<!doctype html public "-//W3C//DTD W3 HTML//EN"> <html><head><style type="text/css"></style><title>Re: string length possible in given cabinet size?</title></head><body> <div>Ron and list,</div> <div><br></div> <div>I've come into this thread late.</div> <div><br></div> <div>Someone posted (perhaps Stephen Airy yesterday I think, I'm at home at present since it's Saturday in Aust.):</div> <div><br></div> <blockquote type="cite" cite>>I'm thinking  2.5" C88, 4.75" C76, 9" C64, 17.5" C52,<br> >32" C40, 60" C28, 72" C16, 80" C4, 81" A1, and 84"</blockquote> <blockquote type="cite" cite>>A-12?  would that be possible?</blockquote> <div><br></div> <div>Ron N replied:<br> </div> <blockquote type="cite" cite>How did you arrive at these numbers?</blockquote> <div><br></div> <div>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.</div> <div><br></div> <div>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.</div> <div><br></div> <div>If we just look at the percentage increase of speaking length per octave, regarding the figures of the previous post, it translates as follows;</div> <div><br></div> <div align="center"><img src="cid:a05010400b6eab408b1ea@[61.8.18.164].1.0"></div> <div><br></div> <div>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 Bösendorfer 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 Bösendorfer Imperial has a C16 of only 162.5 cm (64"). A strange bunch of numbers indeed.</div> <div><br></div> <div>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.</div> <div><br></div> <div>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.</div> <div><br></div> <div align="center"><img src="cid:a05010400b6eab408b1ea@[61.8.18.164].1.1"></div> <div><br></div> <div>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.</div> <div><br></div> <div>Ron O</div> <div>-- <br> Overs Pianos<br> Sydney Australia<br> ________________________<br> <br> Web site: http://www.overspianos.com.au<br> Email:     mailto:ron@overspianos.com.au<br> ________________________</div> </body> </html>