A readily divisible journey into microtonalism

In a recent post ("In defense of 12tet..."), Robert Valentine wrote :

>it has some very interesting properties by being so readily divisible
(diminished chords, augmented chords, tritone substitutions, whole
tone scales)... As one who has composed and played an awful lot of
12tet music, my journey into microtonalism is a stumbling one.

When I first started working with multiple equal divisions of the
octave, I was very interested in seeing what kinds of compositional
conditions I could create that would
strengthen a sense of navigational similarity. My hope was that this
would thereby cultivate sets of modulatory paths (or structural links)
between a wide variety of equal divisions of the octave.

Some microtonalist who use multiple equal divisions of the octave, say
Brian McLaren (in the spirit of Ivor Darreg) for example, will attempt
to exploit a specific characteristic sound, or "mood" of whole
families of equal divisions of the octave. A simple example being 5 &
7e, and their respective families, i.e. 5, 10, 15, 20, 25, etc., and
7, 14, 21, 28 & 35 (where the 5 & 7 would meet), etc. For me, it was
the very kinds of "interesting properties by being so readily
divisible" that Robert mentions in his post, that provided the
catalyst for some of the first things I tried out... for as it was
easy enough to see the 2, 3, 4 & 6 in 12, it seemed to me, that by
compositionally stressing the individual structural fingerprints of
the 2, the 3, the 4 and the 6 inside of 12, that it shouldn't be too
difficult to 'see' say the tritones of 8 & 14, or the augmented 9 &
15, or the diminished 20 and the wholetone 30, in 12e... and it was
precisely these sorts of abstracted paths that would give me some
sense of structural direction when modulating between, or
interweaving, say 8, 9, 12, 14 & 15e.

A lot of what I do here involves processes like mapping the step
structure of certain scales. And most of these create a condition that
clearly favors vertical similarities, and a sense of what could
charitably be called (to paraphrase Daniel Wolf) harmonic rubato
(which more often than not will easily create harmonic distortions of
the sort that most would probably find intolerable)... For example, if
you were to map the familiar 5L 2s diatonic as shown in this periodic
table (where L=s+1, L=s+2, L=s+3, L=s+4, L=s+5, L=s+6, etc.):

(5) 3 1 6 4 2 (7)
12 (10) 8 13 11 9 (14)
19 17 (15)(20) 18 16 (21)
26 24 22 27 (25) 23 (28)
33 31 29 34 32 (30)(35)

It's easy to see the equal divisions in which this 5L 2s mapping will
not work (1, 2, 3, 4, 6, 8, 9, 11, 13, 16, 18, 23 & 5, 7, 10, 14, 15,
20, 21, 25, 28, 30, 35), and those in which it will: 12, 17, 19, 22,
24, 26, 27, 29, 31, 32, 33, 34 & all >35. But as the differences
between the (quarter comma meantonesque) L=5 & s=3 of 31e, and the
(exaggeratedly Pythagorean-esque) L=3 & s=1 of 17e could obviously be
said to stand worlds apart - it's really a matter of whether or not
one can find (or create) a musical condition that can utilize their
shared conditions (e.g., L=s+2, etc.), as it's also not too difficult
to see the thread that runs between them here. Of course in this
sense, it's then not too much of a leap to say that a generalized
diatonic scale such as Paul Erlich's 22e decatonic has a brute
representation in 12e (as 0, 1, 2, 4, 5, 6, 7, 9, 10, 11, 12), and yet
this would no doubt be some sort of near heresy for Paul, as it flies
in the face of most everything that he's very carefully considered his
scale to accomplish... So perhaps it's safe to say that most of what I
do technically here is largely dependant on the types of things I
personally do (or some may say: am willing to tolerate) musically....
and that for others, the various things that these types of structural
abstractions share, could well prove to be utterly useless for their
music.

But for me, they were absolutely indispensable as both specific
exercises, and general concepts... and both ("specific exercises, and
general concepts") would help me start to acquire some useful
structural strategies, and would furnish the first inklings of where
to start cutting potential paths into that which I already knew I
wanted to accomplish aesthetically (a polyintonational use of the
pitch continuum).

Dan

When I earlier wrote:

> A lot of what I do here involves processes like mapping the step
structure of certain scales. And most of these create a condition that
clearly favors vertical similarities,

I wrote the opposite of what I meant, and vertical similarities should
have read horizontal similarities...