23 Mar
2012
23 Mar
'12
4:03 p.m.
Rustom Mody wrote:
If a is say 440 Hz and r is 12th root of 2
then the usual equal tempered scale would be
a
ar^2
ar^4
ar^5
ar^7
ar^9
ar^11
ar^12 = 2a
What if we change r to 7th root of 2
and replace the powers 2 4 5 7 9 11 12 by 1 2 3 4 5 6 7?
I expect it will sound nonsensical but I really dont know...
I assume you chose the number 7 arbitrarily.
It would be possible to compute how 'good' a scale would sound; see
<http://en.wikipedia.org/wiki/Consonance_and_dissonance#Physiological_basis_of_dissonance>.
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
(<http://en.wikipedia.org/wiki/Musical_tuning#Systems_for_the_twelve-note_chromatic_scale>)
suggests that for different equal-tempered scales, you should use not 7
but 19, 31, or 53 steps.
Regards,
Clemens