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First, we have to arrange the twelve tones of the octave into an order of our choosing:

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This will be our twelve-tone series, or our tone row. As you can see, we've numbered each of the tones so we can refer to them by number (trust us, it'll make it much easier to analyze). Now we can begin the actual composition. Let's start off by making a melody:

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As you can see, we've kept the order of the tone row intact. The rule here is that no tone can be repeated (except for immediate repetitions like tones 3, 7, and 11 in the example) until all other 11 tones have been sounded. We could continue constructing our melodies this way, but you can imagine how boring it would be to hear the same twelve notes in the same order over and over. So we're allowed to transpose the whole series so it begins on a different tone, as long as the intervals stay the same. Furthermore, we're allowed to transpose any note up or down an octave:

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Okay, so we've learned how to make melodies, but what about harmony? Don't worry; the tone row can also be applied to harmony. Here's an example of how we harmonized the first two measures of our first melody:

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If you studied the example above, you would see the tone row become apparent in the "blocks" of harmony. In the diagram below, we've replaced the notes with their representative numbers from the tone row. As you can see by the blue boxes, the tone row is repeated not only in melody but in harmony as well.

There are also several other ways to bring variance into a twelve-tone piece such as ours. You are allowed to alter your tone row in three ways: inversion, retrograde, and retrograde inversion. To invert the series, you take every interval and reverse it. For example, our tone row begins with two minor second drops and a major third; the inverted form will begin with two rising minor seconds and a rising major third. Retrograde is fairly straighforward: you take the series and flip it so that the 12th tone comes first and the 1st tone comes last. Retrograde inversion is just what it sounds like: first you invert it, then you flip it.

Press here to play MIDI

Press here to play MIDI

Press here to play MIDI

So there you have it: a quick 5-minute walk through the twelve-tone method. While it may not have turned you into the next Schoenberg, we hope that you gained some sort of understanding of how the system works.