AW.: RE: RE: Re: that scale

In einer Nachricht vom 11/3/99 7:55:37 PM (MEZ) Mitteleurop�ische
Zeitschreibt PErlich@Acadian-Asset.com:

<< Dan Stearns wrote,

>Well yes, but this is no different than the (1/1, 9/8, 5/4, 4/3, 3/2,
>5/3, 15/8, 2/1) syntonic major... and the point of Daniel Wolf's post
>to which you were agreeing... no? What am I missing here!

I was agreeing with Daniel Wolf that the sixth degree of the major scale
should be able to act as _either_ 5/3 _or_ 27/16. Only in the meantone-type
ETs do the major scales you came up with have this property. >>

Not quite right. I wrote:

"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..."

I have no problem in recognizing a major scale in a more limited collection
where only one of the values is represented. If you want to define "major" by
the presence of both ratios (as either exact ratios or tempered
representations), you will then be limiting the definition to a rather narrow
repertoire.