Book "Le génie de stradivari"Book "The Sound of Stradivari"

A Book by Patrick KREIT

Violin maker & Researcher

 THE SOUND OF STRADIVARI

Final edition

Mode B0

 

Frequency of the fingerboard affixed to the neck (Body zero)

 

The fingerboard vibrates at its end and at the center of the neck (through buckling), which allows the B0 mode frequency to be tuned.

The temporary gluing of the fingerboard must be done with precision: otherwise the B0 mode reading could be higher or lower than the true frequency after being permanently affixed.

In the presence of prolonged high ambient humidity, with materials registering 12% moisture content, accurate tuning of the B0 mode is difficult, as the fingerboard's frequency is unstable. This operation is best conducted in a heated workshop.

 

N.B. Gluing the fingerboard onto the neck lowers the B1+ mode frequency.

 

In the presence of high ambient humidity, accurate tuning of the B0 mode is difficult to realize correctly, as the fingerboard's frequency is unstable. Ideally, mode B0 should be tuned on materials registering 6% moisture content.

 

The frequency amplitude (spread) of a good quality free fingerboard is 20 Hz for moisture content between 1% and 12%. This amplitude can increase by approximately 30 Hz, when the ebony is porous and has very low density. Such fingerboards must be eliminated.

 

The pre-tuned free fingerboard must be temporarily glued back onto the set-in neck to monitor the B0 mode frequency and to set up the violin in the white. Depending on the density of the materials, this frequency will sometimes be higher or lower than the A0 cavity frequency with a sound post (by 5 to 10 Hz maximum).

 

If the B0 mode frequency is higher or lower than the A0 cavity mode frequency with a sound post, the frequency of the free fingerboard must be raised or lowered by twice the number of hertz constituting the difference between the B0 mode frequency reading obtained with the generator (or by tapping) and the A0 cavity frequency.

 

Temporary gluing of the fingerboard (5 or 6 small dots of glue down each edge of the flat side) must be done correctly: otherwise the B0 mode frequency will be higher than expected after being permanently affixed. With an improperly glued fingerboard, a temporary set-up of the violin in the white will yield a B1+ mode frequency that is higher than expected.

 

The fingerboard vibrates at its end and at the center of the neck (through buckling), which allows the B0 mode frequency to be tuned.

 

Once the fingerboard has been glued to the neck, using a scraper on the fingerboard in the sector of the neck lowers the B0 mode frequency.

 

It is possible to lower or raise the frequency of the pre-tuned free fingerboard by approximately 10 Hz, by removing about 3 g of wood from the hollow underside to tune the mode B0 frequency. Beyond this limit, the fingerboard must be changed.

 

The B0 mode frequency must not exceed 280 Hz at 6% moisture content in the wood. When it is above 290 Hz, the B1+ mode frequency will be higher than expected.

 

The end of the fingerboard glued onto the neck is very sensitive to variations in humidity, for it has two faces exposed to the air. After varnishing the neck, the B0 mode frequency falls or rises on average, by 10 Hz when the fingerboard’s moisture content fluctuates between 1% and 12%.

 

A tuned free fingerboard weighs from 62 g to 72 g, depending on the density and moisture content of the ebony.

 

To hear the B0 mode tap-tone (without strings) hold the violin by the lower bout of the sounding box (try to find a non-vibrating nodal point); tap the scroll, or the top of the fingerboard near the nut.

 

The fingerboard must be temporarily glued onto the violin in the white, in order to take readings of all the mode frequencies and to make the final adjustments to modes B1- and B1+ when necessary:  this avoids the need to open the violin after varnishing in order to lower the B1+ mode frequency by reworking the thicknesses of the back plate.

 

The B0 mode frequency can be adjusted, preferably when the violin is in the white (but it is also possible after varnishing). Read the frequency of the neck set in without the fingerboard, as well as that of the free fingerboard; then add these two frequencies together. Their sum indicates the frequency to which the free fingerboard must be tuned, in order to obtain a B0 mode frequency identical to that of the A0 cavity mode.

