“Harmonics” refer to the notes that sound when instead of stopping the string firmly with a finger, we just touch it lightly. Harmonics can be divided into “Natural Harmonics” (only one finger touches the string) and “Artificial Harmonics” (a lower finger – usually the thumb – actually stops the string firmly, while a higher finger just touches the string gently). Before we talk about the differences between these two types of harmonic, let’s talk about their similarities.
Harmonics take us into a different physical and sound world from normal stopped notes and can teach us a lot, especially about “not forcing”. For both the left hand and the right hand, harmonics teach us to use delicacy and lightness, rather than pressure. When using harmonics we are transformed from opera singer into child soprano, from bass (or tenor) to falsetto (countertenor). When playing harmonics, volume, vibrato, density and intensity are replaced by purity, lightness and innocence. Compare the following four versions of Mary Had A Little Lamb: one is played normally while the other three are played with harmonics of different types (natural and artificial).
HARMONICS AND THE BOW
For harmonics, we not only can, but probably even need to, use a point of contact somewhat closer to the bridge than for normal (stopped) notes. A harmonic played “sul tasto” (with the bow over the fingerboard) is a harmonic that risks not sounding. In fact, “sul ponticello” doesn’t exist for harmonics: no matter how close to the bridge our bow is, it is quite difficult to get the sound of a harmonic to “break”. Harmonics not only encourage us to play with our bow point-of-contact closer to the bridge, they also encourage us to use faster bow speeds and lighter bow pressure than we would for “normal” notes. The French Impressionists (Debussy, Ravel etc) make very frequent use of harmonics whereas Brahms, Wagner and the other German Romantics basically never use them. What a difference 1000km and 50 years can make !
HARMONICS AND LEFT-HAND FINGER PRESSURE
Harmonics give our left hand the unique, wonderful and almost magically effortless experience of playing without finger pressure. The simultaneous combination of total relaxation of finger pressure with the need for tension in other parts of the hand can however create some curious situations:
- the complete absence of finger pressure in natural harmonics can lead us to unconsciously relax the hand so much that we no longer separate the fingers sufficiently to reach the required distances, especially in the case of extensions. Try the “Mary’s Harmonic Lamb” example above (with natural harmonics) to see if this is also true for you. This problem possibly only significantly affects smaller hands
- in the case of artificial harmonics, in order to produce a clean clear harmonic we need to combine the absolute lightness of touch of the higher (harmonic) finger with a very firm pressure of the stopping finger (usually the thumb). This is quite a feat of fine motor skill and coordination.
- a similar situation occurs in those double-stops (or chords) in which we may prefer to use a natural harmonic on one of the notes in order to give both intonation security and added resonance. Using one finger with very light pressure and the other finger(s) with firm pressure does not come naturally and will probably require practice:
NOTATION OF HARMONICS: DOUBTS, INCONSISTENCIES … AND ERRORS
One of the complications associated with harmonics is that there are usually several different possible ways (fingerings) to obtain the same harmonic pitch. There are not only just several different natural harmonics which give the same pitch but we also have the possibility of using different artificial harmonics to play any possible harmonic pitch. Because of this large choice, composers often don’t know how to notate harmonics in the most practical cellistic way. Sometimes composers will just write the pitches they want, with the harmonic sign over each note, for example:
This type of harmonic notation requires that the cellist work out the most appropriate fingering, and we will often need to rewrite the notes according to how we would like to finger them. We saw above how this “Mary Had a Little Lamb” tune could be played entirely with natural harmonics. But it could also be played using artificial harmonics. In both cases it needs to be almost completely rewritten in a way that, instead of writing the actual sounding pitches, we write what we actually need to do in order to make those pitches, for example: (and see also the version with natural harmonics above)
At other times, composers may try and work out the best fingering. If they get it right then we are lucky …. we don’t need to rewrite anything. But quite often they get it wrong! In these cases, once again, we may need to rewrite the passage or some of the notes in it. The following example, from Stravinsky’s “The Rite of Spring”, illustrates these two situations. First is what Stravinsky wrote …. and then the cellist’s playable (renotated) version.
Often, as in the above example, we will end up using a mix of natural and artificial harmonics for passages in which the composer has simply specified “harmonics”.
OUT-OF-TUNE NATURAL HARMONICS: AN ERROR OF NATURE?
Normally we would expect natural harmonics to be perfectly in tune, according to all the beautiful mathematical Pythagorean laws. How could dividing the string in perfectly equal proportions (in half, in three, in four, in five etc) not produce perfectly in-tune notes? Well, nature and physics play some tricks on us and as we divide the string into smaller fractions the harmonics become increasingly out of tune. Certainly, the harmonic that we get when we divide the string into five equal parts, is consistently flat, no matter on which node of the harmonic we place our finger. For this reason, no matter how it is notated, we will probably be better off playing it with the artificial harmonic. In this way, we can correct its intonation. This is especially important in long, held harmonics. It¡’s a shame that nobody told Ravel this vital bit of information!
For a detailed discussion of both Natural and Artificial Harmonics, click on the following links: