My Contour Choice Ordering Mini-Algorithm Diagram:

The cornerstone of my melody-centric method of designing alternative
tuning systems is the fractal contour choice ordering mini-algorithm
that I discovered in the mid-1980s while working on my larger 12TET
13-note all-interval-class/all-contour (containing the smaller forms
of the six 12TET interval classes: 1,2,3,4,5, and 6 semitones, in
BOTH their ascending AND descending forms) melody-generating
algorithm.

This ordering gives the most compact, minimally redundant,
stylistically neutral, and objective possible contour choice ordering
to use to test out various strings of intervals, 12 TET or otherwise.

Here is how the algorithm accumulates to 16 places(D=descending,
A=ascending):

D-A

DA-AD

DAAD-ADDA

DAADADDA-ADDADAAD

The pattern of repetition is identical at every order of magnitude
(2,4,8,16 places), so that makes it fractal. And contour equilibrium
is re-maintained every 2 places.

In order to create the alternative tuning system of your choice, you
would "plug in" however many/whichever intervals you want to use into
the contour choice ordering algorithm, and then plot out the pitch
class locations on a conventional linear alternative tuning scale
diagram.

The way that alternative tuning systems are normally diagrammed is an
indication of the harmony-centricity and conceptual backwardness of
the
whole alternative tuning system movement, because the intervals are
visualized/conceived of as being laid end-to-end LINEARLY AND
STATICLY, and NOT how they would appear IN MOTION in an actual melody
employing that tuning system.

I haven't been involved with alternative tuning systems for a few
years now, so it will take me a while to catch up and create an
actual concrete tuning system example for you, but I'll start working
on that now, using the most common "pure" or consonant just
intonation intervals to start with.

Bill Flavell

> I haven't been involved with alternative tuning systems for a
> few years now, so it will take me a while to catch up and create
> an actual concrete tuning system example for you, but I'll start
> working on that now, using the most common "pure" or consonant
> just intonation intervals to start with.

Sonuds interesting. I look forward to the example.

-Carl

>
> Sounds interesting. I look forward to the example.
>
> -Carl

Thanks for the response, Carl! :)

Do you have a web site?

Bill Flavell

> Thanks for the response, Carl! :)
>
> Do you have a web site?

Not really. Do you?

-Carl

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

> > Do you have a web site?
>
> Not really. Do you?
>
> -Carl

No, I don't, because I create Yahoo Groups
instead. I guess my most general Yahoo Group
would be my Melody Theory/Analysis one:

/MelodyTheoryAnalysis/

I'll try and get a decent introductory post
up today.

Thanks for your interest! :)

Bill Flavell

--- In tuning@yahoogroups.com, "Bill Flavell" <bill_flavell@e...> wrote:
>
> The cornerstone of my melody-centric method of designing alternative
> tuning systems is the fractal contour choice ordering mini-algorithm
> that I discovered in the mid-1980s while working on my larger 12TET
> 13-note all-interval-class/all-contour (containing the smaller forms
> of the six 12TET interval classes: 1,2,3,4,5, and 6 semitones, in
> BOTH their ascending AND descending forms) melody-generating
> algorithm.
>
> This ordering gives the most compact, minimally redundant,
> stylistically neutral, and objective possible contour choice ordering
> to use to test out various strings of intervals, 12 TET or otherwise.
>
>
> Here is how the algorithm accumulates to 16 places(D=descending,
> A=ascending):
>
>
> D-A
>
>
> DA-AD
>
>
> DAAD-ADDA
>
>
> DAADADDA-ADDADAAD

Hello Bill,

in mathematics this is known as the Thue-Morse sequence.

http://mathworld.wolfram.com/Thue-MorseSequence.html

Kalle

Thank you very much for the response, Kalle! :)

Bill Flavell

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:
> --- In tuning@yahoogroups.com, "Bill Flavell" <bill_flavell@e...>
wrote:
> >
> > The cornerstone of my melody-centric method of designing
alternative
> > tuning systems is the fractal contour choice ordering mini-
algorithm
> > that I discovered in the mid-1980s while working on my larger
12TET
> > 13-note all-interval-class/all-contour (containing the smaller
forms
> > of the six 12TET interval classes: 1,2,3,4,5, and 6 semitones, in
> > BOTH their ascending AND descending forms) melody-generating
> > algorithm.
> >
> > This ordering gives the most compact, minimally redundant,
> > stylistically neutral, and objective possible contour choice
ordering
> > to use to test out various strings of intervals, 12 TET or
otherwise.
> >
> >
> > Here is how the algorithm accumulates to 16 places(D=descending,
> > A=ascending):
> >
> >
> > D-A
> >
> >
> > DA-AD
> >
> >
> > DAAD-ADDA
> >
> >
> > DAADADDA-ADDADAAD
>
> Hello Bill,
>
> in mathematics this is known as the Thue-Morse sequence.
>
> http://mathworld.wolfram.com/Thue-MorseSequence.html
>
>
> Kalle