The bottom number in time signatures has always confused me

The top number in a time signature is easy to understand. Is the song in four? Count “one, two, three, four.” Is it in three? Count “one, two, three.” Is it in five? Count “one, two, three, four, five.” That’s all there is to it. However, the bottom number is another story. What is going on down there? I collected various examples of time signatures in this track I made, but I didn’t understand why “Solsbury Hill” by Peter Gabriel is in 7/4 but “One More Night” by Can is in 7/8.

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Happiness is a Warm Gun

The White Album is full of cobwebby subterranean corners, and this song is one of the cobwebbiest. The title comes from an issue of American Rifleman that John Lennon thought was funny in a bleak way. The joke became quite a bit more bleak after his death.

You can listen to the isolated tracks here. This is probably the most formally complex Beatles song unless you count the Abbey Road medley as a single work of music. “Happiness is a Warm Gun” is a miniature medley unto itself, since John stitched it together from several unfinished fragments. It took a lot of in-studio rehearsal to pull it together, and the band needed more than seventy takes (including false starts) to get the final one. It’s interesting to compare this earlier take, which doesn’t have all the overdubs.
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The Beatles multitracks

As of this writing, you can download a big collection of isolated Beatles multitracks from the Internet Archive. These multitracks have been in circulation for a while, but due to their complete illegality, they can be difficult to find. The Internet Archive is a stable download source, but we’ll see how long it takes for Universal Music’s lawyers to make a move. It’s too bad you have to violate copyright law to share these things, because they are incredibly valuable resources for teachers of music technology, theory, songwriting and popular music history. I use these multitracks in every class I teach, every semester.

The Beatles multitrack collection exists because of a video game, The Beatles: Rock Band, released in 2009 by Harmonix.

The multitracks are MOGG files, the multitrack version of the Ogg Vorbis audio encoding format. You can use Audacity to open and listen to them, and from there you can convert them to WAV or MP3 files. Note that some of these are “fake” multitracks. Harmonix’s production team could work from the original session tapes for the later songs, but some of the earlier ones were recorded straight to two-track tape, so no isolated tracks even exist. For these songs, the engineers had to use sophisticated filtering software to pull out the drums, bass and so on.

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What are harmonics?

For our last day of pop aural skills class, I did a crash course on historical tuning systems. This involved a brief introduction to harmonics. As I was talking, I realized that my verbal explanation of this concept is still clunky and imprecise. This is a problem, because harmonics are important, not just for music theory, but also for audio engineering, as well as many non-music-related subfields in physics. Including quantum mechanics! 

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Back to Black

For my latest column, MusicRadar assigned me to write about “Back to Black” by Amy Winehouse, since the movie of the same name is about to come out. I didn’t have a relationship with the song or with Winehouse generally before starting on the research, but my students are very attached to her. The column gave me the chance to analyze the song’s swing and groove, which I’m always happy to be doing.

Identifying major and minor

This summer I am writing more music theory teaching materials for beginners. In this post, I will be explaining major thirds, minor thirds, major chords, and minor chords.

So, what are these things? The definitions are annoyingly circular.

  • A major third is the interval between the first and third degrees of the major scale. And what makes it a major scale? The interval between its first and third degrees is a major third.
  • A minor third is the interval between the first and third degrees of the minor scale. And what makes it a minor scale? The interval between its first and third degrees is a minor third.

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Identifying sequences

The final topic in pop aural skills is harmonic sequences, strings of chords whose roots move in a predictable interval pattern. Sequences are common in European classical music. Listen to Bach’s Chaconne from the D Minor Violin Partita or Contrapunctus VIII from The Art of Fugue for a million examples. Sequences are also pretty common in jazz. They are not so common in pop. But when people do use them, it can sound like a fun harmonic adventure. 

Circle of fifths sequences

Many sequences are organized around the circle of fifths, so let’s start there. The basic idea is simple. Say you want to write a sequence in the key of C major. You find your chord roots by starting on C and moving through the key in counterclockwise circle of fifths order, like so: C, F, B, E, A, D, G, C. 

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Hypermeter

I didn’t find out about hypermeter until very late in my music theory learning journey. I think it should be part of the basic toolkit, especially for songwriters and improvisers. The explanation that follows might seem abstract, but behind the scenes, hypermeter provides the signposts that orient you in medium-scale musical time.

The term “hypermeter” might be new to you if you aren’t a musicologist, but I guarantee that you already intuitively know what it is. When you feel that a verse or chorus has a front half or a back half, that you can or can’t expect when the next section is going to start, or you sense that things do or don’t align with each other, that is your sense of hypermeter at work. At a club or festival, the crowd can easily feel when a 32-bar section of a repetitive dance groove is coming to an end, not because anyone is counting measures, but because of their orientation in the hypermeter.

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Identifying augmented chords

Augmented chords don’t come up much, but they are on the aural skills syllabus, and they have that specific quality that no other harmony can create. Their uncanny zero-gravity quality is the result of their symmetry. Any note in an augmented triad could function as its root. When you write the augmented chords on the chromatic circle, you quickly discover that there are only four possible ones, shown in the image below.

The one on the top left is C+, E+ and G#+/Ab+. The one on the top right is C#+/Db+, F+ and A+. The one on the bottom right is D+, F#/Gb+ and A#/Bb+. Finally, the one on the bottom left is D#/Eb+, G+, and B+.

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