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Fantasy Pieces examines from several vantage points a vital life-force of Robert Schumann's music, namely metrical conflict. Harald Krebs's imaginative yet.
Table of contents

The compositions I survey in my present study are: String Quartets Nos. They were composed between and , and so cover the composer's three style periods. Stanley Sadie, vol. The three periods are , , and Most of the terminology and definitions used herein originate in his writings. Krebs defines "the meter of a work as the union of all layers of motion i. The layers of a work consist of the pulse layer, micropulses, and interpretive layers. The pulse layer is the most quickly moving pervasive layer, typically the tactus; micropulses move quicker than the pulse layer; and interpretive layers move slower than the pulse layer, and are more important in the metrical interpretation since they group the pulses into larger durations.

Each interpretive layer is denoted by an integer and labeled as an "n-layer"; this cardinality "n" refers to the constant number of pulses between two adjacent attacks of the interpretive layer. In this most recent work, Krebs adopts a different wording for some terms used in his earlier articles.


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For instance, he substitutes the word "layer" for "level. Here, the pulse layer proceeds in quarter notes. A micropulse in eighth notes is offered by the first violin. Two interpretive layers are simultaneously active. The second violin and viola articulate a 3-layer that is a series of dotted-half-notes, in which there are three pulses between consecutive attacks.

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In the cello, a motive lasting 6 J s with slur is sequenced: this grouping structure determines a 6-layer, since there are six pulses between two consecutive beginnings of the motive. Regularly recurring accents may also contribute to the formation of interpretive layers. As Joel Lester notes, accents are emphases on points of initiation and musical 7 events are needed to mark off these accented timepoints. As shown in Example 3. In the piano, the regular recurring dynamic accents, density accents seven-note chord attacks , and new-event harmonic accents B minor-G major-F minor-D minor also mark off a 4-layer.

In Example 3.

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Example 3. Lerdahl and Jackendoff, A Generative Theory, String Quartet N o. Alignment occurs when each pulse of every interpretive layer synchronizes with a pulse of every faster layer, and this state is referred as "metrical consonance. This primary metrical consonance assumes great significance for it acts as a reference point for all metrical perceptions.

There are two types of non-alignment in metrical dissonance. Yeston first explained the concepts of "stratum of motion" and "rhythmic consonance and dissonance" in his book. Krebs extends and refines these concepts, and modifies the terms as "layer of motion" and "metrical consonance and dissonance" respectively. For convenience, Krebs uses a simple method to label these dissonances. In these dissonances, when the interpretive layer e. The following musical excerpts demonstrate these dissonances.

In Example 4.

But the solo cello, alternating with other instruments, articulates an antimetrical 4-layer by repeating a four-note motive. Example 4. Another aspect of metrical dissonance is the difference between direct and indirect dissonance. Superposition means the layers are active simultaneously.

Juxtaposition occurs when one layer stops and is only conceptually maintained by the 7 Krebs, " Some Extensions," , and Fantasy Pieces, J - J-J. Related to indirect dissonance is subliminal dissonance. Subliminal dissonance usually lasts longer than indirect dissonance.

Harald Krebs. Fantasy Pieces

Krebs also distinguishes between simple and compound dissonances. Another related concept is that of pulse streams, which John Roeder has used to analyze the surface rhythms of Schoenberg's complex middle-period polyphonies. His method reveals that regularly recurring accents from different voices create competing pulse streams. These are roughly similar to Krebs's layers of motion, but Krebs focuses on the metrical states of consonance and dissonance resulting from the vertical interaction among the layers while Roeder is interested in the horizontal, concurrent, and distinct continuities hidden behind the apparently irregular surface.

Roeder explains his rhythmic analytical theory as follows: " A pulse is a series of successive, perceptibly equal timespans, marked off by accented timepoints A minimum of two equal timespans is necessary to activate a pulse. When analyzing layers of motion, Krebs remarks that, in addition to the aforementioned phenomenal accents, layers are also created by repetition of patterns, individual pitches and grouping structures.

Perhaps the clearest definition of grouping structure has been given by Lerdahl and Jackendoff in their Well-Formedness and Roeder, "Pulse Streams," Preference Rules, which are part of their generative theory of tonal music. Changes in local details such as register, dynamics, pattern of articulation, and length of notes determines grouping boundaries.

