Atonality for a “Dummy”


When I say atonality for a “Dummy” I am literally talking about myself. When I first started learning about atonality, I felt really dumb trying to decipher and understand it.  I think that many experts in atonality, who’ve authored books on the subject, always feel the need to explain the material in an  overly complicated way. This may be due to the fact that these composers are incredibly intelligent, and the way they express their ideas are simply a product of their extreme intelligence. It could also be that due to the innate dissonance of atonality (and open minded individuals needed to listen to it) by default make it thought of as complicated….therefore a complicated explanation is due.

Now I’m not suggesting that learning, understanding, and performing atonal works isn’t complicated. I’m simply stating that how it’s explained and taught is. While researching what to read and who to study on the subject (aside from Arnold Schoenberg) I kept coming across George Perle as an authoritarian on the subject.  I have to be honest and say that I could not get through his book  Serial Composition and Atonality. It was the second book I read on the subject and I felt that there had to be a better way to absorb the material. Obviously I am speaking for myself as there are probably people out in the world who grasped and understood atonality and his material immediately. However, for those of you out there who haven’t, this article may help.

I do need to quickly preface the material I’m about to talk about with the fact that Arnold Schoenberg who developed the system behind atonality (or the Twelve-tone technique) would probably be upset with me for publishing this article. This is due to the fact that when Schoenberg came to Los Angeles from Europe, he was inundated with requests from composers to teach them his technique. They heard great potential and uniqueness that they could use in their film scores. Schoenberg would only teach composers his technique who were willing to start at the very beginning of music theory and learn the techniques of Bach, Beethoven, Mozart, and the like. This obviously didn’t sit well with composers who were on a deadline to create scores and come up with innovative ideas.

My reason behind talking about this bit of history on Schoenberg, is that this article is just a small sliver of atonality’s depth. Although I’m biased/arrogant and believe that I’m about to explain how to compose the basics of an atonal  piece the easiest way that I’m aware of, further  study and research is recommended for anyone truly wanting to understand this genre.

Schoenberg created atonality as a way to escape the confines of western tonal harmony. Although western tonal harmony is deep and rich in it’s content, it’s still dictated by very observable, discernible, and often times predictable precepts. I believe that Schoenberg wanted to surprise the listener and keep them in suspense as to what was going to happen.

Quite ingeniously, he figured out that the best way to do that is to ensure that the notes he composed had no discernible harmonic correlation to each other, and could not be analyzed by ordinary means. Here is my basic bare essential explanation for beginners atonal composition. It starts with two guidelines. 

  1. All twelve notes (C, C#/Db,D,D#/Eb,E,F,F#/Gb,G,G#/Ab,A,A#/Bb,B) have to be composed so there is no tonal harmonic relation to each other, and  all 12 notes have to be used before a note can be repeated.
  2. A note CAN only be performed/composed repeatedly, before all 12 notes are used, if it is the same note/pitch used consecutively. (this includes ornamentation, like trills & tremolos)

First thing you do is choose 12 non-repeating notes in no particular order. It can’t be an entirely chromatic scale either. Other than that the note choice is completely up to you.   (Here are 12 notes that I chose)


The next step is the most important and also I believe the most ill-defined. To make sure notes were composed, so that they didn’t relate to each other in a traditional harmonic way, a system was developed to make the process easier. This was called a twelve tone row matrix.  (some from the math world call it a magic square)

A twelve tone row matrix is a square grid with 144 boxes.  Each row and column contain all twelve notes from C to B (none repeating). They are arranged in a way that there is absolutely no traditional harmonic relation to the next note in any direction. This gives you your palate of notes to pick from to compose an atonal piece. In a way it’s like Soduku.

To determine the correct notes to be placed in the matrix we will assign our notes a number. This will allow us to create a pattern specifically related to our tone row, that will help us avoid traditional tonal arrangements.

Starting with the first note you’ve chosen for your twelve tone row, (in this case G) place the notes CHROMATICALLY around a circle. Then assign the first note the number “zero”, the second note “one” and so on until you reach 11.

Next you will draw lines from 1 to 11, 2 to 10, 3 to 9, 4 to 8, and finally 5 to 7.  Do not draw lines to or from zero or six! They will stay (for lack of a better word) inert.



