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The Right CAD Curve

The Right CAD Curve

Bezier Curves, Not Splines, Are Truly Smooth Curves

by David Golber

Originally published in American Lutherie #72, 2002 and Big Red Book of American Lutherie Volume Six, 2013



Bezier curves, as opposed to splines, have been known since the 1970s. They are supported by AutoCAD and AutoCAD LT, but not by many other popular CAD packages. What are they, and why do we care?

It’s easiest to start with an example. Fig. 1 shows the outline of a harpsichord. Look at the curved side. The coordinates of the points are from Kielklaviere,1 which describes the curved side of the instrument by listing the coordinates of points along the side. The curve in Fig. 1 is the ordinary spline through those points. Fig. 2 shows that one of the points is erroneous enough that it clearly makes the curve bumpy.

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Shortening Schaller Shafts

Shortening Schaller Shafts

by David Golber

Originally published in American Lutherie #33, 1993 and Big Red Book of American Lutherie Volume Three, 2004



I’ve been making a Yugoslav folk instrument called prim. It’s something like a small mandolin; the scale is 15 1/4". For tuning machines, I’ve been using Schaller M6 minis, but I’ve been modifying them to solve some problems: the peghead is only 3/8" thick, and the threaded bushings that come with the Schallers don’t tighten down this far; the instrument tends to be too heavy at the head; and I have trouble getting enough string angle over the nut.

The photos show what I’ve done to the Schallers. The threaded bushings have been shortened; the metal knobs have been replaced by the proverbial Handsome Pearlescent Plastic; and the shafts have been cut down short and reshaped.

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What You Should Know About The Hardanger Fiddle

What You Should Know About

The Hardanger Fiddle

by David Golber

Previously published in American Lutherie #36, 1993 and The Big Red Book of American Lutherie, Volume Three, 2004

 

Someone has walked into your shop with yet another weird instrument. This time, it’s sort of like a violin, but it has a whole lot of pegs, the top is carved funny, it has pearl and bone inlay, and it’s decorated with flowery drawings. He says his grandfather brought it from Norway in 1890, and he wants you to put it in playing condition.

Well, it’s a Hardanger fiddle (hardingfele in Norwegian). The instrument originated in the area around the Hardanger fjord, whence its name. It is distinctly Norwegian; in fact, it is played in only about a quarter of Norway, the western and south-central areas. The oldest instrument found has a date of 1651. The musical tradition is still very much alive, and continues unbroken up to the present.

Beginning in about 1850, there was an absolutely enormous emigration from Norway to America — something like a third of the population. Those who played fiddle of course brought their fiddles with them. In addition there were tours by professional players who performed for their emigrated countrymen and then returned to Norway. But the instrument and the music died out in America. The children of the immigrants rarely learned to play, and father’s fiddle lay in its case in the attic, or was hung on the wall like an icon of a lost era. Now there is something like a revival here in America, not only among the descendants of the immigrants, but also among those not of Norwegian ancestry who have discovered the music.

Construction

The construction of the Hardanger fiddle is basically like that of a violin. In comparison with violins, however, the amount of variation from instrument to instrument is enormous. Older instruments usually will have smallish bodies, rather tubby, narrow, but with very high arching. About 1850 the outline began to be more like a violin. Nowadays, most makers use a more or less normal violin outline — but there is still a lot of variation to be seen.

Older instruments were made entirely of native materials, using the native spruce for the face, and either native maple or black alder (svartor) for the sides and back. The fingerboard and tailpiece were faced with cow horn, and the inlay was bone and mother-of-pearl from local shellfish. Pegs were from a hard local wood, such as pear or apple. Today, ebony has replaced the cow horn, and many makers buy standard violin wood from the usual sources, although some still use the local spruce and maple or black alder. Older instruments may have no linings and may have a bass bar carved in one piece with the top. Modern construction techniques are the same as for the violin.

Hardanger fiddle by Torleiv Frøysaa, 1921. This is a fairly typical instrument. Note the metal rod that serves as a guide for the understrings. (Photo 1 of 3) All photos by David Golber.
Hardanger fiddle by Torleiv Frøysaa, 1921. This is a fairly typical instrument. Note the metal rod that serves as a guide for the understrings. (Photo 2 of 3)

All that inlay of pearl and bone into the ebony fingerboard is laborious. Some makers instead glue the pearl and bone pieces to a backing piece, fill in around them with one or another kind of black epoxy-like substance, and then file and sand the surface smooth. This can produce very fine results, but, as you can imagine, there are those who regard anything except real inlay into ebony as a kind of cheating. One maker, Sverre Sandvik, uses a material called “Steinkitt,” which he says is used by carvers of cemetery monuments to correct mistakes.

