Scaling, a challenge

[Ron Nossaman]

Reply at bottom

>
>I still think it would be interesting to "run the numbers", just for the sake
>of discussion.  

--trim--

>
>While I did read the flowery embellishment of Ron's post, I disregarded the
>idea that this was a joke.  It is, in fact, how many perceive the very idea of
>any HT, a joke.  "Are you going to tune that piano BACK to ET when you're done
>fooling around with it?, HMMMM?"  I assumed that he really was pondering the
>idea that a varied scale design might be in order if the piano were to be used
>primarilly for HT's.  
>
--trim--

>Since there are so many who truly believe that the modern piano was "designed
>for ET" as Richard seems to, why not explore whether 1/4 comma Meantone
>frequencies really would call for altered string guages?  I say that they
>would not.  And if this is so, then any argumaent that using any HT runs
>contrary to the "intended design" of the piano would be a false assumption.  
>
>Let's prove or disprove it.  It is an often asked question and an even more
>often used argument that I hear from the ET only crowd.  On pages 241 & 242 of
>Dr. William Braid White's book, Piano Tuning and Allied Arts, there is a two
>octave listing of "meantone" frequencies.  I assume it is 1/4 Comma Meantone.
>This would usually be the most extremely non ET that one might want to tune.
>Let's have someone who has a scaling program substitute these frequencies with
>those for theoretical ET and see if it would alter the determination of any
>wire sizes on a typical piano, say a Yamaha or a Steinway.
>
>Bill Bremmer RPT
>Madison, Wisconsin
>
>


I don't believe you've ever read in any of my horticulturally enhanced posts
that I consider HTs to be a joke. What I did say, in this fabricated
situation to which you refer, was that the piano would be tuned in a number
of different historical temperaments. Since the number was unspecified, one
might assume it to be one. Were it not for the fact of the word
'temperaments' in the same sentence this would be a logical and reasonable
starting point. The fact that 'temperaments' is, however, pluralized, would
indicate a number somewhat larger than the singular. Let us therefor assume
a number of at least two as the indicated number of temperaments in
question. At the risk of introducing the unsolicited spectre of practical
probability in this otherwise logical discussion, I would point out the
likelihood of limiting the use of all the available HT schemes to only two
in this instance would be singularly unlikely. However, in the interest of
keeping this correspondence as logically pristine as possible, I will make
no further assumptions as to the number and choice of temperament schemes
used, other than this number being bigger than one.      

You have chosen 1/4 comma Meantone as the antithesis of ET because you have
determined they are each most deviant from the other. This is outside my
education, so I'll take the accuracy of your determination on faith. Any
reasonable effort to conform to the framework of the original post will
require averaging at least one other HT type in with the Meantone
(plurality). To do so would almost certainly bring the frequency averages
closer to ET and make the whole exercise less worthwhile. That's more or
less the point. How do you suppose the result of averaging together all the
HTs ever used would turn out. I'd guess it would be nearly indistinguishable
from ET. In any case, the differences between the 'average' HT, and ET,
would almost certainly not realize any benefit for the 'average' HT by
rescaling. That, again, was the point, and as long as there is no single
definitive criteria for what constitutes a HT (like there is for ET), it's a
moot point. That was the joke and, even having explained it, I STILL think
it's funny.

Since you brought it up, by all means, run the numbers on the Meantone
against ET. I won't make any predictions, but I'd be curious to see the result. 

 Ron Nossaman