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In Vi Hart's video on twelve-tone nursery rhymes, she says that one of the rules of twelve-tone composition is that you're allowed to alternate between adjacent notes in the tone row as much as you want; you're just never allowed to jump back by two notes. For example, if the beginning of your tone row was C#-G-Ab-E-C-..., you could write a melody that began C#-G-Ab-G-Ab-E, but not one that began C#-G-Ab-C#-G.

My knowledge of the subject is pretty limited, but I'd never heard of this rule before, and it doesn't seem to happen in any of the examples on this Wikipedia page (or be stated as a rule there).

How common is this kind of alternation in 12-tone music? Is it universally considered legitimate, or do only some composers allow themselves to do it (or is it just an error)?

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Bliley, I hadn't seen your question but I asked one just a few hours later about the same video. Synchronicity eh? – dumbledad Jul 2 '13 at 20:19
@dumbledad Are we going to need to create a vihart tag? – NReilingh Jul 2 '13 at 22:55
up vote 9 down vote accepted

Wikipedia explains (emphasis mine):

When rigorously applied, the technique demands that one statement of the tone row must be heard in full (otherwise known as aggregate completion) before another can begin. Adjacent notes in the row can be sounded at the same time, and the notes can appear in any octave, but the order of the notes in the tone row must be maintained.

Vi Hart's rule loosens the rule to permit adjacent notes in alternation, rather than sounding them at the same time. This variation is minor, compared to the fact that she deliberately subverts the technique to create familiar tunes.

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Good question here.

It is not considered universally legitimate and may in fact just be a stylistic trait of the person you mentioned, as it is (to my knowledge) not commonly done or practiced.

In 12-tone music, it has been jokingly said that "everyone cheats" and that is more or less true - composers often break away from the rigid structure and follow their ears / intuition in order to realize their artistic goals. It is rare that someone follows every single rule of 12-tone composition perfectly and ends up with something profound or meaningful.

I'm going to refer to the Second Viennese School here for examples of different approaches to 12-tone technique.

Of the three composers most closely associated with the Second Viennese School (Arnold Schoenberg, Anton Webern, and Alban Berg,) Berg was the loosest with his treatment of rules - he would sometimes skip notes of rows or go back a couple of notes and repeat them. Sometimes his rows were incomplete or sometimes he would have gratuitous chromaticism. By contrast, Webern was one of the most strict - with pitches almost never (if at all) ever being repeated.

Other composers such as Stravinsky and Copland further employed their own personal takes on the rules as well.

Generally speaking, in the strictest 12-tone theory each pitch should only be played once and only once, the exception is the repetition of a current pitch such as "C#-G-Ab-Ab-Ab-E" would be acceptable.

Like most things in their respective subjects, it's okay to break the rules if you know the rules and you understand / have reasons for why you are breaking them.

Hope this helps!

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Perhaps we should distinguish two things. First, there is the 12-tone technique as such, which can be rigorously defined to prohibit note repetitions before all notes of the series have occurred. Then there is the actual practice of composers, whose music has been labelled as dodecaphonic. As others have pointed out, composers will often use the series with some flexibility.

Vi Hart isn't really breaking any rules, but rather setting up her own way of concatenating pitches, as we all do. The entire notion of rules can be very misleading. There are simply none to break! Vi mentions one of the reasons for why procedures such as 12-tone rows are used, which is to reduce the combinatorial explosion that occurs if you would pick one pitch, then the next and so on without any system. So rather than a rule, think of it as an aid for the composer to reduce the cognitive load.

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