Scaling

[Richard Moody]

The string lengths, (position and sampe of bridge) were designed for 2:1
octaves. The ratios actually used were under this according to Wolfden.  
Since there are an infinite varitieties of temperaments, ET would be
chosen as the most uiform changing one.  Which scale designers LOVE the
most.  ET triumphs again. 
	The varations from that as far as bridge placement would limit that
instrument to the temperament it was calculated for. BUT choices are
limited according to the size of string.  Because of this limitation, the
choices of string length are of a compass that includes all temperaments. 
Execpt those concocted before noon on a certain day soon after spring
equinox. Perhaps the Steinway M bridge design was hatched on such a day. 
I have always wanted to hear another version of how they figured out the
sway in the bridge at the two breaks.  As in the photo on the APSCO
catalogue.  (Which is almost as meritorius as the M itself.)

Richard Nadafool Moody

ps I have a spread sheet you might be interested in ..rm

> From: Ron Nossaman <nossaman@SOUTHWIND.NET>
> To: pianotech@ptg.org
> Subject: Scaling 
> Date: Wednesday, April 01, 1998 7:06 AM
> 
> 4/1/98
> 
> I've come up against a seemingly insurmountable problem that someone out
> there might be able to help me with. There is a very good chance that
one of
> the instruments in my shop at the moment will ultimately be used in a
venue
> requiring that it be tuned in a number of different historical
temperaments.
> I am rescaling the beast, and my problem is this. Does anyone have
rescaling
> software that optimizes for temperaments other than ET? Since tensions
and
> inharmonicity are computed from speaking length, wire gauge, wrap
diameters,
> length and positioning, and *frequency* determined by position in an ET
> scale, it wouldn't be exactly right for any other tuning scheme. This
could
> have tragic consequences considering the ultimate use to which this
> instrument will be put. Since it is apparently not possible to tune in
ET to
> infinite accuracy in the first place, and - since almost any deviation
from
> ET turns out to be a documented, or surmised, variant of some obscure
> temperament anyway - I suppose I'm looking for a scaling program that
> produces emotionally satisfying screen graphics of scale colorations
that
> will (in use) trigger massive endorphin secretions in the brains of
> listeners of the music performed thereon, no matter what the tuning
scheme.
> Does anyone know of a nice fuzzy, friendly scaling program that will do
> this. I need a 'wild breast' soother, and I'd even take a beta version
for
> testing.  
> 
> Thanks in advance for your help. My endorphin levels are rising in
anticipation.
> 
>  Ron Nossaman