Dear Lute List - I have located the Experimental Musical Instruments magazine article on plain string calculations. I can forward it as a PDF to anyone who requests.
Importantly, the author states that plucked strings sound best when tuned to 50% - 70% of their breaking tension (not 80%, as I mis-reported below) - less tension and they sound too slack; more tension and they're likely to break. Ben Cohen Denver, CO -----Original Message----- From: Ben Cohen [mailto:[EMAIL PROTECTED] Sent: Monday, December 13, 2004 8:53 AM To: 'Jon Murphy'; Lute List Cc: [EMAIL PROTECTED] Subject: RE: Strings Redux, progress report Howdy Jon - I recall a short but very useful article on the physics of vibrating strings in Experimental Musical Instruments magazine in the late 1980s. The author (a physicist) not only gave complete formulae for the pitch of a stretched strings as a function of length, density, gravity, etc., but also gave some practical information on tensile strength. I think he noted that most string materials sound best when tensioned to at least 80% of their breaking strength. The author listed the breaking strengths for some popular string materials (which I think were a function of thickness). I used the information as a high school physics teacher to develop a lab on stretched strings. I had my students build Pythagorean monochords and calculate the pitch of various strings as a function of length, tension and material. Thay matched pitch against my electronic piano. Experimental Musical Instruments magazine is no longer in print, but has a fine web presence at www.windwolrd.com. Give me your contact info and I'll try to mail you the article. Ben Cohen Denver, Colorado -----Original Message----- From: Jon Murphy [mailto:[EMAIL PROTECTED] Sent: Monday, December 13, 2004 3:05 AM To: Lute List Cc: [EMAIL PROTECTED] Subject: Strings Redux, progress report You are all well aware that I've been designing other types of stringed instruments and doing some empirical experiments with a test board that I set up for them a few years ago. (The test board is a piece of hardwood with a range of 30" (@76 cm) with no musical value, so as it can't break the strings can be brought to any tension they can hold - and I can bridge each course at any VL, and set the range from bridge to "tail piece" at will). OK, enough of that. To the point. The real question is the proper tuning (and possible tuning) of our instruments. The various formulae in the string caluculators don't take into account the maximum pitch for a length of string (whatever the guage). And that latter has been argued (sometimes by suggesting ignorance <g>). It is often said that given a VL any string, no matter the guage will break at the same pitch. Within a half tone or a tone and half that is true - if one deals with the usual materials (steel wire, gut, Nylgut and Nylon). My thesis has been that the innate tensile strength of the material, and the different densities are the deciding factor. But as they range all over the lot among those mentioned materials it is difficult to prove. But if tensile strength is a characteristic of the material (given it is in a range of thickness not near the molecular level) then the cross section should increase the amount of force it can resist (force in the form of tension). Yet as the cross section (guage) increases the density per unit length also increases, so a higher tension is needed for a particular pitch (given a length). There is a theory. Now to preliminary results. Using strings near to the calculations from several accepted computer programs I found that the breaking force tended to be about 55 to 65 Newtons. But then forcing thicker guages at the same length I found the "breaking Newtons" off the scale, well over 100 Newtons (can't go above that as I'm back engineering the force into the calculator, but that is another matter). So it appears that the cross section, as it should theoretically, does actually give more "strength". Oh hell, this is too long - I know what I'm speaking of, and the experiments (yet more to come) do confirm it. The point is that given the material there is a maximum pitch for any length of string. But also there is an absolute maximum pitch whatever the material (among the normal string materials). The normal string materials trade off characteristics, the tensile strength, the density, etc (and as I think of it, late at night, those appear to be the only materials characteristics, the rest are the individual string in guage). I solicit suggestions, this will take a while as the process is destructive of strings and I'm not going to buy a bunch of gut until I break the nylon and steel (and bronze, lost one accidentally tonight, while it seemed in range, which might make for a different analysis on bronze which seems to be the early wire - and quite different in the mix of characteristics that put steel, gut and nylon in a similar envelope). Best, Jon To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html -- --
