Balanced word
Let d ≥ 0. A linear or circular word s (representing a periodic scale if circular) is d-balanced if its balance satisfies the following:
[math]\displaystyle{ \operatorname{balance}(s) := \max \big\{ \big| |w|_{x_i} - |w'|_{x_i} \big| : x_i \text{ is a letter of }s\text{ and }k = \operatorname{len}(w) = \operatorname{len}(w') \big\} \leq d, }[/math]
where |u|xi is the number of occurrences of the letter xi in the word u. A scale is balanced if it is 1-balanced.
A balanced word in N letters has a maximum variety bound of [math]\displaystyle{ N \choose {\lceil N/2 \rceil} }[/math].