It has been shown by means of many tests and
actual adjustments to several hundred violin family instruments
that certain frequency relationships of the two lowest cavity
modes, the A zero (A0) or "Helmholtz" and the A one
(A1) body-length mode inside the box, with those of three body
modes below 600 Hz can have a marked effect on the tone and playing
qualities of an instrument. This writing is an effort to summarize
these findings to date and suggest ways in which violin makers
can adjust their instruments to take advantage of these frequency
relationships. It should be noted that the term PITCH is used
for the sound heard, while FREQUENCY is the actual measured Hertz
(Hz) of the sound source, and they are not always the same.
Figure 1 shows the geometry and approximate frequencies of these
two cavity modes, A0 and A1 and the three body modes, B minus
1 (B-1), B zero (B0) and B one (B1) in a normal violin. Three
of these modes, the A0, A1, and B1 are radiating modes, producing
sounds out into the air; while the B-1 and the B0 modes are non-radiating,
as can be seen from their geometries. Once the violin is completed
and strung up it is not advisable to try to move the frequency
of the A0 and A1 cavity modes except in a few cases noted below.
Violin Cavity and Body Modes
PITCH MATCHING OF A0 AND B0
The best place to begin tuning is to try to bring the B0 mode
pitch to that of the A0 mode, for they usually lie fairly close
in frequency. Hold the completely strung up violin in thumb and
forefinger at a point on the nodal line across the widest part
of the lower bout. Damp the strings against your shirt and tap
on the end of the scroll. (Do not damp the strings against the
fingerboard). The sound heard is the pitch of the B0 mode. Then
BLOW across the f-hole on the G-string side (where there is most
air motion) and listen to ascertain whether B0 is above or below
A0. (These are complex sounds and it is not easy to identify their
pitch without practice.)
If the B0 pitch is heard to be HIGHER than the A0, add a small
weight, such as a lump of oil clay, or even chewing gum with a
penny stuck on it, to the free end of the fingerboard. Notice
in the computer visualization of the B0 mode that the end of the
fingerboard is moving most actively. (Added mass on a moving element
will reduce frequency, as will reduced stiffness in a bending
part.) Change the mass slightly until you hear the tapping sound
of the B0 mode at the same pitch as the A0 mode BLOW tone. Other
ways to lower the B0 mode frequency are to remove wood from under
the fingerboard in the area close to the neck, or to thin the
bending part of the neck-fingerboard. Dressing down the fingerboard
when the strings have worn ridges in it will lower the B0 frequency.
The mass of the chin rest as well as that of the scroll and pegs
will also alter the B0 frequency. But first try adjusting the
mass on the end of the fingerboard and have several good players
try the instrument so you can realize the difference. The further
apart these two modes are to begin with the more improvement you
will get when they are matched.
If the A0 pitch is heard to be HIGHER than the B0, a temporary
check can be made by putting various amounts of tape across one
f-hole to lower the A0 pitch. Permanent adjustments to do this
can be done by reducing the mass of the moving end of the fingerboard
either by removing wood from under the end, or sawing thin slivers
of wood off the end of the fingerboard until the desired frequency
is reached. (Less mass in motion raises frequency.) (See Hutchins
1990a, 1990b, 1990c, 1990d)
It is well known from the early work of Helmholtz that the frequency
of a partly enclosed air mass is dependent on the volume of the
cavity, the flexibility of its walls, the area of the opening
and the thickness of the edges of the opening. The larger and
more flexible the cavity, the lower the frequency. The larger
the opening and the thinner the edges of the opening, the higher
the frequency. Enlargement of the f-hole area has shown experimentally
that only a few Hz rise in frequency can be achieved without ruining
the f-holes. However thinning and rounding off the underside of
the f-hole edges will also cause a slight rise in the A0 frequency
since this makes it easier for the air to flow out and in.
