In Search of the Missing Fundamental: by Richard K. Jones
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Review 1

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.

Harmonics

  1. Objects which vibrate with whole number multiples (2f, 3f, 4f etc.) of their fundamental frequency (1f) are said to be harmonic.
  2. The secondary vibrations above the fundamental (1f) are called harmonics.
  3. When these secondary harmonic vibrations are put in sequence they form a harmonic series.
  4. It is the blending together of these harmonics that give definite pitch to a sound and create a composite harmonic wave form.
  5. Instruments that vibrate with a harmonic series  blend together a unique combination of these harmonics to create timbre or tone colour.
  6. An instrument’s harmonic recipe is its unique combination of harmonics at different amplitudes proportions (volumes).

Partials and Overtones

  1. Partials/overtones are frequencies that vibrate above a fundamental frequency (1f).
  2. Partials/overtones do not have to be whole number multiples of the fundamental (1f).  They can be fractions (1.567f), (2.345f) etc.
  3. Every harmonic is a partial/overtone, but every partial/overtone is NOT harmonic.
  4. 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

  1. 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
  2. The more non-harmonic overtones present, the more inharmonicity there is in a sound.
  3. All instruments have natural inharmonicity to some degree.
  4. Inharmonicity becomes more obvious when the vibrating system makes sound by being struck or plucked i.e. a piano string or guitar string.
  5. Inharmonicity is less obvious in a vibrating system which has a steady energy source  i.e a bowed string or a blown reed instrument.
  6. 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.

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