Re: Rothenberg propriety

I haven't followed all this thread, but Rothenberg does not throw out
scales just because they are improper, he merely claims that they are
perceived differently and behave differently in composition. He also
specifically states in another section that there is a
listener-dependent threshold for interval perception. Hence, if one
doesn't hear melodic intervals as different if they vary in span by a
comma or less, then the impropriety of the diatonic in pythagorean
tuning would not be noticeable. This is an example of categorical
perception and his theory is primarily a theory of perception.

Balzano's coherency and Rothenberg propriety are the same. B apparently
came upon the idea independently, but does acknowledge Rothenberg more
or less obliquely in one of his papers.

As for CS, can someone email me an example of an improper one?

--John

>As for CS, can someone email me an example of an improper one?

For example 3 1 1 3 or 0.0 450.0 600.0 750.0 1200.0 cents.

Manuel