The Well-Tempered Timpani
By Richard K. Jones
The contents of this page are the presentation notes from a
lecture presented at the
Nebraska Chapter P.A.S. Day of Percussion in April of 2006.
An interactive WEBook version, which will explore each topic in depth,
is projected for completion in the winter of 2008.
For more information please contact:
rkj@nebrwesleyan.edu
Part I:
The Search for the Missing Fundamental
or
Zen and the Art of Fitting a Round Peg into a Square Hole
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The Competition With all non-percussion instruments in today's modern orchestra (strings, brasses and winds), we hear various pitches according to whether a string or column of air is vibrating as a unit through its whole length or in particular fractions of it. The vibration along the whole length of a string or column of air gives the lowest or fundamental tone. The vibrations taking place at various fractions of the length produce higher pitches called harmonics or upper partials. The stationary points along a string or column of air (i.e., where the waves cancel each other out) are called nodes or nodal points. In mathematical terms, the frequency of each harmonic is in inverse proportion to the size of the fraction. This means that the vibration of equal halves of a string or a column of air produces double the frequency of the whole (and thus sounds an octave higher), the vibration of equal thirds triples the frequency (and therefore sounds an octave and a fifth higher than the fundamental note) and so on. The range of notes produces what is called the harmonic series or overtone series. Use the chart below to see what the harmonic series looks like when it is notated and to hear what the individual partials sound like. |
A Harmonic Series Written as Notes
chart
courteous Reginald Bain
| Show partials: |
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| The first 20 partials of a harmonic series for the fundamental pitch C2 (ca. 65.4 Hz.) expressed in traditional musical staff notation with frequency multiples indicated between the staves. The - and + symbols indicate that the notated pitch is significantly lower or higher, respectively, than the same pitch on a modern piano. | |||||||||
Note that some of the partials are slightly out of tune with our |
What are consider to be musical notes are sounds that have a particular
pitch. The pitch of a musical sound depends on the fundamental frequency
of that sound. The higher the frequency and shorter the wavelength of
the sound waves, the higher the pitch is. Frequency and Pitch
What are consider to be musical sounds generally don't have just one frequency. Sounds that have only one frequency are not at all interesting or pleasing to listen to. They have no musical color or timbre. Conversely, sounds that have too many frequencies, like the sound of a strong wind storm with rain may be interesting and even pleasant to listen to, but these sounds don't have a particular pitch, so they usually aren't considered musical notes. When someone sings a note or plays a note on an instrument,
a very particular set of frequencies is heard. Visualize each note that
is sung or that is played on an instrument as a smooth mixture of many
different pitches. These different pitches are called overtones
or partials and are preferably harmonic, but they can be either harmonic
or non-harmonic. They are generally blended together so well
that you do not hear them as separate notes at all. Instead, the overtones
or partial give the note its color or timbre. Notes which have
many non-harmonic overtones are said to create inharmonicity.
In music, inharmonicity is the degree to which the frequencies of the
overtones of a fundamental differ from whole-number multiples of the
fundamental's frequency. These inharmonic (non-harmonic) overtones are
often distinguished from harmonic overtones (whole-number multiples)
by calling them partials, though partial may also be
used to refer to both. Whether we hear a sound as pitched or unpitched
depends partly on the overtones of that sound. The more inharmonic
a sound is, the less definite it becomes in pitch. Many percussion
instruments such as cymbals, tam-tams, and drums create complex and
inharmonic sounds. Most modern professional-quality wind, brass and
string instruments are designed to limit inharmonicity as much as possible.
Harmonic Vibrating Modes of a String or Column of Air
Harmonic Series Wavelengths and Frequencies
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So, what does all of this have to do with timpani?
Not much
actually, but therein lies the problem of fitting
the round peg into the square hole.
Vibrating
circular membranes (i.e. a timpani head) do not vibrate with a harmonic series
yet they do have an overtone series, it is just not harmonic.
Furthermore,
the fundamental of a vibrating circular membrane
is not very resonant and doesn't produce a pleasant sound.
