There are lots of places to learn about harmonics; all of the books have little blurbs on them and there are plenty of guides online. They all say that you can do this or that, but they all seem to talk about things in isolation, as if the only time you play a harmonic is as a whole note with a rest before and after it. It is very similar to the information, or lack thereof, on double stops. In fact there are many similarities between the performance of harmonics and double stops, so some of the same considerations apply.
First let’s look at the basic types of harmonics: natural and artificial (or false). This will be brief as there are many other resources that go into a lot of details about this. I am going to cut to what is practical.
Natural harmonics are where the player touches the string only on a harmonic node. It is a good idea to commit these to memory as the same math applies when we get to artificial harmonics.
- Touch at the octave, splits string in half, pitch = an octave
- Touch at the 5th, splits string into 3rds, pitch = an octave and a 5th
- Touch at the 4th, splits string in 4ths, pitch = 2 octaves
- Touch at the Major 3rd, splits string into 5ths, pitch = 2 octave and a major 3rd
These can also be played in other positions on the string. For example to get an octave and a fifth, it does not matter which node you touch so long as it ‘cuts’ the string into 3rds. This means the player can access the same harmonic from either end of the string. There are also many other natural harmonic possibilities. The ones I mention are the most common, and apart from the octave, the ones that transfer well to artificial harmonics.
When considering the difference in sound of a natural vs. an artificial harmonic, it is good to just think of them in the same way we think about using an open string vs. a stopped string. While not quite as obvious as it is with normal notes, the difference is still there. Open has a slightly bigger, more strident sound than fingered, where the pad of the finger takes the edge off a bit.
While natural harmonics are very usable on single notes, when you want to play phrases you need to consider artificial harmonics. So far we have been limited to fundamental pitches of the open strings, which limits the notes available as harmonics. But if we look at artificial harmonics, we can use any pitch as the root. To play an artificial harmonic you finger the fundamental, then touch at the node. The math is the same as with the natural harmonic; the only limiting factor is what intervals the hand can stretch to. For example, the first harmonic, the octave, is not possible. The easiest and most common is what I call a “touch 4” (two octaves). This is easy on all of the string instruments except the bass, which I will explain later.
What I have covered so far is the same information that is in most books. There are a few things they don’t say much about, however.
You need to consider the performance of artificial harmonics. In isolation anything is possible, but in reality their performance shares some of the same considerations as double stops, as you are using two fingers at the same time. That means it is hard to play a legato line. If the note moves a step it is pretty easy to quickly move it. But be warned, it is hard to land on the next pitch perfectly. As you move up or down, the distance between the fundamental and the node change. It is not as simple as locking your fingers at a set distance and moving them. This makes targeting a pitch a little difficult, and it is easy to miss the next note in a phrase. You often hear someone in the section miss the harmonic. You might get a dead note, the fundamental, or another harmonic. If the shift is larger than a step, then you will either hear a slide or there will be a gap as they pause the bow and shift the fingers.
There are ways around this, though, and it is possible to get a nice legato line with some careful orchestration.
This is how it will sound, and could be written.
This is how I would write it in order to get a legato result. This is still just the firsts, they will divide on the stand.
You will notice that I have overlapped the notes a little. Strings have a tendency to play notes a little shorter than the written duration, they also ‘tail off’ the ends. By overlapping the notes you counteract this and will get a connected line. You could just write the true duration and ask them to play a little longer but if you are short on time, this way you do not need to say anything. A very cool effect is to lengthen these even more so you really hear the overlap. It works even better when you have Violin I on the left and Violin II on the right and instead of dividing on the stand, have the firsts play the top and seconds play the bottom. It is a great ‘stereo’ effect.
There are several reasons as to why the touch 4 is the most common. Firstly, the math is easy, it sounds up two octaves. Secondly, the shape of the hand on the violin and viola is perfect for the touch 4, it is right where the pinky is by default. The touch 5 is a stretch, so not as ergonomic. As the string is being cut into divisions to play a harmonic, the touch 5 is a slightly bigger sound than the 4. The touch 3’s are not hard to play but as the string is now cut into many pieces, the sound is not as clear. The larger the instrument, the less this is an issue as the strings are longer.
Real World Examples
Here is a little melody that came up in a recent cue. The only way to have it played accurately was to split it up. The top two staves are dividing on the stand. We had 24 violins so it was split 8/8 and then the pizz line was played by the leftover 8. In the studio, all violins are copied on the same part, so these types of divisions are not a problem. By mixing the touch 4 and 5 harmonics, I could leave the hand in the same position for several notes, making the part much easier to play. The fact that different notes came from different players was not noticeable in the resulting sound.
