Troubleshooting Timpani Inharmonicity
Instrument and Head Tolerances
Since the modes of vibration that determine timpani head motion do not generate a harmonic series, there is inherent inharmonicity in the pitch of any timpano. Even though the objective when tempering a timpano is to mitigate this inharmonicity as much as possible, it is often exacerbated by poor mechanical tolerances of the head or the drum itself.
Timpani produce what can be described as an ultra-composite-pitch comprised of a congress of pitch zones competing to agree on a single perceived pitch structure. Much like that of a chorus of voices singing the same pitch, timpani pitch will have voices (areas of vibration) that have slight differences in frequency and color. Ideally, a person should be able to strike a timpano at the normal playing spot anywhere around its circumference and generate the same blend of composite partials throughout the range of the drum. This can be difficult to achieve.
The reality, there is no such thing as a true zero tolerance when it comes to timpani heads (especially in the tucking process). This also holds true in regard to the mechanical integrity of an instrument. Even a slightly imperfect plastic head on a normally stable instrument will create substantial inharmonicity issues. Likewise, a quality head mounted on a timpano with an out-of-round bowl, or an uneven tensioning system will never be in-tune with itself, let alone with an ensemble. Sometimes it can be a combination of poor mechanical tolerances of both the instrument and head that lead to a perceived inharmonicity of the pitch.
Many inharmonicity issues can be mitigated by making sure that the head is properly centered. 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 insures the even tensioning of the fundamental (mode 0,1) frequency of the drum throughout the range 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 principal tone or what we perceive as the pitch of the drum is determined by mode 1,1, which is actually the second partial of the vibrating membrane.
diagram courtesy of the Yamaha Corporation
Mechanical Tolerances
Systemic inharmonicity issues can usually be narrowed down to three mechanical tolerances (both the bowl and head):
- Roundness: This affects the motion (size and shapes) of the Preferred Modes.
- Flatness/leveling : This affects the even tensioning of the head around the circumference of the drum.
- Global Tensioning: This affects the integrity of the overall tensioning system as it applies to chromatic pitch changes.
Roundness: The pitch producing Preferred Modes vibrate in sections like pieces of a pie. (see movie below) If the bowl is out-of-round to any significant degree, the adjacent sections of this pie will be different sizes, hence creating different frequencies. This is particularly noticeable with mode 1,1, which bisects the drum and creates the principal tone(s).
Symptom: struggling to get a consistent principal tone at any tension level around the circumference of the drum is a sign of a roundness issue. Measure the pitch at each lug point with an electronic measuring device. The pitch should deviate no more than +/- 4 cents from zero.
If you can’t get a strong principal tone with some stable harmonic overtones at any pitch level through the range of the drum, check the roundness of the bowl, the roundness of the head, as well as the centering of the head.
The movie below isolates motion of the first six Preferred Modes of an ideal circular membrane in vacuo (i.e. not affected by air loading). Modes are added in order from mode 1,1 to mode 6,1 and then increased in speed. When roundness issues occur with a timpano bowl, the preferred modes will be of unequal size creating an inconsistent and weak principal tone, and extremely inharmonic partials as the motion of the modes moves around the circumference of the head.
A generally accepted tolerance for bowl roundness is <4mm. Anything >5mm will be audible. Tolerance issues become more noticeable as the diameter of the drum becomes smaller. However, it is also important to understand that audible harmonicity issues on smaller drums are also due to the fact that the physical footprint of the head limits the amount of mass that is exerted on the head as a result of air loading. On some drums, roundness issues can be mitigated to some degree with the help of special tools (see Bowl Bounder). If the suspension ring of a timpano is out-of-round due to a miss-aligned frame, send it to a professional for repair.
Flatness/leveling: Anything to do with flatness, or parts of the instrument that should be level, will affect the even tensioning of the head. The lip of the bowl (bearing edge), the counterhoop, and the fleshhoop to which the head is attached, all need to be level and as flat as possible.
Symptom: when you get one pitch level stable with strong harmonic overtones, but the principal tone loses clarity, and a noticeable shift in overtones occurs as you increase or decrease the tension on the head, the usual culprit is a warped or non-level counterhoop, which should be replaced of fixed.
A head with a fleshhoop that is not level or warped should be discarded. An uneven lip (bearing edge) can be fixed, but it is best left to a professional.
Integrity of the global tensioning system. All mechanical parts that tension the head must pull or draw evenly.
Symptom: when you can get one pitch stable with strong harmonic overtones, but there is a noticeable change in the principal tone, and a major shift in overtones occurs as you increase or decrease the tension on the head, the usual cause for major pitch discrepancies throughout the range of the drum is a miss-aligned frame.
This causes the spider to pull unevenly. If you frame is out of alignment, you will need to send the drum to a professional for repair.