Re: Tunings and Cognition (653 #11)

Hello -

I've done a lot of listening to
various just and tempered fifths,
major and minor thirds, etc. both
synthesized and on piano. Without
having done formal mathematical
analyses on various aspects of the
effects of tuning variations on the
intervals, I've gained the impression
that tuning deviations for both
melodic and harmonic intervals become
increasingly noticeable as they grow
larger and that both are important to
the musical effect created. I've also
observed that the locations of mistunings
from what is expected (especially for songs)
greatly affect how they are perceived - as
sounding flattish or sounding fine, etc. -
e.g. if a melodic line has a high point - as
in the second line of "Flow Gently, Sweet Afton",
where the melody climbs to a fifth above the
tonic - a D5 in the key of G - any kind of
deviation which tends to flatten that peak note
will stand out (in this case and at this point
sounding "off" in mean tone temperament, like
a basketball which almost, but doesn't quite
travel high enough to make it into the basket.

I believe the whole matter of musical effects
of variations of intervals is complex and is affected
by quite a few different things.