Let's begin by investigating the acoustic properties of timpani.
Acoustic Properties of Timpani
OK. Got that. |
So, what does all of this mean?
If a timpano's
fundamental is dampened,
from where does the sound come?
What are these "preferred modes"?
All excellent
questions; first we must take a look
at some of the vibrational modes of an ideal
circular membrane.
An ideal circular membrane may defined as an absolutely round membrane, infinitely thin, perfectly flexible, completely homogeneous, evenly and uniformly tensioned where the outer circular edge of the membrane constitutes a fixed boundary condition in an "in vacuo" state (in a vacuum). This type of membrane exists in theory only. For a vibrating timpani head, the conditions are somewhat different, but the mode shapes are almost the same as those of the ideal circular membrane.
12 Initial Vibrational Modes
of an Ideal Circular Membrane
Information and chart courtesy
of Georgia State University
HyperPhysics
Ideal Circular Membrane Modes
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Compare the ratios (f1
1.59f1 etc.)of some of the initial modes of
an ideal circular membrane in the chart above
to the ratios in the harmonic overtone series in the chart below.
Don't worry about the numbers is red yet.
Do you see a difference?
The harmonic series ratios are simple integers (or whole number
multiples) times the fundamental frequency;
the ideal circular membrane ratios are not simple integers
(or whole numbers multiples),they are decimal numbers.
|
Frequency ratios for the first twelve partials of the harmonic series and the corresponding interval names for the notes above the fundamental. |
f1 |
= |
1 |
Fundamental |
1st partial |
2f1 |
= |
2 |
Octave |
2nd Partial/Overtone 1 |
3f1 |
= |
3 |
Octave + Perfect Fifth |
3rd Partial/Overtone 2 |
4f1 |
= |
4 |
2 Octaves |
4th Partial/Overtone 3 |
5f1 |
= |
5 |
2 Octaves + Major Third |
5th Partial/Overtone 4 |
6f1 |
= |
6 |
2 Octaves + Perfect Fifth |
6th Partial/Overtone 5 |
7f1 |
= |
7 |
2 Octaves + Minor Seventh |
7th Partial/Overtone 6 |
8f1 |
= |
8 |
3 Octaves |
8th Partial/Overtone 7 |
9f1 |
= |
9 |
3 Octaves + Major Second |
9th Partial/Overtone 8 |
10f1 |
= |
10 |
3 Octaves + Major Third |
10th Partial/Overtone 9 |
11f1 |
= |
11 |
3 Octaves + Augmented Fourth |
11th Partial/Overtone 10 |
12f1 |
= |
12 |
3 Octaves + Perfect Fifth |
12th Partial/Overtone 11 |
Let's listen to what each of the partial series sounds like.
Both series will begin on C2 (ca. 65.4 Hz.)
First, the first twelve partials of the harmonic series:
Now, the initial twelve
modes of an ideal circular membrane:
Do you hear a difference?
Since circular membranes
are two-dimensional, they can vibrate
in many modes simultaneously and most of these modes are not harmonic;
that is the frequency of higher modes are not simple integers times the fundamental
frequency as is found in the harmonic series.
Furthermore, since it
is vibrating in two dimensions, it has two
sets of nodal points; nodal circles and nodal diameters.
Nodal points are points
of no vibration. The first nodal point (found in mode(0 1)) will always occur
where the bearing edge of the bowl touches the head.
In the customary mode designation, the first number gives the number of
diametric (radial) modes, and the second the number of circular modes.
As we move forward, be
sure to differentiate between modes and nodes.
Modes are the patterns of the vibration and nodes are the
points of no vibration which shape the patterns.
The next section will
give us a detailed look at
modes and nodes. Pay attention to the numbers in red.
