AW.: RE: Re: that scale

In einer Nachricht vom 11/2/99 12:14:46 AM (MEZ) Mitteleurop�ische
Zeitschreibt PErlich@Acadian-Asset.com:

<<
>And that they
>consist of two step sizes: whole and half...

Dan, what could be gained, other that confusion, by saying that a scale with
three step sizes consists of two step sizes? >>

Pardon me for stepping in here, but a lot can be gained from a coarser
definition of step sizes. For one, it's a central feature in the the
tradition of defining tetrachordal genera. For another, it is very often more
useful to define a scale as a collection where a given scale step is
represented by more than one ratio -- e.g. the sixth degree in a major scale
might be represented by either 27/16 or 5/3, depending on the context, and
that difference is important but also important is the fact that both
rational values share qualities that can be group under the term "Major
sixth".

Daniel Wolf