Messiaen’s Modes of Limited Transposition – Part 1

Well, I guess Olivier Messiaen is as good a place to start as any.

And a good place to start with Messiaen would be his choice of scales and modes that he used for composition. Messiaen in general favored synthetic scales, but he gravitated towards the use of scales that have a limited number of unique transpositions. These scales are known as the Modes of Limited Transposition, of which there are seven. We will cover all seven before venturing into their harmonic usages and the Transposition Invariance Inclusion Lattice.

Before we begin, there are a few things that need to be defined.

Unique Transpositions are defined as a transposition in which at least one pitch class differs from the other transpositions. A transposition that has all of the same pitch classes as another transposition is not a unique transposition.

Axes of Symmetry are axes that divide the scale into mirror parts, easily seen with a pitch circle. A common factor with the Modes of Limited Transposition is their internal symmetry, though the exact position of each axis will vary from scale to scale. The visual associated with this has now been added as of 2/5/17.

Each of these scales has at least one mode. These modes are found in the same way that the Greek modes are found in major/minor scales, and can be utilized freely.

Hooray, time for fun!

Mode I – “Whole-tone Scale”

  • 2 Unique Transpositions
  • Forte 6-35
  • Set – {0 2 4 6 8 t}
  • Interval Vector –
  • 1 Mode
    • 2 2 2 2 2 2
  • 6 Axes of Symmetry
    messimode1utr
    Unique Transpositions

    messimode1axes
    Axes of Symmetry

Mode II – “Octatonic Scale”

  • 3 Unique Transpositions
  • Forte 8-28
  • Set – {0 1 3 4 6 7 9 t}
  • Interval Vector –
  • 2 Modes
    • 1 2 1 2 1 2 1 2
    • 2 1 2 1 2 1 2 1
  • 4 Axes of Symmetry
messimode2utr
Unique Transpositions
MessiMode2Axes.PNG
Axes of Symmetry

Mode III

  • 4 Unique Transpositions
  • Forte 9-12
  • Set – {0 1 2 4 5 6 8 9 t}
  • Interval Vector –
  • 3 Modes
    • 1 1 2 1 1 2 1 1 2
    • 1 2 1 1 2 1 1 2 1
    • 2 1 1 2 1 1 2 1 1
  • 3 Axes of Symmetry
messimode3utr
Unique Transpositions
MessiMode3Axes.PNG
Axes of Symmetry

Mode IV

  • 6 Unique Transpositions
  • Forte 8-9
  • Set – {0 1 2 3 6 7 8 9}
  • Interval Vector –
  • 4 Modes
    • 1 1 1 3 1 1 1 3
    • 1 1 3 1 1 1 3 1
    • 1 3 1 1 1 3 1 1
    • 3 1 1 1 3 1 1 1
  • 2 Axes of Symmetry
messimode4utr
Unique Transpositions
MessiMode4Axes.PNG
Axes of Symmetry

Mode V

  • 6 Unique Transpositions
  • Forte 6-7
  • Set – {0 1 2 6 7 8}
  • Interval Vector –
  • 3 Modes
    • 1 1 4 1 1 4
    • 1 4 1 1 4 1
    • 4 1 1 4 1 1
  • 2 Axes of Symmetry
messimode5utr
Unique Transpositions
MessiMode5Axes.PNG
Axes of Symmetry

Mode VI

  • 6 Unique Transpositions
  • Forte 8-25
  • Set – {0 1 3 5 6 7 9 e}
  • Interval Vector –
  • 4 Modes
    • 1 2 2 1 1 2 2 1
    • 2 2 1 1 2 2 1 1
    • 2 1 1 2 2 1 1 2
    • 1 1 2 2 1 1 2 2
  • 2 Axes of Symmetry
MessiMode6UTr.PNG
Unique Transpositions
MessiMode6Axes.PNG
Axes of Symmetry

Mode VII

  • 6 Unique Transpositions
  • Forte 10-6
  • Set – {0 1 2 3 4 6 7 8 9 t}
  • Interval Vector –
  • 5 Modes
    • 1 1 1 1 2 1 1 1 1 2
    • 1 1 1 2 1 1 1 1 2 1
    • 1 1 2 1 1 1 1 2 1 1
    • 1 2 1 1 1 1 2 1 1 1
    • 2 1 1 1 1 2 1 1 1 1
  • 2 Axes of Symmetry
MessiMode7UTr.PNG
Unique Transpositions
MessiMode7Axes.PNG
Axes of Symmetry

Now, I did not make the site I’m about to link, but it is probably the best one for looking at the Modes. I wish I could have done this myself. Jackson Hardaker deserves all of the credit for this tool and more, so I will provide a link to it here ( Specifically, right here ).

This concludes the introduction to Messiaen’s Modes of Limited Transposition. Eventually, I will create a Part 2 and beyond to fully cover the subject.

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