Description
This collection would be great for anyone who is trying to learn the music theory, and it's important for any musician.
This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/ 3.0/) license. This book was accessible as of December 29, 2012, and it was downloaded then by Andy Schmitz (http://lardbucket.org) in an effort to preserve the availability of this book.
Study Set Content:
K E Y T A K E A W A Y S
The student should understand:
• Musical time is represented by symbols called durational values. They
may be dotted or non-dotted.
• Durational values: specific components and specific ways how they are
drawn.
• Durational values are proportional to one another.
• Durational values have equivalent rest values.
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.1 Durational Values: Symbols Representing Time in Music
15
E X E R C I S E S
1. Practice drawing durational values and rests following the model
below. Make sure to draw noteheads correctly (no “stick figures”
please!).
Figure 1.10
Durations and Rests
2. For each value given, draw three lower divisions: for example,
given a whole-note, draw two half-notes, four quarter-notes,
eight eighth-notes. Use flags and beams (ligatures). Make sure to
align and space properly. See sample solution.
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.1 Durational Values: Symbols Representing Time in Music
16
Figure 1.11
Duration Divisions
3. For each value given below, draw the appropriate equivalent
rest.
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.1 Durational Values: Symbols Representing Time in Music
17
Figure 1.12
Equivalent Rests
4. For each dotted value:
a. Draw the appropriate dotted lower divisions, for example, a
dotted half-note dividing into two dotted quarter-notes.
b. Draw the appropriate non-dotted lower divisions, for
example, a dotted half-note dividing into three quarter-
notes.
c. Draw the appropriate durational values that represent the
addition of half the basic value. For example, a dotted half-
note is a half-note plus a quarter-note (“half again as
much”).
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.1 Durational Values: Symbols Representing Time in Music
18
Figure 1.13
Dotted Values
5. For each incomplete example below, add the appropriate
durational value that will complete the background value.
Figure 1.14
Incomplete Values
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.1 Durational Values: Symbols Representing Time in Music
19
1.2 Pulse, Tempo, and Meter
L E A R N I N G O B J E C T I V E S
1. Definitions of the elements of rhythmic organization.
2. Perception of Tempo and commonly used terms.
3. Mapping out meter (time signatures): the perception of Simple and
Compound Time.
4. How these elements interact in music.
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
4
, 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
5
(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
4. Pulse (or beat) is the regularly
recurring background
pulsation in music.
5. Tempo is the rate at which we
perceive the pulse in time. This
is indicated by metronome
markings, pulse value
markings and terms.
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
20
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.
Chapter 19 "Appendix A: Common Musical Terms"
lists common
terms and their commonly accepted meanings along with some
equivalents in other languages.
Meter and Time Signatures
Meter
6
, 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
6. Meter is the “ratio” of how
many of what type of pulse
values are grouped together.
Simple Meter divides the pulse
into two equal portions;
Compound Meter divides the
pulse into three equal portions.
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.2 Pulse, Tempo, and Meter
21
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
7
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
7. Meter is expressed as time
signatures, indicating how
many pulses (beats) are
grouped together into cogent
units.
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.2 Pulse, Tempo, and Meter
22
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.
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.2 Pulse, Tempo, and Meter
23
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
(The fundamental background pulse.)
First Division (The level determining pulse division into two portions or three portions.)
Subdivisions (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.
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.2 Pulse, Tempo, and Meter
24
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:
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.2 Pulse, Tempo, and Meter
25
Figure 1.21
Compound Meter, First Division Groupings
2. Next, sum these groupings of three into dotted values (“two eighth-
notes 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
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.2 Pulse, Tempo, and Meter
26
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:
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.
3
16
3
8
3
4
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.2 Pulse, Tempo, and Meter
27
K E Y T A K E A W A Y S
The student should be able to define and understand:
• Pulse (“beat”), Tempo (“rate”), and Meter (“ratio”).
• Simple Meter: recognizing and analyzing Simple Time Signatures.
• Compound Meter: recognizing and analyzing Compound Time
Signatures.
• Time Signatures that may be perceived as either Simple or Compound
and why they are so perceived.
• Using the Time Signature Table as a tool for graphing Time Signatures.
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.2 Pulse, Tempo, and Meter
28
E X E R C I S E S
1. Using the Time Signature Table, map out all examples of:
a. Simple Duple and Compound Duple.