A1 AND B1 FREQUENCY RELATIONSHIPS
It has been found that the frequency spacing (delta) between the
A1 cavity mode and the B1 body mode is critical to the overall
tone and playing qualities, indicating whether a violin is suitable
for soloists (delta 60-80 Hz), orchestra players (delta 40-60
Hz), chamber music players (delta 20-40 Hz), and below 20 Hz is
easy to play but lacks power (Hutchins 1989). The physical mechanism
taking place as a radiating cavity mode and a radiating body mode
approach each other in frequency is described in Hutchins and
Violins with fairly stiff free plates (mode #5 at 370 Hz and Mode
2 at 185 Hz) often have their A1-B1 delta around 60-75 Hz and
are preferred by soloists for their bright powerful sound and
wide dynamic range, while those with lower free plate frequencies
(360-180 Hz or 350-175 Hz) are more suitable for some orchestra
players and amateurs. (Free plate frequencies do not always produce
the desired delta of A1-B1 since other factors such as stiffness
of ribs, liners, and edge thicknesses enter in.)
Various methods that have been tried to alter the A1-B1 delta
show the following frequency changes of the B1 mode:
|1. Prolonged vibration vibration
|minus 10 Hz
|2. Liners thinned 1/2 mm
|minus 9 Hz
|3. Soundpost thinned through the center
|minus 8 Hz
|4. Wood removal from top plate and bar
|minus 8 Hz
|5. Heavier bassbar
|plus 10 Hz
|6. Heavier liners
|plus 4 Hz
These numbers will probably vary from instrument
to instrument. For violins with an A1 delta B1 of over 75 Hz some
or all of these first four methods might produce desirable results.
Raising the B1 frequency using methods 5 and 6 gave more power
and brighter tone to a violin with an A1-B1 delta of 40 Hz. (Hutchins
and Rodgers, 1992)
Notice that all the above changes involve only the B1 mode frequency.
It is not practical to try to change the frequency of the A1 mode
once the dimensions (especially the length) and the stiffnesses
of the violin body are established. Reducing the thickness of
the top plate near the ends of the bassbar will reduce A1 frequency
a few Hz, but should be done with caution.
WOOD AND WOOD PRIME TONES
It is important to know that when the violin is bowed, the strongest
tone in the A1-B1 range is NOT at the A1 or the B 1 frequency,
but somewhere in between depending on the relative strengths of
these two modes. The effect of bowing is to combine these two
strong resonances into a single strong tone labeled MAIN WOOD
(W) as can be seen at the top of the chart. The MAIN WOOD frequency
is usually the haunt of the wolf-tone because the stored energy
in these two strong resonances is greater than the bow can handle,
and the tone jumps back and forth between A1 and B1, causing a
warble. In cellos the wolf-tone sometimes jumps an octave due
to the near octave relation of the A0 and A1 modes in these instruments.
Also there is a strong bowed tone an octave below the MAIN WOOD,
labeled WOOD PRIME (W') which is due to second harmonic reinforcement
by the MAIN WOOD resonance. WOOD PRIME does not show on a sine
wave curve, but only appears with the broadband input from the
THE HUM TONE AS DIFFERENT FROM THE BLOW TONE
If one BLOWS across the G-side f-hole as described above, the
PITCH of the A0 mode is heard. However; if one HUMS into the f-hole,
a strong tone two to three semitones below the A0 is heard. This
HUM tone can also be sensed by placing the thumb and fingers around
each end of the body and feeling a strong vibration in these areas
when the HUM tone is reached. This HUM tone is at the pitch of
the WOOD prime tone, an octave below that of the MAIN WOOD resonance.
It has been found that in matching the pitch of the B0 mode to
that of the HUM tone an even greater improvement in the overall
sound and playing qualities sometimes results than when the B0
pitch is matched to that of the A0. In this case the match is
related to the octave below two strong resonances, A1 and B1,
rather than just to A0. Also it is sometimes easier, depending
on the frequencies of B0 relative to either A0 or W', to match
B0 to one or the other.
When the article by Deena Spear (1987) was written, we did not
understand the difference between the BLOW tone and the HUM tone.
Considerable research comparing bowed "loudness" curves
with various single frequency tests has shown the mechanism causing
the difference between the BLOW and the HUM tone as given here.
Spear actually described matching the B0 mode to the HUM tone.
