Re: SCALA 19 tone 7-limit scale (was 17 limit j.i. scale - sorry!)

Hi Joseph,

> Yes, I wrote some pieces with it too, before Paul Erlich gave me the
> knowledge that it was a little, er, "peculiar..."

All Paul showed is that it had a smaller number of triads in the 1 3 5 7 lattice
and that one could construct 7-limit scales with 19 notes which are close to
19-tet and with many more triads, which of course he did, and I agree that they
are remarkable scales.

Who knows what the original intentions were of the author of the scale. Presumably
maximising the number of <3,5,7> lattice triads wasn't one of them particularly,
or if that was the objective, and the scale was just poorly constructed, maybe it
will still turn out to have interesting emergent properties.

It's not surprising that it would look poor on that criterion, and that scales constructed
to maximise the number of lattice triads will look better.

But it needn't be ones only objective, to maximise the number of lattice triads in a
scale.

Otherwise all j.i. music would have to be written in harmonic fragment scales, such as
1/1 5/4 11/8 3/2 7/4 (say) as they maximise the number of lattice triads (because every
three note subset is a lattice triad). That particular one is a five note scale with
5*4*3/3*2*1 = 10 otonal triads - the maximum possible in a five note scale.

It's lattice diagram would be a pentad, or a 5-simplex as a mathematician would call it.

Just to suggest some ideas (for scales in general):

One might be interested in some particular type of chord.

One might be interested in near consonances rather than exact ones.

One might want to use particular patterns of scale steps in melodic movement.

One might also be interested in working in a scale with few consonant triads, in order to
help
focus ones ideas.

One might want a scale that gives nice approximations to inharmonic timbres such as
bell sounds, or to gamelan scales.

I'm sure one could come up with many more ideas here.

I don't think one could ever come to a final conclusion about whether a scale is good to
use or not, as there are so many variables to take into consideration.

I think best is to think of a j.i. composer as having the entire space of
rational ratios and n-tet subdivisions, plus irrationals like golden ratio etc.
as an infinite scale to work in, and any other scale as a convenient subset
to aid composition or to help players of the pieces.

Re the text descriptions of scales

> If this could happen, and people would do it, it would be terrific...

Yes, I think so too!

> Er... agreed. Some simple, fast method for making colorful lattices,
> like a "visual construction set" would be a great asset. Let's say
> with lines that one could just easily link together... like a Viseo
> program or something... and perhaps an automatic place for the ratio.

> Well, this is just dreaming, but sometimes things can come of it...

Yes, sounds a nice idea!

I'll keep it in mind - may turn out to be something I could do in either the
VRML Trees program or FTS.

Meanwhile though, it's possible that something like this could have been
developed already, and we just don't know about it yet - lattices are
pretty generally used, and the idea of labelling one of the vertices is a
natural one to have.

If it was in VRML, then adding MIDI clips would be easy too.

If not, I suppose a good musical lattice construction kit would be
found useful in other areas too, like chemistry.

Robert