Pulse
First Division
Subdivisions
b. Simple Triple and Compound Triple.
Pulse
First Division
Subdivisions
c. Simple Quadruple and Compound Quadruple.
Pulse
First Division
Subdivisions
Note: At the Subdivision level, draw one layer of subdivisions
only.
2. Using the Time Signature Table map out the following time
signatures as both Simple and Compound Meters:
a.
3
16
Pulse
First Division
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.2 Pulse, Tempo, and Meter
29
Subdivisions
b.
3
8
Pulse
First Division
Subdivisions
c.
6
8
Pulse
First Division
Subdivisions
d.
9
8
Pulse
First Division
Subdivisions
3. In class (or some group), practice tapping a slow beat with your left foot.
Against that beat tap two equal (“even”) divisions with your right hand
(simple division). Next, keeping that same slow beat in your left foot,
practice tapping three equal (“even”) divisions with your right hand
(compound division). Lastly, switch hands and feet. Good luck.
4. The following exercises alternate between simple duple and
compound duple. Tap these rhythms while keeping the same
constant background pulse. Practice each segment separately at
first: then practice in sequence, switching from simple to
compound time as you go.
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.2 Pulse, Tempo, and Meter
30
Figure 1.26
Rhythm Drill
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.2 Pulse, Tempo, and Meter
31
1.3 Music Notation Practices
L E A R N I N G O B J E C T I V E S
1. Defining and understanding measures and bar lines.
2. Defining and recognizing sectional directions: “Roadmaps” in music.
3. Learning basic conducting patterns.
In
Section 1.2 "Pulse, Tempo, and Meter"
, when describing meter and time
signatures, we spoke of “grouping pulse values together” to form discrete units. In
music these groupings are delimited, or “bounded” by vertical strokes called bar
lines. Bar lines serve as boundaries, defining a “measure” of music.For these
examples we will employ a five-line staff. Use of the staff will be explained fully in
Chapter 2 "The Elements of Pitch:Sound, Symbol, and Tone"
The crossover period between Renaissance and Baroque music at end of the 16th
Century and the beginning of the 17th Century witnessed many changes as to how
music was written. The rise of the “Second Practice,” (
Seconda prattica
) or “New
Style” (
Stile moderno
) of composition (early opera) and the concomitant rise of
instrumental music necessitated changes in notational practice.
Since rhythmic durations in Renaissance music were organized in proportion to one
another (differing forms of
mensural
notation), measures and their separating bar
lines were not in use, nor were time signatures, as we know them. These elements
came into gradual use. Scholars offer many explanations for this: practicality and
ease of reading and interpretation, a shift away from multi-voiced music and
toward solo or homophonic settings in dramatic music, the desire for segmenting
music into discrete segments, and so forth.
Measure and Bar lines
This became common notational practice. A
measure
8
of music constituted beat
groupings (or their durational equivalents) within the context of the stated time
signature, bounded by a bar-line. Composers may use a double bar line to denote
sectional divisions in a piece. A final bar line ends the composition.
8. A measure of music is a span of
music, bounded by a bar line. It
is a discrete grouping of pulse
values dictated by the time
signature.
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
32
Figure 1.27
Measure, Bar lines, Double bar line, Final bar line
Within measures, specified beats received greater of lesser accentuation, referred to
simply as “
strong
” or “
weak
” beats. This perception is based upon how the relative
strength of beats is perceived in a given time signature.
Figure 1.28
Sample Time Signatures and Beat Accents
Conducting Patterns
As performers, as teachers, and as potential ensemble leaders, all musicians must
have a basic understanding of typical conducting patterns. In conducting, the terms
arsis
and
thesis
will be encountered. In this context, synonyms for these terms are
“
upbeat
” (preparatory beat) and “
downbeat
” (commencement beat). The common
conducting patterns are shown in
through
.
The Basic Two-Pattern: for example any simple duple or compound duple time
signature. When practicing this, think “away (from the body)-up, away-up…
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.3 Music Notation Practices
33
Figure 1.29
Two-Pattern
All conducting figures by Michael Paolantonio
The Basic Three-Pattern: any simple triple or compound triple time signature.
Think “down-away-up…”
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.3 Music Notation Practices
34
