A contrast is a linear functional of the sample. Contrasts are a central notion of ANOVA. They are more closely related to the research hypothesis rather than the statistical hypothesis.
A contrast between the means is a functional of the means:
Thus, a contrast is a function , where is the number of groups. More precisely:

where is the -th treatment mean. Additionally, we require that . Thus, the total mean is not a contrast. Moreover, all contrasts are orthogonal to the mean. Hence, under the assumption of normality, contrasts are independent from the total mean.