HARMONIC EXPANSIONS: Watch your harmonies grow!

Harmonic Expansions is designed to introduce the concept of expanding harmonies to first year Music Theory students by using multimedia presentations on the World Wide Web. To this end every four part example is a systematic expansion of the tonic triad. Students also have opportunities to practice their listening skills with dictations which are similarly derived expansions. While acknowledging their limitations in scope, these pages are also intended to provide a glimpse of what a stand-alone web-based text would look like.

Music Theorists will recognize several concepts on these pages that were introduced by Heinrich Schenker, including harmonic expansion (or "prolongation" or "elaboration"), the Urklang (referred to here as the "primordial tonic"), the fundamental harmonic progression and analytical levels. One motivation for writing these web pages was to present these concepts to first year students in a systematic way. However, these pages are not meant to be a comprehensive explanation of Schenker's theories.

This web-based presentation supplements traditional textbook explanations of chord progressions by taking advantage of features which are impossible in printed media:
  • Playback controls can be activated with a simple click right next to the score and the relevant text; there is no need to search for tracks corresponding to passages in the printed text.
    Thus a web presentation eliminates the need for a textbook's CDs, the student's CD or mp3 player or going from the printed page to the textbook's accompanying website. With a web based presentation the number of devices needed for listening and learning is reduced to just one--any device with a web browser.
  • Explanations of unfamiliar terms can be found by clicking on links rather than consulting an index and then searching for the appropriate page.
  • The web can also incorporate visual effects which cannot be conveyed in print. By embedding videos, scores can expand as harmonies expand, the color of notes can change as alternate interpretations are presented, and alternative Roman numeral analyses can appear and disappear depending on the current interpretation.
  • Playback from notation software now uses high quality instrumental sound sampling creating audio clips which are neither offensively robotic nor subject to performers' copyright claims.
  • Social media or forums can be used to communicate suggestions and corrections quickly. In fact a whole community of "reviewers" can discuss modifications and related topics. In Harmonic Expansions suggestions can be made by clicking here or by following a link at the bottom of each page.

Students can begin Harmonic Expansions after
  • having completed a fundamentals course in music theory which includes triad inversions and the spacing of isolated triads in four voices. These subjects are covered in Chapters 1 - 14 in the fundamentals worksheets on this "G Major Music Theory" web site.
  • having completed Chapter 15 of the fundamentals worksheets on this site. This chapter teaches two kinds of simple voice leading between root position chords called Common Tone Stepwise (CTS) and Contrary Motion Nearest (CMN) voice leading. They will be referred to frequently in Harmonic Expansions.
  • having had an introduction to root position dominant seventh chords, as in the first four pages of Chapter 19
  • having gained some familiarity with alto clef (not covered here).

Harmonic Expansions is not a substitute for early voice leading chapters in a traditional textbook. While voice leading is an integral part of the explanations of linear expansions on these pages, students will not learn to write music in four voices satisfactorily without working through traditional pencil and paper exercises found in text books and their accompanying workbooks.

I am indebted to Anthony Kosar and Michael Levi who were my instructors at Advanced Placement Summer Institutes; to Brent Sandene and Janet Waanders, of the Educational Testing Service, who nominated me to the Development Committee of the Advanced Placement Music Theory Exam; and to all the members of this committee, especially my two committee chairs Jane Clendinning and Patrick McCrellis. Thank you, all.