Category Archives: Numeracy

Rock Guitar in 11 Dimensions

Like many pupils, I’m as fond of science as I am of music, and even fonder of situations where the two connect – such as Rock Guitar in 11 Dimensions – one of the talks in this year’s Edinburgh Science Festival. This promises to be an introduction to Superstring Theory – which reminds me of one of the few science jokes I’ve heard:

A string theorist is confronted by his wife with a photograph of him leaving a hotel with a younger woman. He responds, “Darling, I can explain everything!”

Pentatonic Scale

Bobby McFerrin demonstrates the universality of the pentatonic scale and “audience expectations” in this entertaining video from the World Science Festival 2009. This was part of a larger event in the festival entitled Notes & Neurons.

If the notion of the universality of the pentatonic scale interest you, may I recommend the first of Leonard Bernstein‘s Norton Lectures, in which he relates the pentatonic scale (and varieties of it associated with different cultures) to the harmonic series.

Thanks to Pat Kane for flagging this up in Twitter.

False Friends

Yesterday I took part in an interesting CfE exercise at MGS where class each class teacher teamed up with another from a different department to investigate common ground and curricular connections. As an instructor, I was not really programmed into this but was very pleased to be included, having put out some gate-crashing feelers. The power of Maths decreed that many would be paired up with teachers of the subject and I was pleased to see that one member of the Music Department was Maths-bound.

As all expected, there were many overlaps. However, there were also a few false friends – words, the interpretation of which in either subject, is so different that we ought now to be on the lookout for understandable confusion. Examples?

Scale: referring in Maths to order of magnitude but in Music to the various spellings of stepwise movement in a melodic line

Time: time is relative in Music and absolute in Maths

Happily, the connections outweigh the differences by miles – is that a mixed metaphor? I’ll ask the English Department when we pair up with them 🙂


Having been interested at first mention of WolframAlpha, I decided to spend some time on it to see what it’s all about. The site is not short of explanatory material – ranging from an explanation of its goals, through examples to a video demonstrating what’s possible.

I was pleasantly surprised to find that the six major towns of East Lothian featured and decided to find out a little more about population etc. (I imagine that the info might have come from the 2001 census and, in some cases more than others, might be qutie out of date by now). Why not see if you can predict the populations of these towns – or rank them in order before clicking the links? Dunbar; North Berwick; Haddington; Tranent; Musselburgh; Prestonpans

I was also curious about the population of towns which feed into larger secondary schools e.g. East Linton; Longniddry and couldn’t help wondering if all the schools were being located from scratch now, if Cockenzie/Port Seton would merit its own school. The population, at nearly 6,000, must rival that of larger towns at the time schools were establishing themselves.

Then, simply to test-drive Wolfram Alpha, I simply entered random terms in the search box:

a chemical element e.g. Boron; a chemical compound e.g. NaCl (Sodium Chloride); ozone

Pi; a calculation e.g. 7.39 + 17.5%; 10 Factorial aka 10!

today’s date; my date of birth (it seems I’ve been alive for 18,159 days); a random year – 1939

the note Middle C; the interval of the perfect 5th; the major 7th chord; C diminished chord; the term Hertz; human hearing range; speed of sound; speed of light;

the sum of £21.34 which, without asking, was converted into other currencies

a random temperature e.g. 37 degrees C, which was converted into more scales than I knew existed

a random length e.g. 100m; Sun distance Earth; Moon distance Earth; volume of sea;

and finally a random word – sound, which is explored in all its uses – the etymology and first recorded use of words are given – very much like another favourite of mine – etymonline

The results of searches can be saved as pdfs – which must be handy for many classes.

Why not try it out?

Twilight Associations

Spontaneity and inspections rarely appear in the same sentence but yesterday afternoon proved the exception. Upon arrival an mid-inspection NBHS, I overheard mention of voluntary meetings with members of the inspection team and NBHS staff with the intention of discussing ACfE and AIFL. I took the liberty of inviting myself along and was welcomed with open arms.

For obvious reasons I cannot divulge names and details but suffice to say it was the first time I’ve sat round a table with colleagues from such diverse disciplines – and that the debate was very lively. The magnitude of current curricular reform and seems to encourage – in fact, requires – thinking out of the box and I found myself questioning aloud the automatic faculty grouping of Music with its traditional bedfellows. I would describe music as a language with an unmistakable numerical component, yet we rarely pursue these associations.

Magic Numbers

Synchronicity can be the glue that binds ideas together. Alan Armstrong points out that all teachers (including instructors) need to become teachers of numeracy (along with literacy and well-being). I hear that that classroom colleagues in MGS are meeting in groups to discuss how this will be done*. I probe the theory knowledge of a gifted, multi-instrumental pupil and find some cloudiness in the numbers area. This is not due to lack of ability on the pupil, who is in a top Maths set, but due to the multi-modality which music imposes on numbers. With exceptions the numbers involved rarely rise above 7 and therefore we require these few, overworked digits to perform a multiplicity of functions (accidental pun). The big hitters in one area, are Z List celebrities in the next; numbers which seem like immediately family members in one context are, at best, distant cousins in another. Even the most mathematically gifted pupils will feel, at times, that they are drowning in a whirlpool of, polygamous, shape-shifting integers.

Confused? Join the club. That’s why I intend to produce some kind of table to help pupils (and any other interested parties) see at a glance the many faces and functions of these digits. Adapting the Kipling process, I’ll compile a prototype, run it past some pupils & colleagues, make necessary adjustments and additions and post it here – most probably on a new Lesson Support Page.

In the meantime, let me mention just a numerical oddity which struck me the other day while listening to an old mp3 download of Radio 4’s In Our Time. The conversation concerned the Fibonacci series, golden sections etc. and their prevalence in nature, architecture, art and music. It occurred to me for the first time that the Fibonacci series does not feature the number most prevalent in Western music – 4. Strange.

* unfortunately instructors rehearse ensemble at this time and can’t join in.