[CAUT] Moore vs ET

[Fred Sturm]

	I would agree that Broadwood Best meets the threshold of "noticeable"  
at least for many, if not most (this is Ellis tuner #4, one of two  
tunings by "Broadwood's best tuner" that Ellis measured and documented  
back around 1890, along with three done by "the usual tuner"). I  
certainly notice it when I am playing a piano. When I did my "stealth  
Moore experiment," I sampled a few other temperaments, including  
Broadwood Best, in practice rooms mostly. I decided to try Broadwood  
Best in a classroom. A few days later, I got a comment from a prof  
doing harmonic dictation in that room: "Check the piano in room 1106,  
something is strange about the tuning." I switched back to Moore, and  
heard no more comments. (The prof was one who was kind enough to let  
me know whenever something was amiss - in a nice way. I could pretty  
much count on hearing from him if a unison was getting obnoxious, or  
anything was amiss with a piano he used).
	Coleman 11 (C11) looks a little bit milder and more evenly spaced  
than Broadwood Best 4 (BB4), so I presume it would probably be a  
little less pronounced a sound. But they are certainly in the same  
basic ballpark. So I think we can say that Moore is still too close to  
ET to be obvious and noticeable, but BB4 and C11 are far enough from  
ET to be noticeable, at least to those who are sensitive and paying  
attention. Moore varies from ET by a maximum of 3 cents, C11 and BB4  
by as much as 5 cents. It is probably more to the point to compare  
intervals, with M3s as the most representative.
	[It is fairly easy to make these comparisons, using cents offset  
tables: One simply takes each note of the interval, notes how large a  
shift in cents and in what direction, and combines the changes in the  
two notes. So that for the CE M3 in Moore, C is raised 2.5 cents,  
which narrows the interval by that amount, E is lowered 1.5 cents,  
which also narrows the interval by that amount. Hence, the CE M3 is  
narrower than in ET by 4 cents (2.5 + 1.5)].
	Moore narrows M3s by a maximum of 4 cents (CE and GB), and widens by  
a maximum of 2 cents (many M3s). C11 narrows M3s by a maximum of 6  
cents (CE and GB) and widens by a maximum of 4 cents. BB4 narrows a  
maximum of 7 cents (CE only, GB by 6) and widens by a maximum of 4  
cents. So one could say fairly accurately that C11 and BB4 are more or  
less "twice as different from ET" as Moore. Thus, the point at which  
WT variant becomes noticeable probably lies somewhere between Moore  
and C11/BB4.
	Another interesting observation: Moore, which, as we seem to have  
fairly well established, is essentially not noticed as sounding  
significantly different from ET, would score 73% for temperament, 67%  
for mid-range, on the PTG tuning test. (FWIW, which isn't much, C11  
would score 48% and 25%, BB4 23% and 7%. It _does_ give a perspective  
on weighting and the meaning of percentages in this context).
	For those interested in how the cents translate into beat rates, here  
are theoretical beat rates for these temperaments (M3s from C3 to B3).  
I'll list them in order: ET, Moore, C11, BB4.
C  5.2  3.7  2.9  2.5
C#  5.5  6.3  7.1  7.1
D  5.8  5.0  5.0  4.6
D#  6.2  7.1  7.1  7.1
E  6.5  7.5  7.7  8.5
F  6.9  5.9  4.4  4.4
F#  7.3  8.4  9.5  9.5
G  7.8  5.5  4.4  4.4
G#  8.2  9.5  10.4  10.1
A  8.7  8.7  9.4  9.4
A#  9.2  9.3  7.9  8.6
B  9.8  11.2  12.7  12.7
(These numbers are courtesy of a spreadsheet created from instructions  
in A Guide to Musical Temperament by Thomas Donahue. I think I posted  
the spreadsheet to the caut list a while back. You can simply enter  
cents offsets and it generates beat rates, among many other things.  
Very handy).
Regards,
Fred Sturm
University of New Mexico
fssturm at unm.edu



On Mar 20, 2008, at 6:57 PM, A440A at aol.com wrote:

> Fred writes:
>
> <<  I assume the "Broadwood Best" you refer to is "Ellis tuner
> #4" (#5 comes much closer to ET and is pretty bland. I am fond of BB
> #4 myself). I have seen a couple of the Coleman temperaments, but not
> #11. Where are they available?
>
> Rollingball, I think, has all of them.  I use the Broadwood tuning  
> that
> Jorgensen displays on page 558 of "Tuning".  The offsets are
> A    0
> G# +2
> G    +5
> F#   0
> F   +5
> E    -2
> Eb  +3
> D   +3
> C# +1
> C   +5
> B    -1
> Bb  +4
>
>  This tuning is not as "smooth" or refined as the Coleman 11, but as
> Jorgensen states, there is no temperament better than another, they  
> simply have
> different resources.
>
>>> I have seen a
> few "proposed Bach Temperaments" but am not familiar with J. Charles
> Francis. Can you shed some light? (source, whatever). >>
>
>>   From: "J. Charles Francis" <Francis at datacomm.ch>
>>> Subject: Tuning Interpretation of Bach's '1722 Seal'
> you can download at the following link:
>>>
>>> http://www.bach-cantatas.com/Articles/Bach_Seal.pdf
>
>>> And offsets C descending, corrected for A=0.0
>>> C    8.128
>>> B    -2.582
>>> A#   5.959
>>> A    0.0
>>> G#   2.049
>>> G    5.431
>>> F#   -1.861
>>> F    7.914
>>> E    -0.822
>>> D#   4.004
>>> D    4.278
>>> C#   0.0942
>
> Hope that helps.
>
> Ed Foote RPT
> http://www.uk-piano.org/edfoote/index.html
> www.uk-piano.org/edfoote/well_tempered_piano.html
> <BR><BR><BR>**************<BR>Create a Home Theater Like the Pros.  
> Watch the
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