Meantone, my personal adventure

[Richard Moody]

Hi Jim.

	Thanks for the reply.  You wrote..."We both read James Murray Barbour's
> book on the early temperaments. I read it in 1947-9?"

1947 was a good year to be born.  :)  

The Barbour book is next for me to read. As you can probably tell from the
list, most of us know only from Jorgensen's "Big Red", as you (I believe)
put it. :). With the advent of programable tuning machines all of those
tunings are available in a matter of minutes.(I assume it is that easy to
punch in a tuning).  For  aural tuners it is a different story. We have
no one to learn from, meaning, I am afraid any tuner who tuned Meantone
and learned it from the Tradition is long gone.  
	You must know of the Meantone in
Braid White, even that was reconstructed from theory.  It is interesting
that even though MT features pure thirds, the Braid White instructions
show only beating fourths and fifths, and the one I saved from Jorgensen
talks about 1/4 syntonic comma. 
	Your description of you tuning pure thirds and fifths and fourths up to A
and E is quite interesting.  You must have been precocious, or it is
intuitive that the note between the third C..E must lie halfway between,
or at the mean.  And that is how meantone (the sources say) got its
name. But that has to do with pure thirds is beyond me. Braid White
explains the mean between C and E is the square root of the ratio 5/4
(1.25). After this he looses me. How this D or that mean relates to the
calculation of the rest of the scale, I didn't get. 

	My adventure with Meantone began from the idea of tuning pure thirds in a
temperament. Also I had (have) a desire to research historical
temperaments from the point of view of the tuner, or the actual tuning
experience.  
	Before 1750 there were no pianos other than a few prototypes. From 1750
to 1850 the piano was still in its "developmental stage" so its tone
especially to a tuner's ears should be remarkable different from the grand
piano of today. I say "should be" because I have no experience tuning a
piano prior to 1880, unless a few of the square grands I tuned were from
1879.  At any rate, the instrument until 1750 that people had the most
experience tuning was the harpsichord. It would seem tuning instructions
for this time back would be for that instrument. I have left out the organ
because I believe the study of the tuning of that demands a different
approach. The one thing organs do have in common with harpsichords,
clavichords and other keyboard instrumnets is that they were shop
produced. 
	Soon after 1800 pianos began to be mass produced in factories. 
It is the tuning of this instrument onward I would like to really dig
into. It has to be soon after the advent of factories that the profession
of piano tuner came about. The factory system requires a literate work
force if only to insure uniformity of product through written plans and
instructions. There must have been written instructions for the factory
tuners.  Jorgensen hints about this but did not, (unless I missed it in
900 pages) present one. Since it wouldn't need more than three or four
pages, I don't think such a set of instructions would be difficult to
reproduce.  If they do indeed exist.  From Stein and Streicher, to Erard
and Playel to Broadwood especially there should be  tuning instructions
printed at least for the factory tuners, or even some mention from the
maker as to how or what their pianos should be tuned.
	To it me it looks like there were two schools of tuning, one using pure
thirds and tempered fifths (Meantone), the other using some pure fifths
with tempered fifths and tempered thirds.(Welltemered or Wells).  That ET
evolved from Wells that used less and less pure fifths.  
	Its not that Meantone was a dead end in tuning evolution, its that
Meantone is its own system with its own particular characteristics.  It
might be that this system was desired for organs, and this was the system
that Bach couldn't use for WTC. (One might wonder what the other system
was before "well tempered".)  But if in one wants to hear pure thirds on
the keyboard, Meantone is the only system that will give this. 
	Knowing that there was a system of pure thirds, I decided to tune
by pure thirds to see what would come out. That three thirds stacked on
top of each other make an octave, and three thirds are in the white keys
in an octave are the first considerations. 
	Starting at C, the three contiguous
thirds in an octave immediately present tuning problems. Two can be  pure,
but the third one is harshly sharp.(wide) in fact in music theory presents
itself as a diminished fourth. c--e--g#--c1.  But g#--c1 isn't actually
tuned, it is a result. Returning to middle C (c in this essay) we  have
c--e tuned pure. We are now looking at f--a, and g--b and realize that d
completes the tuning of the white keys.  The simplest choice s us to tune
f and g pure from c and tune pure third from them.  This leaves d.  If it
is tuned pure to a it is not in tune with g. 
If d--a is pure, then f# can logically be made pure, which should be nice
for the key of D. So we tune it d pure to a.  Now it follows that Bb can
be tuned pure to d, and then the Bb...f  fifth listened to.  I will leave
this essay with a multiple
choice question, what is the nature of this fifth? Bb...f   
 A. Pure.       B. Narrow.
C. Wide.       D. None of the above. 

Playing around with a tuning such as the above gives an idea of choices,
leeways, and practical results such as the horrible fourth d...g.  It
turns out they flattened g and the rest of the fifths by twice the amount
of ET (4 cents), and left the thirds pure. But how they came to  this back
before there was a conception of cycles per second, cents, and coincident
partials I have not seen explained clearly to me at least. Even the
concept of commas, where does that enter into the aural scheme? 

	For what ever it is worth some scattered thoughts on Meantone and pure
thirds. From C, c--e--g# can be pure but G# is no longer enharmonic to Ab.
 There 8
pure thirds in meantone. If C is the starting note, the pure thirds are
c..e,  d..f#,
eb..g,e..g#, f..a, g..b, a..c#, bb..d. 

Richard Moody  

----------
> From: Jim Coleman, Sr. <pianotoo@imap2.asu.edu>
> To: Richard Moody <remoody@easnet.net>
> Cc: pianotech@ptg.org
> Subject: Meantone, my personal adventure
> Date: Saturday, March 13, 1999 12:49 PM
> 
> Hi Richard:
> 
> You wrote:
> 
> > Good, lets get into Meantone.
> 
> When I was a boy, my father let me practice temperament until I became
> frustrated.
> 
> I started tuning pure intervals from C below middle C. I tuned C-E pure,
> I tuned C-F pure, I tuned C-G pure, I tuned D-G pure, I tuned D-A pure,
> and then it hit me! The F-A 3rd was bad, the E-A 4th was bad. I had not 
> yet read anything about Meantone, but it dawned upon me that if I tuned
> the E-A 4th pure, then the D-A 5th would sound bad; so, I decided to
> split the difference (meantone?) and tune the D flatter so that the
> D-A did not sound so bad, but the D-G would then have beats. In essence
> I was discovering that you can't have your cake and eat it too, so to
speak.
> If you rob Peter, you must pay Paul. Equal temperament is the ultimate
> compromise, but in the process, much of the beauty of tuning and 
> musicality has been lost