How to Write a 12-Tone Composition

Twelve-tone is a 20th-century compositional technique created by Arnold Schoenberg.  Rather than setting a piece of music in a diatonic key, the goal of 12-tone music is to use all 12 chromatic pitches equally.  To create a 12-tone composition, follow these steps:

  1. Begin with a 12x12 grid.  Label your grid as in the example below:

    Original Row
      Inverted Retrograde  
  2. Next, arrange the 12 chromatic pitches in any order you like.  This is your 12-tone row, which will form the basis of your composition.  Fill in the first row of the grid with your 12-tone row.  Check to make sure that you have used each note exactly once.


    Original Row
    C A G D# E F D B A# G# C# F#
      Inverted Retrograde  
  3. Next, calculate the inversion of your row.  Do this by finding the inversion of each interval, and write the inverted row down the left column of your grid.

    Looking at the above example, the first interval is C to AA is a minor third down from C.  The inversion of this would be a minor third up from C, which is E-flat.  While not technically necessary, I like to keep all the accidentals the same; that is, using all sharps or all flats.  I find that this makes proofreading easier, and helps to avoid errors.  Since I've used sharps in my original row, I'll use D-sharp in my inverted row, which is enharmonically equivalent to E-flat.  (You can also write down both spellings of the chromatic pitches, such as D#/Eb.)

    The next interval in my original row is A to GG is a major second down from A, so in the inversion, you would calculate a major second up from D-sharp (E-flat), which is F.

    The resulting inverted row is as follows:

    Original Row
    C A G D# E F D B A# G# C# F#
      Inverted Retrograde  

    Double-check your inverted row to make sure you have used each note exactly once.
  4. Fill in your grid by transposing your 12-tone row into each key listed down the left column of the grid.


    Original Row
    C A G D# E F D B A# G# C# F#
    D# C A# F# G G# F D C# B E A
    F D C G# A A# G E D# C# F# B
    A F# E C C# D B G# G F A# D#
    G# F D# B C C# A# G F# E A D
    G E D A# B C A F# F D# G# C#
    A# G F C# D D# C A G# F# B E
    C# A# G# E F F# D# C B A D G
    D B A F F# G E C# C A# D# G#
    E C# B G G# A F# D# D C F A#
    B G# F# D D# E C# A# A G C F
    F# D# C# A A# B G# F E D G C
      Inverted Retrograde  

    This is your palette.  Reading from left to right, you have your original row in all 12 keys.  Reading from top to bottom, you have the inversion of your row.  Reading from right to left gives you the retrograde of your row, and reading from bottom to top gives you the inverted retrograde.

    Again, you can spot-check your work by making sure any given row contains exactly 12 distinct pitches.
  5. Using the palette that you have created, write your composition.  The following rules apply:

    1. Select any row in your palette:  original, inverted, retrograde, or inverted retrograde.
    2. Once you begin a row, you must follow it to completion:  you must play all the pitches in order, you may not skip any pitches, and you may not repeat any pitches.
    3. Notes may occur in any octave any may last any duration.  You may begin two or more notes simultaneously, as long as they occur sequentially in the row.
    4. Any number of rows may be played concurrently.

    The following is a simple example of a composition based on the above palette.  Click the Play button at the top of the page to listen to the example.

Leave a comment

Beautiful composition! And great explication of this technique, thank you!
Posted by Gregory Tippett on Friday, March 17, 2017
Fantastic! Thank your for the post Carolyn, and the spreadsheet calculator Brent. It has helped me to understand the tonal matrix with greater clarity. Prior to reading here, the tonal matrix was just a mess of meaningless pitches. Now onto my uni assignment. Peter
Posted by Peter on Saturday, March 4, 2017
I have posted spreadsheet that calculates the matrix on my website, and it can be downloaded, used and distributed for free. See ...
Posted by Brent Smith on Friday, January 6, 2017
I had a visitor ask, "Isn't your first interval going up a Major 6th?"

