Constructing a tone through additive synthesis
You say:


  I'm not after any particular timbre, certainly I'm not try to emulate a
       piano, I'm simply after a harmonic tone that is pleasing to the ear.


but I think something that is pleasing to the ear is probably harder to quantify than emulate a piano!

Bill Sethares has done lots of good work (both theoretically in signal processing and practically as a musician).  Bill wrote a book specifically about these ideas.

You can hear an example of his work, called C to shining C here. There is a discussion about it on Wikipedia.

The central idea is that consonance and dissonance are related to psychoacoustics: how the brain perceives sound.  As Bill says:


  For instance, the perception of "timbre" is closely related to (but also quite distinct from) the physical notion of the spectrum of a sound. Similarly, the perception of "in-tuneness" parallels the measurable idea of sensory consonance. The key idea is that consonance and dissonance are not inherent qualities of intervals, but are dependent on the spectrum, timbre, or tonal quality of the sound. To demonstrate this, the first audio track on the accompanying CD plays an example where the octave has been made dissonant by devious choice of timbre, even though other, non-octave intervals remain consonant. In fact, almost any interval can be made dissonant or consonant by proper sculpting of the timbre.


So, now that I've said it's too hard to answer your question, I'll try to give some pointers.

The main parameters to look at are the amplitudes ($A_k$), decay parameter ($\alpha_k$), (relative) phases ($\phi_k$) and frequency ($\omega_k$) relationships between your tones:

$$
s(t) = \sum_{k=0}^{K-1} A_k e^{\alpha_k t} \sin( \omega_k t + \phi_k)
$$

For a harmonic sound, you probably want to select $\omega_k = (k+1) \omega$ where $\omega$ is your fundamental frequency.

For "brighter" sounds, you want $A_k$ for $k&gt;1$ to be larger (i.e. the higher harmonics have greater amplitude).

You can do flanging or phasing by modulating the phase:
$$
\phi_k(t) = \Phi_k \sin(\omega_\phi t)
$$
where $\omega_\phi$ is much lower frequency than $\omega_0$.