Why do two musical notes one octave apart sound the same? (continued)

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When two musical notes are an octave apart, one has double the frequency of the other, but we hear them as the “same” note – a “C” for example. Why is it? (continued)

James whalley Hinchinbrooke, Quebec, Canada

The previous correspondence on this subject refers to the different models of harmonics that allow us to distinguish one instrument from another. This is not the only factor involved.

Many years ago when I was in school some of us were invited to a lecture on instrumental sounds at the University of Birmingham, UK. There, a violinist and a trumpeter, placed behind a screen, played a note at the same pitch on each instrument. It was quite easy to tell which instrument was playing.

We were then asked to listen to a recording of a similar sequence of long notes, but this time the beginning of each note was blocked. Surprisingly, it was now very difficult to distinguish any difference between the trumpet and the violin.

It seems that each instrument has its own “transients,” sounds that occur momentarily before the main note is produced, or that determine how it ends or declines. These can be even more important than the harmonic pattern to give the instrument its special character.

Eric Kvaalen Les Essarts-le-Roi, France

A previous answer explained how a low C contains each upper C and therefore they share a unique mathematical relationship with each other that they do not share with other notes.

But if I play an A with a fundamental frequency of 110Hz, it has harmonics not only at 220, 440 and so on, but at 330, 550 and 990, for example. Why do notes at 220 and 440 Hz sound like A, but notes at around 330, 550, and 990 (E, C #, and B respectively) sound different? Why playing a song two octaves higher (four times the frequency) sounds like it’s in the same key, while playing it three times higher sounds like a different key? I find that confusing.

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