If you are interested in building an instrument, Sverre Sandvik’s Vi byggjer hardingfele (We Build a Hardanger Fiddle) is the one to get. This book includes full-size, well-drawn plans, and a large number of fine photographs. The Hardanger fiddle plan offered by the Guild is very abbreviated, and is at least partly copied from Sandvik’s book.

The chapter on building a Hardanger fiddle in Irving Sloane’s book Making Musical Instruments is based on museum observations and Sloane’s guesses rather than actual visits to contemporary makers, which results in some very strange conclusions. In particular, Sloane carves the bridge of his instrument in a shape which no maker in Norway uses. And Sloane’s guess that the shape of the top is achieved by bending is just plain wrong.

Strings and Tuning

A Hardanger fiddle has four playing strings, which are bowed in the usual way, plus four or five “understrings” which run under the fingerboard. The instrument is tuned in many different ways, depending on the piece being played. The following table shows the most usual tuning, which accounts for about three-quarters of the music. The actual pitch varies, depending on the player’s preference and what makes that particular instrument sound best. The pitch of the “A” string, or kvart, may vary from b­´♭ to c ´´♯, with all the other strings tuned proportionally higher or lower. (The traditional music is solo music, so universal agreement is unnecessary.)

Tuning of playing strings:

Highest: “E” or kvint: tuned to f ´´♯
Second: “A” or kvart: tuned to b ´
Third: “D” or ters: tuned to e ´
Lowest: “G” or bass: tuned to b

Tuning of understrings:

Highest: tuned to b ´ Fourth: tuned to e ´
Second: tuned to g ´♯ Fifth: tuned to c ´♯
Third: tuned to f ´♯

The highest understring is tuned to the same pitch as the kvart. If the instrument has only four understrings, it is the fifth which is omitted.

Another way to understand the tuning: If you start with a violin (tuned EADG), to tune it like a Hardanger fiddle, raise the lowest string one whole tone, and then tune the whole instrument up about one whole tone. (Stop! Don’t actually do this; it would likely damage the violin!)

Fig. 1 shows the arrangement of the strings on the pegs. The arrangement of the understrings is that used in the inland regions; there is another arrangement used by players on the west coast.

Hardanger fiddle by Torleiv Frøysaa, 1921. This is a fairly typical instrument. Note the metal rod that serves as a guide for the understrings. (Photo 3 of 3)
Figure 1. Stringing diagram, after Sandvik. “E,” “A,” “D,” and “G” should be understood as the names of the strings, not how they are tuned. Tuning is described in the text.

The strings are somewhat unusual. The playing strings are in general lighter than violin strings. They come in weights 10, 10.5, 11, 11.5, and 12. For 11 weight, perhaps the most commonly used, the set breaks down as follows. The kvint is .009" steel. The kvart is .027" gut or .011" steel. A Pirastro/Eudoxa violin E “Stark” can be used. The ters is .041" open-wound gut. This is .009" wire wound over .025" gut, with about twelve turns per inch. The bass is .027" gut.

Understrings are steel and are named by their thicknesses in millimeters. Thus, a .0086" string, the most common size, is called “.22”. Understrings are available in sizes .20, .22, .24, and .26 (.0079", 0.0086", .0094", and .0102"). Some players use graduated sizes for the understrings.

If you put violin strings on a Hardanger fiddle, don’t tune it up above A (kvart tuned to A) — this would likely damage the instrument, since violin strings are heavier than Hardanger fiddle strings.

The instrument is traditionally played only in the first position; the highest point on the fingerboard which is actually fingered is approximately at the edge of the body. The traditional music uses double stops almost continually.

