The Elements of Rhythm: Sound, Symbol, and Time

The first musical stimulus anyone reacts to is rhythm. Initially, we perceive how music is organized in time, and how musical elements are organized rhythmically in relation to each other. Early Western music, centering upon the chant traditions for liturgical use, was arhythmic to a great extent: the flow of the Latin text was the principal determinant as to how the melody progressed through time. As Western music moved from monody to polyphony (“single voice” to “multiple voices”), sets of symbols developed gradually that allowed musical time to be established against a recurring background pulse. This also allowed multiple elements in music to be established in tandem with one another. These symbols evolved into the durational values (“note values”) that form the foundation for music notation.

1.1 Durational Values: Symbols Representing Time in Music

Durational values

Durational values are symbols that represent time and action in musical space: they delineate and mark off varying values of sound (and silence) in a composition. Additionally, they are proportional to one another as to how they may be divided from larger into smaller values. There have been many differing notational systems throughout the history of music. In the context of other study, you may encounter these various and sundry systems from early Western notational traditions. Our current system of notation evolved from these early systems, incorporating aspects of many.

Components of Notes

Let us first examine how durational values are drawn:

Figure 1.1 Components

Note values may be “open notes” (not filled in or blackened), or “filled-in notes.” In the context of how musical time is organized (discussed below), these will have greater or lesser lengths or time spans.

Durational Values and Proportional Chain

Below are examples of basic durational values and their common names. Proper names for these values are in parentheses. These names are commonly used in the United Kingdom and Commonwealth countries, as well as by some academics.

Figure 1.2 Durational Values and Nomenclature

There are rare examples of “One-hundred and twenty-eighth-notes.” A notable example is found in the First Movement Introduction to Beethoven’s “Pathetique” Sonata No. 8, Opus 13.

Beethoven, Ludwig vanPiano Sonata No.8, Op.13

Durational values are held in proportion to one another. Observe that each value is proportionally related to adjacent values. If we assign the arbitrary value “1n” to a whole-note, then the half-note equals 1/2n. Therefore two half-notes are required to equal a whole note, two quarter-notes equal a half-note and so on.

Figure 1.3 Durational Value Chain

Tremolo

At times notes may have a diagonal slash (or slashes) through the stem, or below a note value that has no stem. These slashes are interpreted one of two ways:

1. These indicate a tremolo, the performer rapidly repeating the note, or;
2. As a notational convenience, slashes represent flags, denoting embedded smaller durational values:

Figure 1.4 Smaller Value “Slashes” (Tremolo)

These can be interpreted as “eighth-notes in the space of a half-note” (4), or sixteenth-notes in the space of a quarter,” (4) and so on. This is merely a notational convenience employed as needed.

Dotted Values

Durational values may have small periods (“dots”) appended to them. Originally, this evolved as a notational “convenience,” a proportional division indication, or as a segment boundary. Dotted values2 have three different interpretations:

1. A dotted value may represent the addition of half of the original duration, or “half again as much as the original value” (“1+1/2n”).

Figure 1.5 Dotted Values: First Interpretation

2. A dotted value may be divisible into three non-dotted values:

Figure 1.6 Dotted Values: Second Interpretation

3. A dotted value may be divisible into two smaller dotted values:

Figure 1.7 Dotted Values: Third Interpretation

Rests

Just as durational values represent the length of sound in music, symbols of equivalent value represent the length of silence. These are called rests3 . Figure 1.9 "Rests" shows rests and their labels. As with durational values, rests are proportional to one another also.

Figure 1.9 Rests

1.2 Pulse, Tempo, and Meter

We perceive the organization of time in music in terms of three fundamental elements, Pulse, Tempo, and Meter. Use prompts to assist you in understanding these elements:

• Pulse—“beat”: the background “heartbeat” of a piece of music.
• Tempo—“rate”: the relatively fast or slow speed at which we perceive the pulse in a piece of music.
• Meter—“ratio”: how durational values are assigned to represent the pulse are organized in discrete segments in a piece of music.

