Scales scales scales

I would say that a scale is a selection of ladders placed side by side whose rungs are obviously pitches ordered from low to high confined within a period, so that no matter which one you climb or descend, you perceive the same musical emotion.

Cordially,
Ozan
----- Original Message -----
From: Yahya Abdal-Aziz
To: tuning@yahoogroups.com
Sent: 21 Mayıs 2005 Cumartesi 15:30
Subject: [tuning] Re: question about just intonation scales

Graham,

Aline wrote:
> I was wondering what makes a sequence of notes a (just intonation)
> scale. Maybe somebody can tell me about properties of just intonation
> scales, like conditions they have to satisfy?

You replied:
> First of, I don't see why they have to be ordered. That is a scale is
> a set of notes, not a sequence, and therefore not uniquely tied to
> melody. Surprisingly enough, there seems to be disagreement on this.
> ...
> Graham

Let me give you an example where the scale has to be a sequence
of notes, not just a set of notes: the melodic minor scale of
common practice. It's usually taught that the scale has two
distinct forms, one ascending and the other descending. For
example, the C minor scale runs thus -

Ascending: C D Eb F G A B C'
Descending: C' Bb Ab G F Eb D C

- and it's in _both_ those forms that countless music students
for centuries have practiced it.

But of course, you knew that! Just thought I'd remind you :-)

.....

>From the point of view of _tuning_ the scale, what matters are
the pitches of the notes that comprise it, and their (intervallic)
relationship. The order is a secondary consideration. The set
of notes in any scale, I prefer to call the gamut. In the case of
C minor, we have more than the usual 7 pitches per octave; 9 in
fact. It is an abstraction from the scale. Until historically recent
advances in technology (logarithms, calculators and computers)
simplified calculation, scales have usually arisen from _melodic
practice_, rather than from theoretical harmonic ideas.

Which is not to say that building scales based purely on theoretical
reasons is wrong!; merely that you won't know what kind of music
you can make with them until you hear them in practice. But no
matter what its genesis, any scale is just another musical resource.
Human hearing is the essential medium through which those
resources must pass, and individual taste is the final arbiter of
which resources are useful.

To me, a scale is at least two sequences of notes - one ascending,
another descending - drawn from a gamut, which is a set of notes.

(I say "at least", since in my experience, some Indian singers use
more than one alteration (like that of A Ab in C minor) of a single
scale degree, depending on the particular ornament they're using
at the time. I believe that classically-trained Western violinists
do something similar; whether deliberately or not, I couldn't say.)

Regards,
Yahya