Vibrational Modes of a Ideal Circular Membrane
Information and animation courtesy of Dr. Dan Russell, Kettering University NOTE: in the following descriptions of the mode shapes of a *ideal circular membrane, the nomenclature for labeling the modes is (d,c) where d is the number of nodal diameters and c is the number of nodal circles (also known as diametric and concentric modes). *An ideal circular membrane may defined as a absolutely round membrane, infinitely thin, perfectly flexible, completely homogeneous, evenly and uniformly tensioned where the outer circular edge of the membrane constitutes a fixed boundary condition in an "in vacuo" state (in a vacuum). This type of membrane exists in theory only. |
 |
The (0,1) ModeThe animated gif at left shows the fundamental mode shape of a vibrating circular membrane. The mode number is designated as (0,1) since there are no nodal diameters, but one circular node (the outside edge). Remember that a node is a point (or line) on a structure that does not move while the rest of the structure is vibrating. The (0,1) mode of a drum, such as a timpano, is excited when the drum head is struck at its center. When vibrating in this mode the membrane acts much like a monopole source, which radiates sound very effectively. Since it radiates sound so well when vibrating in this manner, the membrane quickly transfers its vibrational energy into radiated sound energy and the vibration dies away. The short duration (fraction of a second) of the (0,1) mode means that this mode does not contribute greatly to the musical tone quality of a drum. In fact, when struck at the center, a timpano, or other large drums, produces a "thump" which decays quickly and has no definite pitch. |
The (1,1) ModeThe next mode is the (1,1) mode, which has one nodal diameter and one circular node (the outside edge). The exact location of the nodal diameter depends on the homogeneity of the membrane and the initial conditions when the vibration starts. The frequency of the (1,1) mode is 1.593 times the frequency of the (0,1) mode. When vibrating in the (1,1) mode a circular membrane acts much like a dipole source; instead of pushing air away from the membrane like the (0,1) mode does, in the (1,1) mode one half of the membrane pushes air up while the other half sucks air down, resulting in air being pushed back and forth from side to side. As a result, the (1,1) mode radiates sound less effectively than the (0,1) mode, which means that it does not transfer its vibrational energy into radiated sound energy as quickly as the (0,1) mode and therefore the (1,1) mode takes longer to decay. Because the (1,1) mode "rings" for a while, it contributes to the musical sound or pitch of a drum. When timpani, or other large drums, are struck somewhere between the center and outer edge, the sound has a definite pitch which lingers for a several seconds. |
 |
The (0,2) ModeThe (0,2) mode, shown at right does not have any diameter nodes, but has two circular nodes - one at the outside edge and one at a distance of 0.436 a (a is the radius of the circular membrane) from the outer edge. The frequency of the (0,2) mode is 2.295 times the frequency of the (0,1) mode. Like the (0,1) mode, the (0,2) mode is excited when the membrane is struck at the center. The sound radiation characteristics of the (0,2) mode are more complicated than the first three modes -- it appears to be a mix between a monopole and a dipole. Its decay time is longer than the (0,1) mode, but shorter than the (1,1) mode. As a result, it contributes to the "thump" sound when a drum is hit at the center, but does not contribute much to the musical pitch of a drum when hit off center. |
 |
 |
The (1,2) ModeThe (1,2) mode has one nodal diameter and two nodal circles. The frequency of the (1,2) mode is 2.917 times the frequency of the (0,1) mode. As you might expect after looking at the first several modes of the circular membrane, the (1,2) mode does not radiate sound very effectively. It has somewhat of a quadrupole type behavior. Thus, the (1,2) mode takes a relatively long time to decay. However, this mode doesn't seem to play a dominant role in the musical tone quality of a drum. |
The (0,3) ModeThe (0,3) mode, shown at right has three circular nodes, but no diameter nodes. The frequency of the (0,3) mode is 3.598 times the frequency of the (0,1) mode. Like the (0,1) and (0,2) modes, the (0,3) mode is excited when the membrane is struck at the center. The sound radiation characteristics of the (0,3) mode are rather complicated. This mode is excited when the membrane is struck at the center, and it dies away fairly quickly. As a result, it contributes to the "thump" sound when a drum is hit at the center, but does not contribute much to the musical pitch of a drum when hit off center. |
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If this true, how do timpani produce musical pitch?
