Given the tone of the debate so far, I didn't want to get mixed up in it (I still don't), but I have to say that in any conceivable temperament the unisons and octaves will be pure.

M

On 13/05/2018 19:11, Rainer wrote:
On 13.05.2018 17:03, stephan.olbertz wrote:
    I don't understand how the practical side of lute temperaments would
    depent on calculating anything. You can just set a fourth fret you like
    and set all other frets by ear via unisons and octaves. No need to
    count beats either.

You cannot tune in any temperament except equal temperament by unisons and octaves.

This can be shown with a little trivial linear algebra.

Rainer



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