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MUSIC LIBRARY^

UNlVERSfTY
Of CALIFORNIA

BERKELEY



SIMPLE METHOD



MODERN HARMONY



CARL IV. GRIMM.



FOURTH Edition.
$1.50



THE WILLIS MUSIC CO,

CINCINNATI, OHIO.



UNIVERSITY

OF CALIFORNIA

BERKEl,EY



Preface to the Second Edition.



There are many reasons for me to feel gratified at the success
of my Harmony method. Without a preface I sent the first edition
of the book into the world, because the work was to speak for itself.
Only in the last paragraph (§ 84) did I add concluding remarks in
order to indicate my standpoint. Composers, teachers and students
have used and praised the book.

As the thorough bass figuring is practicall}' obsolete, and can
contribute nothing towards explaining the chord formations and
chord relationships in modern harmony, it is not employed here.
My signs indicate the tonal functions of chords only. The tonal
functions reveal the fact that all chords are related to each other
in groups, and that these again have subordinate groups. The sev-
eral subordinate groups of chords cannot be ranked in a single alpha-
betical file, as the thorough bass methods vainly attempt to do, but
must be looked upon as clustered around higher chord-groups, and
these again around other points, and so on until the tonic is reached.
The system of modern harmony is founded solely upon the relation-
ship by the Fifth and the Third. The modern key extends far be-
yond the original boundaries, and is not limited to a scale, which is
in itself nothing l '11 a, chord with passing tones.

The principle or "variation" that I brought forward is founded
upon the master works, and adheres to the laws of logic and science.
With this Harmony system, every chord of Wagner's, from Rienzi
to Parsifal, can be so logically explained, that he does not appear as
revolutionist, but as a wonderful explorer in the realm of tones.

My essay on the Ke5'-extension of Modern Harmon}- forms an
addition to the text-book, because it contains illustrations of the
extreme limits of chord relationship.

To the present edition also are added Examination and Review
Questions, which, no doubt, will be welcomed by many teachers.
The well-nigh inevitable typographical errors in the text have been
corrected ; there being no reason to change anything else in the
book.

I hope that this new edition will make manj- new friends and
that the book will be productive of much good in the field of har-
mony study and teaching.

CARL W. GRIMM.
Cincinnati, July IG, lOOG.

Copyright 10(10
IDOl

The Geo. B. Jennings Co.
c inc1nn.\ti, o.






PART I.

CHAPTER I.

INTRODUCTION.

§ 1. RHYTHM, MELODY AND HARMONY are the three
essential factors of music. Rhythm is the change, but systematic
grouping, of tones of various duration. If tones of different pitch
are heard one after another in lo'gical order, we get what is called
Melody; if tones of different pitch are heard together, we get Har-
mony (a chord). In its widest sense Harmony means the science of
chords, their relationship and connection. It is the laws of harmony
that we shall explain in this book, but it will be seen as we proceed
that the question of rhythm or melody is often so closely connected
with that of harmony that it is impossible to treat of one without
also paying some attention to the other.

g 2. INTERVALS.— An interval is the distance and differ-
ence between two tones, heard one after the other or at the same
moment. Intervals have numerical names. These names depend
on the number of letters which are included from one key of the
key-board to another, or from one degree of the staff to another. In-
tervals are measured by means of half-steps (half tones or semi-
tones) and whole steps. A half-step is the term of measurement
for the smallest distance. It is the distance between any one note,
and the nearest note to it, above or below. For example, on the
piano, the nearest note to C is B on the one side (below), and C^ on
the other side (above). From B to C, and from C to C^ are, there-
fore, both half steps. Similarly from F|| to Ftj, and from V% to G
will be half-steps; but from G to A will not be a half-step, for A is
not the nearest tone to G; GJ| (or At2) comes between them. It is
evident that two half-steps together will make a whole step. The
nomenclature of intervals, especially the modified ones, is, unfor-
tunately, in a somewhat confused state and not uniform in all text-
books. The classification adopted here will recommend itself for
its simplicity, because the intervals are arranged into only three
classes: normal, enlarged and narrowed. First of all we will learn
the accurate size of the normal intervals, and then the modifications
(augmentation and contraction) of them. If a tone be sounded and
the same tone be repeated, or sounded simultaneously by some other

