LL-L "Language acquisition" 2005.05.19 (15) [E]

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From: Dave Singleton <davidsin at pt.lu>
Subject: LL-L "Language acquisition/Music" 2005.05.19 () [E]

Moiën Heather,

Have you come across this little gem, I lay no claims to anything -- all
the work was done by Jeff Lee. I have tried the formula and it is
excellent for producing part music !!

  Mathematical Musick

    The Contrapuntal Formula of Dr. Thomas Campion

      By Jeff Lee <http://www.shipbrook.com/jeff/>
      <godfrey at shipbrook.com <mailto:godfrey at shipbrook.com>>

Thomas Campion (1567-1620) was, among other things, an accomplished
musician, lyricist and composer. He was also a musical theoretician; in
1613 he published /A New Way of Making Fowre Parts in Counterpoint/, a
treatise on contrapuntal theory which was republished many times after
his death.

In this book, he proposed a novel means of writing four-part music,
deriving the upper three parts mathematically from the bass line. In his
reasoning, the four parts (of a madrigal, for instance) could be
correlated to the four elements: the /ground/, or bass line, was
analogous to the element of Earth; the /tenor/, to water; the /meane/,
or alto part, was equivalent to the air, and the /treble/, or soprano
part, to the element of fire.

As the upper three parts rested upon the ground, therefore, he concluded
that the bass part was the foundation of the entire piece, and that the
other three parts naturally proceeded therefrom. His theories were
heavily chordal in nature, and in fact (save for passing tones and other
ornaments) each of the three upper parts consisted primarily of thirds,
fifths and octaves above the ground.

Upon the actual composition of the bass line, Campion gave little
direction other than that it should move "/not so much by degrees, as by
leaps of a third, fourth, or fift, or eight, a sixt being seldome, a
seventh never used, and neither of both without the discretion of a
skilfull Composer./" As the writing of an appropriate bass part is made
easier by familiarity with the genuine style, we shall use the grounds
of extant chansons and madrigals for our examples, and compare the
results of Campion's method with the original four-part arrangements of
those madrigals.

Each note of the upper three parts is derived primarily from two
components: the interval between the previous note of the part and the
previous bass note, and the direction of movement of the bass line.

The first rule Campion gives is this: when determining the direction and
distance of the bass line's motion, only intervals of a fourth or less
are considered. Intervals of a fifth or more are replaced by their
inversions: thus, a bass part which rises a fifth is considered to
descend a fourth; a part which rises a sixth is treated as though it
descends a third; and a part which rises a seventh is considered to
descend a second. Likewise, a part which falls a fifth is considered to
rise a fourth, and so on.

Further, many of my musician colleagues remark in passing that they work
either in patterns or colours. I envy them in that they actually have
something they can pin down, on the other hand there are lucky musicians
that are able to use music as a vehicle, which is I suppose, something
that language is -- a vehicle of expression.

******
From: heather rendall <HeatherRendall at compuserve.com>
Subject: LL-L "Language acquisition" 2005.05.17 (04) [E]

Message text written by INTERNET:lowlands-l at LOWLANDS-L.NET

> that I have a "rare dual talent" for both

languages and math/science/logic. I do believe that this is a myth, and
that everybody has, or can develop, both talents - if they are even that
different<

I have always counted  the best maths students among my best language
students and was always sad when at age 14 when moving into the exam
classes, many often found that to cover all 3 science and 2 maths papers,
they had to drop their languages: this was one situation that our much
despised National Curriculum actually rectified - except it did it at the
cost of losing all 3 sciences at 16 and instead offereing a double science.

I frequently use algebraic equations to reinforce sentenc structure. I am
sure there is a cognitive correlation between maths, algorithms, and
language ( perhaps also music???)
Heather

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