Early Indian Heptatonic Scales and Recent Diatonic Theory

Abstract

Two questions are addressed: (1) By what path did ancient Indian musicians make their way from a “chromatic” universe of 22 microtonal divisions of the octave (the śrutis) to a “diatonic” set of seven degrees? and (2) What features do the resulting scale structures have in common with later versions of the diatonic scale in the West? The authors examine the selection principles that appear to have guided these musicians, and explore some of the remarkable features and implications of their solutions. The two basic early Indian heptatonic scales (sa-grāma and magrāma) share a number of features with the Western diatonic scale: (1) distinct step sizes which are consecutive integers, (2) dual tetrachords, (3) exactly one tritone, (4) distinct sizes of fifths which are consecutive integers, (5) a maximal number of consonant fifths (consistent with feature 4), and (6) first- or second-order maximal evenness (as defined by Clough and Douthett). There are three smaller feature sets, each including two or three of the above features, that serve to define both the early Indian heptatonics and the Western diatonic: given the appropriate chromatic cardinality (22 or 12), each feature set corresponds either (a) to all and only the heptatonics specified in the early Indian treatises plus two permissible altered versions or (b) uniquely to the Western diatonic.