Adjustments

The action of a Hardanger fiddle is lower than that of a violin. I suggest the following approximate numbers:

string at nut 1/2" from nut at edge of body

kvint .020" .026" .075"
kvart .020" .026" .075"
ters .015" .021" .070"
bass .020" .026" .075"

These are what I have come to regard as nominal. I have seen them lower, particularly on the kvint side. The action is measured from the fingerboard to the under side of the string. I use an automobile feeler gauge at the nut end. Note that the ters is usually lower than the other strings. If the fingerboard is uneven right next to the nut, then you can use the numbers 1/2" from the nut.

The fingerboard is straight lengthwise. Crosswise, it is much flatter than the fingerboard of a violin. There is a regional difference here: players from the west coast of Norway, where there is less use of double stops, prefer a more rounded fingerboard than those from the inland regions. A fairly normal roundedness (for inland players) would be a radius of curvature of about 2.5" at 2" from the nut, or a rise of .029" between two points 3/4" apart (Fig. 2).

Figure 2. Fingerboard and neck 2" from nut.
Bridge and tailpiece of the Frøysaa fiddle, showing the position of the understrings. (Photo 1 of 3)
Bridge and tailpiece of the Frøysaa fiddle, showing the position of the understrings. (Photo 2 of 3)
Bridge and tailpiece of the Frøysaa fiddle, showing the position of the understrings. (Photo 3 of 3)

What do you do when the fingerboard wears? The strings wear into the fingerboard just as they do on a violin. The ters, with its open winding, cuts in particularly badly. On a violin, one just scrapes down and reshapes the fingerboard, and then replaces it when it is too thin to use anymore. In contrast, the fingerboard of a Hardanger fiddle, with all of its decoration, cannot be scraped down, and to replace it would be to destroy a significant part of the maker’s art (and would be difficult, too).

What I do (and what at least some respectable Norwegian repairmen do) is to fill in the worn spots with superglue. Use several coats. You can level it out a bit before it dries with waxed paper. Then file or scrape it level with the rest of the fingerboard and bring it up to a polish with successive grits of sandpaper. It is even possible to do this without removing the fingerboard from the instrument, but guard against accidental runs of the glue down onto the varnish. You will probably want to remove the nut.

Spacing between the strings should be about .24" at the nut and about .50" at the bridge.

The understrings should be about .10" apart at the bridge. They want to be as high up on the bridge as possible, as close as they can be to the playing strings. However, if you get them too high, they will clang against the underside of the fingerboard. The better the instrument, the more life in the understrings, and the trickier this problem gets! About .10" clearance between the understrings and the underside of the fingerboard at the end of the fingerboard is usual. Look down the tunnel under the fingerboard from both ends. Sometimes I have gotten the needed clearance to prevent clanging just by lowering the understring nut.

Typical mensur (nut to bridge) of modern instruments is 11.9". Fig. 3 shows two typical bridges, with dimensions and usual locations of the soundpost and bass bar.

Because of the playing technique, the bridge is much flatter on top than a violin bridge. Preference will vary from player to player, of course, with the west coast preferring a more rounded bridge. But for inland style, about 8° seems to be the proper angle across the strings, as shown in Fig. 4.

Figure 3. Two typical bridges. Thicknesses of the Viken bridge are maximums of an unfinished bridge.
Figure 4. Angles across the strings.

The tailpiece is held on by wire instead of gut. I suggest .040" hard stainless.

A sickness that sometimes affects Hardanger fiddles is the neck bending forward, bringing the end of the fingerboard down towards the face. Sometimes this is due to movement in the neck joint; sometimes it seems that the whole upper end of the instrument has given way slightly. In any case, it raises the action. Then the end of the fingerboard rests on the understrings. When the fingerboard rests on the face of the instrument, even the most obstinate player will admit there is something wrong.

The standard violin treatment for this would be to reset the neck, or a neck splice: replace the neck and splice on the old head. If the trouble is in the neck joint, which is continuing to move, this may be the only thing to do. However, if there is only a little movement, and it seems to have stopped, then a simpler treatment is to remove the fingerboard and insert a thin wedge of wood under it, to bring the action back to normal. Since one doesn’t play in positions, the slight change in the thickness of the neck does not disturb the player. Many Hardanger fiddles have a thin wedge like this in them.

Some makers in Norway use a white glue called Casco. In some places, this does its nasty, gummy thing. How to remove it? With the help of Sverre Sandvik, I was able to identify that toluene dissolves the stuff and does not affect the varnish.

