Meantone, my personal adventure

[Richard Moody]

Ed writes
	>you tune the G, then D, then A and E. These
> four fifths must be tempered by 1/4 comma each if the C-E third is to
remain
> pure. >      just make all those four fifths equally out of tune,  have
one no better
> than another while keeping the C-E pure. 

	

Today I took the "next step" in the meantone odysey and tried flattening
the fifths to get to (arrive at) a pure C--E third, as you and Jim posted.
 It seems 
I was just about to think of that, it appears so intuitive. And it also
re-enforces my theory that tuners were able to come close to ET by doing
that in the circle of fifths, or "closing the circle" as I have seen it
mentioned. They would have to tune six slightly flat fifths one way and
five the other.  So far that does not seem to me to be harder than tuning
the four fifths "very" flat to get the C--E pure third. 
	When trying your suggestion of the four flat fifths to a pure third I was
struck by the distinct beating of the fifths, (and fourths of course), and
yes,  these fifths should beat the same. Of course eventually they beat
faster as they go up, but they do sound the same when they are the first
four. When tuning the fifths to "close the circle" you don't get these
distinct beats.  However you get very fast thirds which to the ear if used
to pure thirds must have sounded "strange"  But the distinct beating of
the fifths in Meantone sound strange to me.  
	After tuning these four fifths,  pure thirds can then be tuned off of
them.  For instance  F--A the F could be tuned pure. It should beat
against the C.  They must have figured out that the fourth on the bottom
beats the same as the fifth on top. And it should have been noticed that
fourth on top beats faster than the fifth on the bottom.  Twice as fast
actually. At any rate all of the white keys are tuned. Since every black
key is a third away from a white key the it seems now you want to choose
what key signatures you want.  For the key of D you need F#  that leaves
Bb for the key of Bb.  Now you have to choose between G# or Ab.  If you
want the key of A you will choose C# instead of Db. That leaves a choice
of the key of B or the key of Eb. The wolf would lie at Eb--G# (with E--G#
pure)or Ab--C#
with Ab--C pure.   


 
> It is one thing to move the music from pianoforte to the modern grand,
but it
> is entirely more distructive to destroy the intonation in the process! 
>    I suggest that use of its original style temperament  for a piece of
music
> restores   information which the composer installed in the piece.  The
> serenity of pure intervals and the abruptness of contrasting modulations
are
> aspects that ET doesn't have.  The unequal tunings are more complex
> arrangements of the pitches, and the music that results is also more
>complex. 

The study of historical temperaments is an academic pursuit, and as such
must adhere to the rules of academia. Thus the musicians, pianists, and
musicologists can study the effects of temperament on music.  The tuner of
course will have to render these temperaments in a consistant manner. The
historian will try to determine what actually was the tuning Bach had in
mind for WTC, or Chopin for his Perludes and Etudes. What they look for is
direct evidence such as words from the Masters themselves, "I wrote this
piece for this temperament" Or I recommend performing this piece on an
instrument according to _____" 
	As it stands I have not seen any such evidence at least in the English
language. One approach to historiography is the asking of questions and
formulating the answers according to the evidence.  One will naturally ask
"What does the 'Well' mean in Well Tempered Clavier?"  Of all the answers
presented, the student will ask, "What did Bach himself say about Well
Tempered?"  History is full of unanswered questions many appear waiting to
be answered if and when the evidence is uncovered.  One can argue the
possibilites that Bach meant the K or the W, or any of the variations
there of. 
	The music student faced with parctical issues will want to evaluate WTC
on at least two. And with some authority can say, here is what this piece
sounds like in W and here is what it sounds like in K.  I perfer W to K
for these reasons. Of course he and hopefully the lister mighyt wonders
what the "other" temperament was that WTC was NOT written for. That would
imply other Bach music was written in the "other" temp. And another
endeavor in the study of historical temperaments will occur. 
	In our scientific age the student will ask "what is meant by key color?"
and in the process of scrutany and study might also ask, "What did the
composers say" and "can this be demonstrated".  
	And that leads to a BIG consideration of temperament, how practical is it
to play and hear Bach for example anyone of a few besides ET? Someone has
to come and tune it.  With the "revolution" of digital keyboards this
might provide the quick and simple fix. With a push of a button ET can go
to Meantone, or a WT. The player can hear in an instant the differences.
With the record and playback features the listener can hear this also. 
The benefit for tuners is that player who decides to perform or record on
a specially tuned piano.  The tuners who can do this get the call.   
	Hmm I have an idea that some pop style female singers would fall in love
with Meantone.  I bet a few Jazz players would really dig flat fifths in
modern pure fifths temp.  Now if 12 5ths need to be narrow by 2 cents....
would that give pure fifths in an octave stretched 3.77 cents?  Why not
make it 4?  The fourths should be ok if it were 12th root of 2.x  ?

Ric Means Well