what's with the new temperaments?(x post)

[Ron Koval]

Lists,

After the lack of public response to my m3/M3 ratio post, I thought I'd take 
a chance, and stick my neck out again....

Maybe I should have called this post:
What's wrong with the old temperaments?

They are the best efforts of technicians and theorists of the time, created 
with the available tools.  They were recently (in historic time) translated 
into offsets from equal temperament that modern technicians can use to 
re-create (hopefully) what was done in the past.  I watched with a dawning 
awareness of the difficulty of this process, as many people tried to 
quantify the EBVT from the written record.  How many attempts, and different 
sets of numbers were published before one set of numbers were given the 
final o.k.?  And this guy is alive, imagine the possibility for error when 
dealing with only a written recipe.....

Why go to the trouble to design new temperaments?  For the music.  In the 
same way that rebuilders have found that by altering stringing scales of the 
manufacturers, they can come up with better sounding pianos, people are 
continuing the look into what are the strengths and shortcomings of the 
historical temperaments.  Armed with spreadsheets, graphs, available pianos 
and willing musicians, a body of knowledge is slowly coming together.  
First, graphs showed only the progression of major thirds. Next, the 
interval of the fifth and minor third was added.  Finally fragmenting off to 
the projected beat-rates of various intervals, ratios between the m3/M3 and 
the difference between the m3-M3.

There seems to be an added resonance to those temperaments that incorporate 
the m3/M3 in a triad equaling either 2.0, or 1.5, especially in the remote 
keys.  I'll post two temperaments below, that I'd like to get feedback from 
those of you willing/able to give them a test.  Practice rooms are ideal 
candidates, but you can find willing pianists everywhere.  The Wendell 
Natural is very mild, and could safely be placed on just about any piano.  
The Bailey '93 is a full strength temperament for those of you able to try 
that.  The Natural was designed with the m3/M3 ratio in mind (all major 
triads), while the Bailey '93 happened to have 1.5/2 ratios from A around to 
F, following the circle of fifths.  I would avoid choir room pianos and 
vocal studios to start, since their music is keyed by vocal range, instead 
of any circle of fifths traditional order.

Thanks a bunch!

(ET thirds are around 14 cents from pure, for reference)

Bailey '93  (thirds from 5.4 - 21.5 cents from pure)
C      	6.2
C#     	-1.6
D      	1.4
D#    	2.3
E      	-2.1
F      	6.2
F#     	-3.6
G     	4.9
G#    	0.3
A      	0
A#  	4.2
B	-0.1

Wendell Natural (thirds from 7.4 - 17.6 from pure)
C      	4.24
C#     	-1.59
D      	2.41
D#    	2.32
E      	-2.08
F      	2.29
F#     	1.83
G     	3.74
G#    	0.37
A      	0
A#  	4.28
B	-0.12


Ron Koval
Chicagoland





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