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I have recently (about four months ago) taken a healthy interest in music, and about two weeks ago realized the strong interconnections between mathematics and music. It really is astounding. I suppose there are a lot of people on this forum who are similarly interested in both and I'd like to put some questions to them and anyone else who can point me in the right direction.

What I understand of the relation between the two has to do with my limited knowledge of harmonics. The note 'A' is taken to be the base line and its frequency is fixed at 440Hz. Doubling the frequency (the first harmonic) gives the same note, just one octave higher.

There are 12 fundamental notes, and their frequencies are related by the twelfth root of two. For example, if you take the note 'A', whose frequency is set at 440Hz and you multiply it by [tex]2^{\frac{1}{12}}[/tex], you get the next note 'A#' and so on until when you multiply the twelfth time, you get the same note 'A' an octave higher. This mathematical arrangement, I believe, is called the 'perfect temperament', as it forms a perfect geometrical progression between the same notes on different octaves.

When we combine these different notes, we get chords. What I want to ask is this, why do we choose particular notes for a chord, and why do we dwell on particular intervals on a scale (such as 1st, 3rd, and 5th note of a scale for a major chord) to give a particular type of chord?

I may have misunderstood some of the relations between the two so please feel free to correct me where ever I've made a mistake.