 

The pre-tuned free fingerboard must be temporarily glued back onto the set neck to check the B0 mode frequency. Depending on the density of the materials, this frequency will sometimes be higher or lower than the A0 cavity frequency with a sound post (by 5 to 10 Hz maximum).

 

Technique for tuning the B0 Mode of a violin fingerboard

 

Removing wood from regions 3 at 4 raises the frequency of the free fingerboard. Removing wood from regions 1 and 2 lowers it.

 

Chin Rest

 

Particular attention must be paid to the chin rest, for it mainly affects the B1- mode frequency on a violin in the white or varnished. Sometimes fastidious adjustments are required to find the right chin rest that will suit both the player and the instrument.

 

Chin rests weigh from 35 to 70 g. They may have identical frequencies but different weights, according to the density and species of the wood used (ebony, rosewood, mahogany, pear, boxwood or fake boxwood). These chin rests have different signatures, depending on their position (on the left or at the center), their weight (density), and their frequency. Consequently, they modify the B1- and B1+ mode frequencies differently and can lower the decibel level of certain peaks.

 

Certain types of chin rest lower B1+ by 5 Hz and B1- by 25 Hz. This generally depends on the thicknesses in the lower bout of the back and top plates and on the width of the block. In order to obtain an appropriate delta between these modes, the luthier must change the type of chin rest (central or left), use a heavier or lighter one, or one made with different materials.

When a chin rest suits a violin in the white, it must be reserved for that same instrument after varnishing.

 

Example without chin rest:

B1-: 455 Hz; B1+: 550 Hz; delta between these two modes: 95 Hz (the acceptable upper limit).

Once the chin rest has been installed and it has lowered the B1+ mode frequency by 5 Hz and the B1-mode frequency by 25 Hz, the delta between these two modes will be 115 Hz.

The medium register is lacking, the low notes are dry, and the high notes sour. The problem worsens if the back plate becomes deformed, increasing the B1+ mode frequency by 15 Hz (125 Hz delta).

 

Generally, a chin rest lowers the B1+ mode frequency by 8 Hz and the B1- mode frequency by 12 Hz to 25 Hz maximum. Modes B1- and B1+ must have an identical drop in frequency after installation of the chin and shoulder rests, in order for their delta to remain the same as before installation of the accessories.

 

N.B. When constructing free violin back and top plates, the maker must define the frequency range (minimum and maximum) in which they will be tuned for moisture content in the wood at the moment.

With low-density materials having low resistance, or low thicknesses for obtaining the desired frequency (low resistance) –and irrespective of the moisture content in the wood– deformation must be expected on the back and top plates with a normal rise in mode B1+ (5 to 8 Hz), as well as a drop (3 to 4 Hz) in the B1- mode frequency after setting up the violin in the white. These frequencies will again be modified after the chin rest is installed.

 

After varnishing the violin, the delta between modes B1- and B1+ may have changed. To a certain extent, a new chin rest can help in solving the problem.

 

It is also possible to use the chin rest to deliberately modify the delta between modes B1- and B1+, either by increasing the delta to obtain more supple playing, or by decreasing the delta to obtain more firm playing. This is not feasible on all violins.

 

Make sure that the chin rest does not touch the tailpiece: otherwise, there would be a split in the frequency for modes B1- or B1+. In this configuration, these mode frequencies are very difficult to define, both with a generator and with Audacity®.

 

N.B. A shoulder rest lowers the B1+ mode by approximately 5 to 7 Hz (depending on the model).

 

Each instrument is different and has its own acoustics signature. The final tuning of a violin in the white consists of seeking out, understanding, and eliminating certain imperfections.

 

After setting up the violin in the white with a chin rest, read the B1- and B1+mode frequencies, as well as the moisture content in the materials. Place the instrument without a chin rest in the UV cabinet.

The strings must remain taut throughout the UV exposure.

 

A long cycle of creep considerably increases the materials’ stability: 3 to 4 days in the UV cabinet, then 3 to 4 days outside the cabinet, etc. Once the free materials have undergone a sizeable cycle of creep and they are relatively stable, the violin can be left in the UV cabinet for a longer period.

