No one seems to object, and the talk continues as if the very people that gave us all the amazing instruments we play, were totally ignorant as far as the oh, so stupid "tune almost to the breaking point" line goes. The simple truth of the matter is that any string made of the same material will break at the same pitch, no matter its' diameter, as long as the string length is the same. Some here still remember Eph Segerman?.. "The stress on the string (represented by S) is the tension divided by the cross-sectional area, so S=T/A. The tensile strength of a material is defined as the stress at breaking (which we can represent by SB). Then the breaking frequency, represented by fB becomes: fB = (1/2L)sqrt(SB/). This demonstrates that the breaking pitch is inversely proportional to the string stop." In the formula, (as can not be seen here, unfortunately) the invert relation is only between the pitch, length and the breaking point stress. Diameter plays no role. All this means a very simple truth - all the instruments of the same mensura tuned close to the breaking point of a given material, will have the same pitch, to the same degree as an organ pipe of the same length and diameter will produce the same pitch, be it in France or England. I hazard to say that, among professionals who used "no rotten strings" and preferred particular strings made by the same makers and even at particular time of the year, the pitch standard was no worse then nowadays. alexander
On Tue, 17 Feb 2009 18:29:32 -0800 howard posner <[email protected]> wrote: > On Feb 17, 2009, at 5:43 PM, [email protected] wrote: > > > How many of us really follow this "fundamental of lute stringing" > > today? We tune our instruments to arbitrarily agreed upon pitches > > like 415, 392, 440 etc because its practical. If we were to do the > > truly historical thing, Jeff's G lute would be at 449, Joe's at > > 412, Tina's at 463 and Bill's at 398. > > That wouldn't have worked in 1610 either. They all had to use an > agreed pitch if they were going to play together, unless they were > into the whole John Cage thing. > > > -- > > To get on or off this list see list information at > http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
