I recently learned that the wavelength of a note is half that of the same note one octave lower. Do the wavelengths of the notes in a chord have some sort of similarities? Is there another reason that the notes sound good together?
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Yes, in general simpler ratios between frequencies make them sound the more pleasant (in music we call this a consonant interval) and more complex ratios tend to clash (dissonant interval). The simplest ratio is for the octave which is 2/1. Other consonant intervals include 3/2 and 5/4. Meanwhile a dissonant minor second has a more complex ratio of 16/15. Chords are built by stacking intervals, for example a basic major chord has frequency ratios of 4/5/6. It is a little more complicated than that because about the 18th century we figured out that there are some problems with tuning our instruments to these pure ratios so instead we now use a system called equal temperament where distance between all notes is the same and ratios between them are an aproximation of those simple ratios.
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