 

After 20 to 30 days, remove the instrument from the cabinet and wait for the moisture content in the wood to return to the same value as before exposure to UVs, or between 5% and 8% (the free materials must have previously undergone dehydration). Install the same chin rest and read the B1- and B1+ mode frequencies.

A B1+ mode frequency above the original one indicates that the back plate has become deformed under pressure from the strings.

 

After back plate deformation, retune the B1+ mode frequency, when it exceeds the critical limit or when the delta between modes B1- and B1+ exceeds 95 Hz. When calculating the delta, take into consideration the fact that the shoulder rest lowers the B1+ mode frequency by approximately 5 Hz to 7 Hz.

It is advisable to read this frequency with a standard shoulder rest. Then return the instrument to the UV cabinet to obtain uniform color, if the back plate has been sanded.

 

The 5 to 7 Hz (approximate) rise in the B1- and B1+ mode frequencies after varnishing must be taken into consideration for mode tuning.

 

Every week, monitor the tightness of the sounding post. When a longer post is necessary, align it with the center of the right foot of the bridge.

 

The B1- mode frequency may turn out to be too low, with a delta greater than 95 Hz. The bass bar must be changed to raise the frequency of the free top plate “with a bass bar” by the number of hertz in excess of 95 Hz, without exceeding 355 Hz at 6%. The B1+ mode frequency must not exceed 545 Hz at 6% once the back plate has reached its critical limit for deformation.

 

To ascertain the true frequency of the various modes, it is necessary to know the moisture content of the materials at the instant the reading is taken.

 

N.B. If the sound of a violin (in the white or varnished) becomes mediocre some time after the strings have been installed, this defect can be explained as follows:  the back plate becomes deformed, the B1+ mode frequency rises 16 Hz, the B1 mode frequency drops 8 Hz.

These cumulative effects yield an increase of 24 Hz in the B1- / B1+ delta, which will exceed
95 Hz, if it exceeded 75 Hz when the violin was first set up (in the white or varnished).

 

Thus, understandably, fine tone can be rapidly lost if frequencies are tuned to the critical limit without taking the necessary precautions before varnishing the instrument.

 

 

 

Bridge

 

The vibrations of the strings are transmitted to the resonator by the bridge, which plays an important role in the processing of vibrations. Placing a mute on the bridge (thereby toning down the high frequencies) suffices to hear the difference in power and timbre.

 

The bridge is an acoustic filter. The signal it transmits to the top plate will undergo transformations, resulting in a loss of the signal that will generally be greater for high frequencies.

The essential qualities of a bridge depend on the following characteristics: density, celerity, elasticity. Performance should be sought in thickness, shape, cut-outs, and frequency.

The bridge also absorbs part of the vibratory energy: optimization of it is therefore necessary.

 

(2) Hold the bridge by a rubber band looped through the heart or around one foot. Tap the bridge (preferably, with an object made of plastic) to hear its frequency.

 

Bridge blanks have a fundamental frequency from 260 Hz to 395 Hz and weigh from 3 to 4 g.

The bridges available on the market are standardized; consequently, the heavier bridges have higher density. The best ones have high density, elasticity, and frequency.

 

The thickness for the feet of a violin bridge is between 4 and 4.2 mm, depending on the characteristics of the wood. Width is from 41 to 42 mm.

The feet must be adjusted to a perfect fit with the curvature of the top plate’s arching. A good bridge must sit on the top plate naturally. The standardized height is 32 mm maximum. The back side of a properly adjusted bridge must be perpendicular to the line of the ribs.

The thickness of the bridge depends on its density and frequency.

 

A fitted violin bridge weighs from 2 to 2.3 g.

 

A free bridge should be tuned between 260 Hz and 360 Hz. It is advisable to tune the bridge to approximately 270 Hz, which corresponds to the relative top plate coupling frequency, as well as the A0 cavity mode frequency “with a sound post”. A frequency of 360 Hz gives the violin maximal power, but can reveal undesirable high ranking harmonics. Compression by the violin strings does not modify the frequency of the bridge: after installation, it remains identical.

 

The frequency of the bridge is inversely proportional to that of mode B1+.  When the latter is above 550 Hz and the sound is aggressive, harsh, and raspy, the bridge’s frequency should be brought down as far as 260 Hz, leaving more wood in place, to yield a sweeter sound.

