The musical scale

The unnatural scale

Western musical scales (major and minor) are constructed from musical intervals, which (it can be argued) are natural, because they are based on those found in the chord of nature.

But nowhere in nature do we actually encounter a sequence of notes or pitches the same as the musical scales of the kind we now use in music. The scales we use, as an arrangement or sequence of tones, are an invention of Man.

The intervals found in the chord of nature are most obvious in the tones of musical strings and pipes. We can take any two suitable strings or pipes and tune them so that the musical interval between them is the same as one found in the (lower part of) the chord of nature.

Can we arrange a set of strings or pipes with one pipe or string for each note of our scale, so that any two have one of these intervals from the chord of nature between them? We can try to make such an arrangement, but the resulting intervals between the notes, will never all be the precisely the same as those found in the chord of nature. It turns out that no such arrangement can be made, in which all the intervals formed between the notes will be the same as those found in the chord of nature.

In other words, if we choose to regard the intervals in the chord of nature as "in tune", then as a result of arranging the notes in the scale, in this way, some of the intervals between them, will always be "out of tune", by the same reckoning.

Is this some kind of Divine enigma?

Not at all. It is merely the entirely natural result of trying to place the strings or pipes in this Man-made arrangement.

Note:

The chord of nature occurs in strings and pipes, but is actually slightly different in different strings and pipes. It does not occur in all musical tones. It does not occur in the tones of metallophones, xylophones, and many other musical instruments.