Harmony and Voice Leading 4th Edition PDF Download: Master the Art of Harmonization and Melody Writi

Harmony & Voice Leading is a thorough, well-written and well-illustrated book. It deals extensively and exhaustively with the basic musical theory necessary to understand harmony; more advanced topics are then covered, such as dissonance and chromaticism as part of a wider discussion of voice-leading. This fourth edition (it's a volume with a venerable history), published this year, now contains detailed coverage of species counterpoint.

harmony and voice leading 4th edition pdf download

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This article presents a empirical characterization of tonal harmony, the core organization system of Western music. Using the Annotated Beethoven Corpus, one of the largest datasets of expert-annotated harmonic analyses available to date, we adopt a statistical approach to model tonal harmony and to advance the methodological state-of-the-art in music research. We propose an overarching model employing four core dimensions (centricity, referentiality, directedness, and hierarchy) and explore the dataset under that paradigm. Importantly, we do not claim that these dimensions provide an exhaustive characterization of tonal music, as we leave other structural aspects such as meter, rhythm, voice-leading, and hierarchical syntax out of account. Nonetheless, the dimensions considered here constitute central pillars of the Western musical system.

In the baroque era, a set of rules developed for voice leading in four-part harmony. In these rules, the bass voice would be assigned the root of the chord, although it can occasionally be assigned the fifth or the third. If the chord is a triad, the root is generally doubled by one of the other voices. When two voices are harmonized in perfect intervals (fourths, fifths and octaves), repeats of the same interval between the two voices (also known as moving in parallels) are almost always avoided.

Another rule concerns perfect cadences. In such cadences, the leading tone (the seventh scale degree) must resolve step-wise to the tonic. That is, the voice that plays the leading tone must resolve up to the tonic, and if the chord is a dominant seventh chord, the subdominant should resolve to the mediant.

ABSTRACT: This article develops a transformational space based on the concept of guide tones. In jazz pedagogy, guide tones are the chordal third and seventh and are often used to connect consecutive chords through efficient voice leading. Transformational representations of guide-tone syntax illustrate how guide tones provide a pathway for listeners and improvisers to seamlessly traverse the tonally complex harmonic progressions often found in jazz compositions.

[1.4] The presence of guide-tone theory in so many pedagogical works attests to its intuitiveness to jazz musicians and pedagogues. Likewise, its proliferation as a pedagogical tool has facilitated its reception both intellectually and in musical practice: students who are trained to think of guide tones as essential and practice playing and/or hearing guide-tone lines develop an understanding of jazz harmony and voice leading undergirded by guide-tone theory.

[1.7] In many tunes, guide-tone lines support an impression of seamlessness as they provide a means of traversing tonal space through efficient voice leading. Depicting guide-tone voice leading as a transformational space allows us to visualize more clearly these voice-leading relationships and the melodic paths that they afford listeners and improvisers. One of the benefits of transformational spaces is their comprehensive nature, as one can easily visualize the entire gamut of transformations afforded by the space. By taking guide-tone dyads as our transformational object-family and formalizing a transformation-family to relate those objects, we can investigate the possibilities afforded by guide-tone voice-leading syntax in jazz.(15) In the section that follows, I formalize this transformational space.

[2.4] 5-dyads are represented as vertical line segments between two adjacent pc vertices on the Tonnetz. 6-dyads are represented as diagonal line segments extending from southwest to northeast between two diagonally adjacent pc vertices in the Tonnetz. Musical transformations between gt dyads may be visualized as geometrical transformations on the two-dimensional Tonnetz grid.(23) The most familiar of these is the transposition operation, Tn, formalized below.(24) The Tonnetz representation of the Tn operation is shown in Examples 6a and 6b, where gt dyads are translated left or right along the x-axis. Sample harmonizations of each dyad involved in the transformation are shown beneath each of the examples. It is worth emphasizing that, in each case, any chord in the left column may progress to any chord in the right column (or vice versa) and preserve the smooth guide-tone voice leading illustrated in the example. Following the constraints developed above (gt motion may not exceed ic2, total displacement may not exceed 4), only four values are used for n of Tn throughout this article: 2, 1, -1, and -2.(25)

[2.7] Reflections of the 5-dyad are also of analytical use as they model parsimonious voice leading where the moving voice moves by a whole step. These operations, Ru and Rd (reflection up and reflection down, respectively) are formalized below. Their Tonnetz representations are shown in Example 10. The Ru operation reflects a 5-dyad across the x-axis of its upper vertex while the Rd operation reflects a 5-dyad across the x-axis of its lower vertex. Sample harmonizations for each dyad are shown below Example 10.

