harmony and small integer frequency ratios

After going to the extreme lengths of actually listening to chords,
I've come to some conclusions on this subject. Forgive me if I'm
stating the obvious, but here are my opinions:

Just intervals of small interval ratios have a uniquely pure
sound.

This purity is not always desirable.

Differences of tuning as small as 1 cent do affect the sound
of the chord. I'm unable to try smaller intervals at present.

When an interval is detuned by more than a few cents, this
detuning has more of an impact on the sound of the chord than
the particular ratios involved, provided the latter are small
(I haven't worked out how small yet).

All of the above depends strongly on timbre

The idea that dissonance increases with prime limit is
erroneous. The 3-5-7 limits happen to get progressively out
of tune in 12tet, though, which may be the origin of this.


Perhaps the discussion would be more focused if people addressed
these points rather than wallowing around in misunderstandings
about exactly what constitutes a ratio.


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