A question on temperament-Dale

[Avery Todd]

Bill,

    Thanks for the post. I'll definitely be exploring all this.

Avery

At 09:58 AM 01/14/00 -0500, you wrote:
>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