Pulse and Tempo

Pulse , or beat, is the regularly recurring underlying pulsation that we perceive that compels music to progress through time. Pulse makes us react kinesthetically to music: in other words, it compels motion. We tap our feet, we dance, we march, or we may just “feel” the pulse internally. In a piece of music, some durational value is assigned to be the pulse. All other durations are proportionally related to that fundamental background pulse.

Tempo (Latin: tempus-“time”) is the rate (or relative speed) at which the pulse flows through time. This is determined by numerous methods:

1. A metronome marking: for example, MM=120 means the pulse progresses at 120 beats per minute (two beats per second). Often, in practice, the background durational value will be drawn and assigned a metronomic value. (You will sometimes encounter the marking bpm, “beats per minute.”)

Figure 1.15 Metronome Marking and Pulse Marking

2. Around the 17th Century (roughly!), Italian terms came to be used to indicate tempo. These terms were descriptive and therefore rather loosely interpreted as to exact tempo. These terms indicate a narrow “range” of metronomic speeds. For example, the term Andante means “going” or “a walking tempo.” This usually equates to roughly 76 beats per minute, but may be interpreted at a slightly faster or slightly slower pace.

3. In an attempt to refine these terms, to make them more precise, diminutives were added: Andantino indicates a slightly faster pace than Andante. Other modifiers came into common practice as well. For example, Andante con moto (“going, with motion”) is self-explanatory.
Beginning in the 19th Century, composers often used equivalent tempo and performance descriptions in their native languages, or mixed Italianate terms and vernacular terms within the same piece.

4. It is important to understand that the use of these terms exceeded mere indications of relative speed. Often, they also carry the connotation of style or performance practice. For example, Allegro con brio (“lively, with fire or brilliance”) implies a stylistic manner of performance, not merely a rate at which the pulse progresses through time.

Meter and Time Signatures

Meter , expressed in music as a time signature, determines:

1. Which durational value is assigned to represent the fundamental background pulse;

2. How these pulses are grouped together in discrete segments;

3. How these pulses naturally subdivide into lesser durational values, and;

4. The relative strength of pulses (perceived accents) within segments or groupings of pulses.Concerning accentuation of pulse, you will encounter the terms Arsis and Thesis, terms adapted from Hellenistic poetic meter. These have come to mean “upbeat” and “downbeat” respectively. These are nearly slang definitions or, at best, jargon. Arsis is best described as “preparatory,” hence perceived as a relatively weak pulse. Thesis is best described as “accentuated,” hence relatively strong. It is interesting to note that, at various times in the history of music, the meaning of these two terms has been reversed from time to time.

Time signatures consist of two numbers, one over another, placed at the beginning of a composition. They may occur anywhere in a composition where a meter change is required. They are NEVER written as fractions!

Simple and Compound Meter

To understand meter fully, we must first determine the fundamental nature of the
prevailing background pulse or beat. In given meters, we perceive beats as having
the potential (or capacity) of being divided in two ways:

                 1. The prevailing background pulse may be subdivided into two
                     proportionally equal portions. Meters having this attribute are labeled
                     Simple Meter (or Simple time).
                2. The prevailing background pulse may be subdivided into three
                    proportionally equal portions. Meters having this attribute are labeled
                    Compound Meter (Compound time).

We name meters according to two criteria:
                1. Is it Simple or Compound time?
                2. How many prevailing background pulses are grouped together?

Figure 1.16 Simple and Compound Divisions of Given Pulses

So, a time signature wherein (a) the pulse subdivides into two portions, and (b) two
pulses are grouped together is called Simple Duple. Three pulses grouped together,
Simple Triple and so forth. A time signature wherein (a) the pulse subdivides into
three portions, and (b) two pulses are grouped together is called Compound Duple,
three pulses, Compound Triple, and so forth.

Figure 1.17 Time Signatures and Labels

Simple Meter
Let us address simple meter first. Analyze this by answering two questions
concerning the stated time signature:
                     1. For the top number: “How many…?” In other words, how many
                         prevailing background pulse values (or their relative equivalent
                         values and/or rests) are grouped together?
                     2. For the bottom number: “…of what kind?” In other words, what
                         durational value has been assigned to represent the prevailing
                         background pulse?
          So the time signature 2/4 has two quarter-notes grouped together, therefore, we label
          this as Simple Duple.

