Neutral third, 11/9, blues

Johnny Reinhard wrote,

>> >One special characteristic of the neutral third is that no matter
what
>> >kind of 5th there is in a system, the neutral third is always in the
same
>> >place logarithmically.
>
David Finnamore wrote,

>> Do you mean that neutral thirds have the same relationship to the
tonic
>> regardless of how the 5th is tuned, or that the pitch of the 3rd
rises and
>> falls in logarithmic proportion to the height of the 5th, or...?

Johnny Reinhard wrote,

>While the thirds accordian proportionately to the fifth (however large
is
>one third, the other is condensed), the neutral third is always dead
>center, dividing the fifth into 2 identical parts. Just as the tritone
>bisects the octave, the neutral third bisects the perfect fifth.

>The neutral thirds of all the meantones, 12-TET, 31-TET, quartertones,
>Egyptian music, and others are roughly all in the same place because
the
>fifth is so etched in its shape. The difference of a few cents in
either
>direction from 351 cents (at perfect fifth of 702 cents) is negligible
for
>musical purposes.

Though I'm not sure what the neutral third of 12-TET is, I basically
agree. However, there are tuning systems where the neutral third is not
dead center, such as Partch's, where an 11/9 (347 cents) is the neutral
third. But I think that musical uses of the neutral third tend to derive
from a logarithmic bisection of the perfect fifth, and not the 11/9
ratio.

In blues, the neutral third is very common, as is the neutral seventh,
which is a perfect fifth higher and acts as a sort of leading tone. I
think I might know something about the blues because I got a great
response from the audience at a recent gig at Buddy Guy's Legends. The
7/6 or some sort of sub-minor third does occur with some frequency,
though, and I at least hear some consonance when it falls over the IV
chord (so I use it there a lot). The 7/4 is least common of these but I
hear it used by gospel singers and harmonica players over the I and in
passing by guitarists bending up from the 6th to the flat 7th.