Melody-Centric Just Intonation Tuning Design Rule/Constraint List:

Before I respond to Carl's post re the first 5-tone tuning I
posted,I wanted to go back and clarify the additional
rules/constraints I decided to impose on myself before I diagrammed
that first 5-tone tuning.

These are just the constraints I'm choosing to use myself, and
certainly aren't necessary for anybody else to follow.

1. I'm using my contour choice ordering algorithm to supply the
directions (ascending, descending) that the intervals are going in,
which in this case will be DAAD (D=descending, A=ascending). During
my experiments with 12 TET interval strings I discovered that most
of the melodies which sounded the best to me had the first interval
descending, so that's the ordering I prefer, but if you prefer the
first interval to be ascending, use the form ADDA.

2. Since I'm diagramming these out by hand, I'm limiting myself to 5-
tone tunings for simplicity's sake in diagramming them. Also, a 5-
tone tuning perfectly fits the 4-place contour choice cycle
DAAD.

3. I'm only using the smaller forms of each interval class (an
interval class is a pair of intervals which, when combined together,
span an octave). For instance, with the interval class 3/2 and 4/3,
I'm only using the interval 4/3, because it's the smaller interval
in terms of cents distance spanned. That is because I'm
priveleging/prioritizing melodic "flow" over any overall ranking of
the relative consonance of the intervals.

Now I'll get back to responding to Carl's post.

Bill Flavell