# Tangent tuning

### From Hurdygurdywiki

**Tuning a hurdy gurdy 's tangents for playing alone**

On a hurdy gurdy *playing alone* there is no harmony apart from the combination of melody (chanterelle) and drone(s) (bourdons), so the obvious perfect way for tuning the tangents is by making all intervals pure between chanterelle and bourdon(s): a natural harmonic scale ( just intonation ).
In modern equal temperament fifths are slightly impure and thirds very impure. That makes equal temperature not the best choice for a drone instrument playing alone. See Graham Whyte: Tuning and Temperament (PDF) and Table of theoretical tangent positions (PDF).

Due to the distance between chanterelle and lowest bourdon of one or more octaves, the order of priority of pureness in the scale of a hurdy gurdy from important to unimportant is as follows:

1.prime (in fact, one or more octaves distance from the bourdon)

2.fifth

3.major third (easiest tuning with two or one octave added)

4.fourth (easiest tuning with no octaves added)

5.second (easiest tuning with two octaves added)

6.major sixth (easiest tuning with no octaves added)

(and rather unimportant: minor third, minor sixth, minor seventh, major seventh, and the remaining chromatics).

In order to be able to play at least with two different bourdon strings (with a slight deviation from pureness) you get the following tuning system. The bourdon strings differ a fourth or a fifth. The chanterelle is tuned to the highest in case of a fourth difference between the bourdons, and to the lowest in case of a fifth. The tangents are tuned such that fifth, third, fourth, second, sixth (fourth+third) and minor seventh (fourth+fourth) are pure to the ground tone of the chanterelle (open chanterelle). The other tangents may be tuned pure to one of the bourdon strings, but the tunings of these are not so important for the consonants with the bourdons.

For a hurdy gurdy with a chanterelle in g', two bourdons in G and c, this means the following. Tune the G and make G→C, C→F and G→D, D→A pure fifths. Then make C→E, G→B, D→Fis pure thirds. The other tangents are not very critical. In principal, you may finish by making A→Cis, D→Bes, G→Es and C→As pure thirds/sixths. Then the result will be that E-B, B-Fis, F-Bes, Bes-Es and Es-As will be pure fifths/fourths as well.

With this tuning it is possible to play in G (major and minor), in C, where the A is not a pure sixth to the C, if necessary in D, but with the E audibly impure to to the D, and, if really necessary, one could play in F, but with a rather dissonant A. More explanation can be found in Ernic Kamerich: Tuning a hurdy gurdy 's tangents .

**Tuning scheme for a g-c hurdy gurdy playing alone**
Slacken the pullers of the chiens. Be sure that cottoning, resin on the wheel and the pressure of the strings on the wheel are okay.
First check the positions of the nut and the bridge (the ends of the vibrating part of the open chanterelle). The tangent of the fourth tangent (b'-key) must yield a pure third, so the distance to the nut should be 1/5 of the length of the open string (possibly 1/5x345mm), about 2 mm shorter than with modern equal temperament. If the position of the tangent can not be changed enough, the position of the nut must be changed so that the tangents of this third and the following tangent (the fourth) can both be accomodated well. The perfect distance of the fourth is 1/4 of the vibrating length.

The tangent of the highest note without deviation must have the correct position. If this tangent should yield the double octave, the distance to the bridge should be 1/4 of the vibrating length of the open chanterelle. This is true for any normal tuning system. If that is not the case (about 1mm deviation me be acceptable), not any tuning system will work for the highest notes. Then the position of the bridge must be changed. If the bridge is glued to the soundboard, possibly you can change its position a little with the wire that pulls the bridge to the tailpiece (after having slackened the chanterelles). Otherwise, you may better return with it to the maker or consult a violin repair shop.

If you don't have machine tuning pegs or fine tuning adjusters, it is wise to use a tool for easy turning the tuning pegs in order to get precisely what you want. You may test in which direction the tangent is to be moved by pressing the key some more, making the tone a little sharper; listen if it gets better or worse. If you hear a beat (something like vibrato) the tuning is nearly pure: try to get the frequency of this beat to zero. If you are used to modern (equal temperament) tuning, the pure thirds will be considerable flat in your ears. Lower the thirds more than you think untill you hear a quiet sonorous harmony without beats.

1.Tune the chanterelle to g', tune a bourdon to G (pure to the chanterelle) and tune the tangents of g" and g"' (if available) pure to the bourdon G.

2.Tune b' and b" pure to the bourdon. Remember that thirds (the pure b's) are very flat in modern ears.

3.Switch off that G bourdon, use the open g' chanterelle to tune a string to c, c' or c", the highest possible. Tune the tangents of e" and e"' to the c, again very flat.

4.Then tune the tangents of f" and f"' (more difficult!) If you are not content, you may switch off the chanterelle, switch on the G bourdon and tune this to F in relation to that c-string, switch on the chanterelle again, check it to the c-string and tune the f' and f" tangents to this F bourdon.

5.Tune again the chanterelle to g', a bourdon in G,pure to the chanterelle and check the tangents of g" and g"', b' and b". Now tune the tangents of d" and d"' pure to the G.

6.Tune another string (bourdon/chien/mouche) to d or d' as a pure fifth to the G bourdon and check this against the tangents of d" and d"'. Switch off the G bourdon and tune the tangents of a' and a" to the d. Then tune the tangents of fis" and fis"' as pure thirds to that d-string.

You are ready with the critical part. Tuning cis, bes, es and as according to the pure system above is much more difficult. However, don't bother too much: if you can not hear the pureness very well, who cares? You may even dislike the melodic distances of these notes or the differences with the tuning of other instruments if you play together. Then you can change the tuning of these four notes a little: probably your ears will not be offended by the less perfect tuning of these notes to the bourdons. So these other tangents may be left unchanged or you may tune them in equal temperature with an electronic tuner or an other instrument or use a high string of the hurdy gurdy as a reference by tuning it to what you need.

When you have tuned the tangents of the first chanterelle, you may tune the tangents of the other chanterelle(s) simply by tuning them to the already tuned chanterelle. That is easy if they are tuned the same or if the distance is a fifth, an octave or a twelfth (fifth+octave). If the usual distance is a fourth, you may better lower the lowest string one tone for the tuning process. It is essential that the tangents touch the string simulaneously, as accurately as possible. An easy trick to test for the direction in which the tangent is to be moved: pull one of the chanterelles a little with your fingers at the pegs-site of the tangents: the tone will be a little sharper and you can hear if it gets better or worse.