David, You have written an excellent and detailed article on meantone and equal temperament. I have not had a chance to read the details yet (have just printed it). But it seems you limit the "meantone" to the 1/6th comma (and pardon me if I haven't read through it properly). Equal is "equal", as you properly say. and true Pythagorean isn't available to a fretted instrument (or a harp or piano) as it changes as to intervals on the ascending and descending. I'll not get into that here.
But in the article you suggest that "meantone" is a single tuning format. There is the 1/4 meantone and the 1/7 meantone as well as the 1/6. And that only emcompasses the commonly used ones. Pythagoras, along with his other accomplishments (wasn't it he who defined the circumferance of the earth by the varying angle of the sun in Greece and in Alexandria? - and came pretty close to modern estimates), found the anomaly in the overtones of the strings. What Pythgoras found was a "comma", whether it is the one named after him in the discrepancy between 12 fifths and 7 octaves or not. That is natural and uncontrovertible. And the violinists do sometimes play the natural frequencies. But on the whole our Western ear has been conformed to one or another of the several compromises. Most to the "equal temperament" used in many stringed instruments. But yet the trumpets and horns can't do that, the overtone series dictates their pitch (and timbre). But given their limited range the slight discord of the orchestral instrument adds to the timbre of the overall sound. Please pardon a new lutenist, but it seems our instrument is often played alone - or in a small chamber group. Within a range the comma, whichever it is, isn't significant - and may add to the sound. The lute (not my fixed fret attempt) has the ability to set the comma (or tuning) wherever it wants to be, but that won't match with the other instruments if they are present. Again I compliment David on his article, it is detailed and correct. But perhaps somewhere in between this mathematical detail and the simple player there is room for a bit of clarity of expression. David is correct, perfection is impossible with a fretted instrument (unless one can move the frets in the middle of a piece). And is perfection the perfect "equal temperament" that doesn't match the overtone series? Or is it one of the "meantones" that also don't match the natural harmonies. There is no perfection, there is only choice as to which compromise to use. Does one want to make the thirds closer to perfect, or the fifths? They can't all be. The "comma" is present whatever the tuning system, it is just a question of where one places it. Best, Jon ----- Original Message ----- From: "LGS-Europe" <[EMAIL PROTECTED]> To: "lutesmith" <[EMAIL PROTECTED]>; "lute society" <[EMAIL PROTECTED]> Sent: Monday, July 26, 2004 2:18 AM Subject: Re: Happily tuning in Meantone > I've written an article explaning meantone fretting. You can find it on my > website: > > Http://home.planet.nl/~d.v.ooijen/david/ > > David > > > ----- Original Message ----- > From: "lutesmith" <[EMAIL PROTECTED]> > To: "lute society" <[EMAIL PROTECTED]> > Sent: Sunday, July 25, 2004 10:09 PM > Subject: Happily tuning in Meantone > > > > > > For an article going into the next LSA Quarterly I'd like to make a few > > links to sites dealing with fret placement. If any of you have a favorite > > site or even for general meantone information please contact me here or > > privately at the above address. > > > > Many thanks in advance, > > Sean Smith > > > > ================================================================ > > Deze e-mail is door E-mail VirusScanner van Planet Internet gecontroleerd > op virussen. > > Op http://www.planet.nl/evs staat een verwijzing naar de actuele lijst > waar op wordt gecontroleerd. > > > > > > > > >
