<!doctype html public "-//W3C//DTD W3 HTML//EN"> <html><head><style type="text/css"></style><title>Re: Helmholtz and Steinway</title></head><body> <div>At 8:05 PM -0800 11/18/01, Delwin D Fandrich wrote:</div> <div><br></div> <blockquote type="cite" cite>This isn't apples and oranges, more like prunes and</blockquote> <blockquote type="cite" cite>pomegranates. Or prunes and potatoes. Fiber optic cables, and the light<br> traveling through them, do bear some resemblance to telegraph wires, and the<br> electrical current traveling through them, do bear some resemblance to each<br> other but neither is remotely similar to a piano string winding its way</blockquote> <blockquote type="cite" cite>through a couple of offset bridge pins and across the top of a bridge.</blockquote> <div><br></div> <div>Since I'm no greengrocer I'll have to take your word for it, Del, until someone who knows can tell me why a telegraph wire does sing.  And if there are any geologists about, if I produce a certain earpiercing screech with a 3" chalk on a blackboard, what will be the relative frequency of the screech when I break an inch off the end of it?</div> <div><br></div> <div><br></div> <div align="center"><img src="cid:a05100300b81f0096e879@[195.147.149.43].1.0"></div> <div><br></div> <div><br></div> <div>Here's a rough monochord I set up to take an objective look at a few of the things we've been heating the air with.  Two standard upright agraffes driven into a length of 40mm Delignit serve as the end points of the speaking length.  The wire is 12.5 gauge.  A 5 mm drill bit supports the back length between the hitchpin.</div> <div><br></div> <div>I first rolled the drill to tune the back length by sound only, plucking this and the speaking length alternately to get the note.  I then checked the tuning of the back length by plucking only the speaking length and immediately damping it, aiming for maximum resonance of the partial in the back length.  Finally I measured the back length, which come to 87 mm. or 1/8 of the speaking length sounding 3 octaves above the fundamental.  So far as practical measurements can detect, there is no detectable inharmonicity in the main length.  The arrangement is not meant to be typical of anything and is purely for experimental purposes.</div> <div><br></div> <div>Ron O. mentioned in passing Wayne Stuart's use of silicone rubber in his agraffes.  Since I had a sheet of this lying around, I plugged these agraffes with a good firm strip of it and it made not a scrap of difference to anything.  With or without silicone rubber (which is not significant -- I just thought I'd try it), either section of the wire, when struck or plucked, sets up oscillations in the other section.  The back length gives a frequency of ca. 2088 c/s with considerable falseness.  The harmonic induced in the speaking length sings with a much slower false beat and continues for longer if the back length is not muted.  The volume of the induced wave in the speaking length falls markedly as the back length is stopped.</div> <div><br></div> <div>The front section, of length 55 mm, rises directly to the wrestpin giving roughly a G#.</div> <div><br></div> <div>THE LENGTHWISE WAVE.</div> <div> By pure chance, with this configuration, the pitch of the lengthwise wave is also about the same G#.  This wave is set up by stroking the wire between finger and thumb using either a rag wetted with lighter fuel or powdered resin.  This I take to be Theodore Steinway's "whistle".  This whistle is fairly constant and pure at this tension (ca. 100 lbf).  Altering the tension makes no difference to the pitch of the whistle except that at extremely low tensions, instead of a single pitch, it trills about a semitone, like one of those very skilled whistling workmen that I like to be a long way off.  It is as though there are two distinct pitches available.  The trilling effect only happens at very low tension but I have also obtained the two at high tension, alternating but not trilling.</div> <div><br></div> <div>If I place a simple bridge under the wire to raise the pitch of the speaking length a two or three tones, the frequency of the compression wave remains the same.  This would bear out what Stephen seems to be saying.  It would seem to mean that when Conklin talks of getting the correct relationship between the transverse frequency, he means that a meeting point must be found for a given "system", as Stephen refers to it, between the required frequency of the partials for the given note and the lengthwise frequency of the system that will most suitably be used for those partials.  My first impression is that this might be easier said than done.  There is no problem setting up a routine to seek this goal but the goal might not be attainable in view of all the other design factors of the scale.  Have you, Del, or you Ron O, ever allowed longitudinal wave considerations to affect your scale calculations?  I think we should be told.</div> <div><br></div> <div>Before any such thing could be attempted, one would need accurate data to calculate the frequency of a given "system" in the abstact, taking into account, presumably, more than simply the mass of the system.  Conklin may give some information in his patent as to how the lengthwise frequency is calculated, but he gives no hint of it in his lectures.</div> <div><br></div> <div>THE STEINWAY EFFECT</div> <div>Now I've only just set up this rig, so I've only had a little time to play with it and not yet even worked out where to start, but there's nothing like a practical experiment for getting through the trees to the wood and the main points quickly become obvious.</div> <div><br></div> <div>At the moment I'm doing everything by ear and it will be necessary to use electronic recording devices to get the details, but it seems that the sense of Steinway's patent becomes clearer to me using my set-up.  There is no doubt that there is an optimum position for the back length support at which point the discordant clash of certain frequencies between 3000 and 5000, close to the lengthwise wave frequency, becomes still and more harmonious.  This point does seem to be that which gives in the back length the tuned partial of the speaking length.  Further than that I won't say because I haven't had time enough and haven't any electronic help.  What is clear is that certain beats in the very high frequencies, that can jar badly on the highly sharpened ear of the experimenter (though probably completely unheard by the casual observer) can be brought to heel by proper positioning of the back length support (ie. the 5mm drill) and these frequencies then amalgamate with the other partials of the note, even though perhaps somewhat discordantly.</div> <div><br></div> <div>JD</div> <div><br></div> <div><br></div> </body> </html>