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- A Souldiers Resolution - review
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- How to make a fret gauge
A Souldiers Resolution - The First Part of Ayres by Tobias Hume
Miriam Morris, bass viol with Christopher Field, counter-tenor. MOVE CD 3232
Miriam Morris is one of Australia's leading teachers, of both the cello and the viol, and she has a fine reputation as a performer, particularly on the bass viol - a reputation that is further enhanced by this CD. One hears not only technically masterful, refined, and historically well-informed playing from her, but also a thoughtful and artistic shaping of the music, and a tone that is always beautiful (full and warm in the low and medium notes, sweet in the high notes).
Her fine playing is well-served by the high quality of sound-reproduction. The CD consists of a selection of 16 solos for the bass viol, and three songs accompanied by the viol, from Hume's publication of 1605. Happily complementing Morris's viol-playing, is fine singing by the Australian counter-tenor Christopher Field. His three songs are beautifully judged and executed, and Morris's accompaniment is full, but sensitive. The CD booklet is generous, with an erudite and well-written account of the eccentric Hume and his music. Not immediately obvious, is a reproduction on six pages, of some of Hume's fascinating original publication, written in tablature. Also reproduced are several details of Morris's beautiful decorated viol, made by the Australian luthier Ian Watchorn.
Overall, the music chosen for this disc tends to be gentle and poignant in character, apart from a brief reminder of Hume's life-long career as a soldier, in A Souldiers Resolution. There are touches of humour (eg. My Mistresse hath a prettie thing) and of sadness (Death, Adue sweete Love, What greater Grief, and Loves farewell). Just as this music was perhaps an antidote to the trauma and stress Hume experienced as an impoverished soldier, it is well-suited as a soothing antidote to the rush and stress of modern life.
How to make a fret gauge for any size viol or lute without ever having to refer here again
While many makers supply a fret gauge with new viols, such often become lost when the viol is traded and sometimes the bridge moves a bit; so many viol players tend to rely on guesswork for fret placement. Assuming equal temperament is desired, a classical guitar is an ideal paradigm. You will notice on the guitar that the octave fret divides the string exactly in two. Starting from the octave fret & measuring away from the bridge, the sounding part of the string progressively gets about 6% longer at each fret compared with the length at the previous fret. Expressed mathematically, one would expect that 1.06 multiplied by itself twelve times (for the 12 frets from the octave to the nut) should equal 2, that is double the length at the octave fret. Money invested at 6 % interest compounded annually will likewise double in value in 12 years. Taking an ordinary calculator we can enter 1.06 then X and press the = key eleven times to program this calculation. The result is a little over 2. If we fiddle around a bit we shall find that 1.0594630944 is about as close as we can get. But this accuracy is quite unnecessary. The reciprocal of this number, 0.9438743 (divide 1 by 1.059461) allows subsequent multiplication which some people find friendlier than division. Thus if the string is, say, 680mm long, the first fret will be 680 X 0.9439 = 642 mm. Thus the first fret will be 680 - 642 = 38 mm from the nut. Enter on your calculator 0.94387 then X then = up to eleven times and you will generate the second column in the accompanying table.
All you have to remember is that the reciprocal of the 12th root of 2 is easily re-created by hacking away on an ordinary calculator for a few minutes. Multiply this by itself successively seven times and multiply these figures by the string length from nut to bridge and you have the fret distances from the bridge. Make your gauge out of thin Manilla card with a square end. Use a ruler, preferably of metal and the same one used for measuring nut to bridge. Mark the fret positions on the left & right sides of the card & rule across.
In his work Harmonie Universelle, Paris 1636, Mersenne presented the results of his calculation of the above process. Unfortunately he did not have a $5 calculator , so his approximation to the 12th root of 2 was 1.0588285, fortunately the error was almost insignificant. He also records a set of rational approximations. Luthiers at that time and earlier did not need graduated rulers and calculators. They could create these rational approximations with a straight-edge & compasses only. The decimal 0.711111 corresponds to the rational three fifths plus one ninth.
In the fifth column of the table, 1 minus the second column is presented so that the fret distances from the nut may be calculated directly. If this seems a roundabout way of doing things, remember that the important thing is the amount of string free to vibrate, this is from the fret to the bridge. From the fret to the nut is dead, it is thus derived from the former. The final three columns contain information relevant to one sixth of a comma meantone temperament, this may be referenced in a future article.
The above calculations are "theoretical". In tying & adjusting your frets you may feel the need to move them slightly from the theoretical positions. The fret should be measured from the bridge side, as this is where the sounding length is (even when using the numbers in the 5th column). Pushing ones finger down on the string while playing may lengthen it infinitesimally and may change the tension slightly. Therefore slight adjustments may be justified, but any adjustment more than 2mm for a tenor or bass, and 1mm for a treble should be viewed with suspicion. With the open strings well in tune, the frets may be checked with a tuning machine. If you tune the central third to sound sweetly by ear, you may well desire to move some frets more than 2mm in the direction of mean-tone (asterisked entries in the last three columns) this is OK for private practice but not in consort with others tuned in ET.