Source: 'Schoenberg's Piano Concerto: an introduction' by Mitsuko Uchida. Liner Notes for this recording.

Here are the original two pages.

enter image description here For Ex. 1:

  1. Is the C♯ (that I coloured in red) erroneous? To avert writing the same Note Name twice (I colour in blue the C already used), shouldn't it be written as D♭ in green?

  2. Why did Uchida write C♯ in note sequence, but D♭in the chord?

For Ex. 2:

  1. Repeating the same Note Name seems acceptable now. Why?
  • Since there are 12 semitones but only 7 base notes in a scale, you cannot avoid repeating some of them. (This is called the pigeon-hole principle.) Jun 3, 2017 at 7:02
  • Ensure the “superiority” of German music for the next hundred years? My... I've long disliked Schönberg's music, but I didn't know he was such a nutcase. Jun 3, 2017 at 8:30
  • @leftaroundabout Typical German nationalism at that time, unfortunately. He's one of several that made pretty much the exact same statement.
    – Richard
    Jun 3, 2017 at 13:35
  • @leftaroundabout If the subject intrigues you, as Richard wrote, nationalism through music is an old and widespread part of history of music. For the german speaking world you can read the works of Barbara Eichner arts.brookes.ac.uk/staff/barbaraeichner.html for instance. In France, century-long controversies about what should or should not be "french music" or "french opera" or "french melody" as opposed to Italians (in the 17th and 18th) or Germans (essentially Wagner) in the 19th and early 20th are well known.
    – ogerard
    Jun 5, 2017 at 6:36

1 Answer 1


In 12-tone serializm, it doesn't really mater what you call a note the more important is that you maintain the integrity of the tone row which doesn't recognize enharmonic equivalents as different notes for the purpose of the town row. The letter/quality combination comes second to the enumeration of the notes in a row and utilizing the different transformations possible.

It's typical to pick either all sharps or all flats when making a tone row just for consistency, but it's not a requirement and you can switch back and forth as you please as long as you maintain the row. It's even more typical when thinking of the base row and all of its transformations to remove the letter names altogether and just work with numbers then apply the numbers to note names only when you put them on the staff.

To demonstrate why it makes more sense to view theses in numbers rather than letter names and why at the end of the day the exact letter names don't really matter. The following is the matrix for your examples where P0 is ex1 and I5 is ex2:

enter image description here

While you can figure out the relationships, the patterns may not immediately jump out at you. In comparison, this is the exact same matrix just using enumeration to represent the notes instead of letter names:

enter image description here

You can play with the matrix calculator here yourself.

In tonal music this concept is a lot different and you can read it here.


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