I'm trying to learn "Iowa Spring" by Paul Seitz (on the cello) before school starts. in measures 21 through 25, it has repeating half notes that are d and a (on the a string), but the a is 1 octave up from the open a string. I'm pretty new to shifting, so it's quite difficult but I'm improving quickly, as I have been practicing daily. my dilemma is, that the notes each have a small, hollow circle above them. I thought that meant to play the note as an open string but obviously don't have an open strings that are that high pitched! please get back to me ASAP(: thank you!
The small circle indicates a natural harmonic. The D should be played on the D-string by lightly touching the string halfway up with your left hand and bowing as normal. Same thing for the A except on the A-string. The sound is purer than that created when you press your finger all the way down, but the pitch is the same. Obviously, vibrato is impossible.
That is the octave harmonic. Half-way up the fingerboard you will find a spot on each string that if you place your finger lightly on the string without holding or pressing down will emit a slightly hollow sound that is an octave higher than the open string on which you are playing. The D would be played in this way on the D-string, and the A would be played the same way on the A-string. The small circle is notation for a natural harmonic. Flageolets are more complicated, and from your description, are not necessary here. Hope this helps.
The easiest way to approach these octave harmonics is to place your left hand thumb in the curve (underneath where the neck begins to meet the shoulders) of the cello and loosely stretch your third finger up to this spot. Lay it lightly on the string and play. Once you find this "sweet spot" you shouldn't have much trouble finding it again. You'll get used to shifting and finding it very quickly.
Flageolet. You touch the string lightly at the one-octave mark instead of pressing it to the fingerboard, and the string will give sort of a slightly hoarse octave when bowed correctly. Your description is not good enough to guess what the d is about: is appears to be a flageolet as well, but it's hard to guess where.
Flageolets can be played one octave above the string frequency, one octave and a fifth (by fingering a fifth), two octaves (by fingering a fourth) and then stuff gets complicated. Citing just from memory and don't have a string instrument here, so better check with the actual instrument before believing me.
Flageolets become trickier when using higher notes. Also one can play them by fingering one note (typically with the thumb) and touching another one. Which is seriously tricky.
The cello is actually one of the string instruments where flageolets are used most often: with a violin, they tend to get too wheezy to be pretty.