Music and Mathematics Melvyn Bragg BBC Radio 4 -FYI

Hello,

I’m putting this down the phone from the Houses of Parliament where
Big Ben
has just struck 1. Numbers will follow me through many a day. The
numbers,
the numbers – the bells, the bells.

In the Green Room afterwards there was much talk about the similarities
between studying mathematics and studying music, the bringing
together of
several theories, the complications resulting in the final
resolutions. It
is always fascinating to hear people speaking of one discipline in terms
which are thought to be the monopoly of another discipline.
Inspiration,
imagination, all the glowing matters of life have for long been
monopolised
by artists. To discover mathematicians speaking with as much, if not
more,
enthusiasm and in precisely the same terms, is a revelation.

What I would have liked would have been more certainty about the
connections
inside the brain between mathematics and music. But the more I think
about
it, the more I believe that mathematics can be connected with an
enormous
number of activities. With architecture, with football … the reason
might be
to do with the dominance of the heartbeat inside our system and the
measuring
that we do every step we take, every time we count, every blink we make.

Lots of nuggets didn’t manage to get in. I don’t know whether we said
clearly enough that Pythagoras was led to the conclusion that the
basis of
everything that we find beautiful is mathematical. The search for
the equal
temperament was not spelled out as much as I would have liked.

Several people tried to smooth over these difficulties, such as the
early
seventeenth-century Minimite friar Marin Mersenne, a mathematician
who wrote
extensively about music, and the German astronomer Johannes Kepler, who
returned to the Greek idea of musical intervals between the various
planets –
the harmony of the spheres – each planet had its own scale.

And even Isaac Newton got in on the act. Newton spent much time on
musical
scales, and even tried to link the seven notes of the musical scale
with the
colours of the spectrum. That’s why we often say that there are seven
colours in the rainbow – it arises from Newton’s combined researches
into
optics and music.

Temperament relates to the division of the octave – if you play one
physical
pure fifth, then another, then another then after 4 octaves you will
come out
a semi tone higher – even though the maths works, because you haven’t
got
equal temperament. Equal temperament is what’s used to divide the
Octave,
instead of pure mathematical divisions. There is a discrepancy in sound
between a physical pure 5th and an equal temperament 5th – and similarly
between a physical pure octave and an equal temperament octave.

And the search goes on now very self-consciously for more mathematics in
music. Sir Peter Maxwell Davies, Master of the Queen’s Music, has
used magic
squares in several of his compositions. In one piece, he started
with this
8-note piece of plainchant, and this 8 × 8 magic square in which each
row and
column adds up to the same sum, 260. Combining these in a particular
way, he
obtained his so-called Magic square of Mercury, and then by tracing
through
the numbers in it in various ways he was able to generate the pitch
material
for the composition.

I’m off to whistle a happy tune as I do the five-bridge walk, while
the sun
shines, before a late lunch.

Best wishes

Melvyn Bragg

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