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.

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.