What is the general term for a condition where the chromosome number is not a multiple of a complete set?
When a complete set (genome) of chromosome is added or subtracted the condition is called Euploidy. When there is addition or deletion of a single member chromosome the condition is called Aneuploidy.
Euploidy is common in plants but not in animals. There are varieties of fruits and cereals which are polyploid, i.e. in 3n/4n/6n condition.
Animals including humans show aneuploidy. For example children affected with Down's syndrome receive three #21 chromosomes during zygote formation, hence all cells in their body has trisomy 21 condition.
Aneuploidy could be of different types: trisomy, monosomy, nullisomy, etc. Such conditions arise due to formation of abnormal gametes. Most aneuploid conditions are non-viable in humans.