It’s Time to Update the Definition of Hemiola (Again)

By Curtis Madigan April 2, 2019

Musicians: what are your thoughts on this? Hemiola is an extremely useful and vast rhythmic principle in my new definition. It has previously been limited to a tiny meaning (and has already outgrown older definitions/spellings) and it’s barely ever even mentioned in studying music. In my new workbooks there are 4:3 hemiolas, 6:4 syncopated hemiolas, displaced hemiolas, and the ability to play the same type of rhythm at a new tempo, without actually changing the tempo (implied tempo modulation). It is really one of the defining factors of strong grooves and once your ear picks up on these, you hear them everywhere. Onto the article:

There has been continual confusion in the music world around what constitutes a hemiola. Hemiola used to be called hemiolia stemming from the root words hemi or half and holosor whole. This word hemiolia referred to “the ratio 3:2; the interval of a perfect fifth” (see overtone series if that doesn’t make sense), or “a triplet, replacing two notes with three.” We no longer use hemiola to mean a perfect fifth and the modern definition of hemiola (you can’t even find the word hemiolia anymore in modern dictionaries) describes the 3:2 ratio, however specifies a “changing from three groups of two beats to two groups of three beats, thus giving the effect of shifting from duple meter to triple meter.” Other definitions also state that there is a “vertical hemiola” where this duple vs. triple shift occurs simultaneously, thus creating the 3:2 polyrhythm.

This is for sure a limiting and confusing definition, especially because we musicians already use the term polyrhythm to refer to 3:2, 4:5, 3:4 or almost any other rhythmic ratio. There are many intelligent debates on changing and updating the definition of hemiola like this one on Reddit. There are also videos of people talking about patterns like 3+3+3+3+4, and calling it “The Unnamed Rhythm.” The fact that there’s no way to describe this phenomenon of regularly recurring accents, that is prevalent in almost every modern song, especially hit songs, seems strange.

In the DCI (Drum Corps International) world where extreme precision and expertise is required, the term hemiola is often expanded to incorporate patterns like the one described in the above video. When I developed my theory of rhythm, it was very apparent that hemiolas are subdivided polyrhythms. This is beautifully and simply explained in the Level 5 workbook of my rhythm theory. An example from this book is showing the difference between 3:4 polyrhythms and hemiolas and 4:3 polyrhythms and hemiolas (sorry for it being a little out of focus):


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This clearly shows the relationship between hemiolas (as newly defined) and their polyrhythmic counterparts. Hemiolas are essentially a regular accent pattern of subdivisions that creates an implied second pulse or tempo. Thus, hemiolas are the bridge to tempo modulation and metric modulation. This is fascinating because you can then feel the same exact rhythm as another type of subdivision at a new tempo (examples of this are in my book and future workbooks).

The essence of the hemiola and the intentionality behind the shifting of duple to triple via regularly recurring accents, is to imply a second pulse. Creating a second pulse is not limited to 3:2, it works just as well with 3:4 (or any other ratio) and if octaves have taught us anything, it’s that doubling a frequency (which is really just a rhythmic speed) creates the same pitch! For instance the pitch of A440, A220, A110, etc. This is no different in rhythm which means we should certainly have other ratios in our definition of hemiola outside of 3:2 as many other subdivided polyrhythms create beautiful and interesting rhythms that we should be able to concisely describe as educators and performers.

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