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Interactive tool for creating special, retrograde symmetrical twelve-tone series

Create Symmetrical 12-Tone Series Vs 1.2

Use this tool to generate symmetrical 12-tone series. Select the Symmetry Type, then use the pull-down menus in the 12-Tone Series Input frame. The Series Control Buttons will transpose, invert or reset the series. [More user guidelines >>]

Use this page in landscape mode on mobile devices.

Select the Symmetry Type of the Series
Retrograde Symmetry Retrograde Inverse Symmetry
12-Tone Series Input
Pitch 1 to 6:  
Pitch 7 to 12:  
Series Control Buttons
Message Window

Guidelines for the user

This JavaScript GUI generates symmetrical 12-tone series. It is based on a procedure (algorithm) in Hanns Jelinek's introductory book on 12-tone composition (see the Further Reading section below). The GUI generates either Retrograde or Retrograde-Inverse symmetrical series. This GUI is divided into a number of sections:

  • Use the Select the Symmetry Type section at the top to select either a Retrograde Symmetrical (R-symmetry) or Retrograde Inverse Symmetrical (RI-symmetry) twelve-tone series.

  • Then use the Tone Series Input section. The GUI will guide you through the appropriate input sequence. In case of R-symmetry the pitch input order is Pitch 1-2-3-4-5-6 (the other pitches will be generated automatically). In case of RI-symmetry the pitch input order is Pitch 1-12-2-3-4-5-6. Note names represent their enharmonic equivalent, C#=Db, F#=Gb, etc.

  • The Message Window will inform the user about the progress of the input process and suggest the next step in the procedure.

  • After completing the generation of a symmetrical 12-tone series (the Message Window will let you know), the Series Control Buttons will become active and allow the user to transpose, invert or reset the 12-tone series.

  • Navigate to the Tone Series forms GUI on this Website to study the interval content plus the complete set of transposed, inverted and retrograde forms for a given series.

Here are examples of symmetrical 12-tone series that you might want to consider:

  • The series C-E-F-Eb-C#-Ab-D-G-A-B-Bb-F# has the retrograde symmetry property.

  • The series C-Eb-C#-F-A-Ab-B-Bb-D-F#-E-G has the retrograde-inverse symmetry property.

  • The Lyrische Suite, Mvt. 1, (Alban Berg) uses an all-interval series, based on the sequence of two all-interval hexachords, F-E-C-A-G-D and Ab-Db-Eb-Gb-Bb-B. The series has R-symmetry.

Further Reading

The following references discuss twelve-tone series and their symmetry:

  • Hanns Jelinek, Anleitung zur Zwölftonkomposition, 1. Teil (UE 12083) und 2. Teil (UE 12084), Universal Edition, Wien, 1952 and 1958.
  • Reginald Smith Brindle, Serial Composition, Oxford University Press, London, 1966 (ISBN 0 19 311906 4).
  • George Perle, Twelve-Tone Tonality, 2nd Edition, University of California Press, Berkeley, 1996 (ISBN 0-520-20142-6).
  • George Perle, Serial Composition and Atonality, 6th Edition, University of California Press, Berkeley, 1991 (ISBN 0-520-07430-0).
  • Joel Lester, Analytic Approaches to Twentieth-Century Music, W.W. Norton and Company, New York, 1989 (ISBN 0-393-95762-4).