In Search of the Missing Fundamental: by Richard K. Jones
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Frequency, Pitch and Colour

Complex tones, or composite waveforms (harmonic and non-harmonic), consist of many sine waves of different frequency added together. These individual sine waves are called frequencies components. What are consider to be musical sounds generally don’t have just one or two frequency components. Sounds that have only a few frequency components are not at all interesting or pleasing to listen to. They have no musical colour or timbre. Conversely, sounds that have too many frequency components, like the sound of a strong windstorm 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 as shown above. These different pitches are called overtones or partials and are preferably harmonic as described above, but they can be either harmonic or non-harmonic. The human auditory system generally blends them together so well that you do not hear them as separate notes at all. Instead, the overtones or partials give the note its color or timbre. Notes that 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 (integer) 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 composite waveforms that are inharmonic sounds but yet they add a peculiar or colorful amount of inharmonicity or harmonic distortion to music, which is found to be palatable to the ear. Conversely, most modern professional-quality wind, brass and string instruments are designed to limit inharmonicity as much as possible in order to bring harmonicity to music.  In the hands of a master, timpani can bridge the gap and provide both.

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