Rustom Mody wrote:
I assume you chose the number 7 arbitrarily.
It would be possible to compute how 'good' a scale would sound; see
The equal-tempered scale evolved because one of its halftone steps (r^1)
is big enough to be audibly different, and, more important, the scale
allows many consonant intervals.
To be precise, equal temperament is not as consonant as other tunings,
but it is used because it is equally usable in all scales. Wikipedia
suggests that for different equal-tempered scales, you should use not 7
but 19, 31, or 53 steps.
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