Interesting intervals

Regular readers will know that I have been attending lunchtime lectures at the City Recital Hall this year on various topics associated with music.

Firstly, there was Music and Philosophy.  I am sure that the concepts would have proved very interesting had the speaker and I shared the same vocabulary.

Then there was Music and the Periodic Table of Elements, which showed that scientists are always looking for patterns in nature, whilst musicians, painters and the like thrive by creating their own visual and aural patterns.

The third was Music and Mathematics.  Now that should prove interesting, I thought, as my degree is in maths.  Mind you, I only just got my degree as I seemed to spend most time at uni in non-academic activities such as music of various sorts and helping to run the Students’  Union.  Oh – and, of course, meeting Anne……..

Going to the lecture was going to be a bit tricky as it fell on the second day of a romantic interval in everyday life organised by our children in honour of a recent wedding anniversary – top seats to see Madama Butterfly, preceded by dinner overlooking the Harbour and followed by an overnight stay in the penthouse of one of those luxurious hotels overlooking Circular Quay.  It was all absolutely magic.

Anyway, Anne found a lunchtime organ recital at St James’ King Street at the same time as my lecture – much more her cup of tea.  And I said as we parted, each with our own pack of sandwiches, that if they mentioned Fourier Transformations, the point at which my mathematical comprehension ran out, I would leave.

The professor of mathematics who spoke is also an amateur chorister, so there was an immediate bond.  He started by talking about intervals – such as taking a string tuned to C, halving the length and getting C an octave higher.  And, as is well known, different ratios give different notes: one quarter off the string length gives F and a third gives G.

It was only shortly afterwards that the dreaded Fourier Transformations raised their head.  If I had not still been contentedly eating my sandwiches, I would have left.  They were the last thing I expected in a talk about music.  But apparently they are fundamental to digital communications, such that, for example, file formats for recorded music such as MP3 would not exist without them.

Then, like my degree maths, my comprehension suffered a catastrophic failure.  There followed some very erudite comments and questions, but for me the sandwiches proved more interesting.

The other memory I have of the lecture is the speaker’s missing out all the other musical intervals except one.  C to F# is the dreaded “tri-tone”, which sounds rather dissonant.  The fraction of the string to be stopped is mathematically interesting, as it involves dividing something, I cannot remember what, by the square root of 2.  Maybe that is one reason why, in Medieval times, the tri-tone was reputedly barred by the authorities from Church music for being the work of the Devil.

Of course, Mozart uses the once diabolical interval to good effect throughout the Great Mass in C minor, as we discover every Thursday evening.  Not that knowing it’s mathematical basis makes it any easier to sing!