Examination of Neutral Intervals and Parent Scales in Persian Art Music: A Step toward the Standardization of the Musical System

Abstract

Neutral intervals between minor and major intervals have been used in Persian/Iranian art music for centuries or even millennia. During the medieval era in the Muslim world, several scholars proposed ratios for the various intervals used in their recognized musical species and presented systematized parent scales. However, this did not result in unanimously accepted or standardized neutral interval sizes or fretting systems in practice, either in the past or in modern times. This article examines neutral intervals and parent scales in Persian art music in four sections. First, the neutral intervals according to the main medieval theorists of the Muslim world (specifically, from the eighth through the fifteenth centuries) are reviewed. Second, the opinions of several twentieth-century mu sicologists and their measured/proposed neutral intervals are critically examined. Third, several ratios for neutral seconds are considered based on different theoretical approach es, and a unique ratio, close to the current practice, is proposed. Finally, the arithmetic mean calculation method is directly applied to an 18-tone scale (for the fretting of a Persian tār/sitār) as an example of a standardized parent scale.