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.

  1. Algebraic tunings C. P. Dettmann and L. Taylor-West, J. Math. Music 18 203-216 (2024). pdf supp.7z.

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