Author: Robert Lennon

Pythagoras and the Music of the Future

Three of four planned articles in a series that explores the acoustical foundations of key developments in western music over the centuries.  Since they first appeared several years ago, these articles have proved valuable sources for students, academics and for those with basic musical knowledge who are curious about why music has developed the way it has.

In the first article – possibly the most widely-read item on the site – we discuss the role of the harmonic series in the perception of timbre before exploring how it has influenced the evolution of melody & harmony, as well as rhythm and tempo, since the Middle Ages. The fourth and final article Synthesis, which is in preparation, will propose ways in which the principles discussed in the first three can continue to inform musical creation now and in the future.

Read the articles here;

Pythagoras and the Music of the Future Part I – Timbre

Pythagoras and the Music of the Future Part II – Melody & Harmony

Pythagoras and the Music of the Future Part III – Musical Time

Pythagoras and the Music of the Future Part III – Musical Time (contd.)

Risonanze for Clarinet & Electronics

Risonanze was composed in the summer of 2016. The title (in Italian because I was based in Milan at the time) means ‘resonances’ or, in the literal way I have used it here, ‘re-soundings’ which occur after the clarinet soloist plays, or at the same time, by way of multiple delays allied to pitch shifters or multiple pitch shifters. Then there is the ‘freeze’ reverb where the soloist’s staccato notes are prolonged and built up into ‘chords’ which are then sampled to form the basis of new, bell or gong-like, inharmonic timbres. In fact, every sound you hear in this work is derived, directly or indirectly, from the sound of a clarinet. Also, ‘pre-echoes’ of fragments from later in the piece can be heard superimposed on the live clarinet part, most noticeably towards the end of the first part. Finally, particularly at the beginning of the second section, we hear very faint ‘overtones’, derived from routing the soloist’s sound through several pitch shifters, transforming the timbre of the solo clarinet’s long, sustained notes.

Follow the clarinet part and listen here,

Continue reading “Risonanze for Clarinet & Electronics”

Pythagoras and the Music of the Future – Updates

imagesQ3JSZSG3Today, the first four articles in the series tracing the acoustical origins of the major developments in western music over the centuries, revised and ‘refreshed’, are published. Since they first appeared several years ago, these articles have proved valuable sources for students, academics and for those with basic musical knowledge and curiosity about how music works.

Continue reading “Pythagoras and the Music of the Future – Updates”

Practice Makes Perfect – Really?

Actually, I prefer ‘practice makes permanent‘!

Here is a short article exploring some of the often contentious issues regarding music practice. In it, I discuss how informed practice works to consolidate learning and thus the importance of appropriate preparation on the part of the students before commencing.

I also examine how the teacher’s guidance during the lesson can make practice more meaningful and productive for the student, and how careful a choice of words can make affect attitudes towards it.  This is all of vital importance, because, as we know,  the majority of the learning takes place away from the lessons – and away from the teacher!

Click here to read: Excuse me, how do I get to Carnegie Hall?

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Keeping Everyone Involved in Group Lessons

This article deals with one of the problems that, for many teachers, is the most challenging: how do we keep everyone involved while at the same time, giving due attention to the problems of individuals?

You will find several solutions and discover why this calculation is correct!

. Group Instrumental Teaching III – Keeping Everyone Involved

Group Teaching & Mixed Abilities

Let me start by telling you a story…

When I was a lad of about 11, I played in a local brass band. I was something of a novice which meant that, with relatively rudimentary sight-reading skills, ‘keeping up’ was a real challenge – the notes just seemed to fly past! The conductor’s and older players’ advice to me was; “sit there, play what you can, and if in doubt, leave it out!”

One summer’s Saturday or Sunday afternoon, the band was engaged to play at a garden party or the like. Part of our task was to accompany a troupe of folk dancers; ‘Morris dancers’ as they are known. To accompany their performance, we played a short ‘jig’ style piece that I had never played before. We must have played it over a hundred times! When the dance finally came to an end, I could play it note perfectly without anyone having  ‘taught’ me anything at all: I had looked at the notes, listened to those around me, imitated the more experienced player who sat next to me and played whatever parts I could. Gradually, I was able to add more and more until I could do the whole thing. Once I had mastered a particular part, I was able to consolidate what I had learned by way of seemingly endless repetition.

