One more 12-tone tuning . . .

[Richard Moody]

Paul Erlich writes,....

" 	For example, the first version of the tuning is
> notated in meantone for a reason -- e.g., C-D# is _not_ a minor third, it's
> an augmented second, and approximates a 7:6 ratio (not a 6:5 ratio) very
> closely. Etc. etc." 

The confusion arises when you say "meantone".  In Meantone, to keyboard tuners, for
at least  the past 400 years there has been no C--D#.   It has always been Eb, or
three fifths (1/4 comma don't forget) down from C.  It was that way to form a pure
third with G. (but forms a wolf with G# (and not Ab))  I saw your D# but when put
into the spread sheet it took it as a 6:5 ratio, since the cents you posted were
from ET and in ET, D# and Eb are the same.   The spread sheet is not set up to
compute 7:6 ratios, but further calculation with the cents you gave do give a "close
enuf"  pure ratio.
Never-the-less the 6:5 is lower and theoriticaly "louder" and beating at 20+ so that
must be heard as well.  If you would like me to tune it on a piano and post the
results I certainly will. 

	I am sorry you perceive all this as negative, but this is a list of piano tuner
technicians.  We are fault finders in many aspects.  We must make sure the piano you
are performing on will not "fault on you" especially when it is in front of 10, 100,
or 1000 or more audience, or even in practice. So from tuning to mechanical, and
__________  
 yes we do deal with a lot of "negatives" but we hope the result is positive. 
---ric

ps, You might be interested in Helmholtz and Ellis on resultants and combination
tones, and perhaps  experiments to obtain audible tones from beat frequencies of
supersonic pitches. 

----------
> From: Paul H. Erlich <PErlich@acadian-asset.com>
> To: 'Richard Moody' <remoody@easnet.net>; pianotech@ptg.org
> Subject: RE: One more 12-tone tuning . . .
> Date: Sunday, September 05, 1999 9:54 PM
> 
> Richard --
> 
> (a) You're totally missing the point of this tuning! Clearly you're coming
> at this with a negative attitude rather than taking the time to understand
> the content of my messages. For example, the first version of the tuning is
> notated in meantone for a reason -- e.g., C-D# is _not_ a minor third, it's
> an augmented second, and approximates a 7:6 ratio (not a 6:5 ratio) very
> closely. Etc. etc.
> 
> (b) Beatings _do not_ sound as tones, even if they are fast enough to be in
> the audible range. That's because tones are fluctuations in air pressure,
> while beating is merely a periodic variation in the _amplitude_ of these
> fluctuations. If you're interested in learning more about beats, combination
> tones, virtual pitches, and their interactions, I would recommend Reiner
> Plomp's _Aspects of Tone Sensation_.
> 
> -Paul
>