+------------------------------------------------+
| Note: |
| |
| Bold surrounding =text=. |
| Italics surrounding _text_. |
| |
+------------------------------------------------+
ESSENTIALS OF
MUSIC THEORY
ELEMENTARY
BY
CARL E. GARDNER
AUTHOR OF "MUSIC COMPOSITION"
[Illustration]
NEW YORK
CARL FISCHER
1912
COPYRIGHT, 1912,
BY
CARL FISCHER
International Copyright Secured
PREFACE.
The primary object in the following pages is to supply the teacher
and student with a text book to accompany the work on instrumental or
vocal technic. Because of the great amount of time required to obtain
proficient technic, text books are often neglected, and, if exhaustive,
are usually ignored. Brevity and conciseness characterize this volume
and it is planned to meet the needs of the busy teacher and student.
Many pupils may not see the importance of some of the following
text, such as the research for theoretical keys; but the results
thus obtained are nothing more than the natural outcome of simple
mathematical reasoning, and are inevitable if the -structure- of the
scales is understood. Pupils should be impressed with the structure of
scales rather than be taught their keys and signatures by rote. Rote
methods have little to recommend them in modern pedagogical ideals,
and are used principally in teaching the young. The lack of knowledge
of the -whys- and -wherefores- of scales, intervals, and chords among
instrumentalists and singers is appalling, and is due partly to the
neglect of text books and partly to incompetent teachers.
A further object of the text is to offer a course of preparation
for the study of harmony, composition, and appreciation. Music
Appreciation, as a cultural course of study, is growing in popularity
and large enthusiastic classes in this subject are to be found in
all our colleges. These students are frequently handicapped by poor
preparation in the essential rudiments of music such as are treated in
this volume.
The author's gratitude for valuable aid, criticisms, and suggestions
is due his wife, Marion Dillon Gardner, and his sisters, Mabel Gardner
Bankart and Lena Gardner Lewis.
CONTENTS.
PAGE
PREFACE iii
I. RHYTHM: NOTE VALUES: TIME SIGNATURES: TEMPO 3
II. THEORY OF SCALES (Major and Minor) 10
The Major Scale 11
The Minor Scale 21
III. INTERVALS AND CHORD BUILDING 32
Inversion of Intervals 36
Chord Construction 38
Inversion of Triads 40
The Seventh Chord 41
Inversion of Seventh Chords 43
IV. EPITOMIZED ACOUSTICS 47
V. EAR TRAINING 51
The Normal Intervals of the Major Scale 52
The Normal Intervals of the Minor Scale 55
Altered Intervals 56
Arpeggio Chords 60
Two Voiced Chords 61
The Four Voiced Chord 63
ESSENTIALS OF MUSIC THEORY
CHAPTER I.
RHYTHM.
Sound is the effect produced by propagated atmospheric waves which
affect the sense of hearing. Irregular impulses, propagated through the
air, produce noise. Regular impulses produce musical -tone-.
The duration of tone is indicated by symbols called -notes-. Following
is a list of notes:--
[Double whole note] or [Breve] Double whole note or -Breve-.
[Semibreve] Whole note or -Semibreve-.
[Minim] Half note or -Minim-.
[Quarter] Quarter note or -Crotchet-.
[Eighth] Eighth note or -Quaver-.
[Semiquaver] Sixteenth note or -Semiquaver-.
[Demisemiquaver] Thirty-second note or -Demisemiquaver-.
Occasionally the sixty-fourth note ([Sixty-fourth note]) is used.
Following is a table of the relative value of notes:--
[Illustration]
The -breve- or double whole note is not given in this table as it is
but seldom used. The value of it is twice the whole note, four times
the half, etc.
The whole note is represented by an open oval; the half, by an open
oval and stem; the quarter, by a closed head and stem; the eighth note
is the same as the quarter with a flag; the sixteenth, the same with
two flags; the thirty-second, the same with three flags. As is seen
in the table, the eighth, sixteenth and thirty-second notes are often
grouped when more than one occurs in succession.
Suspension of tone is indicated by symbols called -rests-. Each note
has its equivalent rest. Following is a list of rests:--
[Double whole rest] Double whole rest.
[Whole rest] Whole rest.
[Half rest] Half rest.
[Quarter rest] Quarter rest.
[Eighth rest] Eighth rest.
[Sixteenth rest] Sixteenth rest.
[Thirty-second rest] Thirty-second rest.
The rate of vibration is called -pitch-. Rapid vibrations produce
"high" (shrill) tones. Slow vibrations produce "low" tones. More
complete information on sound, tone and pitch is given later under the
heading "Acoustics."
The notes are written on the staff which consists of five horizontal
lines together with their spaces. The duration of a tone is determined
by the note used; the pitch, by the note's position on the staff.
A dot placed after a note or rest adds one half its value. A "tie" is
a curved line connecting two notes of the same pitch. Examples of dots
and ties:--
[Semibreve with Augmentation dot] equals [Semibreve tied with
Minim] or 1 + 1/2.
[dotted half note] equals [half note tied to quarter note] or
1/2 + 1/4.
[dotted quarter note] equals [quarter note tied to eight note] or
1/4 + 1/8.
etc., etc.
A double dot adds one half and one fourth its value, thus:--
[double dotted whole note] equals [tied notes; tied whole, half
and quarter note] or 1 + 1/2 + 1/4.
[double dotted half note] equals [tied notes; tied half, quarter
and eighth note] or 1/2 + 1/4 + 1/8.
[double dotted quarter note] equals [music symbol; tied quarter,
eighth and sixteenth notes] or 1/4 + 1/8 + 1/16.
etc., etc.
