Werkemeister III

[Richard Moody]

----------
> From: Paul N. Bailey <103445.713@compuserve.com>
> To: INTERNET:pianotech@ptg.org
> Subject: Re:Werkemeister  III
> Date: Friday, September 03, 1999 2:52 AM
> 
> I think these would be the cents deviation for the Werk. III  in 
> Owen Jorgensen's  little book The Equal Beating Temperaments:
> 
> Fred Tremper worked this out, a couple years back he offered to
> send SASE the cents dev. for all the temperaments in that wonderful
> little yellow chapbook. I highly recommend, if he will still honor
> requests.
> 
> c       0
> b       -6.3
> a#      -3.9
> a       -10.2
> g#      -7.8
> g       -2.6
> f#      -11.7
> f       -2
> e       -8.2
> Eb      -5.9
> d       -6.7
> c#      -9.8

Here are beat rates of above figures. The order of notes is reversed.  The rates are
from the given note as the bottom note. Thus first f , that sixth is f--d'     
 
5th	4th	3rd	6th	Note
0.01 	0.02 	2.77 	5.53 	f
-0.02 	3.13 	11.47 	11.45 	
-2.05 	2.06 	5.66 	5.69 	g
-0.02 	-0.02 	12.91 	12.88 	
0.02 	2.76 	8.93 	8.97 	a
-0.02 	-0.02 	7.33 	11.43 	
-3.13 	0.03 	10.05 	10.09 	b
-2.06 	-0.03 	4.15 	4.12 	c'
0.02 	0.04 	17.21 	17.25 	
-2.76 	4.10 	7.36 	13.62 	d'
0.02 	0.04 	15.29 	19.41 	
-0.03 	-0.03 	13.40 	13.36 	e'
0.03 	0.04 	5.54 	11.06 	f'
-0.04 	6.26 	22.95 	22.90 	
-4.10 	4.12 	11.32 	11.38 	g'
-0.04 	-0.04 	25.82 	25.76 	
0.03 	5.52 	17.87 	17.94 	a'


Lots of  pure fifths but no wolfs. Can't say they are "equal beating" But look at
the beat rates of the thirds and Sixths, they are equal to one beat in 10 seconds. 
"Equal beating" if I had to name it. ---ric
> 
> 
> The Jorgensen-Tremper numbers represent an "equal beating" tempering 
> scheme, while the SAT numbers represent a more modern tempering approach, 
> where the tempered fifths are all the same size in cents.

 5th	4th	3rd	6th	Note
-0.02 	-0.02 	1.97 	4.95 	f
0.01 	2.51 	11.55 	11.58 	
-1.99 	2.67 	5.58 	5.61 	g
0.02 	0.03 	13.00 	13.03 	
0.02 	2.98 	10.01 	9.98 	a
0.02 	0.03 	6.64 	10.62 	
-2.51 	0.03 	11.26 	11.23 	b
-2.67 	0.03 	3.04 	3.00 	c'
-0.03 	-0.03 	17.33 	17.29 	
-2.98 	3.99 	8.34 	13.36 	d'
-0.03 	-0.03 	14.12 	19.45 	
-0.03 	-0.03 	14.92 	14.98 	e'
-0.03 	-0.04 	3.95 	9.91 	f'
0.03 	5.01 	23.10 	23.16 	
-3.99 	5.34 	11.16 	11.22 	g'
0.03 	0.05 	25.99 	26.06 	
0.03 	5.96 	20.02 	19.97 	a'	(440)

These are from the SAT manuel numbers that were posted. Where the C--G is beating
2.67, 
that is contracted by four cents, or the 696 fifth which is 6 cents tempered from a
pure fifth (702) which is more than 1/4 comma but less than 1/3 comma, ---ric