New Werkmeister III Direct Interval Program

[Billbrpt@AOL.COM]

Dear List,

Because today was a holiday, I got an itch to tune that Werkmeister III 
temperament which has been discussed lately on my own piano which is a new 
scale Walter Console with Pianodisc system.  It is not a temperament I tune 
often and have previously only done it by ear, the last time, many years ago. 
 Since I could see that a Direct Interval approach would work, it will work 
with any Meantone or Equal Beating Well-Tempered tuning, I decided to make a 
new Werkmeister III program for my own piano.

My basic idea worked but the post I sent recently should be disregarded.  I 
made an error in the procedure and said that the G3-B3 3rd should be pure and 
this was not correct.  However, tuning the series of 4ths & 5ths starting on 
A3 0.0, D4 3.0, G3 6.0, C4 9.0 (all values read on Octave 5) works perfectly 
on a High Inharmonicity scale such as this Walter or a Steinway, not to 
mention Kimball, Wurlitzer, Baldwin Acrosonic and Kohler & Campbell.

You tune your fist pure 5th E4 from A3 by Direct Interval.  Then you do your 
series of 3 tempered intervals.  Once at C4 you tune your series of 6 
remaining pure 5ths by Direct Interval starting by going down to F3 (then up 
to the octave F4), up a 4th to A# (Bb)3, Up another 4th to D#(Eb)4, down a 
5th to G#9(Ab)3, up a 4th to C#(Db)4, then down a 5th to F#3.  Now you tune 
you last tempered interval, up a 4th to B3 by finding the value for B3 as a 
perfect 4th from F#3 then adding 3.0 cents to that value.

I tuned out my octaves as I usually do, a way that I believe to be the 
easiest to determine, the most natural and best sounding for general 
purposes.  The octave is always made to be an Equal-Beating compromise with 
the 5th.  Once two octaves have been tuned, the double octave is always made 
to be an Equal-Beating compromise with the octave and 5th.  This is carried 
all the way to the top and bottom.

I had guests over later and we played the piano both ourselves and with the 
Pianodisc system.  While I have known some technicians who regularly use the 
Werkmeister and even one who tuned it on a Yamaha Disklavier, I know that 
there are some people who do not like it or at least consider it too limited 
to ever use except by specific request.

My guests all thought it sounded just fine and even when I pointed out what 
was supposed to be considered out of tune, most of them could not even tell 
at all and one could say that he recognized something that sounded very 
slightly out of tune to his ear but that it was something very slight, that 
wouldn't bother him.  

That interval was the 5 cent narrow C3-G3 5th, which has an obvious beat.  I 
showed him how the Equal-Beating feature has the ability to cancel out that 
objectionable sound.  Sure enough, when a full chord was played, you couldn't 
hear that sound at all.  I told him that I was able to take advantage of the 
same phenomenon in the Equal Beating Victorian Temperament.  All of the 
Well-Tempered Tunings have some of this effect.

None of my guests ever heard anything that they considered to be the 
slightest bit out of tune.  However, as the disc played different kinds of 
music, I did hear things that I knew some people would not like.  In short, 
the Werkmeister III sounded even better than I thought it would but I still 
would not choose it as an all-purpose temperament.  I would want to know that 
it would enhance specifically the music to be played.

If anyone is interested in the detailed procedure and/or the 88 note program, 
I can write it up.

Bill Bremmer RPT
Madison, Wisconsin