What is a scale?

A friend emailed me the following. I can't answer it. Anyone care to
have a go?

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This will sound silly but this question has been bothering me for
quite
some time. I've studied music theory extensively over the years and
have
pretty much accepted most theories as fact without question. However
one
question I have which has always puzzled me is why a scale? After one
determines a "bunch" of intervals that sound pleasing in relation to
the
tonic the theorists of all time then arranges the frequencies in
ascending order from the lowest frequency to the highest. Ex: C, D, E,
F, G, A, B, C Why?

Is the reason because they want to "fit" all the pleasing intervals
"between the tonic and octave to "lock in" the that particular sound?

If so, I and any one else can also arrange the frequencies so they fit
between the tonic and octave but they are NOT in ascending order from
the lowest to the highest frequency. They are scattered here and there
in no particular order between the tonic and octave. Ex: C, F, D, A, G
,
B, E, C Why not this way?

Is it because when a scale starts on the tonic the brain will remember
that frequency as "Home Base" and subconsciously relate all remaining
frequencies to it? If so, then I can still construct a scale beginning
with the tonic BUT the remaining frequencies can still be scattered in
no particular order. Again like : C, F, D, A, G , B, E, C - As long
as
the tonic and the octave are both on opposite ends????

We can also get into the topic of whole step, half step, etc (which I
know determines major/minor sound) but how does that relate to why
scales are organized into ascending and descending order?

This confuses me. I guess my real question is, "What is defined as a
"scale"?
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-- Dave Keenan

This person should be made aware that only relatively recently has C
come to be considered the "best" tonic for the diatonic scale -- most
others were previously considered "better" -- only with the
development of the Western common-practice style, characterized by
tritones resolving in contrary motion through half-steps at cadences -
- did "C major" become the "default" mode.

As for why the scale is in ascending/descending order, I guess that's
simply the definition of "scale"! It's not a melody, it's simply the
set of stepping stones, arranged in order of pitch, on which a melody
may be built!

Here is my belief along these lines.

First of all, I percieve this to have been, basically, two questions:

* Why use a tuning, meaning a preferential set of pitches, rather than just using whatever
arbitrary pitches you want at a time?
* Why have a scale, meaning an ordered sequence of the pitches in your tuning?

I believe that there are three reasons to choose a tuning: First of all, from a historical
perspective, only a small percentage of instruments could, except through "extended techiques"
produce any arbitrary pitch. Johnny Reinhard has proven that extended techniques can indeed
produce pretty nearly any pitch (at least on some instruments), but what Johnny does is innovative
much more than historical.

Secondly, limiting yourself to a framework of accepted and excluded pitches makes the problem a
lot more tractable.

The third, and I believe definitely the most important, answer to the question, "why build music
around a tuning?" is much the same answer as to the question, "why play games with rules?"
Because it makes the results more interesting. If a game player can do any ol' arbitrary thing
s/he wants, the result is also arbitrary and thereby seemingly pointless. Only within a framework
of limitations can you give the impression of clever musical ideas and development of those
ideas. Without a framework of limitations, you can't have a clever solution to a problem because
there are no problems to be solved.

So then what about the second question, "why have a scale?" Well, there's also a number of ways
to look at that. First of all, such a scale could highlight the notes of a subset mode, in which
case, you're extending the limitation idea. Second, a scale is a very basic melody, and can be
manipulated to build more-interesting melodies. Third, from a historical perspective, partly
because of the second reason, it has become a valuable element of musical learning. Do we have to
learn that way? Well no, but learning that way does "work," historically.

> From: Gary Morrison <mr88cet@austin.rr.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, July 20, 2001 6:10 AM
> Subject: Re: [tuning] What is a scale?
>
>
> The third, and I believe definitely the most important,
> answer to the question, "why build music around a tuning?"
> is much the same answer as to the question, "why play
> games with rules?" Because it makes the results more
> interesting. If a game player can do any ol' arbitrary
> thing s/he wants, the result is also arbitrary and thereby
> seemingly pointless. Only within a framework of limitations
> can you give the impression of clever musical ideas and
> development of those ideas. Without a framework of limitations,
> you can't have a clever solution to a problem because
> there are no problems to be solved.

Hi Gary,

Thanks for a great post. This is the clearest explanation
I've ever seen relating to Schoenberg's frequent invocation
of the phrase "compositional problems".

Of course, that term refers to many other aspects of composition
besides tuning, but tuning was *definitely* a big part of what
Schoenberg was considering!

-monz
http://www.monz.org
"All roads lead to n^0"

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--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> This person should be made aware that only relatively recently has C
> come to be considered the "best" tonic for the diatonic scale ...

Thanks for those points Paul. I'll pass them on.

My friend just found this excellent answer by one Andrew Milne.
<http://dspace.dial.pipex.com/andymilne/Scales.shtml#what%20is%20a%20s
cale>

-- Dave Keenan