Something remarkable had taken place, and I don’t pretend to be able to explain it fully, but

Continue reading “Group Teaching & Mixed Abilities”

Music Education’s Love Affair with Literacy (it’s complicated)

There has been much debate recently regarding an article that appeared in The Guardian on March 27th bemoaning the ever-diminishing provision and status of music education in the UK: a valid subject, well worth any number of column inches, given the decline in school music provision not “since 2010, when the baccalaureate was introduced” as the author Charlotte C. Gill states, but since the early 1980s at the hands of Margaret Thatcher[1] and Sir Keith Joseph[2]; a trend that shows no sign of being reversed – at least in terms of government policy. Ms Gill makes some valid points concerning the importance of music education albeit in a confusing and sometimes self-contradictory manner. The two key issues she sees are that music education in the UK has become the preserve of a predominantly white, middle-class, academic mindset (in other words, ‘elitist’) and that teaching with an emphasis on music notation is a dominant symptom of the overly academic approach to musical pedagogy. This, she claims, renders the subject inaccessible and irrelevant to the needs of many if not the majority of school age students. As she puts it, ”music has always been taught in a far too academic way, meaning that theoretical knowledge is the main route to advancement”. In response, there has been an outcry of indignation in the form of a letter published in The Guardian, with several musical luminaries among its signatories, and a plethora of articles and blog posts shared on social media. Several of these demonstrate a clear grasp of the issues surrounding music provision, but others, unfortunately, also contain contradictions and mixed messages even to the extent that, in effect, they lend support to some of Ms Gill’s claims. It is not possible, therefore, to come down firmly on one side of the debate or the other since there appear to be extremely valid points as well as errors and assumptions on both sides. Continue reading “Music Education’s Love Affair with Literacy (it’s complicated)”

Why We Shouldn’t Stop ‘Defending’ Music Education

Why We Shouldn’t Stop Defending Music Education

A few years ago, I came across an interesting and thought-provoking article by Peter Greene, entitled Stop ‘Defending’ Music.  His basic premise is that music has so many affective – or if you like ‘human’ – benefits that it shouldn’t need defending. He tells us that it is “universal’; he mentions its omnipresence in our lives and asks the popular rhetorical question, “Would you want to live in a world without music?”  Most musicians, music teachers or just ‘music lovers’ would find it nigh impossible to disagree with many of the points he makes, but I think Continue reading “Why We Shouldn’t Stop ‘Defending’ Music Education”

Pythagoras and the Music of the Future

Harmonic Wave 2Pythagoras and the Music of the Future is a series of articles in which I discuss, in accessible terms, I hope, the central influence that the harmonic series has had on the development of western music since the Middle Ages. I look closely at the connection between the harmonic series and the conventions of the musical structures of timbre, melody and harmony and musical time i.e. rhythm meter and tempo.

 Ironically, or so it might seem, I also argue that whereas the development of functional harmony, and therefore tonality, was strongly influenced by our (probably subliminal) awareness of  the interplay of frequency ratios of the harmonic series, the ‘modern’ music that, quite fittingly, has nothing to do with functional harmony, tonality or indeed the notion of regular pulse and tempo  is, or should be, equally bound up with the very same underlying proportions.

The planned fourth article will make the case for a musical ‘language’ that utilises the gamut of proportions inherent in the naturally occurring overtone series first postulated by Pythagoras. I will further argue that the realisation, and indeed the performance, of such a music, is made possible only via the availability of manageable and affordable digital computers together with allied software for sound generation and organisation.

Although the earliest article was published over two years ago, the series as a whole maintains a steady flow of views, which seems to have gathered momentum recently. Why not take a look yourself;

Klee Connections for Piano



Klee Connections for Piano was composed in February 2013. It works by connections being formed between superimposed variants of very simple rhythmic and harmonic series. Some of these connections are made by the composer – using them as a means of developing basic material – and by the listener who may well perceive patterns that weren’t deliberately put there, but which arise out of the interactions of these elements. For example, the sequences, inversions and cadence-like configurations that are often suggested are, to a greater or lesser extent, coincidental or even ‘accidental’.

This is something that the painter Paul Klee made use of in his work: interactions between lines or shapes often give rise to configurations that are not independently drawn and/or which have an aspect of familiarity.

Although this work is written in a post-tonal idiom the word series is used here not in the sense of ‘twelve-tone’ or serial music. An alternative might have been sequence, but of course, that too has a musical definition that would, in this context, be even more misleading.

Click below to listen while following the score on YouTube.

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