A Hemiola by Any Other Name

  The term "Hemiola" has, like many things, evolved.  I myself am guilty of using it in ways that stretch the limits of it's many definitions. 

FIRST DEFINITION
    The earliest use of the word is simply to describe the conditions that create the Musical Interval of the Perfect Fifth - two notes that have a FREQUENCY ratio of 3:2 - for example:

                                             E660 : A440    a Perfect Fifth

        Simple enough.....then there's the
SECOND DEFINITION:
  The term evolved to mean a RHYTHMIC Ratio of 3:2    -- 3 Beats of Equal Value in a space normally occupied by 2.  This is the traditional dictionary defintion of the HEMIOLA. 

  This is extremely common in Afro-Cuban music and Jazz and is the essential feel of the Jazz Waltz.
It is so common to those of us that play Jazz, in fact, that it hardly seems worth naming.

                            
THIRD DEFINITION
      Here in the trenches, we use "hemiola" much more loosely, to refer pretty much to anything that has a "whacky" rhythm relative to the bar-line. 
   This is  a use of  the word "hemiola" that pushes the envelope  - the music below is better described as a "RHYTHMIC DISPLACEMENT"  or "Polyrhythm" or even "Cross-rhythm", but many people will just refer to this as a hemiola.  Probably not a great way to describe it, but that's language evolution for you.   In Zez Confrey's classic solo piano novelty, Kitten on the Keys, there is a 6/8 melodic phrase plastered onto a 4/4 harmonic accompaniment - it is the displacement or polyrhythm  that makes it sound like a cat wandering up and down the keyboard with an expected disregard for the underlying music. 

Here is Zez Confrey himself playing the tune - notice the exaggerated "swing-feel" eighth notes unlike most contemporary performances of this piece.

A FOURTH CURIOSITY
   Here's a clever "Note-Sequence Displacement" where a sequence of notes is displaced in the bar by ONE 1/8 beat and  the rhythm of those notes is modified as well - on first hearing this,  the word "hemiola" comes to mind, but it is really much more curious than just that.   Felix Arndt's ear-catching composition, NOLA.

   And just to cement that tune into your psyche, here's the unforgettable version by Liberace:

A FIFTH CURIOSITY
   THE MYSTERIOUS CASE OF THE DISAPPEARING HEMIOLA -
      ( more correctly "rhythmic displacement" )

From the 1962 musical, The Music Man, comes this most memorable tune "Gary, Indiana"  - look at this melodic line below without the words -  it's really not an interesting melodic phrase AT ALL - in fact, it's straight out of Hanon Studies for the Piano ( the main character of the movie was a Music Teacher - nice touch!)  BUT,  add the 6 syllable Word-Phrase and all of a sudden there's a rhythmic HOOK, completely "lyric-dependent".  A 3 beat word-phrase stuck into a 2 beat musical phrase.  Take away the words and the "hook" just vanishes!   Is this a hemiola in the contemporary use of the word?
   Probably not.  But just as interesting by any other name, whatever that might be.  

        Listen.....

And just to close, while we're speaking of cats with disregard for the music, I include a special cat, Nora, performing a composition by Mindaugas Piecaitis with refreshing regard for music...in fact, she LOVES music....