Re: Prime rarity -- hemiola

Hello, there, everyone, and hemiola may be common to lots of music, but
it's something I'm especially familiar with in the 14th and 15th
centuries. As mentioned, it involves two ways of combining an
"imperfect" (twofold) with a "perfect" (threefold) division -- expressed
in modern notation as 6/8 in one voice and 3/4 in another.

The four rhythmic divisions or mensurations which become standard in the
early 14th century, and provide the basis for late Gothic and Renaissance
notation, are in modern notation 9/8 (3x3), 3/4 (3x2), 6/8 (2x3), and 2/4
(2x2).

There's a really beautiful piece in an English source from around the late
14th century which sounds lovely in Pythagorean with some cadences
featuring this idiom -- fun to play on keyboard while trying to express
the contrasting rhythms of the different melodic lines.

In this era there are also things like 6/8 in one voice combined with 2/4
in another, irregular or less usual groupings like units of 5/8 and 4/8
(as expressed in modern notation), and proportions, given the same names
as the interval ratios (e.g. hemiola or sesquialtera for 3:2), such as a
division of a 9/8 measure into two equal 9/16 parts.

Willi Apel, Ursula Gunther, Suzanne Clercx, Richard Hoppin, and others
have written about this era, immensely sophisticated and beautiful: here's
one epoch where practice and theory go together.

Most appreciatively,

Margo Schulter
mschulter@value.net

Lovely, Margo! Thanks for the contribution!

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
> Hello, there, everyone, and hemiola may be common to lots of music,
but
> it's something I'm especially familiar with in the 14th and 15th
> centuries. As mentioned, it involves two ways of combining an
> "imperfect" (twofold) with a "perfect" (threefold) division --
expressed
> in modern notation as 6/8 in one voice and 3/4 in another.
>
> The four rhythmic divisions or mensurations which become standard
in the
> early 14th century, and provide the basis for late Gothic and
Renaissance
> notation, are in modern notation 9/8 (3x3), 3/4 (3x2), 6/8 (2x3),
and 2/4
> (2x2).
>
> There's a really beautiful piece in an English source from around
the late
> 14th century which sounds lovely in Pythagorean with some cadences
> featuring this idiom -- fun to play on keyboard while trying to
express
> the contrasting rhythms of the different melodic lines.
>
> In this era there are also things like 6/8 in one voice combined
with 2/4
> in another, irregular or less usual groupings like units of 5/8 and
4/8
> (as expressed in modern notation), and proportions, given the same
names
> as the interval ratios (e.g. hemiola or sesquialtera for 3:2), such
as a
> division of a 9/8 measure into two equal 9/16 parts.
>
> Willi Apel, Ursula Gunther, Suzanne Clercx, Richard Hoppin, and
others
> have written about this era, immensely sophisticated and beautiful:
here's
> one epoch where practice and theory go together.
>
> Most appreciatively,
>
> Margo Schulter
> mschulter@v...

"M. Schulter" wrote:

> Hello, there, everyone, and hemiola may be common to lots of music, but
> it's something I'm especially familiar with in the 14th and 15th
> centuries. As mentioned, it involves two ways of combining an
> "imperfect" (twofold) with a "perfect" (threefold) division -- expressed
> in modern notation as 6/8 in one voice and 3/4 in another.
>
> The four rhythmic divisions or mensurations which become standard in the
> early 14th century, and provide the basis for late Gothic and Renaissance
> notation, are in modern notation 9/8 (3x3), 3/4 (3x2), 6/8 (2x3), and 2/4
> (2x2).
>
> There's a really beautiful piece in an English source from around the late
> 14th century which sounds lovely in Pythagorean with some cadences
> featuring this idiom -- fun to play on keyboard while trying to express
> the contrasting rhythms of the different melodic lines.
>
> In this era there are also things like 6/8 in one voice combined with 2/4
> in another, irregular or less usual groupings like units of 5/8 and 4/8
> (as expressed in modern notation), and proportions, given the same names
> as the interval ratios (e.g. hemiola or sesquialtera for 3:2), such as a
> division of a 9/8 measure into two equal 9/16 parts.
>
> Willi Apel, Ursula Gunther, Suzanne Clercx, Richard Hoppin, and others
> have written about this era, immensely sophisticated and beautiful: here's
> one epoch where practice and theory go together.
>
> Most appreciatively,
>
> Margo Schulter
> mschulter@value.net

I remember studying this and thinking how close all this was to a lot of modern rhythmic and
metrical thinking. It is somewhat paradoxical that the highly structured and codified metres and
rhythms led to such apparent rhythmic freedom. I also remember Willi Apel giving an excerpt from a
medieval piece which would not have been out of place in a work by Ferneyhough. I maintain that
composers would do well to dig deep into the pre-tonal eras for new ideas.

Regards

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

/tuning/topicId_31951.html#32098

>
> I remember studying this and thinking how close all this was to a
lot of modern rhythmic and
> metrical thinking. It is somewhat paradoxical that the highly
structured and codified metres and
> rhythms led to such apparent rhythmic freedom. I also remember
Willi Apel giving an excerpt from a
> medieval piece which would not have been out of place in a work by
Ferneyhough. I maintain that
> composers would do well to dig deep into the pre-tonal eras for new
ideas.
>
> Regards

Great idea, Allison!

J. Pehrson

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> /tuning/topicId_31951.html#32098
>
> >
> > I remember studying this and thinking how close all this was to a
> lot of modern rhythmic and
> > metrical thinking. It is somewhat paradoxical that the highly
> structured and codified metres and
> > rhythms led to such apparent rhythmic freedom. I also remember
> Willi Apel giving an excerpt from a
> > medieval piece which would not have been out of place in a work
by
> Ferneyhough. I maintain that
> > composers would do well to dig deep into the pre-tonal eras for
new
> ideas.
> >
> > Regards
>
> Great idea, Allison!
>
> J. Pehrson

Bob:
Composer have been doing just that for a very long time. A lot of
modern music takes its inspiration from medieval roots.