Patrick, The "swinging tangent" on an Equal Temperament HG only just allows the setting of Just Temperament I suspect you have not actually done it Tangent angles at the low end can approach 45deg It is normally necessary to move the nut to reduce these This means that the octave tangents are not at right angles This is not a problem Setting the key positions halfway between Equal and Just is a good solution You can then set either temperament with minimal tangent angles
Please don't refer to Equal Temperament as "the tempered scale" Almost all scales (temperaments) are tempered Equal Temperament is just one of several THOUSAND named temperaments Each of these has 12 possible root notes Equal Temperament is more accurately described as Twelfth Comma Meantone Temperament This means that the ratios of all the intervals in every key are identical Hence the name "Equal" Although this allows playing in all keys it does serious musical damage to some intervals In paticular major thirds are 14% of a semitone (half step) out of tune (sharp) One reason for the need to temper is that 3 sucessive pure major thirds don't make an octave Try tuning an E true to a C Then tune a G# true to that E Then tune a C true to that G# You will end up with a C which is almost 1/2 a semitone flat (midway between B and C) It is the distribution of this 42 cent error called "Diesis" that is known as "tempering" Different temperaments distribute this error in different ways Read my paper at http://www.luthiers60.freeserve.co.uk/pdfs/tuningandtemperament.pdf Graham -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Behalf Of Patrick Brown Sent: 09 March 2007 00:14 To: [email protected] Subject: Re: Re[2]: [HG] Key placement calculator Long time ago, at least as far back as fretted instruments conforming to the newer than fretted instruments 'tempered scale,' which tempered scale goes back to the ca 1600's(?) and placed in our laps by a fellow appropriately named Werckmeister(sp), (and fretted instruments going back to the 1400's or earlier, depending on where you were),,,derived, as Alden says, from using the 12th root of 2,,was known as the 'Rule of 18,' which means that each successive distance for each next fret, or tangent, closer to the bridge one goes, in order to find its placement, you divide that distance by 18, and that resulting distance by 18, and so on ad infinitum (literally,,like the frog jumping halfway across the pond,,then halfway again). The actual number is generally agreed among luthiers to be 17.817, if memory serves, though I've read 17.835, but that's an obscure and only one or two source memory,,but 17.817 is the divisor, if that's the right word. The number you use to divide, at any rate. This is, of course, assuming you are after a tempered scale. If you want just temperament,,then you'd use fractions of the fundamental. The swinging tangent should allow either choice. Pat
