The methods for both Dowland's fret calculations, as well as the modern mathematical spacing, are given here for those who are interested.
An MS-DOS executable is also available; the zipfile also contains the C source code for the program, which should compile on non-MS-DOS systems with little or no modification.
NEW! Now the Lute Fret Calculator is available for PalmOS-powered devices! Click here for more information.
The following instructions are taken from Robert Dowland's book, A Varietie of Lute Lessons; it is excerpted from a larger section written by John Dowland (Robert's father) that also gave instructions on how to select good strings.
Wherefore take a thinne flat ruler of whitish woode, and make it iust as long and straight as from the inward side of the Nut to the inward side of the Bridge, then note that end which you meane to the Bridge with some small marke, and the other end with the letter A, because you may know which belongeth to the one and to the other : then lay the ruler vpon a Table, and take a payre of compasses and seeke out the iust middle of the Ruler : that note with a pricke, and set the letter N. vpon it, which is a Diapason from the A. as appeareth by the striking of the string open. Secondly, part the distances from N. to A. in three parts, then the first part giues you the seauenth fret from the Nut, making a Diapente : in that place also set a pricke, and vpon it the letter H. Thirdly, deuide the distance from the letter H. to the letter A. in eleauen parts : two of which parts from A. giues the first fret, note that with a pricke, and set the letter B. thereon, which maketh a Semitone. Fourthly, diuide the distance from H. to the letter A. in three parts, one of which parts from A. vpward sheweth the second fret, note that with a pricke, and set the letter C. vpon it, which maketh a whole Tone from A. Fiftly, diuide the distance from N. to A. into two parts, there the first part sheweth you the fift fret, sounding a Ditessaron : in that place also set a pricke, and vpon it the letter F. The sixt fret which is a G. must be placed iust in the middest betwixt F. and H. which maketh a Semidiapente. Seuenthly, diuide the distance from the letter B. to A. in three parts, which being done, measure from the B. vpwards foure times and a halfe, and that wil giue you the third fret, sounding a Semiditone : mark that also with a prick, & set thereon the letter D. then set the fourth fret iust in the middle, the which wil be a perfect ditone : then take the one third part from B. to the Bridge, and that third part from B. maketh I. which soundeth Semitonium cum Diapente, then take a third part from the Bridge to C, and that third part maketh E. which soundeth Tonus cum diapente, or an Hexachordo maior. Then take one third part from D. to the Bridge, and that third part from D. maketh L. which soundeth Ditonus cum Diapente. Now take your LVTE, and lay it vpon a table vpright, and set the Ruler edgewise, betweene the nut and the bridge, and thereby set little marks vpon the necke of the Instrument euen with those on the ruler, because those are the places on which your frets must stand.
Thus haue you the perfect placing of your ten frets, which taketh away that scruple by which many are deceiued, when they say the frets are false. Note here also, wee doe not try the frets, as wee trie the strings : but (now knowing their places) size them rightly, for which any kind of string will serue, I meane whether they be true or false, new or old, onely take heed that you set not a great fret where a small one should be, & so by contrary : for euery fret doth serue as a Magade : therefore doe this; let the two first frets neerest the head of the Instrument (being the greatest) be of the size of your Countertenor, then the third and fourth frets must be of the size of your great Meanes : the fift and sixt frets of the size of your small Meanes : and all the rest sized with Trebles. These rules serue also for Viols, or any other kinde of Instrument whereon frets are tyed.
In the last paragraph, Dowland instructs that the first two frets be of the same diameter as the strings in the F course; the third and fourth, that of the A course; the fifth and sixth, the D course, and all the rest should be of the diameter of the top course (or string), G.
Although I corrected a couple of typographical errors in the above paragraphs, I did not modernise the orthography. For a version with modern English spellings, click here.
Footnote 1. Misprinted as D. in the original.
For modern mathematical spacing (which, to my ears, sounds extremely out of tune compared to Dowland's spacing), use the following formula:
Measure from the nut to the bridge, and divide that distance by 1.059461, giving the distance from the bridge to the first fret. Repeat that calculation for each fret, dividing the distance from the bridge to the previously calculated fret by the magic number (1.059461).
In all cases, the frets calculated by Dowland's method are within a few millimetres of those calculated by the modern method, but those few millimetres can make all the difference!