Werkemeister III by Direct Interval

[Jim Coleman, Sr.]

Hi Bill:

Just one comment about the paragraph below. Did you intend to say "play the
F4 note and stop the lights"? One might think that you intended them to play
the F5 note.

Jim Coleman, Sr.

On Fri, 3 Sep 1999 Billbrpt@AOL.COM wrote:

<snip snip>
> You can use the old Stretch Calculator sampling 
> method to make this determination.  In the Tune mode, set the SAT to F5, play 
> the note and stop the lights.  Press Octave Up to F6 and stop the lights 
> again. A reading below 5 would be considered Low, 5 to 5.8 would be Moderate 
> and 5.9 or above would be High, as simple as that.
> 
> Next, you do the same as you would do to tune a 1/4 Comma Meantone 
> Temperament.  Take the value for the Syntonic Comma, which is 21.5 and divide 
> it by 4 to get 5.38.  Subtract 2 that is already built in between each 5th 
> the SAT has to get 3.38, round that off to 3.4.  This is the theoretical size 
> of the 5th to be programmed.  Now you must adjust that size for 
> Inharmonicity.  For a Low Inharmonicity piano, subtract .2 to get 3.2, for a 
> Moderate, subtract .3 to get 3.1 and for a High Inharmonicity piano, subtract 
> .4 to get 3.0.
> 
> If you have a Steinway, which has a relatively High Inharmonicity scale, it 
> is particularly easy to program in the figures, they are all multiples of the 
> number 3.  Starting on A3 reading on the 5th Octave, program in 0.0.  Press 
> Shift and Store to store the value for that note. Move up to D4 and adjust 
> the SAT to read that note on D5 and program in the figure 3.0. Press Shift 
> and Store to store the value for that note. Move back down to G3 which will 
> automatically read on G5 and program in the figure 6.0.  Press Shift and 
> Store to store the value for that note.  Move up to C4, adjusting the SAT to 
> read on C5 and program in the figure 9.0.  Press Shift and Store to store the 
> value for that note.  Now tune carefully all of these notes according to the 
> program you have established so far.
> 
> Now you must tune the G3-B3 3rd.  Theoretically, it would be pure but because 
> your octave will be stretched, the 3rd will be just slightly expanded but 
> below the threshold of where you would hear a beat, less than 1 cent.  Move 
> to the Tune mode and set the SAT to G5.  Play the note G3 and stop the 
> lights.  Press Shift and reset so that the SAT now reads 0.0.  For a Low 
> Inharmonicity piano, dial in 0.7, for a Moderate, dial 0.8 and for a High, 
> such as this Steinway, dial in 0.9.  Now tune the note B3 to that setting.  
> Now, cancel out your offset and return to your page and set the SAT to the 
> note B3 which will automatically read on B5.  Play the note B3 and stop the 
> lights.  Press Shift and Store to store the value for that note.
> 
> Now, to get the last of your tempered intervals, subtract your adjusted 1//4 
> Syntonic Comma value from the figure you now have for B3.  In the Steinway, 
> that value is 3.  Let's say the B3 ended up reading 1.0.  If you subtract 3 
> from that you would have     -2.0.  Program that value for the note F#3 which 
> will automatically read on F#5. Press Shift and Store to store the value for 
> that note.
> 
> Now from here on out, you can use Direct Interval Programming to tune the 
> remaining pure 4ths and 5ths.  It is very easy.  You have already tuned F#3, 
> leave the SAT there and play C#4.  Tune that note to stop the lights.  Now 
> set the SAT to C#4 and adjust the SAT so that C#4 will read on C#5.  Play C#4 
> and stop the lights.  Press Shift and Store to store the value for that note.
> 
> Move the SAT down to G#3 which will automatically read on G#5.  Play the note 
> C#4 and stop the lights.  Now tune G#3 to that reading.  Press Shift and 
> Store to store the value for that note.  Now continue through the rest of the 
> temperament the same way.  You will get D#4 from G#3.  You can get the F3 
> from C4 and the A#3 from the F4 after you have tuned you octave or from D#4.  
> They will all match up.
> 
> With DIP, you can now tune the kind of octaves you really want by selecting 
> the coincident partials you want and either tune them perfectly or make 
> whichever kind of compromise you want.  You have the choice, you are in 
> control.  You are telling the SAT what to do, it does not offer you 
> information that may be incorrect.
> 
> Good Luck!
> 
> Bill Bremmer RPT
> Madison, Wisconsin
>