The Music

Well, look: I wouldn’t be deep into this instrument if I wasn’t crazy about the music. And so I have to have my chance to infect you.

First some orientation: What do most Norwegians listen to now? Well, normal Western pop music, of course. Going further back to the middle of the 19th century, there was a big industrialization, which brought in all sorts of foreign laborers. They came with their accordions, and polkas, mazurkas, waltzes, and reinlanders. In Norway, these are now called gammaldans — old dance — and the music is gammaldansmusikk.

But before this, and miraculously surviving up to the present, was an older tradition of solo Hardanger fiddle playing, and a parallel tradition on violin in areas where Hardanger fiddle is not played. The old tunes are called slåttar (struck: as the bow on the strings) and the corresponding dances are called bygdedans (regional dances: they vary greatly from region to region.) It is this slått tradition that I am preaching to you. I’ll say just a little about the music; the references include recordings and sources.

I feel that this music has a certain strictness and seriousness that is more akin to “classical” music than to what we call usually call “folk” or “pop.” The music is handed down aurally, but with great emphasis on exact preservation. The rhythms and melodic organization will be unfamiliar to you. The best players are truly virtuosos, and this you can hear in an instant even without understanding the music. Most of the tunes are at least nominally dance tunes, and there is something very special in dancing to fine and subtle music.

Most Norwegians are not into this stuff. It’s somewhat analogous to the relation of the average American to real old-time Appalachian hill music. (But only somewhat!) On the other hand, there’s an association (Landslaget for Spelemenn — The National Fiddler’s Association) of people involved with this music and dance, with about 5,000 members, and this is in a country with a total population of about 4,000,000. They publish a substantial magazine and organize numerous concerts and competitions. More and more, even those Norwegians who personally do not like this music recognize it as a substantial tradition and an important part of their national artistic heritage.

If you go to Norway, be sure to contact the National Fiddler’s Association to find out about concerts and competitions (a music and dance competition is a kappleik). The competitions range from a one-afternoon affair in a small town with all of thirty people in attendance, to the Landskappleik (country-wide competition) which lasts for four or five days with a thousand competitors in various kinds of music and dance, several thousand in the audiences, and concerts and parties until late into the night. Don’t be afraid to go; you’ll be sure to find someone who speaks English who will point you in the right direction.

And be sure to contact the Hardanger Fiddle Association of America (HFAA) for news of players and dancers visiting America.

Decorative pen-and-ink drawing on the back of the Frøysaa instrument
Peghead of an instrument thought to be by Trond Botnen, 1713–1772.
Peghead by Frøysaa.

How Much Is It Worth?

Sigh... that old exasperating question.

NO, NO, NO! The right questions are “What does the music sound like?” or “How can I learn to play it?” or “Can I hear another tune?”

But people persist in asking, so here’s an attempt at an answer. First of all, there are no public auctions to establish prices. There are no factories producing bottom-end fiddle kits, with fiddle, bow, and case for $119.95. I have seen beginner fiddles for about $800; these are instruments that look right, are solidly put together, and have some sound in them. Reasonably good current instruments seem to go for about $2,000 to $3,000. “Name” instruments (some famous names are Helland, Steintjønndalen, and Røstad) might start at $3,000 and move up towards $5,000, with the very best perhaps up to $15,000. The best instruments are rarely sold publicly at all, but pass from one player to another within the circle, or are passed down within a family. The right strategy for getting a good instrument begins with getting a not-so-good instrument, learning to play a little, and then going to Norway. Learning to speak some Norwegian somewhere in-between helps. There are good instruments to be found in the United States too, often gathering dust in an attic or on a back shelf in a shop. But you may well be looking at $1,000–$2,000 in repair costs to make such an instrument playable.


Associations

The Hardanger Fiddle Association
of America
www.hfaa.org
The HFAA publishes a quarterly magazine, The Sound Post, and sells strings, teaching aids, videos and books. The Sound Post is your best source for what’s happening with Hardanger fiddle in America: Norwegians on tour, instruments for sale, and so on.

Landslaget for Spelemenn
(The National Fiddler’s Association)
Tollbugata 28, 0157 Oslo, Norway.
Phone: 22 41 45 48
If you are visiting Norway and want to attend folk music events, this is the group to contact for information. Their magazine, Spelemannsbladet, sometimes has ads for fiddles for sale.