The reason why we’re drawing lines between these numbers is to find the atonal inversion of our chosen 12 tone row. This obviously isn’t an inversion in the traditional sense, but this creates the pattern on the grid that ensures that the notes are unrelated. This pattern is used for every 12 tone rows you create. Once you understand the pattern it’s easy to implement. As you can see 1 will always invert to 11, 3 to 9 and so forth.

Now we’re going to plot our chosen 12 tone row as well as it’s inversion into the 12×12 matrix. Our initial chosen 12 tone row is written on the top row, with it’s corresponding number we’ve assigned it from above circle. Our inversion of our chosen 12 tones is written along the furthest most left column.(Ab becomes F#, C becomes D etc..) Remember that Zero and Six do not invert. They are the only notes that will stay the same when doing your inversions.

12 Tone Row.png

Obviously we have 120 more squares to fill in and now that we have the top line and the most left column filled in, it’s easy to do. (I will preface that my way to determine the correct pattern of notes is just one way to do it. There are many different ways to complete the matrix, but I believe this way to be the most consistent)

A) We will be filling in the notes from left to right in rows. We will start on the first note of the second row.  In this example it’s F#.

B) Then we look at the next empty box next to the F# in our second row. We can see the number in the top of that column is 1.

C) Now we look back at the the chromatic 12 tone circle and count that amount clockwise. The note we land on in that circle is the next note to place in the matrix. In this example that would be the note G.

Since that’s a pretty simple demonstration, let’s do one more example with a chart to explain further.

If we look at the next empty box in the second row and look at the top of the column the number is 5. We then count 5 away from F# on our chromatic 12 tone circle and we come to the note B.

Atonal Arrows.png

We apply this technique to each row until the matrix is complete.

Atonal 12 tone.png

The example above includes the names that are given to each side row and column. I wanted to explain what the numbers meant without any additional information in the previous matrix. When you do a 12 tone matrix the left side of the grid is called Prime, the top is called the Inversion, the bottom is called the Retrograde Inversion, and the right side is called Retrograde.

All these really do is tell you what direction you’re reading the matrix from. If you’re reading from right to left, that’s retrograde, if you’re reading bottom to top that retrograde inversion etc.. You can read the matrix from any direction and the notes won’t have any correlation to each other and it gives you a plethora of patterns to choose from. I now have my matrix completed and am ready to compose an atonal piece.

With our 12 tone matrix completed, the question may arise, what about rhythm? Is there some sore of atonal rhythm structure I have to follow? Lucky for us everything that relates to traditional rhythm studies applies to atonal music as well. There’s really no specific set of rules with regards to rhythm and atonality. Whatever rhythms you liked in traditional tonal harmony, are completely applicable here too. You just have to follow the 2 guidelines about harmony I posted above.

We can now move forward composing an atonal piece. The piece that I composed is only atonal for the first 15 seconds of the entire composition. It was composed for a film score for a documentary called “On Deterrence.” The film’s subject matter was about nuclear war, so atonality was the perfect choice to create a sense of uncertainty and unrest.

In the music below, you’ll see that the violin and viola repeat an “F” over and over through out the first 12 measures. The cello and bass are playing the atonal melody based upon the notes that were completed in 12 x 12 matrix above.

The Edge.png

I believe that the information above is a great starting place for someone to start composing atonal music. However, I didn’t touch upon the use of chords in atonal composition as that is another chapter all it’s own. Chords become a bit trickier, as another system has to be put in place for chords. This is to avoid creating traditional harmonic chord progressions when harmonizing your atonal melody. That I may save for another time.

Atonality is not a widely listened to genre. Although it has many different uses for different applications, it’s not something that I think will become a widely popular genre. With that said, if you’re new to atonality and interested in knowing about it, you will find that not all 12 tone rows sound alike. The arranging of your first 12 notes of your matrix will have an absolutely profound affect on the feeling and emotion on music it helps to create. Your 12 tone row can evoke moods like warmth or darkness or fear. It’s not just a medium that only sounds really strange and unnerving or even the same. Not unlike traditional tonal harmony, the method may be the same in creating a piece, but the results of how it sounds and is heard is always different.