Music
Most western music is based on the 12-tone equal temperament (12TET) tuning,
where ratios between frequencies are powers of 2^(1/12)=1.05956... making
intervals sound the same however the music is transposed. However, sums
and differences of frequencies are almost all not exactly in the scale.
Here, we propose a class of tunings (focusing on one involving the golden
ratio) where many sums and differences are in the scale,
but there are many different sizes of interval.
If you would like to try out the golden ratio tuning, download the
supplementary files, which include "patches" for
https://www.websynths.com/microtonal/, usable with either a computer keyboard or a MIDI keyboard. This is
an external site, for which we are not responsible.
If you have any questions
or suggestions for using this tuning, we would be very happy to hear from
you.
- Algebraic tunings C. P. Dettmann and L. Taylor-West, J. Math. Music (published online). pdf supp.7z.
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