Vibration

Vibrations per second

The page Klang-Spektrum gives the basic example: if flute and violin both play the A above middle C, both vibrate 440 times per second. The pitch is identical, measurably identical. The frequency is given in hertz; the page Tuning & Cents describes the standard pitch A4 as today usually 440 hertz, many orchestras tune to 442 or 443, historical ensembles to 415. See Standard pitch.

The article Why the fifth sounds hollow explains what intervals have to do with vibrations: two notes sound the more fused together, the simpler the ratio of their frequencies.

According to the article, this connection is neither a convention nor a matter of habit. At 3:2 the common pattern of the two waves repeats after every two and three vibrations respectively, a very short common period that the ear perceives as one sound. With the tritone there is no common period at all, which is why it stays floating and undecided.

Beats: vibrations compared

The page Tuning & Cents describes how vibrations mix audibly: the beat frequency corresponds to the difference of the two frequencies. If 440 and 442 hertz sound together, the sound pulses twice per second. Piano tuners work with exactly this: they count beats per second.

Vibration and timbre

According to Klang-Spektrum a string never vibrates only as a whole, but at the same time in halves, thirds and quarters. The sum of these partial vibrations gives the note its colour. See Partial and Harmonic series.

Common mistakes

• Mixing up frequency and loudness: The frequency determines the pitch, not the loudness.
• Hearing the octave as “equally high”: It has double the frequency and only sounds similar.
• Taking beats for a mistake: They are a tool for tuning.