Introduction: Reductive analysis strips away details such as reiteration, doubling and linking notes to reveal the "bones" of a work. This online lesson explains the rationale and signs used in a procedure derived by Gerald Warfield from the work of Heinrich Schenker.

In this procedure, notes in a harmony are written as beamed half notes. Neighbor tones are beamed black note heads and passing tones are free (unbeamed) black note heads. A few terms will be used such as:

verticalize:

reduce arpeggiation to a block chord

simultaneity:

notes sounding together (same as block chord in this lesson)

domain:

span occupied by one chord

The following examples and exercises are of short excerpts. The process by which one arrives at the Ursatz (overall pattern) of a passage or movement is not shown in this lesson. What is important is the act of seeing below the surface to find underlying generalized patterns.

The approach to an Ursatz is based upon a "wheels within wheels" process where successively broader levels of abstraction and generalization are tied together by an underlying macro pattern. The ingrediants of an Ursatz in "tonal" music is a step wise line that descends to the tonic and a 1-5-1 bass (see Example 9).