Here is another figure from the same cue. I notated the first ‘B’ as a touch 5 as the hand is then in an easy position for the next harmonic. I could have just written the pitches with circles as in the guide staves, but I will put money on someone playing the E as a natural harmonic and thus not balancing with the other notes.
For natural harmonics you place a diamond note on the node and specify the string with a roman numeral or “Sul [string name]” (unless it is only possible on one string).
Historically, it has been common to write all natural harmonics as hollow diamonds, which means that you have to write the rhythm above if it is not obvious. On occasion, I have written using solid diamonds and not had an issue, but this is a place where I feel the traditional way is not the most ideal! In 99.9% of the work that I do, I never use this system anyway. The easiest way is to write the sounding pitch and put a circle above (see the first ‘sounds like’ example above). If it is an obvious natural harmonic, it will be played as such.
In the studio, I prefer to use artificial harmonics. The advantage of artificial harmonics is that the players can tune them to the context, whereas natural harmonics are locked in.
There are two ways to notate the artificial harmonics: write the sounding pitch and put a circle above it, or write the fingered notes. Over the years I have gone back and forth a bit on what is best, but in most cases now I write out the fingered version. It is clear for the players and it also helps me visualize what the player has to do, including where their hand will be, and you can ensure they play an artificial, not natural, harmonic. If you are unsure of what you are doing, go for the sounding pitch and the circle. If you do know how to create the harmonic, then I think it is better to write out the fingering. One problem with using the sounding pitch method is that when you get high, you need to use 8va or 15ma and that can get confusing to read and interpret. It can also take time for the players to work out the best way to do it and which nodes to use. The circle method also presents issues when it comes to basses, as there is a school of thought that harmonics in treble clef (written with the small circle) are written at pitch (not transposed), so you need to clarify. If you write the fingered notes there is no confusion.
You will often see the sounding note written above the fingered notes in parentheses. This can be helpful in academic situations or if you are writing lots of different harmonics, but it is more a convenience for the score reader and not the players. After all, the fingering can only produce one outcome. In my scores I do not add the sounding pitch, as I know what the note will be and so do the players.
I have also seen people get confused and merge aspects of these different methods. For example, adding a circle above a diamond. The diamond indicates a harmonic node, so it is thus… a harmonic! The circle in this case is redundant and incorrect, as it means ‘harmonic at this sound pitch.’ String players are pretty intelligent people and will work most things out, but just like it is possible to read text with spelling mistakes, it is not necessarily pleasant. One should always strive to be correct, not just close enough.
Something else that seems redundant to me is the continuation of harmonic circles on long tied notes.
This is the correct way to do it, but I question whether the circles are needed after the first note. I have never done this, and have never had my section all of a sudden swap to a normal note.
Who can do what?
Violins can play all of these harmonics, as they can easily reach a fifth. Violas can also do it, however the fifth is harder for people with smaller hands. It gets more interesting with the cello. As the notes are much further apart, they can only reach the fourth by moving the whole hand on top of the fret board and using the thumb to hold down the fundamental. The stretch of the fifth is not possible until a fifth up the string, so G on the C string is the first time they can reach a node to create the harmonic. The bass has an even harder time. They can’t reach until a major sixth up and like the cello, they also have to move the thumb on top. The notes are far apart on the lower part of the fretboard, so it is impossible to stretch. The added difficulty with the bass is that due to the positioning of the fretboard, they cannot comfortably get their hand on top until the sixth. At this position, the touch 3 and touch 4 harmonics are possible. When they move up to the octave, touch 5 is also an option. These are all safe rules for orchestral playing. For soloists, the boundaries can be pushed and certain players with big hands or limber shoulders can do more, but check with the player before writing.
Remember, though, that natural harmonics still work on the ranges where the hand cannot reach.
There are some very cool effects you can create with harmonics. Harmonic slides are easy and very effective. A natural harmonic slide is where you lightly touch the open string and slide the finger around. As it moves it hits different nodes and the pitch changes. The pitches will all be based on the harmonic series of the open string. A more interesting version with a more random sound outcome is the use of artificial harmonics. As I mentioned earlier, the distance between notes gets closer as you go up the finger board. If you want to slide the same pitch, you have to adjust the distance between your fingers. But if you don’t adjust, and keep them locked, you will touch different nodes as you go up and down. When you have a whole section doing this, it sounds pretty cool, like a flock of seagulls.
There are many ways to notate something like this. You could come up with some crazy graphics, but I always prefer to use standard notation and a ‘to the point’ text description. I love it when I see crazy graphics and then a huge explanation of what the crazy graphic means.
By default, players do not play harmonics with vibrato. They can though; it’s best to check with a player and see if that is a sound you want. It can be a cool effect, but in general we expect harmonics to be glassy and static.