thirteen equal

David J. Finnamore wrote,

<< The key to 13 EDO (Equal Divisions of the Octave, since we seem to
have a few newbies posting :-), in my experience, is to emphasize
thirds and to minimize fourths and fifths. >>

The main scale I used in "With Eyes so Blue and Dreaming" is 0 3 4 6 7
9 11 13. And though this was yet another purely ear derived scale, the
nice 11 and 13th (and the 'not so nice' 3rd) harmonic approximations
did jump right out at me, and if one wanted to look at it as a
consistent temperament of sorts one could actually call it a harmonic
series subset of 1/1 19/16 5/4 11/8 23/16 13/8 29/16 2/1. But this is
not the way I approached it at all -- it was the augmented second
scale-step that really fired me up with this scale. That particular
melancholic ache that I associate with many eastern European scales is
very
vividly recast in this scale.

Most all the 11 and 13 equal scales that I use have an 'exotic' scale
quality (and I mean this in the traditional "Hungarian major" etc.
sense), where the unfamiliar proportions and alignments of 11 and 13
equal add something special to the equation. When I said crude but
effective yesterday, this sticking to a simple scale is what I meant.
So in other words a simple 'modal' approach where the unusualness of
the tuning supplies enough complexity to make the whole not seem quite
as straightforward as it actually is. (I also will often use different
1/1s as way to heighten the interest/tension/complexity as well, as is
the case with some of the ensemble in "With Eyes so Blue and
Dreaming". This too is "crude but effective", and a favorite and much
used structural device of mine.)

<< A fun way to approximate 13 and get a feel for it was discussed
here some time ago. On a guitar with a movable bridge, move it back
and slant it until you get octaves on the 13th fret on each string. >>

Yes, I've used this too, and it's quick but increasingly dirty, and
dirty = inaccurate here, the farther you get from the bridges original
position (Paul Erlich posted the math for this a while back, but I've
forgotten it now... anyone care to spell it out again?).

About 8 or 9 years ago now, I had an old Kay Jumbo loaner for a while,
and you could actually push the bridge up towards the soundhole until
you had the octave just about at the 10th fret, and all the way back
until you had the octave nearly at the 15th fret -- way cool! This
guitar in various bridge positions appears in many places on my piece
"Day Walks In".

--Dan Stearns