[2.8] When both guide tones of a 5-dyad move by semitone in contrary motion and form another 5-dyad, this is represented by the C (contrary motion) transformation. The C transformation is best visualized as a translation along the southwest/northeast axis, shown in Example 11. Sample harmonizations for each dyad are listed beneath Example 11. Note that a translation northeast results in the same dyad as a translation southwest due to the redundancy of the ic6 axis. This motion may also be understood as either RuT-1 or RdT1 (shown in Example 12). However, neither of these combinations captures the semitonal voice leading involved in the C transformation, and both require more voice-leading work. For this reason, I prefer the visualization found in Example 11.(28)

[2.10] Transformations where each gt moves by greater than ic2 may be diagrammed on the gt Tonnetz, but are less likely to be heard because the tones are moving by more than a step. Because this article is chiefly concerned with smooth voice leading, I have left all such transformations in the space unformalized.

[2.11] As with many, if not most, geometric and graph depictions of voice-leading relationships, following transformations on the gt Tonnetz can feel more alien than simply following the same transformations on a musical staff. It is worth emphasizing that the purpose of using the gt Tonnetz is not that the space is easier to follow, but that it more accurately represents the ways in which the gts in harmonies progress from one to another without direct reference to the contexts to which they belong. In some ways, this is similar to the Neo-Riemannian Tonnetz: while it may not be easier to think in terms of moves on a Tonnetz, it is an alternative means of notation that clarifies its syntax. Indeed, both the Neo-Riemannian and gt Tonnetze are useful in part because they defamiliarize otherwise familiar music-theoretical objects. This opens new avenues for interpreting their relationships. Unlike the Neo-Riemannian Tonnetz, however, gt space also helps to separate the relationships between gt dyads from their surrounding context. This separation has two uses: First, it allows us to see the various transpositional and inversional relationships that are established between particular gt dyads; second, it suggests that even when tonal coherence is not found through other harmonic-analytical ventures, coherence may be established through gt transformations. Thus, the gt Tonnetz helps to visualize a significant alternative space, where coherence is established solely through the voice-leading properties of guide tones.

[4.1] In the previous sections, we formalized a transformational space that visualizes the voice-leading syntax established by guide tones and explored some of the ways in which the space may be used to model various kinds of harmonic structures. It will now be useful to consider how guide-tone syntax relates to tonal, diatonic syntax. To do this, let us more closely examine the parallels between neo-Riemannian theory and gt space.

[4.3] Though differences exist, guide-tone dyads and consonant triads share a few notable properties. Like consonant triads, gt dyads can be generated from one another using parsimonious voice leading. These smooth voice-leading procedures form a syntax by being constrained in particular ways (following the transformations codified above): no single gt may move by more than ic2 and the total voice-leading displacement may not exceed 4.

[4.4] Yet gt dyads establish a much more complicated relationship with their musical surroundings. Unlike consonant triads, which may often faithfully represent the entirety of pitch material over a given span of time, gt dyads are always situated within a larger harmonic context as chord members, and the harmonies to which they belong are often at least somewhat indeterminate due to the improvisational circumstances of jazz performance. Indeed, although an isolated 5-dyad would be acoustically resonant, such resonance is mostly irrelevant when the dyad is placed in its larger context as the third and seventh of a given harmony. This makes establishing relationships with parent collections problematic as well. In pan-triadic syntax, the handful of distinct triads generated by chains of L and P operations may be considered subsets of a parent hexatonic collection, the symmetric properties of which avoid establishing tonal hierarchies found in the diatonic collection. The voice-leading syntax of gt dyads is more varied and is always in dialogue with these tonal hierarchies, within which gt dyads are subsumed. 2ff7e9595c