The science
behind how timpani produce sounds which constitute musical pitch
has been a fascination of scientists and physicists for well over a century.
Remember
the definition of an ideal circular membrane; a absolutely round membrane,
infinitely thin, perfectly flexible, completely homogeneous, evenly and uniformly
tensioned where the outer circular edge of the membrane constitutes a fixed
boundary condition in an "in vacuo" state (in a vacuum).
Well, the fact that a timpano head cannot conform exactly to and ideal membrane
may actually help the drum produce musical pitch. Factors such as the thickness
and stiffness of the head alter some of the higher partials helping coax the
head into vibrating with near harmonic relationships which in a sense "fine
tune" the drum.
Probably the most important contributing factor however, is air. A timpano head vibrates in an ocean of air both inside of the bowl and outside of the bowl. The air mass outside of bowl significantly lowers the frequency of the principal mode and the resonance of the air enclosed in the bowl interacts with other modes. All of this air working against the head is called "air loading" or simply "loading" which is believed to be the main contributing factor in coaxing the drum into having a "near" harmonic series. Together, the air inside and outside of the bowl and the head work together to create a single vibrating system.
Let's now take a look at some of the studies.
Studies on the Acoustic Properties of Timpani
Lord Rayleigh's
(John William Strut) seminal work
The largest factor for the "correction" of the overtones into a close approximation of a harmonic series stems from the mass of the air against which the membrane vibrates. A drum's bowl (kettle) features a large surface area and thus interacts with a large volume of air. This air mass serves to lower the frequencies of the principle modes of vibration. The shape of the drum's large conical shell exhibits resonance properties of its own. Modes with similar shapes interact and reinforce each other through the medium of the air trapped inside it the bowl. The stiffness of the air in the kettle raises the frequencies of higher overtones. All of the above properties shift or coax the partials (overtones) and result in a close approximation of a harmonic series (from which we are able to discern a pitch). |
Taking into consideration
that Lord Rayleigh did not have modern laboratory equipment to work with and
the fact that the "English" timpani of his day were less than desirable,
it is nothing less than remarkable that his results were what they were. In
fact, they may have been different if he had used timpani of quality. Benade
in his book Fundamentals of Musical Acoustics relates
that in personal correspondence with P. R. Kirby, Kirby stated that the drums
used in Lord Rayleigh's experiments were second hand and not properly tuned.
Perhaps this accounts for the interval of a major seventh in his analysis.
Thomas
D. Rossing/Garry Kvistad 1976
Northern Illinois University
Ludwig Professional Symphonic Suspended Bowls
(plastic Weathermaster™ -750db heads)
Information and charts courtesy of
Georgia State University
HyperPhysics
The Preferred Timpani ModesAssuming that these selected modes are excited, the relative frequencies and intervals in cents are given compared to the 1,1-mode. The preferred vibrational modes for timpani are a subset of the modes of a circular membrane. 
The interval values in cents here are calculated from the mode frequencies given by Berg & Stork. They can be compared to equal tempered intervals. The actual sounding frequencies are affected by air damping. |
From; Benade, Arthur H., Fundamentals of Musical Acoustics, Oxford
University Press, 1976
Ch 9, p143-144. Measured timpani of Cloyd Duff of the Cleveland Orchestra
in 1973
(Duff owned Dresdner Apparatebau Anheier/Jaehne & Boruvka timpani)
Sounding Frequencies of TimpaniThe timpani sound involves the vibrational modes of a circular membrane, but the technique of playing specifically excites the preferred modes of the membrane. These are further affected by air damping, which finally leads you to the set of frequencies which are actually produced by the instrument. An actual set of frequencies is reported by Benade for an instrument which is tuned to C3 (130.8 Hz).