Yes, C to A can either be a minor 3rd down, or a Major 6th up.  It doesn't matter which one you use.  On the inversion row, you just use the same interval going the opposite direction.  So a minor 3rd up from C is E-flat, and a Major 6th down from C is also E-flat.  It works out the same.
Posted by Carolyn on Monday, November 7, 2016
Hi Michelle,
For your palette, you get to choose what order to put the notes in for your original row. That's part of your composition. Then, when you create your music, you can choose whatever row you want, in any direction and in whatever key you like, and start it at any time you like. And you can have as many rows playing simultaneously as you please.
Posted by Carolyn on Thursday, July 21, 2016
This looks so interesting but I'm confused as to where you got the notes in the order they are presented? I can't see it following in a pattern like the circle of 5ths. is there any particular order or is this the order of the notes in the composition.
Posted by Michelle on Thursday, July 21, 2016
great stuff you are a boss lolololo trolltrolltroll
Posted by ggg on Monday, March 21, 2016
Sure, if you like, the audio file is located here:
Posted by Carolyn on Wednesday, March 16, 2016
This is fantastic and very well done, thanks so much for helping me understand this concept. Is there any way you can supply a download for the audio file of the example composition? I would love to have it to bring into my DAW software i use to compose to compare against my own 12 tone composition. Thanks!
Posted by Andy B on Wednesday, March 16, 2016
this article was very helpful and informative. Thank you very much. And the piece you made is really good
Posted by Brandon on Friday, February 12, 2016
Learning this stuff at uni, couldn't get my head around the rules until I saw your coloured diagram, made it much easier to comprehend. So cheers!
Posted by Cal on Sunday, June 7, 2015
The labels are placed on the side from which you begin reading the row. So, if you are reading from left to right, you are reading the original row; thus the label on the left says "Original Row". If you begin reading from top to bottom, this is the inversion, so the label on the top says "Inverted". Likewise, if you read from right to left, you're reading the row backwards, or retrograde, so the label on the right says "Retrograde". Hope that helps!
Posted by Carolyn on Tuesday, February 24, 2015
All clear to me except labeling in the margins: if the top row from left to right the original (prime) row, then why is it labeled "inverted". same with the others R and IR. I find this confusing!
Posted by if the top row from left to right the original (prime) row, then why is it labeled "inverted" in on Tuesday, February 24, 2015
Thank you.
Posted by Geetha on Saturday, April 19, 2014
Thank you! I am working on 12 tone serialism for my IB composition, and this has helped a lot!
Posted by Dupyo on Friday, March 14, 2014
Best of luck, Alexander!
Posted by Carolyn on Wednesday, January 15, 2014
You are awesome. Writing a Tone Row composition to prove to my teacher it can sound good. We'll see what happens haha.
Posted by Alexander Piechowski on Wednesday, January 15, 2014
Zoe, thank you for your feedback. You are absolutely correct, and I have amended my entry.  What is true is that the tritone occurs in the same position in both rows.
Posted by Carolyn on Saturday, January 4, 2014
It's not right that the inverse must end at the same note as the original.  Take for example this matrix that I formed:
Posted by Zoe on Saturday, January 4, 2014
I stumbled upon this after watching a video about twelve tone composition. I compose and arrange in my free time and after reading this I found one thing was unmistakably clear. I write music and have little technical understanding of theory. =P I guess that's what I get by playing with my ears instead of learning the mathematical language music is comprised of. In either case, it was a fun read even if I had to wrack my brain to make sense of some of the terminology. Which, really, convinced me that I need to brush up on musical language to retain my music nerd status. On to more relevant things. I find twelve tone music is fascinating. It's like trying to communicate with things that sound like words, but are structured differently. Certainly they follow similar rules and in certain stretches they seem like the patterns of words we've come to understand in our respective languages but then it pulls a fast one and turns into something nonsensical. At least, when you're trying to look at it from the standpoint of the patterns of said language. It's an interesting challenge to try to hear it without limiting it to the formations and patterns we associate with music. I'll cut this off because it's late and I'm at risk of rambling so I'll conclude with this; a fun read and a thorough explanation as well as a nice piece as demonstrated above.
Posted by C.J. on Sunday, August 18, 2013
It creates harmony (or dissonance) only by virtue of the fact that you have more than one note sounding at a time. It does not have to create *tonal* harmony; that all depends on what rows you choose and how you put them together. That's up to you. Because you are working with 12-tone rows, you never really have any tonal center, which is one of the aims of 12-tone composition.
Posted by Carolyn on Saturday, July 13, 2013
I stumbled on this while looking for an answer to my question. I know how to make a tone matrix and how to use it, but I can't figure out what the left hand plays. I thought that you could play two rows at the same time, but doesn't that create harmony, making it tonal and not atonal? What do I do?
Posted by Lapo on Saturday, July 13, 2013
It doesn't really matter which way you start your original row. If you prefer to call right-to-left your original row, then the opposite, left-to-right, is the retrograde.