Figure 1.18 Typical Simple Meters

In Renaissance music, specialized symbols were employed that were the forerunner of time signatures. These symbols determined how relative durational values were held in proportion to one another. We continue to employ two holdovers from this system.

Figure 1.19 “Common Time” and “Cut Time”

“Common Time” and “Cut Time,” are slang terms. Other names for “Cut Time” are “March Time” and the proper name, Alla Breve.

The Time Signature Table The characteristics of individual time signatures are perceived in multiple layers that can be reduced to three basic levels:

1. The prevailing background Pulse or beat.

2. First Division: the level wherein we determine if the pulse divides into two equal portions (simple meter) or three equal portions (compound meter).

3. Subdivisions: how First Division values subdivide into proportionally smaller values. Therefore, we can graph time signatures using the following table.

Table 1.1 Time Signature Table

Pulse 

First Division

Subdivisions

(The fundamental background pulse.)

(The level determining pulse division into two portions or three portions.)
(Subsequent divisions into smaller values.)

Figure 1.20 Time Signature Table Example

Use this table to map out time signatures and their component organizational layers.

Compound Meter
Understanding compound meters is somewhat more complex. Several preparatory
statements will assist in comprehension:
                             1. Compound Meters have certain characteristics that will enable
                                 prompt recognition:
                                               a. The upper number is 3 or a multiple of 3.
                                               b. The prevailing background pulse must be a dotted value:

           remember, in compound meter, the pulse must have the capacity
to divide into three equal portions.
                                               c. Subdivisions of the background pulse are usually grouped in sets of
                                                    three by the use of beams (ligatures).
                              2. In theory, any Compound Meter may be perceived as Simple
                                  Meter,depending upon the tempo:
                                                a. If a tempo is slow enough, any compound time signature may be
                                                    perceived as a simple meter.
                                                b. In practice, this is limited by style and context in compositions.
                              3. In Compound Meter, the written time signature represents the
                                  level of First Division,not Pulse:
                                                a. In order to find the pulse value in compound time signatures, use
                                                    the Time Signature Table. List First Division values (the written
                                                    time signature) in groupings of three.
                                                b. Sum these to the dotted value representing Pulse. List these
                                                     accordingly in the Table.

As with Simple time signatures, let us employ the same Time Signature Table to
graph Compound time signatures. Reviewing Statement 3 above, we will follow a
slightly different procedure than that used for graphing Simple Meter:
                                1. For the Compound Duple time signature 6/8
                                    list six eighth-notes in two groupings of three in the First Division row:

Figure 1.21 Compound Meter, First Division Groupings

2. Next, sum these groupings of three into dotted values (“two eighthnotes equal a quarter-note, the additional quarter-note represented by a dot”); list the two resulting dotted quarter-notes in the Pulse row:

Figure 1.22 Sum to Find Compound Pulse Value

3. Lastly, draw subdivisions of the First Division values in the Subdivision row:

Figure 1.23 Subdivision

Below are typical compound meters and their respective labels.

Figure 1.24 Typical Compound Meters

Note that Simple meters divide all values into two subdivisions in each level of the Table. Compound meters divide the First Division level into three (see Statement 1 above). Subsequent subdivisions divide into two.

Simple Triple Interpreted as Compound Meter

Some Simple Triple time signatures may be perceived as either simple or compound, again depending upon tempo. In practice, this is a limited list: The time signatures:
3/16 3/8 3/4

may be perceived as Simple Triple if the tempo is relatively slow. In other words, you perceive the “lower number” of the time signature as the fundamental background pulse value. As the tempo for any of these becomes relatively faster, we cease to perceive the lower number as Pulse. Instead we perceive the lower number as the First Division of a Compound meter.

The Time Signature Table will show this:

Figure 1.25 Simple Triple, Compound “Single”

In the next section, these fundamental elements of sound, symbol, and time will be placed in full musical context by uniting them with common notational practices.

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