Bach and ET (or was that Meantone?)

[Billbrpt@AOL.COM]

In a message dated 4/19/00 7:57:32 AM Central Daylight Time, 
remoody@midstatesd.net (Richard Moody) writes:

<< >    After Bach's death, his son, CPE Bach was asked about his father's
 > preference and stated that the old man did NOT prefer equal temperament.
 
     This is evidence that ET did exist in Bach's time because how could he
 have a preference one way or the other for something that did not exist?  >>

How can it be certain that Bach was not actually referring erroneously to 
Well-Tempered Tuning when he spoke of not liking ET?  Much of the WT Clavier 
music works well in 1/4 or 1/5 Comma Meantone (1/4CMT), only those in the 
remote keys, the ones that WT is designed to make acceptable don't sound 
right in 1/4 or 1/5 CMT.  I have ironically heard just the opposite of the 
commonly raised question posed:  How do we know that Bach didn't actually 
prefer Meantone (1/4 or 1/5)?

**************************

In a message dated 4/19/00 7:58:34 AM Central Daylight Time, 
remoody@midstatesd.net (Richard Moody) writes:

<<  In this light one wonders how a tuning that is well tempered can contain 
fifths that are not tempered at all.  I believe that most of the so called 
"wells"  have two or three 5ths that are not tempered.  If "well tempered" 
means that ALL of the fifths are tempered, and we imagine this means  
tempered so well that the circle of fifths "comes out", ie the last fifth 
sounds like the first fifth, then we have ET.   >>

By the Rules, a Well Tempered Tuning does not have to contain pure 5ths but 
in fact the early ones have as many as 8 of them.  The 18th Century ones 
usually have 6 and some of the 19th Century ones have 5.  My EBVT has 4 of 
them and 2 which are tempered but by an even smaller amount than an ET 5th.

I have often heard that a WT is a combination of ideas:  Meantone and your 
favorite, Pythagorean.  The simple keys, 0-3 sharps or flats represent the 
Meantone side and the remote keys, 4-6 sharps or flats represent the 
Pythagorean side.  Combining the best that each of these ideas offers a 
solution that "works" in all keys.

*************************

In a message dated 4/19/00 8:04:41 AM Central Daylight Time, 
remoody@midstatesd.net (Richard Moody) writes:

<< Beyond 1/4 comma to get pure thirds I have yet to fathom the thinking of 
1/5
 comma, 1/6, 2/7, 2/9  etc, and how they figured out from that how to make
 the thirds.  (snip)  I don't understand how commas were set up on the 
monochords, and how from that they could determine what flavor meantone was 
being used. I could put them in my spread sheet quick enough, but that 
doesn't tell me how the
 early theorists could realize temperaments from how much the syntonic comma
 was altered.  (execpt for 1/4 tone)    ---ric

Well, Rick it boggles my mind too.  I don't have any idea how they did it.  
The Aural instructions all give theoretical beat speeds that you can only 
guess at.  There are however aural comparison checks that will tell you if 
you are on the right track as you progress through the temperament.

Several years ago I was reading in Owen Jorgensen's Tuning The HT's By Ear 
when I read a statement that said that all of the Meantones were defined as a 
chain of 5ths all tuned exactly the same size.  For me, a light went on that 
told me this could be done electronically.  Now I know that you are an Aural 
Tuner and I was too for some 21 years.  I found the SAT difficult and 
cumbersome to work with at first but fascinating nevertheless.  I was not 
interested in the FAC program however and still never use it.  I found Direct 
Interval programming where I was in command, not some calculation, to be what 
held my interest.

I theorized that I could create *any* Meantone, from 1/3 to 1/11 by tuning a 
chain of 5ths, all the same size.  The fraction merely needs to be *adjusted* 
for Inharmonicity.  That is the trick and the key factor which makes the plan 
work.  I have tuned 1/3, 1/4 (once for a recital by Owen Jorgensen at a 
Convention), 1/5, 1/6, 1/7 & 1/8.  The 1/9 and 1/10 are also worth exploring 
as Quasi-Equal Temperaments which may substitute for ET.

The other odd fractions may also reveal interesting properties that I have 
yet to hear.  For me, however, the search for a temperament that restores 
true Cycle of 5ths based "color" to the *modern* piano without creating a 
sound which a contemporary user would reject is my usual goal.  Therefore, I 
have been most interested in the 1/7 and 1/8 Comma ideas and variants of 
those.  I rarely tune a piano that will be used exclusively for an Early 
Music performance.  When I do, I choose something which will be specific for 
it.

As far as ETD's go, I have to agree with Ed in this respect.  The SAT allows 
me to explore and construct these kinds of temperaments accurately.  However, 
I think that merely plugging in some sets of deviation figures to another set 
of deviation figures does not teach the student very much, not unless the 
results are compared with what the Aural Instructions say and some serious 
music is enjoyed and carefully listened to as a benefit of this work.

Simply tuning to a program which is "fed" to you and then standing back and 
saying, "Wow, does that ever sound *weird*!, then, with the muting strips 
still in, rushing back to the "safety" of ET, and saying, "Whew! I'll never 
try *that* again!" will not do much to promote advancement in the varieties 
of the way the modern piano can sound.
 
Bill Bremmer RPT
Madison, Wisconsin