Once you have your palette filled in, just choose whichever rows you like the sound of for any particular place within your composition.
Posted by Carolyn on Thursday, November 8, 2012
Very interesting ... As you know , Japanese read from right to left and top to bottom, and it's supposed to give me the retrograde but no inverted retrograde. I don't have a talent to compose you have any right to left & top to bottom samples ?
Posted by Mitsuyo on Thursday, November 8, 2012
Why is a-tonal or serial music any less expressive than music from the Common Era? Isn't a piece of music, despite the method of composition from which it was brought into being, an inanimate object and thus incapable of expressing anything nay mean anything? If inanimate objects express anything then they do only by virtue of us saying so. In other words, music cannot be literally sad, glad, happy or mad because inanimate objects do not have the capacity for human emotions. Perhaps inanimate objects like music or sunsets can be all those things in a metaphorical sense. However, to say that serial music is not "truly expressive" or as expressive as tonal music is like saying rivers are not as expressive as sunsets. I love your peice by the way. Joe Composer
Posted by Joe on Friday, September 28, 2012
The dynamics are totally at the discretion of the composer. The 12-tone theory only dictates the pitches that must be used. The composer has complete freedom to choose timing, dynamics, rhythm, orchestration in short, everything else.
Posted by Carolyn on Monday, January 23, 2012
I am working on 12 Tone compositions in my Music Theory class and I was wondering how exactly dynamics are calculated into this randomness. Could you help me out here?
Posted by Aaron on Sunday, January 22, 2012
I like the resulting piece though I do believe serialism to be expressive. The idea of consonance and dissonance goes back to Plato and the harmonic proportion. This meant that only 4ths and 5ths of the octaves were consonant and gradually other 'proportions' were introduced or accepted (like 3rds and 6ths). I also think it is a common mistake to call it a 'technique'. It is not actually a technique at all, it is a philosophy. In that by using the linear patterns of all the notes the music was ultimately unified. Thus, the completion of the tone row "...provided a philosophical base and singular unity of expression that is based on musical truth and meaning" (2011, SC). Just some of my thoughts...
Posted by Gerald on Thursday, January 12, 2012
You're most welcome!
Posted by Carolyn on Wednesday, April 29, 2009
THANK YOU you have made 12 tone composition make sense and it has helped me so much! x
Posted by Rachel on Wednesday, April 29, 2009
Agreed.  I've always believed that music should come from the heart, and speak to the heart.  20th-century compositional techniques are rather like working through an interesting puzzle.  (In fact, I wrote this document in response to a friend who was telling me about Soduko.)  It's an entertaining intellectual exercise, which might yield some aesthetically pleasing results, but I can't see how it could ever be truly expressive.
Posted by Carolyn on Saturday, June 7, 2008
Interesting. Weird, but interesting.
Posted by Thomas on Friday, June 6, 2008

Sing to the Lord, you saints of His,
praise His holy name.
For His anger lasts only a moment,
but His favor lasts a lifetime;
weeping may remain for a night,
but joy comes in the morning.

You have turned my mourning into dancing;
You removed my sackcloth and clothed me with joy,
that my heart may sing praise to You and not be silent.
O Lord my God, I will give thanks to You forever.

— Psalm 30:4-5,11-12