Category Archives: Rick Louie

Advanced Music Theory Lesson 8 – Thinking Outside the Box

Breaking through the “theory” box

Ah the final lesson. This week we’ll be discussing ways to break out of the theory box. If you’ve read and understood all of the lessons in this course, chances are you’re fairly serious about music and have enough theoretical knowledge to start getting tired with the theory of it all. Not to fear, music is a lifelong journey, and half the fun is in trying to create things that have never been done before, and in seeing things in ways that have never been seen before. It’s from these out of the box ideas that a good portion of your compositional girth will come from. I, personally, went through a period where the knowledge in my head began to irk me. It took me awhile to figure out I could take this knowledge and use it toward something new. It’s important to look at everything you’ve learned as a simple foundation on which to build the building- each piece of theoretical knowledge works to sure up the foundation. However, the foundation is not what people see- people see the building, in whichever way you choose to display it.  

In this post, we’ll take our already assumed knowledge and use it to explain other concepts. We touched on this idea in last week’s lesson about symmetric scales.

For example, how many different ways can we see a major scale? It’s something you’ve looked at for ages, ever since the first year of theory or playing an instrument. But, there is so much more to a major scale than just being a major scale.

For starters, let’s talk about tetra-chords. All tetra-chords are, are the first four notes of any given scale. Which tetra chords can you see in a major scale?

C Major Scale

Here, I see a C Major tetra-chord and a G Major tetra-chord a 5th apart.

What if we were to look at it in terms of chords? Which chords could potentially make up a C Major scale? How about a D minor triad superimposed over a C Major 7th chord.

What about looking at something as banal as a C major 7th? It could be written as Em/C, a major third starting on C plus a major third starting on G, two perfect 5ths placed a major third apart, A minor 9 with no root, and any other categorization you can think of for it. What this exercise does is open your eyes a bit. Nothing is too ridiculous or obvious to think about, as every categorization is a possible new door toward something you’ve never thought about.

Of course, more complicated concepts will have more ways to be parsed. Take the diminished scale we learned about last week:

C Diminished Scale
What do you see in the diminished scale? How about two minor tetra-chords a tri-tone apart, two fully diminished 7th chords superimposed, a C minor-augmented major 7th chord and a F# minor-augmented major 7th chord a tri-tone apart, etc.    

This method of doing things, is, perhaps, the most difficult thing about theory. It takes true command of the material to create something new from it; or is it, through creating something new with the material you learn command of the material? Either way, it’s the next step in theoretical evolution, and the point where you realize a teacher cannot help you along the path any further.

Questions to think about:

How many ways can you quantify an Augmented Scale starting on A?

What could you call the first 4 notes of an auxiliary diminished scale?

How can you write Phrygian as a slash-chord or poly-chord?

Which two tetra-chords make up a locrian scale?

How can you write Harmonic Major as a poly-chord?

Which chords do a diminished scale and augmented scale have in common?

How many ways can you think of to represent a minor 7th chord?


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Music Fundamentals – Lesson 8

Building Triads

This post builds on last weeks lesson. Where intervals are comprised of two notes, triads are comprised of three. They are also the first instances of chords that you’ll see. A chord occurs when several notes are played simultaneously.  One of the most basic chord structures is the root position triad.

How to construct a triad

Just like intervals, there are major, minor, augmented, and diminished triads. Each of these triads is constructed differently, and each has a different sound quality.

Let’s start with major

C Major Triad


C major.mp3 C Major Triad

This is a C major triad. It is comprised of a root, a third, and a fifth, which are the first, third, and fifth notes of the C Major scale. Notice the intervals between the notes. The first interval, between the root and the third is a major third. The interval between the third and the fifth is a minor third. We’ll use the major triad as the base chord for the following triads in the lesson. Now, onto minor. To create a minor triad, take your major triad and “flat” the third. When you “flat” something, you lower it by a half step.  When we do this to C Major, we get:

C Minor Triad



C Minor.mp3 C Minor Triad


This is a C minor triad. The interval between the root and the third is a minor third, and the interval between the third and the fifth is a major third. Now, how about flatting the fifth as well? If we do that we get:

C Diminished Triad


C diminished.mp3 C Diminished Triad

This is called a C diminished triad. This is the “tensest” type of triad because it is comprised of all minor thirds and contains the dissonant tri-tone interval.

