Category Archives: Numeracy

The Art of Fugue

I always look forward to notification of a new YouTube upload by Smalin aka Stephen Malinowski. I’ve linked to several here before but this one is a cracker and features: 

  • his uniquely colourful system for portraying pitch and duration
  • the option to watch in 3D – with the right specs
  • mention of the following musical concepts:
  • augmentation – doubling the length of notes in the theme
  • diminution – halving the length of notes in the theme
  • inversion – turning the theme upside-down; as he explains the M-shape becomes a W-shape
  • if you watch the hands closely you’ll also see ‘finger substitution’ – where a finger, which is keeping a note down, is ‘relieved’ by another so that it can move on to its next job; the complexity of the music comes through here as many of the notes are effectively being played twice

Afro Cuban Rhythm

Bouncing from one YouTube video to another, I recently came across a great series of films on Afro Cuban Rhythm – with very clear explanations of how the rhythms are layered. The central protagonist is maestro of Cuban rhythm, drummer Ignacio Berroa. There are some very good musicians involved, but I’ll let him introduce them to you.

Key to understanding the whole thing are the two main rhythms of the clave (although the qutoed graphic below from Wikipedia includes three – the extra one begin in 6/8). Note the interesting etymology of the word clave:

cla·ve [klah-vey]
noun – one of a pair of wooden sticks or blocks that are held one in each hand and are struck together to accompany music and dancing. Origin: 1925–30; American Spanish, Spanish: keystone < Latin clāvis key

This little graphic from Wikipedia may help to outline the key rhythms:

At the end of the 5th video (and running well into the 6th) there is a chance to see if you can keep the clave part going once they temporarily drop out of the music. Now there’s a challenge for you.

Happy Birthday Heinrich

If you are a guitarist then today is the day joyously to play D# – string 4, fret 1. The reason to celebrate the 155th birthday of Heinrich Rudolph Hertz (1857-94), the man after whom the calibration of pitch frequency is named. That D# (the one below Middle C)  is the nearest note to 155 Hz.

1 Hz = 1 cycle per second – that is to say that the D# in question makes the air vibrate 155 times per second.

Orchestras in the west tune to A  = 440 Hz, with the exception of the French who prefer 444 Hz.

But the situation has not always been stable. Harpsichords in the Baroque were tuned to A = 415 Hz; some organs were tuned to A = 465 Hz. The French preferred 398 Hz.

Human hearing range is 20 Hz to 20,000 Hz (20 kHz).

The range of a piano is 27.5 Hz (no point in going much lower) to 4186 Hz (we could perceive notes which are much higher than this, but would we enjoy them?)

Creativity

great article in The Guardian (Mon 2 Jan) featured artists from various disciplines offering tips on creativity, inspiration and realising ideas. Placed in the arts section, it would be silly to criticize the piece for lacking a wider field of professionals, but I did find myself wishing for contributions from those in other areas of expertise e.g. science, engineering, social policy, education. The wider the field, the more boldly common themes tend to stand out.

In this regard I have to say that I’ve always found it something of an irrelevance that, in school life, Music is grouped together with, say, Art or Drama. As far as academic side of Music goes, I feel it has most in common with Language(s) and then Maths. Actually, on this point, let me bore you with another possibly pedantic personal opinion: it is often claimed that Music and Maths are very closely related. I think this is an overstatement. Music and Arithmetic are closely intertwined but Calculus, Trigonometry, Algebra and Geometry rarely darken my door – unlike alliteration. Certainly as regards the honing and analysis of technique, then Music has as much in common with PE as any other subject – and let’s not forget teamwork!

Returning to the article, I was pleased to see that composer, Mark Anthony Turnage, scotched the idea of inspiration allowing us to avoid hard graft. Fortifying this take on the creative life, he cited various details of working method: routine; a quiet place to work; the difference that time of day can make. He opines that “the afternoon is the worst time for creativity.” It can feel like the worst time for learning and teaching. Many pupils (and possibly staff) seem to undergo a dip around 2.00-3.00 and perk up when within sight of the home straits. In the unlikely event that I am charged with redesigning the school day, I will opt for 7.00-2.00, freeing up the afternoon for siesta, meditation, reading or sport. Turnage also feels his critical eye/ear to be more lenient in the evening, often necessitating morning revision.

Susan Philipsz, has some very straightforward suggestions: “keep it simple” and “be audacious” and, in similar spirit to Turnage, “if you have a good idea, stick to it. Especially if realising the project is a long and demanding process, try to keep true to the spirit of the initial idea.”