 

Give the bridge the standard thickness, then adjust the feet on the top plate. If the feet are left
too high, there will be a shortage of wood at the head of the bridge; if the feet are too short, there will be too much wood above the heart. In both cases, the frequency of the bridge and the sonority of the violin will be modified.

After fitting the feet to the top plate, adjust the height of the bridge. Note down its frequency, refine the final thicknesses, and remove wood from the various regions in order to obtain the desired frequency for the free bridge.

 

Thinning a bridge blank to the standard thickness lowers its frequency by 45 to 65 Hz.

 

Reducing the height of the bridge head to its standard value lowers its frequency by 45 to 65 Hz.

 

Irrespective of the properties of the bridge, once its thickness has been adjusted, its frequency rises by as many hertz as it dropped when the height of the bridge was reduced.

 

Removing wood from the various regions of the bridge yields the following outcome:

 

¨ (C) -  raises the frequency by                                               5 Hz

¨ (E) -           raises the frequency by approximately       10 Hz

¨ (F) -           raises the frequency by approximately       10 Hz

¨ (D) -          lowers the frequency by                                              10 Hz

¨ (B) -           lowers the frequency by                              10 Hz to 15 Hz

¨ (G) -          lowers the frequency by                              25 Hz to 30 Hz

¨ (A) -           Thinning the bridge lowers the frequency by approximately 5 Hz.

 

To obtain satisfactory results, the frequency of the bridge blank must be at least equal to that
of the desired adjusted bridge.

 

 

Tuning the free bridge is necessary. However, according to the regions from which wood is removed in order to tune the bridge, the violin’s sonority and equilibrium are modified. Enlarging the heart and the eyes gives a clearer timbre, enhancing the higher harmonics. Beyond a certain limit, the sound becomes sour and aggressive.

 

A string lifter is absolutely necessary for improving a violin’s sound by successive bridge adjustments. The device must remain in place throughout the process until the strings are retightened and the bridge is once again under tension.

Slacken the strings: the tension on the neck and plates relaxes, increasing the B1- mode frequency and lowering the B1+ mode frequency by a few hertz. Once the strings have been retightened, the violin gives the impression that it breathes, has lovely sound and a perfectly adjusted bridge. But two days later, once the instrument has stabilized under the tension of the strings, the bridge setting is no longer correct, nor is the violin’s tone (which occasionally is even worse than with the previous bridge).

 

N.B. The vibrations transmitted to the bridge by the strings do not function like the frequency of an electric current, but more closely resemble a trepidation or an oscillation of the bridge, making the plates vibrate top plate mechanically and the back plate via the sound post in a multitude of nodal and antinodal zones depending on the frequency, as well as certain parts of the ribs.

 

Not all vibrations pass through the bridge. The strings also make the neck, fingerboard, tailpiece, upper and lower blocks vibrate by setting a part of the ribs in vibration and the top and back plates extremity (mode C2 or CBR).

 

After assembly of the violin, as each piece of the “puzzle” is set in vibration, the whole forms
a resonator whose outcome depends on several variables: quality of the materials, thicknesses, weight, tension, load and deformation of the materials, moisture content in the wood, A0 mode frequency, B1- and B1+ mode frequencies and the delta between them, and varnish.

 

 

Violin strings’ tension: 30 kg to 40 kg (66.14 to 88.18 pounds) depending on the diapason and the type of strings.

 

Calculation of string pressure on a violin top plate with a 158° angle and a 2.5 ratio.

 

Lower nut height: 6 mm  (0.24 inches) – Bridge height: 32 mm (1.26 inches)

 

Example:   32 kg  ÷  2.5 = 12.8 kg pressure on the top plate, and via the sound post, on the back plate.

             (70.55 lbs  ÷  (2.5 = 28.22 lbs)

 

              Copyright © 2010  - 2018 Patrick Kreit.            Reproduction of any content of this site without my express written permission is prohibited.

 

  Contact   Patrick KREIT

Home

Italian method

Arching

Mode 5

Mode B1

Mode A0

Varnish

Violin