Diatonic definition

Ehem... first a note on post 57696

pi is known to be both irrational and trascendental. However, as far
as I know, it is not known whether pi x e is trascendental.

Then, onto the diatonic issue:

As I think it's clear from the discussion, there are several
definitions of the term. The greek definition of (or what we think
they imply by) such expressions as "diatonic" and "chromatic"
differs from the 'modern' (?) use. There is no problem with this
divergence, as long as we don´t insist on arguing whether a certain
scale is diatonic because it has x different letters or because "x
tethrachord... this and that".

I assume it would be difficult to generate a unique definition
comprenhating this variety of terming. Who knows, consensus may
overrule this statement.

As for what I think of when hearing the word 'diatonic', I would
like to sketch the following lines of reasoning:

1) First, I assume a 'complete' series of notes conforming a scale
[this is the 'chromatic' scale]
2) I recognise a pattern of notation defining base notes and altered
notes. In most cases, I would expect that the notation have some
connection with the tritriadic (or 12-eq) naming; however, i accept
this might be just a preconception.
3) I interpret (as stated repeatedly before this post) 'diatonic'
as 'implying a selection of notes from the 'chromatic' scale
explained above, such that:'
'a) it contains all (7 in my "preconception") names of notes'
'b) the scheme of altered notes included is such that no unison
or case of "higher note followed by lower" is present [eg. b#-c or
e##-f ruled out]'

Of course, according to our accustomed, tired 12-eq ears, many
scales 'diatonic' following this definition, won't sound at all like
the diatonic character we remember from 12-eq cdefgab pattern.

Lastly, assume this is to be taken as my humble view on the issue; I
welcome critisisms or comments.

Dear Maximiliano, it is a pleasure to meet a Westerner who can agree to such a possibility even though the scales are sure to sound quite alien.

Cordially,
Ozan
----- Original Message -----
From: Maximiliano G. Miranda Zanetti
To: tuning@yahoogroups.com
Sent: 23 Mart 2005 Çarşamba 17:35
Subject: [tuning] Diatonic definition

Of course, according to our accustomed, tired 12-eq ears, many
scales 'diatonic' following this definition, won't sound at all like
the diatonic character we remember from 12-eq cdefgab pattern.

--- In tuning@yahoogroups.com, "Maximiliano G. Miranda Zanetti"
<giordanobruno76@y...> wrote:
>
> Ehem... first a note on post 57696
>
> pi is known to be both irrational and trascendental. However, as far
> as I know, it is not known whether pi x e is trascendental.

It's trivial to prove that pi+e and pi x e cannot both be algebraic,
but it seems to be way harder to show neither is.