Why Use a Contour Choice Ordering Algorithm?

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:

>The precise details of why this algorithm is your favorite aren't
clear
>yet -- hoping you'll take the time to explain that.

I guess you're referring to my contour choice ordering algorithm.

That goes back to the late 1980s when I had narrowed my choice of
12TET intervals to use to generate melodies to the six smaller forms
of the 12TET interval classes (1,2,3,4,5, and 6 semitones).

Six intervals in succession can have 2 to the 6th power or 64
possible contours, so what I wanted to do was to find a bare minimum
standard or reference contour choice ordering that would have the
minimum stylistic "expression", and the maximum stylistic neutrality.

I was interested in concentraing on the other melodic variables: (1)
interval content, (2) interval order as melodic generators and pitch
class
as the resulting scales embodied in the melodies.

I come from a mechanical engineering/drafting background (and more
specifically automotive hot rod engineering) and this would be
referred
to as "locking down" the contour choice ordering variable in order to
be able to perceive the interval content/order/pitch class resultant
variations more clearly.

I didn't stumble on the ordering through algebraic means. I just used
a simple graphic technique of "zooming out" from the first 2-place
ordering (DA), and then making that the first place item in the next
order of magnitude (DA-AD), and repeating that on every order of
magnitude (2,4,8,16,...etc.).

I hope this helps, Carl! :) If not, fire away some more questions! :)

Bill Flavell

>> The precise details of why this algorithm is your favorite
>> aren't clear yet -- hoping you'll take the time to explain
>> that.
>
> I guess you're referring to my contour choice ordering algorithm.

Yes.

> That goes back to the late 1980s when I had narrowed my choice
> of 12TET intervals to use to generate melodies to the six smaller
> forms of the 12TET interval classes (1,2,3,4,5, and 6 semitones).
>
> Six intervals in succession can have 2 to the 6th power or 64
> possible contours,

Isn't that 6^6 possible contours, or maybe 6! possible contours
if you only use each interval once?

> so what I wanted to do was to find a bare minimum standard or
> reference contour choice ordering that would have the minimum
> stylistic "expression", and the maximum stylistic neutrality.
>
> I was interested in concentraing on the other melodic
> variables: (1) interval content, (2) interval order as melodic
> generators and pitch class as the resulting scales embodied in
> the melodies.
//
> I just used a simple graphic technique of "zooming out" from
> the first 2-place ordering (DA), and then making that the first
> place item in the next order of magnitude (DA-AD), and repeating
> that on every order of magnitude (2,4,8,16,...etc.).
>
> I hope this helps, Carl! :) If not, fire away some more
> questions! :)

I'm still not sure I could produce a string of Ds and As of
any length according to your procedure. Can you give some
examples of increasing lengths?

Also, this shows only how to get the interval directions. It
does not show how to choose the intervals. Correct?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:

> >> The precise details of why this algorithm is your favorite
> >> aren't clear yet -- hoping you'll take the time to explain
> >> that.
> >
> > I guess you're referring to my contour choice ordering algorithm.
>
> Yes.
>
> > That goes back to the late 1980s when I had narrowed my choice
> > of 12TET intervals to use to generate melodies to the six smaller
> > forms of the 12TET interval classes (1,2,3,4,5, and 6 semitones).
> >
> > Six intervals in succession can have 2 to the 6th power or 64
> > possible contours,
>
> Isn't that 6^6 possible contours, or maybe 6! possible contours
> if you only use each interval once?

My apologies here. I should have said that I was only thinking of
using
each of the six intervals once in the string, so there would only
need to
be 6 contour choices, hence the 2 to the 6th power total possible
contour orderings per 6-interval string.

> > so what I wanted to do was to find a bare minimum standard or
> > reference contour choice ordering that would have the minimum
> > stylistic "expression", and the maximum stylistic neutrality.
> >
> > I was interested in concentraing on the other melodic
> > variables: (1) interval content, (2) interval order as melodic
> > generators and pitch class as the resulting scales embodied in
> > the melodies.
> //
> > I just used a simple graphic technique of "zooming out" from
> > the first 2-place ordering (DA), and then making that the first
> > place item in the next order of magnitude (DA-AD), and repeating
> > that on every order of magnitude (2,4,8,16,...etc.).
> >
> > I hope this helps, Carl! :) If not, fire away some more
> > questions! :)
>
> I'm still not sure I could produce a string of Ds and As of
> any length according to your procedure.

Sure. Each successive order of magnitude doubles the length of the
contour choice string. You add the opposite ordering or inversion to
whatever length of string you start with.

> Can you give some examples of increasing lengths?

Sure. Here's one to 64 places (I've put dashes every 4 places and
underscores every 16 places, so you can see the patterns easier).
Also note that the 2nd row is the reverse or inversion of the first
row. This holds true at all orders of magnitude that are powers of 2:

ADDA-DAAD-DAAD-ADDA_DAAD-ADDA-ADDA-DAAD_
DAAD-ADDA-ADDA-DAAD_ADDA-DAAD-DAAD-ADDA

> Also, this shows only how to get the interval directions. It
> does not show how to choose the intervals. Correct?

Right. That's up to the user. But contour is NOT tuning-system-
specific,
so the algorithm can be used either to generate 12TET
melodies/subscales
OR to create non-12TET just or other froms of tunings. I'm only
interested
in just intervals right now, but I don't see why the algorithm
couldn't
be used for non-just microtonal intervals, too.

Thanks very much for the response and interest! :)

Bill Flavell