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Editor’s Message

[1] MTO volume 9.3 presents work on contrasting topics by three authors. In his article, “Klein-Bottle Tonnetze,” Robert Peck relates transformational theory and musical analysis to the four-dimensional topology of a Klein bottle. In order to more faithfully render the mathematical equations and graphic examples, we offer this article in Adobe PDF format. Robert Peck also contributes a report on the special session, “Mathematical Techniques in Musical Analysis,” presented at the American Mathematical Society’s 2003 Spring Southeastern Section Conference in Baton Rouge.

[2] Diane J. Urista’s “Beyond Words: The Moving Body as a Tool for Musical Understanding” is the second in a group of articles we are preparing on topics in music theory pedagogy. The movement-based approach to aural training described in the article is illustrated with video clips of students’ movement improvisations.

[3] “The Role of Set-Class Identity in the Estimation of Chords” by Tuire Kuusi examines subjects’ ability to aurally discriminate between chords of varying set-class. Graphic and audio examples are included.

[4] Also provided in the issue are listings of recently completed dissertations, job opportunities, and general announcements.

[5] Submissions to MTO are welcome at any time. We encourage readers to post their reactions to this issue's articles and review. The mto-talk email list is available to MTO subscribers (subscription is free) for online discussion of any MTO-related topic. To post to mto-talk, simply send an email message to Longer responses may be submitted for publication in the Commentary section of the next issue. These should be formatted and submitted according to MTO Author Guidelines.

[6] All MTO volumes dating back to our first issue in 1993 can be accessed from the contents page at

Timothy Koozin, Editor
Music Theory Online
Moores School of Music
University of Houston
Houston, TX 77204

Updated 03 July 2013
Brent Yorgason