octave equivalence and voice leading

I'm wondering what about voice leading really depends
on octave equivalence.

In barbershop, the tenor part typically has a lot of
repeated notes (zero voice leading motion) or motion
of a scale step. The lead and baritone have some 3rds
and 4ths, and the bass often has jumps of a 5th or
sixth. The pictre is much the same in evangelical
SATB arrangement, where

S is like barbershop lead
A " " tenor
T " " bari
B " " bass

in terms of voice leading motion. In either case,
octave equivalence doesn't seem to change much, as
jumps of an octave or more are rare. Even swaps
often don't require octave equivalence (though where
they do I agree the voice leading motion is less
than what an octave-specific measure would give).

Meanwhile, octave-equivalence quickly runs into
problems above the 5-limit, and even in the 5-limit
(it's why Schubert voiced few close-position triads
in the bass).

-Carl

--- In tuning-math@yahoogroups.com, "Carl Lumma" <ekin@...> wrote:
>
> I'm wondering what about voice leading really depends
> on octave equivalence.
>
> In barbershop,

Carl,

voice leading in Barbershop is a great topic, especially as it is
saturated in seventh chords. One place to start, Ithinks, would be to
take a few pieces and analyze the voice leading both a melodic step
motions (are the neo-Riemannian operations I, R, L, L', P, P', R, R'
sufficient for barbershop? ) and as lattice moves, and see how closely
the two analyses match. The two constraints on voice leading that I
would follow most closely are (1) fixing the melody to the lead (which
may cause the other voices to use less efficient voice leading) and
(2) the treatment of the bass voice, usually on the root or fifth, but
sometimes filling in the voice-leading above. And, if I may be
excused for heresy on pitch drift, once you've drawn a lattice, you
might want to see if there is an optimal temperament (and geometry)
for that lattice, and see what that might imply for additional voice
leading possibilities.

DJW

>> I'm wondering what about voice leading really depends
>> on octave equivalence.
>>
>> In barbershop,
>
>Carl,
>
>voice leading in Barbershop is a great topic, especially as it is
>saturated in seventh chords. One place to start, Ithinks, would be to
>take a few pieces and analyze the voice leading both a melodic step
>motions (are the neo-Riemannian operations I, R, L, L', P, P', R, R'
>sufficient for barbershop? )

I'm not familiar with them.

>The two constraints on voice leading that I
>would follow most closely are (1) fixing the melody to the lead (which
>may cause the other voices to use less efficient voice leading)

Actually the tenor has usually by far the least motion.

-Carl