On 08.03.2018 13:18, Martin Shepherd wrote:
I should just point out that there are no pure fifths in meantone temperaments.
The fifths are close to pure in equal temperament, just 2 cents narrow, but in
meantone temperaments they are much more narrow.
I usually use 6th comma, and I do find the fifths useful as a tuning check, but
only because I know by ear how flat they should sound. I often play (as
arpeggios) a sequence:
c1c2a3, a1a2c4, d2d3a4, etc.
To check that all the fifths are equally narrow. (and the octaves are perfect).
Many years ago I checked which tuning methods have perfect octaves and unisons.
That's a simple problem in linear algebra - trivial.
There is only one solution: Equal temperament.
Rainer
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