RE: Answering J. Reinhard and others

Bringing up the tempo of a piece is actually a good point. I have claimed
that just intervals can be tuned with greater precision, by ear, than
intervals that are based on logarithmic (equal cents) constructions, only if
simultaneities (and the resulting beats) are examined. Another caveat is
that the simulataneities must be listened to for long periods of time, while
in melodies, equal vs. unequal intervals can be heard even at fast tempi.

Tuning two guitar strings a quartertone apart does not require tuning to the
11:8. As long as the beat rate of one quartertone is between those of the
two adjacent quartertones, the result will not be more than 0.7 cents off.
This is better than the 1.3 cent error from using 11:8, and usually better
than the 0.6 cent error from using 11:6. Needless to say, all of these
methods are better than just trying to divide the semitone into two
melodically (=logarithmically) equal parts, but only if one can listen to
the intervals for longer than a fraction of a second at a time.


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