Bars are lines drawn vertically across the staff dividing music into
-measures-. The contents of the measure is determined by the fraction
at the beginning. The denominator of the fraction shows the kind of
notes, and the numerator, the number of that kind contained in a
measure. Each measure must contain the number and kind of notes or
rests designated by the fraction, or their equivalents.
-Artificial groups- are groups of notes played and summed in other
than their fractional value. The most common artificial groups are the
-triplet- and -sextuplet-. A triplet is a group of three notes played
in the time and summed in the value of two of its own kind. A sextuplet
is a group of six notes played in the time and summed in the value of
four of its own kind. A group of five notes is played in the time and
summed in the value of four of its own kind. A group of seven notes
is played in the time and summed in the value of six of its own kind.
Occasionally a group of two notes occurs. This group differs from other
artificial groups inasmuch as it is played more slowly than the tempo
notes. A group of two notes is played in the time and summed in the
value of three of its own kind. Artificial groups are designated by a
curved line over or under the notes with a figure showing the kind of
group, thus:--
triplet [Illustration: [triplet]]
sextuplet [Illustration: [sextuplet]]
group of two notes [Illustration: [2-note group]]
In "counting" music, it is customary to give as many counts to each
measure as the numerator of the fraction indicates. Each of these
counts is called a -pulse-. Pulses should occur regularly unless
otherwise marked. Irregularities in the occurrence of pulses are
marked in various ways. The -ritardando-, the -hold- ([Fermata]),
and the -accelerando- are the principal marks of irregularities. The
-ritardando- (abbreviated -ritard.- or -rit.-) means to lessen the
speed, the -accelerando- (abbreviated -accel.-) to quicken the speed,
and the -hold- ([Fermata]) to hold the note, over or under which it is
placed, as long as musical taste dictates.
This occurrence of pulses is called -rhythm-. The most common rhythms
are =4/4= or [common time], =3/4=, =2/4=, =6/8=,
=3/8=, =4/8=, =9/8=, =12/8=, and =2/2= or [2/2
alla breve] also called -alla breve-. Other rhythms not so common are
=6/4=, =8/4=, =1/4=, =2/8=, =1/2=, =6/2=,
=3/2=, =4/2=, =3/16=, and less often =1/1=,
=5/4=, =5/8= and =5/16=, etc.
On the first pulse of all kinds of rhythm is a primary accent called
-thesis-. Secondary accents, called -arsis-, occur in =4/4= on
the third count and in =6/8= on the fourth count. These natural
accents give a "swing" to the music. They can only be displaced or
overshadowed by artificial accents which are designated in various
ways. The most common artificial accents are the -forzando- (designated
thus: [Sforzato], [Marcato], or -fz-), meaning a sudden strong
accent to the note or chord over or under which it is placed; the
-rinforzando- (which is not quite so marked as the -forzando-); the
-staccato- (designated by a dot placed over or under the note or
chord) which makes the note thus indicated short and crisp, and the
-syncopation-, which is a form of rhythm displacing the natural accent
by the note's entrance on an unaccented part of the measure and its
sustentation through the pulse.
The rapidity of the occurrence of pulses is called -tempo-, which is
indicated at the beginning of a movement by Italian words usually, the
most common of which are as follows:--
-Grave-, slow and solemn (the slowest tempo).
-Largo-, slow, a trifle faster than Grave.
-Larghetto-, a trifle faster than Largo.
-Adagio-, a trifle faster than Larghetto.
-Lento-, slow.
-Andante-, moderately slow.
-Andantino-, translated literally means slower than Andante, but it is
more often used incorrectly meaning faster than Andante.
-Moderato-, moderate; the mediate between fast and slow.
-Allegretto-, cheerful.
-Allegro-, quick.
-Vivo-, quick.
-Presto-, very quick.
To many of the above words is added the ending -issimo- which gives
the word to which it is added its superlative degree. Other terms are
oftentimes combined with the above words to characterize the movement.
Every pupil should have a dictionary of musical terms for constant
reference.
The majority of piano students have an absolute disregard for note
values and tempo marks which are so important that the pupils fail to
gain any good results from their study unless they understand and pay
strict attention to these marks. The incompetency of so many teachers
is somewhat responsible for this state of affairs, but the majority of
piano studies and methods is more largely responsible. In second grade
studies, there are many which, if written in a judicious manner, would
be excellent second grade work, but when played as they are written
and as their tempo mark demands require a virtuoso to execute them
correctly. These studies have led pupils to playing -allegro- movements
in -largo- tempo. At the end of a week's practice a -moderato tempo-
may be the result. Continued enforced disregard can produce nothing
but habitual disregard for tempo marks. The teacher should constantly
remind the student of these facts and, in as far as possible, omit such
studies as cannot be played -a tempo-. Many exercises may be rewritten
in a playable manner by the teacher, who, by so doing, would not only
impress the pupil with the importance of tempo marks, but would develop
his ability to read from manuscript, an ability which, unfortunately,
is almost universally lacking in pupils.
EXERCISES.
ORAL AND WRITTEN.
1. What is sound?
2. Tell the difference between noise and musical tone.
3. What is a note?
4. Describe the most common notes.
5. Write a table of the relative value of notes commencing with the
whole note.
6. Write a table of the relative value of notes commencing with the
dotted half note.
7. Describe the rests.
8. For each dotted note, show its equivalent by two tied notes.
9. For each double dotted note, show its equivalent by three tied notes.
10. Describe measure and bar and upon what the measure's contents
depends.
11. Describe the manner of counting the different rhythms.
12. Name the marks that designate irregularities in rhythms and
describe the character of each mark.
13. Describe the natural accent.
14. Name the most common artificial accents and describe the character
of each.
15. What is meant by tempo?
16. Name and define twelve different tempo marks.
17. Explain and notate artificial groups.