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THE BOTTOM LINE ON WHICH ALL * The mass of the air contained inside
the bowl lowers the frequencies of the diametric modes [(1,1), (2,1),
(3,1), etc.]. * The principal tone is derived primarily
from mode (1,1) * The air inside and outside of the bowl and the head make up a single system, the two parts of which are of equal importance in determining the frequencies and overall vibrational shapes which define the pitch of the instrument. All of the above properties shift or coax the partials (overtones) and result in a close approximation of a harmonic series (from which we are able to discern a pitch). |
| But what about that missing fundamental? Why do timpani still sound low, or do they? |
The Missing Fundamental Effect
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|
The Missing Fundamental This demonstration explores the relation between the
frequency content of a musical note and the pitch perceived by listeners.
Musical notes are complex tones consisting of a fundamental frequency
and higher harmonics (known as partials) that are integral multiples
of the fundamental frequency. The particular mix of partials is
part (but only part!) of what gives different musical instruments
their individual character. The pitch of the note is
related to the fundamental frequency of the complex tone. However,
the pitch of the note remains unchanged even if this fundamental
frequency is removed. |
So, how do you make your timpani sound like musical instruments if they don't vibrate with a harmonic series? How do you get timpani to blend with other instruments? How do you achieve this"correction of the overtones into a close approximation of a harmonic series" as Lord Rayleigh prescribes while clearing heads on timpani or, as I like to refer to it, "tempering" the timpani? Are we able to
hear the missing fundamental? |
| Start by eliminating as many variables as possible. The following ingredients are essential for good timpani tone.
Assuming all of the above exist you can proceed to tempering or clearing the drum.
|
Nomenclature of a Yamaha Timpano
courtesy of
the Yamaha
Corporation
|
Tempering & Adjustment of
a Mylar Timpani Head or |
For timpani to produce a true pitch, one that is clear (rich with near harmonic overtones), well-defined, and a pitch that will project, the instruments must be adjusted or tempered properly. I use the term temper which means to adjust. You may also hear or use the terms clear or balance when working with timpani heads. These terms refer to the process of adjusting each tension lug until the pitch at each tension lug point is uniform and consistent and the drum has a long sustained principal tone, and is rich in near harmonic overtones. When the instrument's heads are clear or tempered, the instrument is easier to tune, blends better with the ensemble and is much easier to play. You will be able to produce a pure and focused pitch as well as a beautifully sustained principal tone throughout the range of each drum. The strong near harmonic overtones produced will not compete with those of your colleagues, but rather compliment them. This process should be done routinely, but only when necessary. The mishandling of timpani when moving the instruments from one location to another is often blamed for why timpani sound bad when in fact it could be simply a change in climatic conditions, especially atmospheric pressure. I'll bet you never thought that climate change had anything to do with timpani with plastic heads, well it does. A very important component to the sound of timpani is air, especially the equalization of the air inside the drum (both temperature and moisture content) to that of the air in the room. A very delicate dance between the air mass inside of the drum to the air mass outside of the drum contributes significantly to the perceived pitch of timpani. Even subtle changes in air temperature and/or barometric pressure can affect the perceived pitch. It is a well established fact that atmospheric changes (especially humidity) can affect timpani with calf heads and it is true that mylar heads are not affected by atmospheric change but, the irony is that these plastic heads don't "breath" like calf heads do and actually impede the exchange of air between the inside and outside of the bowl. This is good for the most part however, it does contribute to a slower exchange of air between the inside and the outside of the bowl which is critical when differing air masses need to be equalized. The worst thing you can do is start to clear or temper you heads after the drums have been moved from one location to another with differing conditions, e.g. a dry air conditioned room to a warm/hot humid outdoor venue or a cold storage room to a warm stage. The best thing to do in this type of situation is to just let the drums sit for forty-five minutes to an hour and acclimate to the new environment. Playing on them won't hurt them and it will actually help equalize the air mass in the bowl with the outer air, but it will play tricks with your ears. When moving percussion equipment, I always move the timpani first. If a drum is sounding good and has a long sustained principal tone with clear near harmonic overtones present at each tuning lug, leave it alone. In general, I like to clear the heads on my drums after a rehearsal rather than before giving them time to settle a bit so they will be ready for me the next time I need to play them. Don't be afraid...just do a little bit at a time and try to do a little bit every time you play the drums if possible and only if needed. Just remember that there is no magic bullet or perfect