Singer/song-writer, Martha Wainwright, confesses to a piecemeal approach: “I write in short spurts – for five, 10, 15 minutes – then I pace around the room, or go and get a snack.” Playwright, Polly Stenham, touches on the physical side, advising us to “go for a walk.” Author, Haruki Murakami (in another article) takes this much further. “When I’m in writing mode for a novel, I get up at 4:00 am and work for five to six hours. In the afternoon, I run for 10km or swim for 1500m (or do both), then I read a bit and listen to some music. I go to bed at 9:00 pm. I keep to this routine every day without variation. The repetition itself becomes the important thing.”

Artist, Polly Morgan, stresses the fruitfulness of a cross-curricular approach: “Don’t restrict yourself to your own medium. It is just as possible to be inspired by a film-maker, fashion designer, writer or friend than another artist. Cross-pollination makes for an interesting outcome.” Harking back to my first paragraph, I would widen this field considerably. Morgan also seems willing to embrace the tough choices which many of us would prefer to avoid: “Don’t be afraid to scrap all your hard work and planning and do it differently at the last minute.” I have certainly found this approach indispensable upon arrival at gigs which differ widely from their description.

Director, Ian Rickson, encourages us to “embrace new challenges. When we’re reaching for things, we tend to be more creative.” This reminded me of an inspirational idea by Joe Zawinul, keyboard player and founder member of Weather Report (and incidentally one of the few who seemed able to write music which was happy but not inane). In his 7th decade, there was more chance than ever that his improvising would fall into favoured patterns. In a bid to stumble upon new sounds, he programmed one of his keyboards so that pitch ran in reverse order. Playing this, along with others formatted in the normal way, many novel ideas emerged which would not have occurred to a trained hand and ear.

Musician, Gus Garvey (Elbow), recommends the practice of bringing together two unrelated ideas. I recall coming across this in Edward de Bono‘s 1973 book, Po.

Perhaps my favourite sound bite from the piece comes from opera singer, Kate Royal who reminds us that, “art is everywhere.” Taking the word art as a synonym for inspirational practice then, with providers and consumers of public service having to produce more with less, this seems like as good a way to step into 2012 as I can imagine. Happy New Year!

You can access the full article here.

But let’s leave Joe Zawinul with the last word:[kml_flashembed movie="http://www.youtube.com/v/Ae0nwSv6cTU?rel=0" width="425" height="350" wmode="transparent" /]

The Science of Sound

If you like the mix of music/sound and science – plus a bit of comedy – why not listen to this episode of The Infinite Monkey Cage?

The programme features Professor Brian Cox; Robin Ince; University of Salford’s acoustic expert Professor Trevor Cox; neuroscientist Professor Chris Plack; violinist Julian Gregory; comedian and former acoustics student Tom Wrigglesworth.

Topics covered include major/minor-happy/sad correlation; why some sounds fill us with horror; acoustics of concert halls; musical intervals and maths/ratios – including the tritone also known as Diabolus in Musica (The Devil in Music).

European Day of Languages

Tomorrow (Mon 26 Sept) is European Day of Languages. Like all Mondays I’ll be spending it in two primary schools. A really good way to involve pupils, without major distraction from the task in hand, is to have them ‘count in’ the tunes in a variety of languages. This table is very helpful. Handy time-saving hint to avoid lengthy scrolling, for those not already addicted to keyboard short-cuts:

  1. Control+F
  2. Type the name of the language you want in the search box which should appear at the top-right of the screen

TeachMeet 2011

This evening I’m heading up to TeachMeet 2011 chez Scottish Book Trust as one of the 7-minute presenters.

My theme is Literacy, Numeracy and Games in Instrumental Lessons. Seven minutes will allow a an average of 6 seconds per slide. So it will be a broad brush, hurried affair with the intention that people can download the ppt from here.

So here it is: Literacy-Numeracy-Games-in-Instrumental-Lessons

Music: An Explanation by a Guitar Hero

Better late than never? Having been on holiday I’m a little late with this short write-up of an Edinburgh International Science Festival event but, as it was so good, here goes.

Dr. Mark Lewney is a physicist and a guitarist. Last year I went to his excellent Rock Guitar in 11 Dimensions and reviewed it here. This year he presented Music: An Explanation by a Guitar Hero – a look at the physics underlying sound/music. Without wishing to spoil the show for those who may have the chance to see it later, let me say that he took us on an engaging journey from the sine wave – through the world of harmonics (overtones), the importance of the fundamental, 4th and 5th notes, the short step from there to the pentatonic scale, which is used in folk musics across the world – notably in the blues.

