Re: [tuning] Re: Diatonicity

Jacky Ligon wrote,

> Please explain the difference between "strictly proper" and
"proper".

I'm sure Carl will post some helpful and insightful details to all
your questions here, but here's a brief bit on the differences between
some the terms anyway...

A scale like the familiar 12-tET diatonic scale is a "proper" scale
because it has at least one instance of ambiguity, i.e., shared
intervals between distinct classes; in this case the augmented 4th and
the diminished 5th which are both represented by the 6/12ths half
octave.

A scale like the syntonic major scale is a "strictly proper" scale
because it has no instances of ambiguity; no overlapping or shared
intervals between interval classes. To my mind this is made all the
more clear and distinct if you look at how this sits in say 19-tET,
where the distinction between the 64/45 and the 45/32 is a very
non-commatic 1/19ths of an octave.

A scale like the Pythagorean major scale is an "improper" scale
because it has overlapping (or conflicting) interval classes, i.e.,
the augmented 4th is larger than the diminished 5th. And much like the
"strictly proper" syntonic major example, to my mind this is made all
the more clear and distinct if you look at how the Pythagorean major
sits in say 17-tET, where the distinction between the 729/512 and the
1024/729 is a full 1/17ths of an octave.

hope that's helpful,

ds

Thanks Dan!!!,

Yes, this has been hugely helpful. If I remember correctly, when I
analyized the "All Prime Scale" with the Scala program, it informed
me that the scale was "strictly proper".

--- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:
> Jacky Ligon wrote,
>
> > Please explain the difference between "strictly proper" and
> "proper".
>
> A scale like the familiar 12-tET diatonic scale is a "proper" scale
> because it has at least one instance of ambiguity, i.e., shared
> intervals between distinct classes; in this case the augmented 4th
and
> the diminished 5th which are both represented by the 6/12ths half
> octave.
>
> A scale like the syntonic major scale is a "strictly proper" scale
> because it has no instances of ambiguity; no overlapping or shared
> intervals between interval classes. To my mind this is made all the
> more clear and distinct if you look at how this sits in say 19-tET,
> where the distinction between the 64/45 and the 45/32 is a very
> non-commatic 1/19ths of an octave.
>
> A scale like the Pythagorean major scale is an "improper" scale
> because it has overlapping (or conflicting) interval classes, i.e.,
> the augmented 4th is larger than the diminished 5th. And much like
the
> "strictly proper" syntonic major example, to my mind this is made
all
> the more clear and distinct if you look at how the Pythagorean major
> sits in say 17-tET, where the distinction between the 729/512 and
the
> 1024/729 is a full 1/17ths of an octave.
>
>
> hope that's helpful,
>
> ds