tool that will do this this for you. At best, the results will always
be a compromise since timpani do not vibrate with a natural harmonic
series as do all other standard orchestral instruments, but with
good tempering you will hear clear near harmonic overtones and a
strong principal tone at all dynamic levels throughout the range
of the drums. When the drums are well-tempered, the illusive "missing
fundamental" can be found. |
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1. Clean the surface of the head thoroughly with a non-caustic glass and surface cleaner to remove any salt, dirt or grease which may have accumulated, and which can keep the head from vibrating evenly. If the head shows any dryness or damage from indirect sunlight or heat, evenly apply liberal amounts of a vinyl protector such as Armor All®; let it set for at least ten minutes, then work the protectant into the head evenly, and then wipe off any excess. It is best to do this after you have completed the tempering process. The vinyl protector will help restore some of the natural elasticity in the head. It is a good idea to apply this to the heads routinely. The heads come from the factory with a film coating on them but it dissipates over time. Be sure that the protector has been worked well into the head and that no excessive residue remains. For balanced action timpani (Ludwig, Yamaha, Adams, Ajax, Majestic etc.), set the foot pedal all the way back to the floor with the heel of your foot. This will remove the head tension and should place the drum near the low end of the MSR. Center the head & check for a uniform collar. The head can become off-centered simply by moving the drum improperly. If the head is not centered, loosen each lug the same amount and center the head on the drum. Measure the distance from the lip of the bowl to the counterhoop at four points on the drum (north, south, east and west) making sure that they are exactly the same. With a felt tipped pen, place a small mark on the head directly where the at the lip touches the bowl at these four points (NSEW). Use these marks as reference points to make sure that the head is always centered. It is best to place these reference marks on the head before it is mounted on the drum in which case you would simply measure the diameter of the drum at two adjacent points at the lip and then the diameter of the head. You then find the difference of these two measurements and then divide that number by two. Use this measurement and mark on the head at four points (NSEW) measuring from the very edge of the head inward towards the center. When you mount the head, center the head on the drum making sure that the NSEW marks are right at the lip. For more information on this process, please see my article on mounting mylar/plastic heads. If the head is not centered, the drum cannot be tempered properly and will never be able to create a desirable overtone series throughout the range of the drum. This crucial step, which is often overlooked, is easily fixed and "makes or breaks" the overall sound of the drum. This process defines the actual fundamental (mode 0,1) frequency of the drum, a frequency which is not heard as being the actual pitch of the drum yet it has a strong influence on the preferred modes that do. The actual principal tone or what we perceive as the pitch of the drum is determined primarily by mode (1,1).
Return the lugs to the low note position of the MSR
(the lowest and highest pitch at which you want the instrument to
sound) once the head is centered. |
|
Sample MSR pitches for various timpani are:
The size of the drum is generally determined by the diameter of the bowl, not by the diameter of the head or the counterhoop. To determine the size of the bowl, measure the lip of the bowl (the bearing edge) at opposing tension lug points. The size of the head is determined by the counterhoop. Some timpani manufacturers use non-standard counterhoop sizes. Be sure to consult the owner's manual for the correct size of heads needed for your instruments before ordering replacement heads. |
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Make sure that the drum itself is level and pick a point at which to begin. Position the block on the head so that the pointer (set screw and cap-nut) is centered in the middle of the counterhoop directly in front of a lug. Adjust the pointer so the cap-nut barely touches the rim and lock it in place with the wing-nut. Following the cross-tuning sequence below, place the gauge on the head and adjust each lug until you do not see any daylight between the block and the head.
MAKE ADJUSTMENTS IN SMALL INCREMENTS ONLY. Repeat this process until all lugs have been leveled. ALWAYS make sure you keep the drum within its MSR.