References

Vi byggjer hardingfele
(We Build a Hardanger Fiddle)
Sverre Sandvik
Tiden Norsk Forlag, Oslo, 1983
ISBN 82-10-02357-8.
Available from the HFAA.
This is the introductory book on building Hardanger fiddle. It is well-illustrated with both photographs and drawings, and includes full size plans. It is in Norwegian; be aware that the bridge is stol, i.e. “chair”.

Norwegian English Dictionary
Einar Haugen
University of Wisconsin Press
Madison, 1977
ISBN 0-299-03874-2.
This is the dictionary.

Hardingfela (The Hardanger Fiddle)
Sigbjørn B. Osa
Musikk-Huset A/S, Oslo, 1952.
Write to: Musikk-Huset A/S, Karl Johansgt. 45, Oslo, Norway.

A pamphlet of about 15 pages, in both English and Norwegian, describing playing and tuning the instrument, with exercises and a few transcriptions.

The following two articles explain more about the nature of the music, the playing technique, and the context of the music. Each article includes photographs of instruments, and a transcription of a simple traditional piece.

“Hardingfele: The Best-Kept Secret
of European Ethnic Music.”
Loretta Kelley
Strings, March/April 1990
Vol IV No. 5, pp. 59–63.

“Hardingfele: The Nordic Survivor”
Loretta Kelley
The Strad, June 1991
Vol 102, No. 1214, pp. 520–527.


Some American Makers

Ron Poast
728 Mills St, Black Earth, WI 53515

Lynn Berg
1630 Cameo Drive, Eugene OR 97405

Joe Baker
Hunger Mountain Instruments, Box 332, Monterey, MA 01245


In Norway

Halvor Lisland
Svinten 10, N-3940 Heistad, Norway.
Phone: 35 51 10 32
Has a considerable assortment of fiddles for sale.


Some recordings

Fire of the Amazons (Skjoldmøyslaget)
Hallvard T. and Torleiv H. Bjørgum
Sylvartun CD SYLVCD 2
cassette SYLV2.
Highest quality performances of electrifying traditional music of the Setesdal region, with an extensive English text.

Edvard Grieg: Slåttar/
Norwegian Peasant Dances, Op. 72
Knut Buen, hardanger fiddle
Einar Steen-Nøkleberg, piano.
Simax CD PSC 1040.
In 1902, Grieg composed seventeen piano pieces based on Hardanger fiddle pieces from the Telemark region. The originals have survived in the traditional repertoire. This CD presents Grieg’s pieces in juxtaposition with the fiddle originals, in master performances, with extensive English text.

Sigbjørn Bernhoft Osa
Sigbjørn Bernhoft Osa
Hardanger fiddle and violin.
Buen Kulturverkstad CD BKCD 1.
Osa was a classically trained violinist who returned to the folk tradition. He played both violin and Hardanger fiddle with brilliance and beauty. The recording contains a great deal of gammaldansmusikk, which will be more familiar to the ears of the newcomer than the older slått tradition.

Spel til dans (Playing for Dancing)
Vols. I, II, III and IV (cassettes) or one CD
Knut and Hauk Buen, Hardanger fiddle.
Buen Kulturverkstad cassettes BKMC 4, 30, 31, 32 or CD BKCD 10.
Traditional dance music from the Telemark region, played with driving dance rhythm. The performers are considered by some to be the best two players in Norway today.


Some sources for recordings

Norsk Ltd.
770 Linden Avenue, Boulder CO 80304

Haug Forretning
2428 NW 56th, Ballard WA 98107

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Letter: Installing Pegheads

Letter: Installing Pegheads

by David Golber

Originally published in American Lutherie #102, 2010



Dear American Lutherie,

A couple years ago a customer asked me about installing Pegheds/Knilling Perfection Planetary Pegs in his instrument. I read the instructions, sent by Mr. Herin, for installing them: he said to use Gorilla Glue. Now I get nervous. I’m being told to glue something into a $5000 instrument with Gorilla Glue. Hmm. I wrote to him asking how to remove them. I got no reply.

These are mechanical devices. What lifetime do they have? Ten years? Twenty? Thirty? (Thirty years is a good lifetime for industrial products.) Does the manufacturer put a warranty on them? For how long? Will the manufacturer even be in existence thirty years from now?

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