A question on temperament-Dale

[Billbrpt@AOL.COM]

In a message dated 1/14/00 5:49:53 AM Pacific Standard Time, avery@ev1.net 
(Avery Todd) writes:

<< One of our theory professors took a class with Owen and has told
 him that Owen said he was pretty convinced that Chopin used a
 Marpurg. Comments?
  >>

You can always call Owen and ask him any question you have.  He is retired 
but remains active.  You will often find him available and quite happy to 
answer your questions.  You can find his number in the directory.

Marpurg created many temperaments but there is only one which most people 
think of as "Marpurg".  It is often the only other temperament that an ET 
tuner will dare to try.  If you ask me, I think it was doubtful that Chopin 
used it and furthermore, I don't see the advantage it would make.  However, 
you personally may like it and if the artist you tune for wants it, then you 
need to know what it should sound like.  It is what is known as a Quasi Equal 
Temperament (QET), "quasi" means almost.

You can create your own program for this.  I personally never use FAC 
"Correction" figures, I prefer to understand and create my own temperament 
aurally, but using the SAT for the initial pitch and sometimes to prove pure 
4ths & 5ths and in the Direct Interval mode to create a 3rd of a specific 
size.  When I am satisfied with the arrangement, I program it into the SAT 
and have it for all time afterwards.  It works very well for me.

The Marpurg is very easy to describe and to remember how to construct.  Tune 
A4 and A3 as usual.  Then tune F3-A3-C#4-F4-A4 contiguous 3rds exactly the 
same as you would for a regular ET.  You could use the FAC program to set 
this up.  Just be sure to aurally verify that it is correct.  Then from each 
of the notes you have tuned so far, tune whichever 4th or 5th from that note 
which is available perfectly pure.

If you have used the FAC program to tune the initial contiguous 3rds, go to 
the note C4 and press Tune.  It will read on C6.  Change that to C5 and press 
program.  Then stop the lights on that setting and press Shift and Store to 
make the SAT start to read the 4th octave on Octave 5 rather than 6.  Read 
all of your notes from C4 to B4 in octave 5, even though you haven't tuned 
them yet.  You could even program in the same number or 0.0 for each one, the 
idea is to have the SAT reading the 4th octave in octave 5 rather than 6.

Now, you can use the SAT to help you tune those pure 4ths and 5ths.  From A3, 
you want to tune E4 a pure 5th.  Set the SAT on E4 (which will be reading on 
E5, the coincident partial for these two notes).  Play the note A3 and stop 
the lights.  Now tune E4 to whatever that is and press SHIFT and STO.  To 
tune the 4th, A3-D4, set the SAT to A3 and play the note D4 and tune it so 
that the lights stop.  Then move the SAT up to D4, play the note, stop the 
lights and press SHIFT and STO to store that value.  

Do the same with the 4th and 5ths from C#4, F#3 and G#3, and the 4th and 5th 
from F3 and F4 which would be Bb3 and C4.  Now you have only 3 notes left to 
tune.  G3, B3 and D#4.  You have to now do what is called Equal Beating.  The 
classic way to do this is to temporarily tune G3 pure to C4.  Then play the 
5th G3-D4 and notice the strong beat.  Flatten G3 until the G3-C4 4th beats 
exactly the same as the G3-D4 5th.  These intervals will end up beating 
(tempered) about twice as fast as they would in ET. 

With practice, you won't need to do the "temporarily tune" part, you will be 
able to just park the note in the place where it is an exact compromise as a 
4th and 5th.  When you have the note where you want it, press SHIFT and STO.  
Do the same for the remaining two notes, B3 (form F#3 and E4) and D#4 (from 
G#3 and A#3).  The results should give you 3rds and 6ths which sound 
identical to ET.  But when you play the 4ths and 5ths, they will all be pure 
except for the 3 "wobbly" ones.  That is essentially the compromise you are 
making.

In my view, this is a much better alternative than the ET with pure 5ths.  It 
produces a very "clean" sounding piano tuning with just a touch of "color".  
As you tune out your octaves, if you try to make your double octaves agree 
with your octave and 5th, you will maintain that very "clean" sound.  When 
you are tuning the octave that is associated with the tempered 5th, you can 
stretch it a bit more so that the double octave has the same slight beat as 
the octave and 5th (another form of Equal Beating). 

This will tend to "clean up" the 3 tempered intervals so that really, the 
only "impure" sound that you will hear is in the temperament octave itself.  
Outside of it, virtually all the Slowly Beating Intervals (SBI) will either 
be pure or have a barely perceptible beat.  All of your Rapidly Beating 
Intervals (RBI) will have the same smoothness expected of ET and none of the 
harshness that occurs in any of the HT's or the kind of harshness produced by 
the overly stretched octave required for the ET with pure 5ths.

In my view however, Chopin is better served by a Victorian or other 19th 
Century Temperament.  The extra vibrancy of the wider 3rds, 10ths and 17ths 
makes the music written in Ab and Db sound more alive.  Some people are 
sensitive to this however and if this is the case, the Marpurg will be the 
temperament to use.  It will be just as useful for virtually any kind of 
music as regular ET is.

Good luck.

Bill Bremmer RPT
Madison, Wisconsin