All great pieces for the cello have their danger spots, and no one is immune from them. In Cello Practice, Cello Performance, I devoted an entire chapter (Chapter Seven, "Composing Your Own Etudes,"pp. 87-104) to how we can teach ourselves to master these virtuoso sections.
I wrote a lot about the Saint-Saëns Concerto No. 1 in my book, because it's usually the first of the great Romantic concertos that a student learns. For this reason, it's often thought of as an easy piece, but that's simply not true--there are some very challenging passages. For example, this section in the third movement where, following a heart-rending theme in the lower register, the solo cello takes off on an ascending scale that morphs through several keys up to the very top of the fingerboard, and then takes the pitch up into the stratospheres using artificial harmonics.
When played well, the effect is magically, spellbindingly glacial. But everything depends on being able to get your artificial harmonics to work. Many players are able to make it as far as the second B-flat before the harmonics fail, or are so scratchy that we can't get the bell-like clarity Saint-Saëns demands.
So what can we do to make this passage in harmonics (a) reliable and (b) effective?
The starting point is a rational left hand position: gently rounded, more or less the same position we use for playing octaves. The base knuckles in particular must be curved, not flattened out, so that you can have the flexibility to contract the third finger closer to the thumb the higher you climb. Here's a picture I took of my hand, with the camera positioned parallel to the fingerboard.
Although you can't really see this in the picture, my thumb is touching the string at a point in the middle of my thumbnail. I find that this is the way to get the cleanest harmonics. My third finger just grazes the string at the interval of a perfect fourth above my thumb.
My next point may seem almost too obvious to mention, but to succeed in this passage, you have to make sure that your thumb is playing the "base pitches" in tune. In the downloadable PDF below, I recommend starting to learn the scale with thumb only for intonation. Note that the scale goes through several transformations in the last two full measures: we start with B-flat major, briefly tonicize G major, and end up in F. Study the orchestral score so that you can keep the orchestra's harmonies in your mind's ear, and memorize the patterns of major and minor seconds. After you've done this, maintain the "perfect fourth" hand position and practice the third finger in stopped notes to make sure you have it in the right place.
Many players make the mistake of assuming that if something goes wrong in artificial harmonics, it's the fault of the left hand. But as with many techniques, I actually feel that artificial harmonics are a both-hands technique (see Cello Practice, Cello Performance, Chapter Two and Chapter Four). Here's what you can do with your bow to make sure your harmonics "sound."
1. Play in the upper half of the bow. The weight of the lower half, or any too-accented bow change, can disrupt the equilibrium of your sound during bow changes, which puts the harmonics "off."
2. Use a contact point about an inch from the bridge. You want to be relatively close so that the harmonics speak, but any closer and you run the risk of getting a hairy, unfocused tone.
3. Play the harmonics with a straightened arm, not bending your elbow. This looks disconcertingly like bad technique, but for artificial harmonics you don't want weight or vertical movement disrupting the side-to-side horizontality of your bow strokes.
4. Use only a little bit of bow. Too much bow speed and hair coverage can disrupt the harmonic.
Click here to download a PDF of preparatory exercises for this passage.