Determining The Sparsity or Density of a Chroma Vector
I am considering a similar problem as well and I found Gini index as one of the solution: Gini Index as Sparsity Measure for Signal Reconstruction from Compressive Samples. Please have a look at the definition in page 3. It is normalized in the range from 0 to 1 as the least sparse or the most sparse the vector is, respectively. 

The code below is an implementation in Python, though I am not sure about returning 0 if the input is a zero vector:

def gini(v):
    v = np.array(v)
    sort_v = sort(abs(v))
    norm_v = sum(sort_v)
    if norm_v==0:
        return(0)
    else:
        sig = 0 
        for k in arange(len(sort_v))+1:
            sig+=(sort_v[k-1]/(norm_v))*((len(sort_v)-k+0.5)/len(sort_v))
        return(1-2*sig)