Describing families of 12-tone temperaments
Donald E. Hall · The Journal of the Acoustical Society of America · 1984
All possible temperaments of a keyboard with 12 pitch classes can be represented by points in a 12-dimensional space. Certain subsets are of special interest, such as all temperaments in which the octaves are unstretched (11-dimensional) or the “regular temperaments” (1-dimensional). It is interesting to ask what might be useful 2- or 3-parameter families that would serve to generalize the regular temperaments. Some possible choices and the analysis of their residual tuning errors will be discussed.