(C.M. Hutchins, personal communication)
Experienced violin makers are well aware that a tail-piece, when
tapped sometimes gives out a strong singing vibration that seems
to enhance the sound of the whole instrument. Various methods
are used to achieve this condition such as tuning the string-ends
between bridge and tailpiece to certain pitches, adjusting the
length of the tail gut, and changing the weight of the tailpiece
Experiments are now showing that this desirable condition is achieved
when the vigorous motion of the tailpiece as a whole is matched
to that of the frequency or to a sub-multiple of a strong body
or cavity mode frequency. This frequency of the whole tailpiece
is found between 120 and 140Hz, usually around 130 Hz. Thus far,
tonal enhancement has resulted when the tailpiece frequency is
matched to: (a) the B-1 mode, (b) 1/2 the frequency of the A0-B0
combination, (c) 1/2 either A0 or B0, (d) 1/2 WOOD PRIME or 1/4
MAIN WOOD frequency (which are the same). (Hutchins 1993)
THE TWO CHARTS
summarize these desirable mode tunings and indicate various methods
of achieving them without very expensive electronic equipment.
It should be noted that HUMMING into the f-hole does NOT give
the octave below the pitch of the A1 cavity mode, but rather that
of WOOD PRIME (W') which is somewhat lower. A forthcoming article
by Alan Carruth in this Journal will describe a relatively inexpensive
setup for pressure testing for the frequencies of the A1 and B1
modes inside the cavity. This is the only test method we know
so far that will give the correct relative frequencies of the
A1 and B1 modes (Hutchins 1989). Measurements made off the body
of the instrument or the top of the bridge may be useful, but
the frequencies, particularly of the B1 mode, are altered depending
on how far the measurement point or the feet of the bridge are
from the nodal lines of a given mode.
The approximate relative frequencies of B-1, B0, B1 and the tailpiece
can be found by soft mounting the violin horizontally at the nut
and at a nodal line across the body (see chart) over your plate
testing loudspeaker. Sprinkle glitter on the end of the fingerboard
and the string-end of the tailpiece and sweep through the range
of 100 to 1000Hz until the glitter bounces off at the approximate
frequency of each of these modes. (Ekwall 1990)
There is still much to be learned about how the body and cavity
modes of the violin interact to produce the wonderful sounds we
hear from a fine violin in the hands of a skilled player. There
are many more of these interactions at higher frequencies that
are not yet understood at all. No wonder the crafting and the
physical parameters of every piece of wood that goes into the
construction and final adjustment of a violin can make a difference
to the tonal qualities! It is a tribute to violin makers over
the centuries that they have been able to cope intuitively with
all these subtle variations to create such beautiful sounding
Prominent Modes of the Violin below 600Hz
Strong Bowed Tones and "Subharmonic" Tones Based on
Tailpiece Mode Tuning
Condax, L.W. (1988), "The soundpost of the violin," J. Catgut Acoust. Soc. Vol. 1 (Series 2) p. 28. Reprinted from
Catgut Acoust. Soc. NL. No. 2, Nov. 1964.
Ekwall, A. (1990) "Tuning air-body resonances for the violin
maker," Catgut Acoust. Soc. J. Vol. 1, No. 6 (Series 2) p.
Hutchins, C.M. (1989), "A measurable controlling factor in
the tone and playing qualities of violins," J. Catgut Acoust.
Soc. Vol. 1, No. 4 (Series 2), pp. 10-15.
Ibid. (1990a) "The cavity (air) modes of the violin," J. Catgut Acoust. Soc., Vol. 1, No. 5 (Series 2), pp. 34-35.
Ibid. (1990b) "Some effects of adjusting the A0 and B0 modes
of the violin to the same frequency," Ibid. pp. 35-37.
Ibid. (1990c) "Acoustical effects of "dressing down"
the violin finger board and/or thinning the violin neck." Ibid. p. 37
Ibid. (1990d) "Sympathetic vibration and coupling of resonances." Catgut Acoust. Soc. J. Vol. 1, No. 6 (Series 2), pp. 40-41.
Ibid. (1993) "The effect of relating the tailpiece frequency
to that of other violin modes," Catgut Acoust. Soc. J., Vol.
2, No. 3 (Series 2), pp. 5-8.
Hutchins, C.M. and Rodgers, O.E. (1992) "Methods of changing
the frequency spacing (delta) between the A1 and B1 modes of the
violin," Catgut Acoust. Soc. J., Vol. 2, No. 1 (Series 2)
Spear, D.Z., "Achieving an air-body coupling in violins,
violas and cellos: a practical guide for the violin maker." Catgut Acoust. Soc. J. #47, pp. 4-7.