Tag Archives: Functional Harmony

Muse – Take A Bow

By: Aaron Zimmerman

This is an ongoing series of posts called “Music Theory Rocks”, for an intro to the series and some music theory fundamentals, check out this post.

One of the eye-openingly cool things about music is the circle of fifths. A fifth (often called a “perfect” fifth) is 7 half steps. Moving by fifths up or down creates a circle that touches every note before starting over at the note you began with. If you start on a C and go up by fifths, the notes you will play will be:

Moving Up by Fifths

Moving Up by Fifths

As you move left to right in the above series, you add a sharp to the major scale that starts on that note.

Key Sharps
C Major no sharps
G Major F#
D Major F# C#
A Major F# C# G#

The inverse of this is also true, as you move right to left, you subtract a sharp (or add a flat).

Key Flats
C Major no flats
F Major Bb
Bb major Bb Eb
Eb major Bb Eb Ab

Both of these patterns will lead to the same place, and then back around, hence the name circle of fifths.

Circle of Fifths on Wikipedia

Circle of Fifths on Wikipedia

The circle of fifths is featured in Take a Bow by Muse. This piece takes a single chord progression and modulates it repeatedly downward through the circle of fifths.

Take A Bow

Take A Bow Chord Progression

This chord progression features an Augmented triad, represented with a ‘+’. This triad is formed with a major third and a minor sixth from the root. The only other chord used is the minor IV, which is only one note different from the I+.  This is a stable, easy to follow chord progression, hovering around the I chord, the lowest note never actually even changes. As the piece moves through keys, this simplicity helps the listener maintain a sense of continuity through dramatic key changes.  If it were a more complicated progression, the piece would feel scattered, confusing, rather than dramatic and sweeping.

The piece is organized in two large sections separated by an interlude. The first section features the above progression modulated 6 times through the circle of fifths, starting in D Major, and ending in Eb Major. The interlude picks up in Eb and ends up solidly in F Major. The second section picks up in F Major and goes all the way through the circle of fifths to B major, where the piece ends, just three steps in the circle of fifths from the D Major the piece started in.

Here are the elapsed time marks in the piece at which modulations occur, the new key, the number of times the chord progression sounds before moving on, and any notes.

time key times notes
0:00 D 2
0:23 G 1
0:34 C 2 Vocals
0:56 F 1
1:07 Bb 1
1:18 Eb 1+ Vamps a little bit on the end
1:40 Interlude See notes on interlude progression
2:13 F 2 Second time guitar comes in
2:35 Bb 1
2:47 Eb 1
2:58 Ab 2 Vocals back in
3:20 Db 1
3:31 F# 1
3:41 B 1
3:53 CODA

Types of Scales

By: Aaron Zimmerman

In this post, I’ll list and briefly explain different types of scales commonly used in music today.   I’ll break them into 4 categories, Common, Symetric, Modal, and Other.

Common Scales

Common Scales

Common Scales

Major is the best known scale.  The key characteristic is the major 3rd (E) and a seventh that is a half step down from the root (B). It is a pattern of whole steps W-W-H-W-W-W-H.

Natural Minor is identified by lowered third, sixth, and seventh (when compared to a major).  Natural minor keys share key signatures with the major chord that is 3 half steps higher.  That is, A Minor has the same key signature (no sharps or flats) as C Major, the note 3 half steps higher.  A Minor is the relative minor of C Major.  Eb is the relative major of C Minor (above).

Harmonic minor is a natural minor with a raised 7th degree.  In a minor key, we usually use a major V chord to create a stronger V-I cadence.  In C minor, the V chord is G Major (with a B natural, even though B is flat in the key signature).  This creates a clash between a melody using the natural minor scale, and an accompaniment playing a major V chord.  So the harmonic minor scale addresses this by adjusting the scale to be what the harmony expects.

Melodic Minor is a comprise between the natural and the harmonic minor scales.  When descending, the scale is identical to a natural minor scale. When ascending, the 6th and 7th are both raised a half step (from the natural minor).  This allows for smoother voice leading (no jumps in melodies that move up and down the scale), while maintaining compatibility with harmonic progressions.

