## 1.1 Durational Values: Symbols Representing Time in Music

#### Durational Values and Proportional Chain Figure 1.2 Durational Values and Nomenclature
Beethoven, Ludwig vanPiano Sonata No.8, Op.13

#### Tremolo Figure 1.4 Smaller Value “Slashes” (Tremolo)

#### Dotted Values Figure 1.5 Dotted Values: First Interpretation Figure 1.6 Dotted Values: Second Interpretation Figure 1.7 Dotted Values: Third Interpretation

## 1.2 Pulse, Tempo, and Meter

#### Pulse and Tempo Figure 1.15 Metronome Marking and Pulse Marking

#### Meter and Time Signatures

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 1.19 “Common Time” and “Cut Time”

## 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

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 Figure 1.22 Sum to Find Compound Pulse Value