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;

‘Classical and ‘Modern’ Music – Are They Really So Different?

 In essence, ‘No!’Portrait Ludwig van Beethoven when composing t...

 The works we know as the classics, the work of composers such as Bach, Mozart, Beethoven, Wagner and others beloved of so many, and the ‘difficult’ music of Schoenberg, Webern, Stockhausen, Boulez, the source of bewilderment for just as many, in fact, share a clear common heritage. Continue reading “‘Classical and ‘Modern’ Music – Are They Really So Different?”

Pythagoras and the Music of the Future Part II

It’s Harmonic Wave 2a relief finally to be able to post the next article in my series about the relationship between musical structures and the harmonic series. It’s a relief because my crowded schedule, which included writing a new (now finished) piece for solo piano, meant that I could only work on it sporadically. However, it’s done now!

Whereas the first article dealt with timbre, this one focuses on melody on harmony (well, mostly harmony actually) and, after tracing the development of harmony in relation to the proportions inherent in the harmonic series, illustrates the premise that music based on functional harmony (tonal music) and atonal music are very similar in at least one very important regard.

The two are often thought of as very different and even in opposition to one another, but in fact one grew out of the other and both are founded on proportions to be found at points – distant points perhaps – but nonetheless, points on the continuum which is the harmonic series.

It’s all becoming reminiscent of Heraclitus and the ‘unity of opposites’ once more I think! Read more here.

Pythagoras, Heraclitus and Hucbald…

It shouldn’t be too long before I  can post my next article in the series  ‘Pythagoras and the Music of the Future’. It has taken me some time partly because I have made a start on ‘digitising’ some of my earlier compositions to enable sharing.

The first fruits of this will appear in my next post introducing my composition, Songs of The Aristos for brass & computer-generated tape. The accompanying sound file was created using Sibelius 7 and the marvellous, free sound recording software Audacity. I am still ‘finding my way’, especially with the latter, so any audio clips that I post may leave something to be desired in terms of ‘engineering’. Please forgive.

Going back to Pythagoras and the harmonic series for a moment, I want to share a quote I recently came across, which I have a great deal of sympathy with. It’s from A Monk’s Musical Musings – an excellent, very comprehensive blog by a scholarly guitarist who goes by the nom de plumeHucbald‘.

“Lacking in all music theories that I am aware of from Western history is a neat and tidy description of why music works, and why it has evolved as we see from the historical record. There is no Einsteinian General Theory of Musical Relativity… yet.

For such a proposed theory to be compelling, it would have to relate directly – in all of its aspects – to the very nature of sound itself. Harmony, counterpoint, rhythm, melody, and form would all have to be explained as having originated within some feature that God and nature have given to sound, and sound alone. There is only one candidate for the feature I am describing, of course, and that is The Harmonic Overtone Series.”

I couldn’t agree more with the second paragraph. In fact, I think that study of the harmonic series could probably lead to a musical ‘Theory of Everything’ let alone Relativity! The problem for me is that Hucbald doesn’t seem to have much time for ‘modern’ i.e. non-tonal music judging by subsequent comments in his blog. It’s almost as if he holds the belief  (and if he doesn’t many others do) that post tonal music has somehow become divorced from the properties of the harmonic series. I can only agree to a certain extent and this is something I’ll be addressing in my forthcoming articles.

Nevertheless, for those interested in such things, there is a lot to be gained from looking at;

A Monk’s Musical Musings: Musical Implications of the Harmonic Overtone Series: Introduction.

Tuning tips for teachers of young/amateur bands and wind ensembles

tuning_fork

Many will be used to tuning to a sustained note, usually A, or in the case of brass or wind bands, it could be a B flat. The problem with this is that many players will, consciously or unconsciously, compensate by correcting the pitch with the embouchure. Once the music starts, the tuning is ‘out’ again.

I have found the following sequence for tuning instruments very useful. It is a lengthy process initially, but it speeds up as you and the players get used to it and it pays dividends.

  1. Tune the first player to a digital tuner. This is optional because the main objective is to have the players in tune with each other not necessarily to the exact concert pitch, but of course you won’t want to be too far out.
  2. Have the first player play a short ‘open’ note. Short means about one second, but not less.
  3. Immediately, get the next player to do the same. You will find it is very easy to compare the pitches and give the necessary ‘pushing/pulling’ instructions to the players.  After a while, this process can become quite quick.
  4. Go through this process with each of the players and the first player, occasionally back-tracking to check those who have been tuned.
  5. When a section has been tuned in this way then have them play long unison note ‘forte’.
  6. Listen, and you will hear either beats or the octave above the tuning note ‘ringing’ out!
  7. Repeat the above until you are satisfied.

We hear the beats or octaves because of ‘sum tones’ and ‘difference tones’:  When two notes are played simultaneously, they produce additional frequencies which are the sum of, and the difference between, the frequencies of the notes being played.  If the frequencies are just 2-3 Hz out, then the sum/difference tones will be below our hearing threshold, but they will create ‘amplitude modulation’ of the basic tone creating the familiar ‘wah-wah’ effect. If they are in tune, the clear octave above will be heard.

For the sake of clarity, let’s take A as an example. Everyone knows that in standard concert pitch A = 440 Hz.

440 + 440 = 880;  in tune so ‘A’ one octave higher would be heard.

440 – 440 = 0;  no lower pitch would be heard, but

440 – 438 = 2; one note is flat so ‘beats’ would result

It gets a tiny bit more complex when one note is sharp, but this serves to illustrate the point.

Of course, after this and when your rehearsal is under way, the focus will be on intonation (the players) rather than tuning (the instruments).  However, you will find that once these tuning habits are well established and the players are encouraged to listen critically to, and correct, their own intonation, a considerable improvement in the richness of sound – across the entire ensemble – will result.

Pythagoras and the Music of the Future

Harmonic Wave 2I am just about ready to introduce the first in a projected series of articles discussing, in accessible terms I hope, the influence that the harmonic series has had on musical development since the Middle Ages. I will be discussing not only the connection between the harmonic series and timbre (the obvious one), but also the connections between this and the conventions governing musical structures such as rhythm, melody and harmony.

Ultimately, I will arrive at the conclusion that there needs to be a clear, natural (as opposed to contrived), relationship between the the diverse sets of proportions inherent in the harmonic series, and musical expression – now and in the future. Ironically, or so it might seem, I will also argue that whereas the development of functional harmony and therefore tonality was strongly influenced by our perception (maybe subliminal – I don’t know) of  the ‘inner workings’ of musical sound, the music that has already left, and will leave, tonality where it belongs – in the past – is equally bound up with these inner workings – particularly as represented by the harmonic series.

Many will know a great deal about the relationship between the harmonic series and timbre already, so may not find anything particularly new in the first article which sets the scene, so to speak.  To find out if you’re one of them, click here.