Enharmonic Equivalent Notation

Extra-Chromatic Pitches. Non-western musical systems such as the Arabic maqam system, and the Holdrian and Syntotic comma systems provide a notation for notes outside the chromatic scale, but adopting these notations systematically introudces complexity in both notation and interpretation. Notations that allow overloading accidentals are not widely supported in scoring software and reading the score would be even harder than with standard notation.

This section establishes the semantics for idiomatic use of enharmonic notation for use on extra-chromatic pitches that would otherwise require symbol overloading.

Quarter Tones. Extra-chromatic notes in the Arabic maqam system are often notated with the half-flat (𝄳) symbol where half-flat means one quarter tone lower than the nominal pitch. For example, in the lower tetrachord of Rast in D, the third note is F ♯ (𝄳) half-flat, a quarter tone below F♯ and a quarter tone above F.

A problem arises when notating a pitch like F ♯ (𝄳). The notation requires symbol overloading. Overloaded notation is not widely supported in scoring software and the score is more difficult to read than standard musical notation which is already a challenge for many guitarists.

To avoid overloading, we allow the use of enharmonic equivalents using the symbols quarter tone flat (𝄬), quarter tone sharp (𝄰), three quarter tone flat (𝄭) and three quarter tone sharp (𝄱).

Example 1 illustrates the enharmonic equivalent of (C♯𝄳) as C half sharp (C𝄰) the pitch one quarter tone above C. Similarly, Example 2 illustrates the enharmonic equivalent of the pitch denoted by B flat (B♭) half-sharp (B♭𝄲), the pitch one quarter tone below B as (B𝄬) which could also be denoted by C𝄭 as in Example 3.