Etude 2: Harmonics
If we produce sounds with different timbre but of the same pitch, obviously the frequency of such sounds will be the same. Frequency is expressed in Hertz (Hz), which is 'vibrations per second'. Like the pitch of A has about 440 vibrations per second or simply 440 Hz. High pitches vibrate much quicker and have higher frequencies. Like the A in the octave above will have a frequency of 880 Hz, so vibrating twice as much. But again, where is the timbre if there is just one number for the frequency?
When we produce a sound, we do not only produce the fundamental frequency of the pitch, but also a package of additional higher frequencies. And it is exactly this package of frequencies, which adds the specific timbre of the instrument so that our ear can recognize that a sound is produced by a flute or a violin, and that we can hear the difference between [o] and [ee].
To put this all together: if we produce a sound, we not just produce one frequency, but a complex of frequencies. From this cocktail of frequencies, we will perceive the fundamental (lowest) frequency as the pitch. The presence of the frequencies above this fundamental describe to us the timbre of the sound. If we speak about harmonics, we are actually referring to this complex of frequencies. Now have a look, and click the play button to listen, to the different frequency images and note that the [ee] has much more higher harmonics compared to the [o].
Please take a moment now to sing [o] and [ee] for yourself. Do so without moving the lips.
The Harmonics Series
The frequencies above the fundamental are always an integer multiple of the fundamental. If the fundamental has frequency N, then the additional harmonics will have a frequencies of 2xN, 3xN, 4xN, 5xN, etc. This results in a fixed series of harmonics and is called the harmonics series. How strong each of these harmonics is present in a certain sound decides its timbre.
In the image the fundamental frequency is represented by a one-segment vibration. The other vibrations have more segments (2, 3, 4 etc.), so a shorter wave length, resulting in a higher pitch.
About Pasta and the Salsa
In a similar way, we combine and balance the harmonics to add a unique timbre to a somewhat dull fundamental pitch. Using timbre in music is the art of balancing and controlling the harmonics, parallel to balancing the taste when preparing some food. Good music is like a good food: an amazing creation with a delicious taste!
Audio samples: Harmonics
Approach for playing Harmonics on the Flute
On a string instrument we can play a harmonic by softly touching the string in the middle, or at 1/3rd, 1/4th, 1/5th, etc., like we can hear performed on the guitar. Sometimes also called ‘flageolet’ or ‘overtone’, they basically all refer to the same concept. On the flute we are playing harmonics with traditional fingerings for example when playing the octave from the low E. To perform such a harmonic, we could simply:
- blow with more strength
- squeezing the lip-opening, so airspeed will be increased
- using tonguing to initiate the higher note
To find a suitable alternative, let's bring back the circle image, which I have introduced to you in the Introduction. There we concluded that we should avoid to study 'that what we already master' (the center). Instead we better focus on studying those difficulties which we do not yet master (remote areas). By integrating the techniques from the more remote areas into our daily studying we will increase our effectiveness and flexibility. This tells us that we should study harmonics in the following way:
- play p instead of f
- strive for a high, open and relaxed lip-opening, which will open the sound
- play legato, instead of tonguing
- use vocalization, varying the acoustic of the mouth cavity
To change our vowels when speaking, we are constantly changing the acoustical space of the mouth cavity. All these different shapes result in different harmonic characters. It is like we use the mouth cavity to decide how much of which harmonic we want to activate for a certain sound, similar to filtering a sound with an equalizer. If you look to the frequency spectrum analyses in the image you can clearly see the differences between the [o] and [ee]. Compared to the [o], the [ee] has less presence of the lower harmonics, but much more presence of the higher harmonics. So this vocalizing is actually a very common thing, since we use vocalization all day long when we speak and create all the different vowels of our language.
Vocalization is one of the most fascinating and useful aspects in relation to performing harmonics and to flute playing in general. It makes us realize that we should not only ‘blow the flute’ but also use our body, especially the mouth cavity, to support and ‘shape’ the sound. This may feel like you become part of the sound, or the sound part of you. Or like you are singing the sound, and feeling the resonance inside your very body. To do this correctly, one should consiously use the mouth cavity - and not the lips - to create the desired vowel.
Audio samples: vocalization techniques by the mouth cavity
So now let's include all this information into one study: vocalization, decrescendo, legato and breath support. A great study which will lead us towards developing more flexibility and a more relaxed embouchure, resulting in a more open and clear sound. So let's grab the flute and move on to the study below.
In this study we perform most gradual transitions from one note to its next harmonic. It means, there are always two notes on one full breath. Perform these transitions extremely 'poco a poco' especially at the very moment, where you move from the lower to the higher note. In the notation, we use a diamond note-head to indicate the fingering and the usual note-head for the actual pitch, whenever the fingering and the sound do not coincide (see score). While moving towards the higher harmonic, keep in mind the following remarks:
- Use an open vowel like [o] to support the lower sound, and change your vocalization gradually towards a smaller vocal space like [ee] for the relative higher sound.
- Start with a mf or f and make a decrescendo until the next harmonic appears.
- Use legato.
- Keep an open and relaxed embouchure without any squeezing the lips.
- Start with a relaxed breath support but when making the decrescendo, intensify the breath support.
We will start the exercise on the low-C fingering (or low-B if you have a B-foot-joint). At first produce a low-C (or B) sound and transform this into its octave. Take a breath after each transition and move on to the next step of the harmonic series. After some steps, you may realize that things are getting more difficult. At that point, when you can’t produce the higher harmonics anymore without unwanted squeezing, it is time to change the fingering and to repeat the same study half a note higher. In this way you move on chromatically until the low G fingering to finish this exercise. All together it might be just a 10 minutes exercise, but once repeated on a daily basis it may improve your harmonics and general flute sound dramatically.
Etude 2: Harmonics
After you have worked on the study above, you can move on to the Etude 2: Harmonics of my book For the Contemporary Flutist. This etude, actually quite entertaining, is structured as a rondo with an increasing excitement. The beginning material uses only two fingerings: the low-C and D. While alternating between these two fingerings you combine the harmonics of both fingerings and resulting in a melody. It is like a one-finger melody, just for the right-hand little finger! Especially with the higher harmonics one should take care not to tense the lips, but instead use vocalization and breath support to create round-character, enchanting harmonics.
The Road is our Goal
Remember when studying extended techniques, that the study itself is both the road as well as the goal. When we enjoy the road, the result will come without force and without stress. The same goes for the harmonic study. Our goal is not to play the next harmonic. Our goal is to 'invite' the next harmonic by preparing our body (by vocalization with mouth cavity and by breath support) so that the next harmonic may sound. If we force the harmonic it will not sound beautifully, but just stressed and dull. If we 'invite' the harmonic, maybe it will not sound, which is no problem because the road is our goal. But if we 'invite' again and it does sound it will be full of charm, open sounding, and with a relaxed expression for both the listener as well as the flutist.
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