Inner Machinations

My place for writing about things I find interesting.

24 August 2019

Music Analysis and Decomposition - 2

Even Odds

This is part 2 of a 7 part series on musical analysis and decomposition! It’s been a while, but it’s back.

Last time, we talked about and analyzed music that is simplistic in nature, mostly diving into Vulfpeck. This week, we’re gonna talk about music written in “odd” time signatures and how that leads to music that is varied and interesting.

First, let’s define terms. In (Western) written music, we have a concept of time signatures, which is a notational convention that is used to specify how many beats (pulses) are contained within one measure (bar) of music, and which note value is equivalent to one said beat. In a musical score, the time signature is (usually) written as a fraction, where the numerator describes how many beats are in the measure, and the bottom number describes which note gets the beat. Here’s a helpful image for reference on what “notes”, are: notes
Common note values used in modern Western music

Some of the more common time signatures in modern music include 6/8, 12/8, 4/4 (arguably the most common), 2/4, and 2/2 (think 4/4, but faster). Chances are, your favorite pop song is in one of these time signatures. An interesting thing to note is that a lot of these time signatures sound nearly the same, just with a different feel. For example, 4/4, 2/2, 12/8, and 6/8 all can (arguably) be interchanged, as can 2/4 and 6/8, sort of. Of course, this isn’t really true, but I digress.

The observant among you may have noticed that all of the time signatures I have mentioned have even numbers in their numerators. This isn’t a coincidence; even time signatures are quite common due to their regular, predictable nature. However, given the name of this post, you can probably see where this is going.

An “odd time signature” is used to describe music where the time signature has an odd number in the numerator. Adam Neely, from YouTube, has a bunch of great videos about odd time signatures like this one about being able to “speak” in odd time signatures. The most common, in my opinion, is arguably 3/4, though it can also be argued that 3/4 is so common that it may as well be an even time signature. 3/4 is heard often in waltz music, like this Mozart waltz. Odd time signatures often make the listener feel a bit uneasy, due to each measure feeling like it’s being cut short (since it sort of is).

Okay, terms have been defined. Let’s listen to some music.

Song 1: Whiplash - Don Ellis Band


Whiplash (the movie was named after the song) is a track from the 1973 album Soaring by the Don Ellis Band, composed by Hank Levy. The piece is orchestrated for a big band consisting of a few strings (mostly violins), 5 saxophones (2 Bb Tenors, 2 Eb Altos, 1 Eb Baritone), 4 Bb trumpets, 3 trombones, 1 bass trombone, guitar, piano, bass, and drums. The piece runs approximately 4:27, played at a lively BPM of 192. The song is in C dorian mode, with hints of a C blues scale thrown in. We’ll talk more about modes in a later post, so don’t worry about that. This song has a time signature of 7/4, meaning that there are 7 quarter notes in every measure of music. As you’ve undoubtedly noticed, this is one beat shy of being two full measures of 4/4, meaning that the song will have a lilting feel where it feels like every other measure is being shortened prematurely.

The song starts with an explosive intro of the full band doing a call-and-response with the rhythm section (bass, drums, piano). The band plays homophonic lines (meaning they all play the same rhythm) that are very harmonically rich. At measure 9, around 0:17 into the song, the main groove of the song is established via the rhythm section.

A common technique when playing odd time signatures is to subdivide the measure into smaller beats to help with counting the complex rhythms that may pop up, and this song makes extensive use of this. Each quarter note can be subdivided into two eight notes (fractions at work), so our 7/4 song can also be alternatively written as 14/8. The majority of the song is counted as 4 groups of 2 eight notes followed by 2 groups of triplets (groupings of 3 eight notes), written as 2 + 2 + 2 + 2 + 3 + 3. This subdivision mainly comes from the bass line, which features the aforementioned triplets and help give the song a natural pulse, despite its odd nature.

The song breaks into a brief B section, reprises the hook and intro, then launches into a huge trumpet solo all with the same subdivision, before going into some of the coolest odd time signature music in existence. The post solo section all the way to the end of the song fully takes advantage of the 14/8 subdivision idea by shifting around the groupings of eight notes to produce measures which differ in feel from bar to bar without actually changing the number of beats in the measure. As an example, the opening 4 measures are, in order, subdivided like so:

  1. 2 + 2 + 3 + 3 + 2 + 2 (same as the main one, just with the two triplets in the middle of the 4 groups)
  2. 3 + 3 + 2 + 2 + 2 + 2 (two triplets in front, 4 groups after)
  3. 3 + 3 + 2 + 2 + 2 + 2 (same as line above)
  4. 2 + 2 + 3 + 3 + 2 + 2 (same as the main one, just with the two triplets in the middle of the 4 groups)

If you’re feeling up to a challenge, try subdividing the rest of the measures of this post solo section without looking up the chart. It’s a fun exercise in counting.

That shifting subdivision is a fun way to toy with the feel of the song without actually changing anything, and is commonly employed by our next two songs.

Song 2 and Song 3: Blue Rondo à la Turk - Dave Brubeck Quartet and Bird on the Wing - Sungazer


Now, I know it seems strange that I’m grouping these two different songs together, but there’s a reason for this: 9/8.

9/8 is a very interesting time signature, so much so that there’s a whole video about it. For starters, 9/8 is an isochronal time signature, meaning that it has regular pulses. This can make it feel more like 3/4, and indeed, 9/8 is literally what you get if you take a 3/4 piece and turn each quarter note into a eight note triplet. 9/8 written this way is extremely common, with examples you’ve probably heard, like The Sorceror’s Apprentice by Paul Dukas or in Irish Slip Jig music. That said, 9/8 can also be grouped in ways that aren’t evenly divisible by 3, and this is common in Balkans folk music. The history of both of these songs is that they’re 9/8 pieces that are inspired by that traditional Balkan music, and as such follow their subdivisions. The video I linked about 9/8 dives futher into it, but specifically, the former follows a subdivision of 3 measures that are quick + quick + quick + slow (a.k.a. 2 + 2 + 2 + 3) with a measure of regular triplets 9/8, and the latter follows a quick + slow + quick + quick (a.k.a. 2 + 3 + 2 + 2). Both come out to be 9/8, just with drastically different feels. Also, Blue Rondo does have that entire solo section in 4/4 but we’ll ignore that.

The video I linked covers 9/8 way, way better than I can, so I’ll leave it at that. Listen to the songs and watch that video to get a better feel for the music (also it’s a great video), and I think you’ll come to appreciate odd time signatures and the joys they bring.

Additional Songs

If you like what you’ve heard, here are some more in a similar style:

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tags: music - music-theory - music-analysis - decomposition