Symmetric Scales

These scales are based on symmetric, repeating patterns of intervals.  It is the asymmetric-ness of the major and minor scale that give it a strong sense of tonic, of a “home” key.  As these scales are symmetric, they do not have a strong tonic.  If you start a C Major scale in the middle, after a few notes, it is still clearly a C Major scale.  Whereas, there is no “middle” to a symmetric scale, wherever you start, you start.

Symetric Scales

Symmetric Scales

The chromatic scale features every note.  It is made up entirely of half steps. Rimsky-Korsakov’s “Flight of the Bumblebee” makes heavy use.

The whole tone scale consists of only whole steps, so it contains 6 notes.  There are two whole tone scales.  That is, the whole tone scale that starts from C is the same collection of notes that starts from D.  Likewise, C# and D# whole tones scales share the same pitches. Stevie Wonder’s “You Are the Sunshine of my Life” uses an ascending whole tone scale in the introduction.

The octatonic scale is formed by alternating half steps and whole steps.  This leads to a scale of 8 notes, hence the name.   You can further classify an octatonic scale by whether it starts with a whole step or a half step). The introduction to Radiohead’s “Just” uses a whole-half ascending octatonic scale.

Modal Scales

modal scales

Modal Scales

The concept of modes comes from ancient greece, where modes were given names due to regional associations.   Today modal scales are used a lot in jazz.  When improvising over a given chord progression, it can be helpful to play the notes from a mode whose notes go well with a particular chord progression.

Dorian is a natural minor scale with the sixth raised one half step.  The key distinction between dorian and minor is that a dorian mode will have a major IV chord, whereas minor will have a minor iv.  (In C Dorian, you have a F Major chord, whereas in C Minor, you’d have F Minor).

“Billie Jean” by Michael Jackson is an example of a dorian piece.

Phrygian is a natural minor with a lowered second degree.  It is featured in this piece “Phrygian Gates” by John Adams.

Lydian is a major scale with a raised 4th degree.  The Simpsons main theme song is an example.  Listen for the raised fourth degree, it is the second note you hear, on the first half of the word “Simpsons”, and again the third note of the wordless melody

Mixolydian is a major scale with the seventh lowered a half step.  It is characterized by the presence of a flat-seventh chord rather than a diminished.  In C Mixolydian, the VII chord is a Bb major, whereas in C Major, it is a B Diminished.

Gun’s N Roses “Sweet Child of Mine” is predominantly in Mixolydian.


Other Scales

Other Scales

Pentatonic is more of a classification than an actual scale.  Taken literally, it just means a scale with 5 notes.  However, two pentatonic scales have emerged that, without further qualification, ‘pentatonic’ probably refers to.  One sounds vaguely major, the other minor.

The first two lines of the folk song “Oh Susanna” use the pentatonic scale.

The blues scale is featured heavily in the genre of the same name.  It is used extensively in blues improvisations, as each of its notes can sound consonant with the 12 bar blues. Pretty much every blues piece uses this scale, here’s Clapton with “Crossroads”, jump to 1:28 for the guitar solo

Music Theory Rocks

By: Aaron Zimmerman

Music Theory Rocks

Music theory sometimes gets a bad rap.

People tend associate music theory with tediums like naming notes, labeling chords, and determining form.   These are good skills to develop, they help answer questions about music that come up frequently.  But they are not at the core of music theory.

Music theory is an attempt to answer a simple question:

Why is this music good?

This is a different question than what makes music good.  That is a rabbit hole I’ll not venture down at the moment.  Rather, lets first just assume that a given piece is good, and try to figure out why.  What worked for this symphony?  What made this rap song memorable?  Theory is observations about music that has been created.  We learn about chords, scales, harmonies, because these form the basis for almost every piece of music we encounter.  When someone discovers a new way to make good music, we label it, share it, and discuss it.  Music evolves over time, as innovators discover new ways to create it.  Music theory is a reaction, a formalization of these discoveries.

Music theory is context, vocabulary, and enjoyment.

Most people can identify the chorus of their favorite pop songs.  This is an internalization, a labeling, of something they like in music.  Verse-chorus is a form, a pattern for organizing musical ideas.  It is an easy form for the listener to identify. There is a chorus that is always the same and a verse that is the same except for the lyrics.  By giving this pattern a name, we create three advantages:

Context –  We can identify where we are in the song, we can understand how the music will flow.

Vocabulary – We can talk about the song together – “I really like the chorus of that song”.  “I like American Pie, but it has way too many verses”, etc.