There’s one more type of triad which we get by “sharping” the fifth of a major chord. When you “sharp” something, you raise it by a half-step. When we do this, we get:

C Augmented Triad



C augmented.mp3 C Augmented Triad

This is a C augmented triad. While the diminished triad is  comprised entirely of minor thirds, the augmented triad is comprised of entirely major thirds.

Listen carefully to each audio example and try to get a feel for how each chord sounds. Every chord has its own unique quality, and it’s these qualities which makes the music we listen to exciting. If your goal is to become a complete musician, the ability to pick out these chords by ear is paramount.

Triads, and all other chords, can also be inverted. When you invert a chord, you simply put the notes of the chord in a different order. Triads can be inverted twice. In classical notation, first inversion is denoted by a super-script 6, and second inversion is denoted by a super-script 6/4. Pay careful attention to the sounds of the inversions in the examples below.

C Major Inversions



C Major inversions.mp3 C Major Triad Inversions


C Minor Inversions


C Minor Inversiosn.mp3 C Minor Triad Inversions


Diminished Inversions


C Diminished Inversions.mp3 Diminished Triad Inversions


Augmented Triad Inversions


C Augmented Inversions.mp3 Augmented Triad Inversions


I stress again, listen well to all of the above examples and get a good feel for the sounds of the different triads. Also, do the worksheet!!

Lesson 8 Worksheet

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Advanced Music Theory Lesson 7- Atonality and Serialism

Atonality, Serialism, Organized Chaos

Ah, the penultimate lesson. I want to cover a few things during this one. First, a final important theory concept, atonality. Atonality arises when there is no discernible key or tonic to a piece. This style of writing was developed by Arnold Schoenberg, though others like Charles Ives and even Strauss were experimenting with it around the same time. Schoenberg was the head figure of what Musicologists call the “Second Viennese School”, a group of Austrian composers whose ranks also included Berg and Webern, two of Schoenberg’s students. His compositions, initially, were very romantic in nature. However, he soon started experimenting heavily with the rearrangement  of the chromatic scale. Eventually this atonality evolved into something bigger, its own musical genre called Serialism.

I noted earlier in the poly-chord post how atonality and polyphony developed in the same decade around the same time, and how both their founders (Stravinsky and Schoenberg) both wound up settling in California. Well, I think it’s also worth mentioning that later in life, Stravinsky turned form Polyphony to neo-Classicism, to Serialism. Also, around this time, in the 1940’s, the film industry was just taking off, and in film scores composers began to use elements of polyphony and atonality, a trend that continues today. Whether or not this has any correlation to Stravinsky or Schoenberg, I have no idea, but it’s an interesting tidbit.         

Ok, onto the meat of the discussion.

Tone Rows

Tone rows are groups of the 12 notes from the chromatic scale, where no notes repeat, and where tonality is clearly not established. They also serve as a compositional tool, a starting point for a serial piece. When constructing a row, you want to be wary of any sequences of notes that might suggest tonality. Though, there are a few rows that use “hinting at tonality” to their advantage. Let’s look at a row:

Prime Row


prime row.mp3 Prime Row

This is the basic row, which we call the “prime row”, denoted by “P-0”. Since there is no tonality, it helps to think about rows in more theoretical and mathematical terms. For example, in addition to the prime row, there are three transformations we can make to the row. These are: retrograde, inversion, and retrograde inversion.

First, retrograde.

Retrograde 0



retrograde row.mp3 Retrograde Row

Retrograde simply takes the prime row and asserts it backward, denoted by “R-0”.

Second, inversion


Inversion 0


Inversion row.mp3 Inverted Row


Inversion, denoted by “I-0”, takes the pitches of the prime row and inverts them by interval. Think of inversion as a mirror. If there is a descending fourth in the prime row, the inversion will have an ascending fourth, and so on.

Finally, retrograde inversion

Retrograde Inversion 0


retrograde inversion row.mp3 Retrograde Inversion

Retrograde inversion takes the inverted series and sets it backward, it is denoted as “RI-0”.