Move the pedal into mid playing range and strike the
drum in the normal striking position with a medium hard stick a
few times softly and once loudly. Place your ear close to the head
and listen for clarity of pitch and near harmonic overtones. The
idea throughout the tempering process is to find the differences
in pitch at each tension lug point and correct them until the pitches
of the soft strokes and loud stroke match. More than likely the
drum will still need more tempering. More often than not, after
measuring equally at each tension rod, the pitch at each rod will
be extremely different and the head will be completely out of tune.
This is usually due to a counterhoop that is not flush. The maker
of this product states that additional head clearing may be needed
after initial leveling. |
5. Another device that can be very useful is a DrumDial™ or a Tama Tension Watch which precisely measures the tympanic pressure at each lug point. However useful these tools maybe, they are not a solution for fine tuning timpani. Since they don’t measure pitch (but only the timpanic pressure of the head at specific points) and since pressure doesn't’t determine pitch, these pressure readings are probably best used as a guide to get you in the general range of the drum’s optimum sound rather than a mechanism for fine tuning. If the head has been excessively stretched at any point (i.e. the playing area), the timpanic pressure readings may not be accurate. This device works best on new or lightly played heads. There are just too many variables involved with the way timpani work to rely solely on pressure readings for accurate pitch but these devices are very useful for getting you to that sometimes elusive "fine tuning zone" where you can begin to fine tune and temper your drum.
The DrumDial™
and the Tama
Tension Watch work very well and do accurately measure the timpanic
pressure, but the pitch clarity of your drum may not be100% accurate.
Although it works much more consistently than most measuring devices,
it can sometimes produce an unclear head. After adjusting the head
tension (or timpanic pressure) at each tension rod to a point where
the gauge indicates the tension to be exactly the same, the sound
and clarity of pitch may still be false. If the DrumDial™
or the Tama
Tension Watch produce unsatisfactory results, you may have a
head that is excessively stretched at some point, or, have a false
head and/or tolerance issues with the drum itself. They work best
on new, non-coated heads or smooth heads. Coated heads may not be
the same thickness at each measuring point yielding slight variations
in measurements even though the tension may be the same. |
|
I use an electronic tuner to measure and adjust the pitch of the principal tone (mode 1,1) at each tension lug. I have found that an inexpensive tuner such as the Korg CA-20 (ca. $15.00) works very well for this process and saves my ear from fatiguing so quickly. The tuner is also able to register very low frequencies which are difficult for me to even discern as a pitch. I focus on the pitch of the principal tone only, not the overtones or partials. The tuner needs to respond to the sound quickly, so make sure that the tuner has a "fast" mode or that it will respond immediately to low frequencies. If the tuner will not respond quickly to low frequencies, this process will not work and may produce an inferior result.
The objective with this step is to to unify vibrating mode (1,1)
which is the frequency from which the perceived pitch of the instrument
is defined. This can be accomplished by exciting the lowest frequency
possible on the drum, which is generally the lowest note of the
MSR on a balanced action drum. (If your drum has a master tuning
screw, loosen the tension on the head to the threshold of pitch.)
If the pitch of the principal tone [mode (1,1)] at each lug point
matches, a near harmonic series can be created using virtual pitch
(difference tones) and the air baffling/dampening process of the
bowl (explained in Part I), creating a clear tone and well-defined
pitch throughout the entire range of the drum. In order to get the principal tone to speak clearly, I use a relatively large and heavy mallet covered with a very soft felt. A hard or light mallet will not produce a strong principal tone. It is a good idea to experiment with different mallets until you get a solid reading on the meter. If at all possible, it is best do do this process in a completely quiet room .
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This process will to go slowly the first few
time you attempt it. |
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| In a Nutshell A Quick Guide to Tempering Timpani
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Some General Timpani Do's and Don'ts
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Online References HyperPhysics, Georgia
State University
Other Timpani Links Yamaha
Corporation Mike
Crusoe, Principal Timpanist, Seattle Symphony Orchestra Timpani
picture album featuring antique instruments |
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©2005 Timpani Analytic International TAI
All Rights Reserved
Please send comments
to:
rkj@nebrwesleyan.edu
Last updated 9/24/06