On a larger-level, symmetry equal length and parallelism motivic, thematic, rhythmic, or harmonic help define the extent of a group. Lerdahl and Jackendoff do not discuss layers of motion, but they do treat meter and they explore some musical situations in which the grouping and metrical structures are "in phase" and "out of phase. The authors hear tension in out-of-phase music, and consider this quality to be an essential rhythmic feature in music.

In addition to these factors, however, Hindemith has other unique ways to mark off layers in his music. They will be considered systematically in this section, in order to characteristic Hindemith's rhythmic style, and provide a basis for the analysis presented hereafter. Within one single voice, Hindemith creates layers by regular grouping, "oom-pah-pah" accompaniment patterns a kind of grouping , regular accent, ostinato pattern repetition , motivic or rhythmic repetition, regular attacks, weak-beat durational accentuation, and slurs.

These factors are similar to those of Krebs's theory. Between voices, Hindemith establishes layers by the separation of pitch-class content or root content, and by the distribution of regular attacks through several voices these are slightly different from Krebs's factors. Very often, several kinds of accents act together to generate a layer. For the purposes of clear demonstration, each musical example cited below will deal with only one type of accent. In Example 5. On a larger level, repetition marks off a 6-layer, that is, dotted-half-note pulse.

Similarly, in Example 5. In Examples 5.

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Regular accent within a single voice also creates layers of motion. The dynamic accents of Example 6. In Example 6. Sonata for Oboe and Piano 8 , first movement, mm. In Example 7. Similarly, the cello of Example 7. More generally, Hindemith frequently creates layers by motivic or rhythmic repetition within a single voice. For instance, in the left-hand part of the piano in Example 8. In the right-hand part of the piano in Example 8. In the Cello Sonata example, 8. The second violin and viola in String Quartet No. Example 9. Solo Solo B. At mm.

In the Viola Sonata, a 3-layer is also determined by durational accents in the piano, as shown in Example Example See his Fantasy Pieces, For instance, one way that Hindemith creates distinct layers is by separating their pitch class content. In an Interludium from Ludus Tonalis, shown in Example 12, a 3-layer conforming to the notated meter at mm. It is the result of a repeated rhythm J Y J J y J that keeps an A in the uppermost voice as a pedal point, and uses only the white-key chords, so that it seems to imply a D-Dorian mode.

Another 3-layer, on the notated off-beat, is articulated by the left hand in the same register. In contrast to the other layer, it contains only black-key chords, and so implies the pentatonic scale. A similar method is used in mm. In these few measures, layers are distinguished by interval content: the on-beat 3-layer consists of major and minor triads; the off-beat 3-layer, one single dyad P4. The left-hand chord maintains D as a root, while the right-hand chords have Example Another illustration is given in Example Layers are often created by distributing attacks regularly through several voices.

In the Violin Sonata of Example The solid line shows the distribution. In Example In Hindemith's theoretical system, the root of a chord is the root of its "best interval. To identify the root of a chord, one determines which of its intervals is best according to this list.

Although layers involve regular motion, Hindemith sometimes creates a sense of irregularity by shifting from one layer-cardinality to another within single voices and by gradually shortening or lengthening the group lengths. A simple illustration is given in Example At first, the combination of cello and piano stresses the metrical 4-layer with durational accents every whole note.

But in mm. Another illustration is in Example The motive J J J J transferring from one voice to another activates a 2-layer. But the loud dynamic and density accent on the first quarter at m. Sometimes the new group length is not maintained, but the lengths of successive groups keep varying, creating irregularity within the voices. In a passage from the Wind Quintet shown in Example Transpositions of the three-eighth-note ostinato establish some large group lengths, each characterized by a distinct key.

That is, the lengths gradually decrease until the very last group. With all these means of creating layers, there are many interesting and artistic ways to combine them in metrical consonance and dissonance. Some of these combinations are like those covered by Krebs, but Hindemith invents other combinations as well. A short passage from the Wind Quintet, Example In the clarinet, three 15 J groups are prominent.

The flute, seeming to be a shadow to the clarinet, has two prominent groups, which result from the repetition of a segment at a temporal interval of 15 J s.