Now, after you’ve written out the prime row and its 4 inversions, you can transpose each 12 times. A transposition of the prime row up a major third will be denoted as “P-4”, indicating “P” the prime row, has been transposed up “4” half steps. This same formula works for all of the different transformations. What would RI-7 be? Well, “RI” retrograde inversion, up “7” half-steps. So, RI-7 would be retrograde inversion up a perfect 5th. There is a useful tool you can use to map out called a 12-tone matrix (a free matrix generator is available at Let’s plug our row into a matrix:

Row Matrix

So, lets take our row and compose a short piece:

Short Atonal Piece


row composition.mp3 Short Atonal Composition

I’ve labeled the elements so that you can compare this to the rows and the matrix. The trick to atonal musical, at least in the Schoenberg sense, is to get a series of notes with no tonality to sing. You can do this with extensive use of motivic development, expression, and use of dynamics. Listen to the row you’ve created first, then try to hear what you hear. For this piece, I heard a kind of marchy beginning, followed by bursts of loud melodic statements and calm chords. Each song should tell a story. In this piece I imagine a pompous General walking in the room to have a confrontation with his wife. They heatedly argue, and the wife tries to calm him down. By the last phrase they’ve reached an accord and settle down, the tension subsides. In any kind of composition, atonal or otherwise, a clear path makes for better music. 
Work through the worksheet!

Worksheet 7

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Music Fundamentals – Lesson 7

Key Signatures

Before explaining key signatures, I suppose we’ll have to discuss what a key actually is. Key signatures sprang up in what Musicologists call the “Common Practice” period of music. This era of musical development spanned from the Baroque period to the end of the Romantic period (roughly, though the dates are negotiable, from 1650-1900). Key signatures came into use to fill the need for greater organization in music. As music grew to become more complicated, equal temperament was developed, and theorists firmed up the rules of harmony, there arose the need for a organizational system to help players read the music in front of them.  Prior to the advent of the key signature, during the Medieval and Renaissance periods, there was a great amount of polyphony, with no regard for key.

Each of the 12 notes has a major and minor key associated with it (two concepts we will get to later). Key signatures serve to let the person reading the music which key the music is in and which notes will always be either flatted of sharped.

Eb Major

This is the key signature for Eb major/ C minor. The three flats in front of the clef tell us so. To tell the root key of a flat key signature, look one flat back from the last flat- in this case, Eb. When reading music, it is important to look at the key signature first. the key signature lays out for you the notes which will always be flatted or sharped (unless marked with a natural ♮sign). In this way, key signatures present a short had way to write out music, so that composers will not have to constantly fiddle with writing sharps and flats, and so that performers will not have to read copious sharps and flats.

A Major

This is a sharp key signature. Specifically, it is the kay signature for A Major. To tell the root key of a sharp key, look at the last sharp and go up one half step. In this case, the sharp is G#, up one half step is A.

There is, however, a more technical way to learn your key signatures- the Circle of 4ths and the Circle of 5ths.

There is a simple pattern to each block of flat and sharp key signatures:
Circle of Fifths

Let’s break this chart down piece by piece.

 You’ll notice, if you move from C to the left, the intervals are increasing by perfect 4ths. This move to the left represents the flat key signatures. You’ll also notice that the order of flats also moves in perfect 4ths, starting with Bb.

Moving to the right denotes the order of sharp keys. The order of sharps in the key signatures move by perfect 5ths, starting with F#.  

The numbers in the gray circle represent how many sharps or flats each key signature includes.

The inner green circle represents the corresponding minor keys to the major keys. Minor keys are always one minor third down from the corresponding major key, and, as is shown in the chart, share the same key signature.

I know this is quite a bit of material to wrap your head around, but luckily, music is cumulative, and this concept will keep coming up, over and over again.

Worksheet 7

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Intermediate Music Theory Lesson 7 – Analysis


Often, I’ve been teaching a first piano lesson to a student, and they’ll play something for me so I can assess their level. After finishing, for example, a beautiful Chopin piece, I’ll ask the student to explain what they’ve just played. What chords are you playing? How does this progression work? Most of the time I’m greeted with blank looks. For the budding composer, one of the most important things to know and understand is how to analyze a song. We’ve already started to learn some analysis techniques in past lessons, but now, we’ll try to define a set of “guides” for analyzing a song. There are the rules to “baroque” 4 part harmony analysis, but that’s a whole different beast, something that may be covered in a special lesson segment.

