the tuning effort.
This though is a record of what the theorists proposed. Mersenne was not a tuner
although he may have witnessed a spinet and organ being tuned. He states that the
imperceptable amount the fifth is tempered, is the art and "secret" of the  masters.
 The tuner probably never thought of publishing his ideas.  Bach didn't even bother
to specify the tuning he had in mind for WTC and Bach was also a tuner.   It is only
the historians reading the theorists and us reading the historians if we are to
propose a tuning Bach would have concurred.  And it seems historians are more
theorists than they are tuners.   
	Translations of the early theorists into English has given new views on actual
tuning methods.  Barbour (1952) when reading Pietro Aaron finds instructions for
tuning which the FIRST step  gives C--E   tuned pure.  Certainly different from
circle of fifths Mersenne and others published. Aaron himself probably practiced
tuning,  as aurally attempting 1/4 meantone by his instructions certainly gives
better and faster results than going through the theorists perscribed circle of
fifths and 
hoping for the desired result in the end.  
	Another consideration of the differences is that it was
centuries before science caught up with the theorists. 
>From the time of Pythagoras theorists were able to compute the syntonic
and Pythagorean commas accurate to 7 decimal places.  This meant
nothing to tuners who could only rely on their experience, and
the agreement of other musicians as to what a pure thirds
Meantone sounded like and how much "the eare could bear" with
tempered Fifths.   Even in 1885 after the discovery of beat
rates as a function of coincident harmmonics,  according to
Ellis (inventor of cents), tuners did not use the rates of thirds
and tenths as checks or proofs.   In 1930's Barbour expressed
dismay at the differences of beat rates he heard in piano
tunings with those on paper.  Even Jorgensen implies that the
practice of tuning varies widely unless institutionalized
standards and testing are observed. 

I would agree that today translating the intervals and temperings into cents has
greatly bridged the gap between theory and practice, especially with the use of
electronic tuning devices, (ETD's) that can be programmed directly using cents and
produce any theoritical tuning within moments.  
 ---ric