A short review of the concepts and terms introduced in chapter 1 may aid the reader in developing his/her own ability to listen to and better understand timpani pitch.
- Objects which vibrate with whole number multiples (2f, 3f, 4f etc.) of their fundamental frequency (1f) are said to be harmonic.
- The secondary vibrations above the fundamental (1f) are called harmonics.
- When these secondary harmonic vibrations are put in sequence they form a harmonic series.
- It is the blending together of these harmonics that give definite pitch to a sound and create a composite harmonic wave form.
- Instruments that vibrate with a harmonic series blend together a unique combination of these harmonics to create timbre or tone colour.
- An instrument’s harmonic recipe is its unique combination of harmonics at different amplitudes proportions (volumes).
Partials and Overtones
- Partials/overtones are frequencies that vibrate above a fundamental frequency (1f).
- Partials/overtones do not have to be whole number multiples of the fundamental (1f). They can be fractions (1.567f), (2.345f) etc.
- Every harmonic is a partial/overtone, but every partial/overtone is NOT harmonic.
- In order for a partial/overtone to be harmonic it HAS to be a whole number multiple (2f, 3f, 4f etc.) of the fundamental frequency (1f).
Differentiating between partials/overtones and harmonics is important because Chapter 2 will show that timpani head vibrations are not harmonic in fact, they are extremely non-harmonic. It is the taming of these inherent inharmonic partials into a near or quasi harmonic partials that is the challenge when clearing timpani.
- Inharmonicity is the degree to which the frequencies of the overtones of a fundamental differ from whole-number multiples of the fundamental’s frequency. i.e. 1f, 2.767f, 3.123f and not 1f, 2f, 3f
- The more non-harmonic overtones present, the more inharmonicity there is in a sound.
- All instruments have natural inharmonicity to some degree.
- Inharmonicity becomes more obvious when the vibrating system makes sound by being struck or plucked i.e. a piano string or guitar string.
- Inharmonicity is less obvious in a vibrating system which has a steady energy source i.e a bowed string or a blown reed instrument.
- Inharmonicity is “generally” not desirable in musical sounds. It destroys intonation, pitch center and blend.
Harmonic partials/overtones are not inherent in timpani tone so herein lies the problem of fitting a round peg into the square hole as it were. The sound created by timpani is not generated by a vibrating column of air or string, but rather from striking vibrating circular membranes. Vibrating circular membranes 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.
Chapter 2 will investigate the acoustic properties of vibrating circular membranes which is the mechanism or system for creating timpani sound.