He finished the talk with some thoughts on music’s purpose in our evolution – the topic of much debate – such as from 2:24 – 7:03 in this video). One thing is clear, though: prosody (the music of speech) matters – it’s not just what you say it’s how you say it.

This was an excellent, funny and informative presentation. This cross-curricular take on life is, I feel, at the heart of CfE.

You can see Mark Lewney in action in YouTube videos here.

My further explorations on prosody took me here to a fascinating series of lectures by Peter Roach

p.s. 

I forgot to mention one of the most elucidating facts of the evening – and one of the simplest. 

When non-musicians ask musicians why orchestras need conductors, there are many common answers: 

  • apart from waving the baton, the conductor is the person who has led rehearsals and is in charge of the interpretation
  • orchestral players can end up sitting many metres away from their colleagues and it’s hard to hear – conductors can ensure the overall balance and timing of the group
  • the conductor is the fore-runner of drummer and mixing desk

 However, Mark Lewney’s audience participation illustration was much better and more direct and more memorable. He asked the audience to clap to a beat which, having started, he left in our hands – with out eyes shut. The timing soon began to drift. He asked us to open our eyes and sync with him. The timing improved. Closing our eyes again, the timing deteriorated. Opening them, and following his lead, we were back in sync. The reason? Light travels approximately 874,000 times faster than sound*. Relying on the sound, we had to wait for it to bounce off the back wall of the hall. Syncing to the beat, we were exactly in time.

 * Speed of sound

  •  343.2 metres per second
  • 1,236 kilometres per hour
  • 768 miles per hour

 Speed of light 

  • 299,792,458 metres per second
  • 1,079,000,000 kilometres per hour
  • 671,000,000 miles per hour

Rock Guitar in 11 Dimensions (review)

On Saturday I attended an excellent event in the Edinburgh International Science Festival:  Rock Guitar in 11 Dimensions, presented by Dr. Mark Lewney:

This was science presentation at its best: great guitar playing; comedy; conjuring; audience participation; information presented in a stimulating way; enthusiastic response in the Q&A; the feeling that science is about you, your life, the universe in which you live and, most excitingly of all, the idea that some of the mysteries of the universe could be solved within our lifetime (well, to be fair, I think he was addressing the many younger members of the audience..). On that note, I was pleased to see a pupil there, with his dad, and to discover that he had already been at another event in the festival.

Starting with a very clear explanation of the world of sound, vibrations, acoustics, amplification etc., Dr. Lewney’s talk went on to explore: dimensions; spacetime; the origins and future of the universe and string theory. Rather than describe content here, let me direct you to Dr. Lewney’s entertaining and informative YouTube videos all of which, I feel, are tailored made for the pupil who feels all learning to be connected:

Highlights of a similar talk in Japan:
[kml_flashembed movie="http://www.youtube.com/v/OOJXzlB2qXM?rel=0" width="425" height="350" wmode="transparent" /]
The Physics of Rock Guitar:
[kml_flashembed movie="http://www.youtube.com/v/vPNPcyWSuzo?rel=0" width="425" height="350" wmode="transparent" /]
Cool Acoustics Part 1:
[kml_flashembed movie="http://www.youtube.com/v/y3SotmBmLRg?rel=0" width="425" height="350" wmode="transparent" /]
Cool Acoustics Part 2:
[kml_flashembed movie="http://www.youtube.com/v/AU-BJv0QKGc?rel=0" width="425" height="350" wmode="transparent" /]
Cool Acoustics Part 3:
[kml_flashembed movie="http://www.youtube.com/v/mVKprDUHqQs?rel=0" width="425" height="350" wmode="transparent" /]
Dr. Lewley’s lovely Ibanez guitar

had been airbrushed by Jim Fogarty. It features pictures and equations of Albert Einstein and Max Planck which you can see close up here.
This festival, I feel, is one of Edinburgh’s best – and possibly underestimated – events. It is also the greenest, in terms of booking: one visit online; one e-ticket number entered into my phone’s notepad; no printed matter!
For the record, I have been to two other events: The Mind is Somewhere North of the Neck and Seven Deadly Sins and
have tickets for two further events: Because God Made It That Way – Paul Dirac and the Religion of Mathematical Beauty in Fundamental Physics and The New Intelligence: Working Memory.