Quarter Tones vs. Three Quarter Tones

As I’m reading this dissertation by Dr. Obeida Madi, “The Violin in the Arab Music Tradition: History and GDgd Tuning,” I’m struck by his usage (presumably taken from Mohamed, 1984) of quarter tones. Usually we refer to quarter tones as the intervallic relationship between two pitches that is one quarter the distance of a whole tone (hence the “whole tone” to “quarter tone” ration).

Several times throughout the piece, Madi refers to a pitch with an accidental altered by a quarter step in pitch as a quarter tone. These are actually three quarter tones. In section 3.2 The Intervals of Arab Music (al-bo’d al sawti), (pp. 21-22) he clearly shows that he knows the difference between a quarter tone and three quarter tone.

In contrast to western music, where the whole tone is divided into two half tones, a tone in Arab music is divided into four quarters. There are four types of melodic intervals (al-bo’d al-sawti): the whole tone containing four quarters, the quartertone containing three quarters, the half tone containing two quarters, and the augmented tone containing six quarters.

Yet in Figure (3.2.2) used to illustrate this quartertone we get:


We can be charitable and say that Madi is simply designating the word “quartertone” (as opposed to “quarter tone” with spacing) as a convenient shorthand to reference a three quarter tone, yet in 3.1 Accidentals and Pitch in Arab Music, he uses “quartertone” in a different manner:

Besides the flat, sharp and natural tones, many maqamat (modes) include quartertones, which are a rarely precise quarters falling halfway between two semitones and the intonation of the same quartertone may vary withe each maqam (mode).

Here, Madi isn’t being clear about the difference between accidentals, which indicate a change in a stated pitch, and the intervallic relationship between pitches.

Most folks who have any Western Music Theory background will understand what Madi is talking about, but the lack of clarity and consistency could be problematic for novices, or untrained musicians. I’m going to make it a point to always refer to intervallic relationships with that are 3/4 of a whole tone (i.e. three quarter tones) as a three quarter tone and leave the quarter tone to refer to an intervallic relationship of an actual quarter tone.