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For the Contemporary Flutist

introducing the 12 flute etudes on extended flute techniques from the etude book 'For the Contemporary Flutist' by Wil Offermans


Etude 3: Difference Tones

In this chapter we will look to Etude 3: Difference Tones from the book For the Contemporary Flutist. This etude is primarily to experience, to sharpen the hearing and to enjoy the phenomena of the difference tone. Like we did with the harmonics, we will again talk about frequency. Once you have some understanding about the difference tone, you will listen to sound with greater care and more detail.

Mozart's vs. Tartini's Philosophy

You may have heard about the famous expression by W.A. Mozart: "What's even worse than one flute? …Two flutes!". Why was he saying so? And what Mozart would have thought about the flute ensemble, which is gaining popularity now-a-days? (4 flutes, 10 flutes, 100 flutes!!!).

If we try to understand Mozart and look seriously to his statement then the explanation might be related with an acoustic phenomena, where the purity of the two flutes is disturbed by a resulting third sound: the difference tone. The difference tone teaches us some very special logic: 1+1=3! This means: [something] + [something] equals not 2x, but 3x [something]! To put it simple, if two sounds vibrate in the air, they will meet and as a result produce a third sound. Throw 2 stones into a quiet pool and watch what happens when the waves of each stone meet. The same happens with sound waves…

But when an orchestra is playing it must be a wild pool of sounds, in which 60 or more sound waves interfere and create other waves? Yes indeed, and that is why it is so good to know a little about the difference tone. It actually always exist when more instruments play together, however it may be more apparent with higher pitches and in certain circumstances.

WA Mozart
Wolfgang Amadeus Mozart (1756-1791)
Giuseppe Tartine (1692-1770)

The Difference between two Frequencies

When two notes are played simultaneously, there is a simple rule to calculate the pitch of the difference tone: 'the frequency of the difference tone' equals 'the higher frequency' minus 'the lower frequency'. So the difference of the frequencies of the two sounds will be audible as a third sound: the difference tone. Indeed amazing!

Difference Tone

The image below shows us an illustration of an example with simple numbers. If one sound has a frequency of 10Hz and a second sound has a frequency of 8Hz, there will be a difference tone of 2Hz (10 minus 8). A more realistic example could be: frequency 1 = 2400Hz; frequency 2 = 2480Hz; so the difference tone will be 80Hz.

By the way, the difference tone is also known as the combination tone, sum tone or beat frequency and was discovered by the violinist Giuseppe Tartini (1692-1770). That is why we sometimes also call it the Tartini-tone.

Difference Tone

Difference Tone by Singing and Playing simultaneously

But how does a difference tone sound? Can we hear it? Well. if you are alone in the room… mmm… it might be difficult (Mozart complained about two flutes, not about one flute). So call your flutist-friend and invite him/her to come over, because now we need two flute sounds! And while waiting for your friend to arrive, let's already enjoy some difference tones by yourself by singing and playing simultaneously. Indeed in that way you can also play two sounds, or actually three. Remember 1+1=3!

pasta y salsa
Sing a high pitch using your falsetto voice. Don't worry, it doesn’t need to be a beautiful sound, it just should be high and a kind of stable. Remembering the vocalization as discussed with the Etude 2: Harmonics, use a small-throat vowel, like [ee], for singing this high pitch. Find the same pitch on your flute and now play and sing both simultaneously, combining your falsetto voice and the flute sound. Listen most carefully, while trying to have both sounds well in tune. You may clearly hear some distortion, a kind of waving or beating in the sound. That’s right, this is our difference tone at work! Because there will be easily some difference in pitch between the two, you may hear a wave with one or more beats in one second (so a few Hertz). This beating is a sound wave, however it is below the human hearing. We can only hear from about 20 Hz upwards. The difference tone becomes audible when we increase the difference between the flute and the voice. The most simple way to do so is to lower the voice slowly (glissando down). Now, you will hear that the waving will accelerate until reaching something like 20 Hertz. From that point we will hear the difference tone as an extreme low sound. This sound will further rise if we continue to lower the voice. Isn't it fascinating. In this way you can produce three pitches!

Ah, someone is ringing your doorbell. Your flute-friend has arrived to share the difference tone. With the two flutes, we can enjoy even more difference tones. Here are three exercises to experience with your friend:

Difference Tone by two Flutes

1/ Ask your flute friend to repeat a long high-G note. Do not play too loud and be sure to keep a stable pitch without any vibrato. Now, you are going to play the same high-G simultaneously. Listen carefully to play the same pitch. When you are out of pitch you will hear a slow waving. There is a point where there is no waving. At this point you are playing exactly in tune! At that moment there is no difference in pitch, so no difference tone. Next change role, so that your flute friend has to find the no-waving correct high-G pitch while you are playing the stable high-G.

2/ One player performs again the stable high-G repetitively. The other player plays a high-G, but on purpose a bit out of tune by rolling the flute inwards and outwards, so changing the pitch. When making a small pitch bending, you can clearly hear the resulting wave either accelerating or slowing down. If you make a wider pitch bending the resulting wave may even become audible as a difference tone!

Difference Tone Two

3/ Again one player performs the stable high-G. The other player starts from the high-G and slowly plays chromatically upwards. You now should hear some clear difference tones. You can also play chromatically downwards and again you will hear a rising series of difference tones, however a bit less steep. Remember that the difference tone will rise if the difference in pitch is increased.

Difference Tone Three

Etude 3: Difference Tones

To enjoy more difference tones, have a look at Etude 3: Difference Tones. This piece has indeed three staff lines: two for the flutists and one for the difference tone. So indeed 1+1=3! We can also see that the difference tone becomes more and more audible during the etude. A quick analyze of Etude 3:

  1. The piece starts similar to the above studies with both players performing high-G and small fluctuations (by pitch-bending). Consequently the difference tone only appears as waves (1~5 Hz?).
  2. As soon as other notes than the high-G are being performed we can hear extreme low difference tones becoming audible (from about 20 Hz onwards).
  3. In the second half of the piece the pitch difference between the two flutes widens. As a result we hear higher difference tones (100 Hz and higher), creating some entertaining difference tones melodies.
  4. At the end of the etude, when our ears are totally accustomed to the presence of the difference tone, both flutes suddenly perform low sounds and a low-C# unison at the end. This sound - in contrast with the part before - is so extremely quiet and peaceful, because of the surprising absence of the difference tone. This quietness is further accentuated by the second flute, who performs some special fingering on the F with the ring-finger of the right-hand (R4) down. These are actually some bamboo tones producing some really enchanting sounds to finish the piece quietly.

Etude 3

Final Thoughts

This etude is to enjoy the difference tone. You might agree with Mozart's philosophy ("I don't like two flutes!"), but at least we now should be able to understand a little about the difference tone and that what attracted Tartini while he was playing his violin.

When playing the flute alone, we also sometimes can hear some difference tones. This can happen when the room has enough reverberation, so that the echo of the original sound interferes with the live sound. This will be more apparent with quick note changes (trills!) and high pitches (yes, the piccolo!).

A similar effect is produced by many ethnic flutes, especially small flutes, often in combination with big drums. During my world-wide flute performance Round About 12.5 (see the Introduction) I could meet several of such a small flute ensembles where an ensemble of small flutes generates lots of exciting difference tones. On the photos you see the flutes from Zipaquira, Colombia and Nara, Japan.



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