Musical acoustics

The pioneer of music acoustics was Hermann von Helmholtz, a German polymath of the 19th century who was an influential physician, physicist, physiologist, musician, mathematician and philosopher.

When the original sound sources are perfectly periodic, the note consists of several related sine waves (which mathematically add to each other) called the fundamental and the harmonics, partials, or overtones.

[citation needed] Variations in air pressure against the ear drum, and the subsequent physical and neurological processing and interpretation, give rise to the subjective experience called sound.

In a very simple case, the sound of a sine wave, which is considered the most basic model of a sound waveform, causes the air pressure to increase and decrease in a regular fashion, and is heard as a very pure tone.

All of the frequency components that make up the total waveform, including the fundamental and the overtones, are called partials.

Overtones that are perfect integer multiples of the fundamental are called harmonics.

Additionally, the two notes from acoustical instruments will have overtone partials that will include many that share the same frequency.

Although the mechanism of human hearing that accomplishes it is still incompletely understood, practical musical observations for nearly 2000 years[10] The combination of composite waves with short fundamental frequencies and shared or closely related partials is what causes the sensation of harmony: When two frequencies are near to a simple fraction, but not exact, the composite wave cycles slowly enough to hear the cancellation of the waves as a steady pulsing instead of a tone.

When two notes are close in pitch they beat slowly enough that a human can measure the frequency difference by ear, with a stopwatch; beat timing is how tuning pianos, harps, and harpsichords to complicated temperaments was managed before affordable tuning meters.

Helmholtz proposed that maximum dissonance would arise between two pure tones when the beat rate is roughly 35 Hz.

The diatonic scale appears in writing throughout history, consisting of seven tones in each octave.

As forms of the fifth and third are naturally present in the overtone series of harmonic resonators, this is a very simple process.

Temperaments, though they obscure the acoustical purity of just intervals, often have desirable properties, such as a closed circle of fifths.