Enjoyment – We can identify what we like in music, and compare one piece to another.  A lot of music is an aquired taste, you have to develop a base line theoretical understanding of that music in order to appreciate the beauty therein.

Music theory changes how you listen.

If you listen to a pop song that doesn’t follow verse-chorus, it might take longer to appreciate, it might feel a bit awkward, and the end result could be something you like or something you don’t like. The more music you listen to, or study, the greater experience you will acquire.  The more music you have experienced, the larger your vocabulary, the more context you will have from which to appreciate a new piece you listen to, and the more enjoyment you will get from music of all kinds.

Music Theory Rocks

Along with other posts about teaching and learning piano, I’ll post an occasional analysis of a popular piece of music.  I’m not really sure how to define popular music, so I’ll just stick to the self-evident definition of “music that people seem to like”.

The purpose of the analysis is to think about why people like the piece in question.   Along the way I’ll try to point out core music theory concepts where they apply.  I’ll also be forced to use some of the jargon, I can’t explain what a scale is in every post, etc.  If you need a refresher on some basics, check out this post.

photo credit: rockfingrz Photography via photopin cc

FUNctional Harmony

By: Aaron Zimmerman

hognestad083008-4.JPGYou turn on the TV.  You see 20 or so people dressed in bright colors and helmets.  They are just standing around, and then suddenly they run full force into each other.  One person runs as fast as they can and another person throws him an oblong ball.  The receiver catches it and runs a little ways before flinging the ball at the ground and starting to dance.

To the average American adult, this is not such an odd sight, but imagine if you had never seen a football game.  How much more do you appreciate the game after learning the rules, understanding the objectives, and appreciating the strategy?

This is what it is like to learn harmony.  Harmony is the language of music, learning even a little will change the way you listen to music forever.

The three building blocks of harmony are intervals, scales, and chords.




An interval is a name for the distance between two notes.  Starting from a C, a ‘minor second’ or ‘half step’ takes you to the note directly to the left (B) or right (C#)  A whole step would be two half steps, so a D or a Bb.


C Major Scale

C Major Scale

A scale is a pattern of whole steps and half steps.   The most common scale, “major”, is the pattern, w,w,h,w,w,w,h.  This pattern can be started on any note to create the “major” scale for that note.  The vast majority of melodic material in music comes from a single scale.  A composer selecting a scale is like an artist picking out the colors of paint they will use for their next work.


C Major Chord

C Major Chord

A chord is three notes played simultaneously.    Chords are named for their lowest note (called the “root”), and the scale from which the other notes come from.   A “C Major” chord starts on the note C and uses thirds from the major scale.  (A third is the interval that you get by skipping one note of the scale.)


Now comes the clever bit.

We can take the C Major scale and build a chord for each note, sticking with the same collection of notes (the C Major scale itself), for each root note.   This results in the following 7 chords:

Chords built off C Major Scale

By convention, we label these chords with Roman Numerals (numbers are used for so many things in music, this helps distinguish those that designate harmony). We also give them impressing sounding names so we can sound smart at dinner parties.  The I chord is called Tonic, the IV chord the Subdominant, and the V chord Dominant.

Harmony is a pattern of chords, a “chord progression”.  Usually, chord progressions are designed to create a feeling of departure and return.  Think of it like running the bases, we move away from home plate, touching on other chords, before returning home to the I chord, the Tonic.

Sample Chord Progressions:

Pop Music is full of the chord progression I, V, vi, IV.

Pachelbels “Canon in D” uses a longer chord progression:  I, V, vi, iii, IV, I, IV, V.

“Hang On Sloopy” and “Wild Thing” both follow I, IV, V, IV…. for the whole song.

Beethoven’s Ninth Symphony “Ode To Joy” melody alternates mostly between I and V (with a few harmonic flourishes here and there).  For the last twenty seconds of the piece, Beethoven repeats and repeats the I chord.  This gives the piece a strong sense of finality, of completeness.  It is how you can tell that the piece is over.

(Jump to 4:52 to see what I mean about the ending.)

And that’s most of it.  Bam!  You are now a functional harmony expert.  Well, not quite, there are many more exciting twists and turns, but this is a great start.  Harmony is the language of music, learning to recognize it is like learning to read.  An entire world of appreciation and discovery awaits.