Balzano proposed the study of pitch sets as an alternative to the study of timbre or harmonicity for psychoacousticians. His analysis and discussion was devoted to various subsets of this 12-note collection, with extended discussion of the diatonic subsets. Below are the general definitions of each word. If you would like to read a more complete discussion of a word, click on that word.
Uniqueness contributes to the emergence of a 'tonic' element.
It refers to the ability to individuate the elements of a set by virtue of their relations with one another. If more than one element in a set have the same intervallic relationship to all the other members of that set, it is NOT unique. This requires that the same distance is not traversed in one part of the scale by one step and in another part of the scale by more than one step.