string length possible in given cabinet size?

Ron Overs sec@overspianos.com.au
Sat, 31 Mar 2001 13:58:46 +1000


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Ron and list,

I've come into this thread late.

Someone posted (perhaps Stephen Airy yesterday I think, I'm at home 
at present since it's Saturday in Aust.):

>  >I'm thinking  2.5" C88, 4.75" C76, 9" C64, 17.5" C52,
>>32" C40, 60" C28, 72" C16, 80" C4, 81" A1, and 84"
>  >A-12?  would that be possible?

Ron N replied:

>How did you arrive at these numbers?

Good question Ron, because there would be little chance of C88 (with 
a speaking length of 2.5") getting to pitch without breaking wire. 
Too often piano scales are designed by pulling numbers out of the air 
at random. Most of us have a computer handy these days, so what about 
using some of that computing power? We could teach ourselves a lot. 
We might even design better pianos while we're at it.

The subject of this thread is one which must be considered with 
regard to a number of other design factors. However, the numbers 
originally posted seem to be a pretty strange bunch. While I would 
like to write about the process of scale designing at some point, 
which would also cover the question of sensible speaking lengths for 
a given size of piano, it would likely be a little too long a topic 
to consider publishing on the list.

If we just look at the percentage increase of speaking length per 
octave, regarding the figures of the previous post, it translates as 
follows;



The percentage increase is somewhere within the ball park of many 
other contemporary scales, but the chosen string lengths are way too 
long for any degree of safety, if indeed a piano with such a scale 
could get to pitch at all without breaking wire. C16 down is 
obviously in the bass section. However, the bass lengths also look a 
bit strange. I note A1 is almost identical in speaking length to that 
of a B=F6sendorfer Imperial (which goes on down to the C below). 
Whereas C16, at 183 cm is about the length of the longest note on a 
Steinway D treble bridge, F21 at 183 cm. I don't know where the C16 
length came from, even a B=F6sendorfer Imperial has a C16 of only 162.5 
cm (64"). A strange bunch of numbers indeed.

When designing a string scale, inharmonicity, percentage of breaking 
strain and impedance should all be considered together, hopefully 
resulting in a scale design which satisfies all factors without any 
wild excursions.

The end result of such a scaling exercise should result in speaking 
lengths which tend to increase in length in a uniform way throughout 
the scale. Your post encouraged me to browse over some of the seventy 
odd piano scales I have on my computer. What I found interesting was 
that the increase in speaking length for all instruments, expressed 
as a percentage increase per octave, followed a definite trend. 
Consider the following examples I prepared for four grand piano 
scales.



What is interesting is the very uniform percentage increase of the 
speaking lengths of all of these pianos when compared to the speaking 
lengths of the perhaps fictitious piano of the earlier post.

Ron O
-- 
Overs Pianos
Sydney Australia
________________________

Web site: http://www.overspianos.com.au
Email:     mailto:ron@overspianos.com.au
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