© 1998 by Susan Fowle
Natural | Artificial | Notation | Physics
Harmonics are based on physical principles (see Physics for a short explanation), but more important to string players, they are fixed points on the vast expanse of pitches possible on a stringed instrument. They also allow one to play notes otherwise difficult to reach. I learned to value them for both these virtues, and that's why I remember where they are on the instrument. I've been surprised by the number of people who have asked me how to produce some particular harmonic, and thus the incentive for this little description.
On the cello the comparable locations are valid, although you'll have to interpret fingering and position for yourself, and it's likely you'd use the thumb instead of the first finger for artificial harmonics.
The first octave above the open string is the first one I learned, being one whole step above the 4th finger in 3rd position, or the top note in 4th position. This is also quite convenient as a fixed point when shifting into or checking the intonation in any of the positions from 4th through 7th. The note is the same pitch whether produced as a harmonic or a firmly pressed note.
The octave plus a fifth is also a very useful harmonic. The lower place is with 4th finger in first position or 2nd finger in third position. The note produced by pressing firmly with the finger (stopping the note) is one octave below the note produced as a harmonic at this point. Example: play an A on the D string; producing a harmonic here sounds an A one octave above the open A string. String players, perhaps especially cellists, use a combination of the first octave harmonic on the A string and the octave plus a fifth on the D string to produce two identical pitches to check their tuning. The upper place on the string is again the same as the stopped note.
The note two octaves above the open string is produced with the 3rd finger in first position. This becomes especially important in artificial harmonics. Play the natural harmonic A on the A string with the 3rd finger (where a D would be the stopped note). Now create this same relationship 1/2 step up: lift your 3rd finger, press firmly with your first finger on the Bb and touch the Eb lightly with your 4th finger. You've just produced the most common "artificial harmonic" by essentially moving the nut up 1/2 step using your first finger and substituting your 4th finger for your 3rd. You can create tones two octaves above wherever you place your first finger if you maintain the relationship of 1st and 4th fingers.
An artificial harmonic of an octave and a fifth higher than the first finger can also be played if you can stretch your 4th finger one whole tone higher: press Bb firmly, touch 4th finger at F. This becomes more practical in higher positions because the notes will be closer together.
Play around with both natural and artificial harmonics on all strings so you learn for yourself what notes are available and where to find them (otherwise known as "it is left as an exercise for the reader..."). Have fun!
You will see harmonics notated in several different ways.
The composer or music publisher may show you how to produce the desired pitch: for natural harmonics, a diamond shaped note generally means to touch the string where you would stop the note if it were not a diamond. An ordinary note with a diamond note a fourth or fifth above it is an artificial harmonic. Two diamond notes one above the other indicates 2 natural harmonics, played as a double stop.
You may have to figure out for yourself how to achieve the proper pitch, in some cases whether this is possible as a natural harmonic or it must done as an artificial harmonic. A 0 as a fingering indicates the note is meant to be played as a harmonic. It's possible the composer used the 0 as a substitute for the diamond. The word "harmonic" or just "harm." may be used instead.
One of the more difficult harmonic calculations for me to sightread is to have a passage written in a particular octave with 8va----- written above it, indicating it should sound one octave higher, and to know I have to think down one octave from what I see so I know where to place my first finger for the artificial harmonics! Good luck with your calculations.
Touching the string in the middle of its length divides the string into 2 equal parts, and causes each half to vibrate at twice the open string frequency, producing a tone one octave higher than the open string.
You divide the string into 3 equal parts when you play the octave plus a fifth harmonic, each third vibrating at 3 times the frequency of the open string.
Touching the string at either two octaves higher location divides the string into 4 equal parts, each part vibrating at 4 times the frequency of the open string.
You may be able to see the harmonic vibrations on a cello or string bass. I can see the first octave vibrations on my viola's C string.
Last updated: 8-29-2001
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