As an example, we’ll use the first few measures of the Movement 2 from Beethoven’s Piano Sonata No. 8, the “Pathétique”.

Pathetique sonata


Pathetique first 8.mp3 First 8 Measures of Pathetique Movement 2

Step 1- The foundation

What is the key signature?

Noting the key of the song is the most important. If the song has a key, that gives you the base from which to analyze all other chords and melodic development. In this case, there are 4 flats, so it’s either Ab major or F minor. You can usually tell whether a piece is major or minor by the first few chords. In this case, the first chord has an Ab, C, and the next note in an Eb. These three notes make up an Ab triad, to its pretty safe to say this piece of the movement is in Ab major.

What is the form?

From this excerpt, we cannot determine a form. However, it is important to look through a piece and decide on what the form could be, AA, AABA, sonata, etc. Most pop tunes don’t follow a form like this, but they follow something akin to: Intro, verse, verse, chorus, verse, chorus, bridge, chorus, outro- or some other variation.

What is the Time Signature?

In this case, 2/4.

Step 2- The Harmony

Now we can move chord by chord. What we’re looking for is not limited to which chords pass, but also includes which cadences we see, if there are any modulations, pedal points, strange motions, suspensions.

Measure 1

As we said, the song starts in Ab major with an Ab major chord. The harmonic motion is moving at one chord per beat. On beat two, the chord changes to Eb7, which is the V chord in Ab major. Remember the thirds and sevenths! There is no fifth in this Eb7 chord, and the 7th appears in the base. It’s an easy leap to guess that the Eb7 will resolve to Ab major, with the third and seventh moving properly. Let’s see…

Measure 2

Just as we predicted! The first chord in this measure is Ab major with C in the bass, as the seventh moved to the third, just like we though it would. Meanwhile, the third moved to the root. In the second chord, Beethoven moves it to Eb again with G in the bass, and in the second half of the beat, there’s that seventh again, I wonder if that seventh will move to the third again….

Measure 3

Aha! It did. The Db moved to C. The first chord is Ab major again, this time with the root in the bass. We can also see that the harmonic rhythm has changed, it’s now moving twice as fast, one chord every eighth note. The second chord is Eb with G in the bass again, but this time no seventh. Then, in the third chord, Beethoven switches it up and does what’s called a “deceptive” cadence. A deceptive cadence happens when the V chord moves to the relative minor or vi chord- in this case, it resolves to F minor. Then, Beethoven does something tricky, moving to a Bb7 chord with F in the bass, or in Ab, the V/V (the five chord of the five chord). He used the F minor as a sort of ii chord to do a ii-V-I cadence to Eb….

Measure 4

And there’s the Eb chord, tonicizing the V chord. This measure remains in Eb, and Beethoven has switched the harmonic rhythm back to one chord per beat. The only wonky thing that happens here is the E natural passing tone on the second half of beat two leading to….

Measure 5

Gb half-diminished over Db. This is the vii7 chord of Ab major which often works as an extension of V7, which Beethoven eventually moves to in beat two, briefly touching on V7 moving to…

Measure 6

Another tonic! Ab major over C to start the measure. Next is an out of place chord, F7. F7 is the V/ii (five chord of the ii chord, which is Bb), will it move to Bb?

Measure 7

Yes! He moves to ii then to V and eventually, after some harmonic motion….

Measure 8

To a pedal point of Eb7 over Ab, finally to Ab to ease the tension.

For you classical theorists, if we were to write this out in “classical” roman numerals, the first 8 measures would look like this:
Analysis Roman Numerals

Some roman numerals have superscripts. This is just the classical way of writing inversions. The only two here are V4/2, which is a 7th chord in third inversion, and I6 which is a triad in first inversion.

For this week’s homework, take one of you favorite tunes and analyze it piece by piece. Paste your analysis to the comment board!   


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