instrument (or voice), a "prime" is formed, for example: F^ —J

The word prime means an interval of one degree; it also means
the starting note, the one from which the other notes are counted.
A prime makes use of only one letter for two sounds which have
the same pitch, or very nearly the same, as the paragraph on

fa



02:]02



"modified" intervals will show. This prime is also called "per-
fect." Instead of always writing down the name of an interval, we
will use figures. For the word prime the figure 1, seconds are in-
dicated by 2, thirds by 3, etc.

A "second" (2) is an interval between two conjunct degrees;
it includes two letters. A "normal" second contains one wiiole

step, for example : pi^ m — ~ ^~| This second is also called a " major "

2
second.

A " third " (3) is an interval of three degrees; it includes three
letters. A " normal " third contains two w^hole steps, for example:

i±. J

^ -j This is also named a " major " third.

T
A " fourth " (4) is an interval of four degrees ; it includes fojr
letters. A " normal " fourth contains two whole steps and one half-
step: p ^— -^ zii^ This is also called a " perfect " fourth.

4
A " fifth " (5) is an interval of five degrees ; it includes five let-
ters. A "normal" fifth contains three whole steps and one half-
step: ^ fe "^^^-^ '^^^^ '^^ ^^^° called a " perfect " fifth.

5
A "sixth" (6) is an interval of six degrees; it includes six
letters. A " normal " sixth contains four whole steps and one half-

step: : ^ — /p — j This is also called a " major " sixth.

6
A "seventh" (7) is an interval of seven degrees; it includes
seven letters. A "normal" seventh contains five whole steps:
p^— u— ziiH It is a whole step smaller than the octave. This is also
F ^ ~" ^^ H called a "minor" seventh. It is to be borne in mind
•^ -^ that our term " normal " and our figures do not indicate
merely a -degree, but an exact size of the interval. Our figure 7

always indicates the "minor" (dominant) seventh

therefore, we indicate the "major" seventh Ffe^^^J as a "raised"

7<
seventh. The mark: < (short crescendo sign) means "raised,"
as will be further explained in the paragraph on " modified " in-
tervals.

An "octave" (8) is an interval of eight degrees; it includes
eight letters. It is always the distance from one tone to the next



(above or belowj of the same name
six whole



normal " octave contains
octave.



steps : EfeE^^B This is also called a " perfect

jrees; it
second.

d This is also called a



A " ninth " (9) is an interval of nine degrees; it includes nine
letters. It is composed of an octave and a second. A " normal"

ninth contains seven whole steps : p^z

C)

" major " ninth.

A " tenth " (10) is an interval of ten degrees; it includes ten
It is composed of an octave and a third. A "normal"

also called a



letters

tenth contains eight vi^hole steps



ffi==J This is



terms.



" major " tenth. Intervals larger than tenths and even tenths are
commonly reduced to the nearest octave, and so to their lowest
r~§~ ^~^ — 1
Thus the tenth F r t ^ ~ "| is usually spoken of as a third,
TT :^

as if it were counted from the c on the third space. It will be
found useful to impress upon the memory that:

the normal or " major" second (2) is midway between the prime
and third; it is at an equal. distance of a whole step from each;
the normal or "perfect " fourth (4) is between the third and fifth;
there is an intervening space of a half step from the third and
a whole step from the fifth ;
the normal or " major " sixth (6) is next to the fifth; a whole step
farther away from the prime than is the fifth.
EXERCISE. — Write out the normal intervals up to the tenths
of the following notes: g, d, a, e, b, fif, c^, g^^, d||, att, e^, h^, f, bl?,
et2, al2, dl2, g\z, ct2, f^.

§3. NORMAL UNDER-INTERVALS.— Intervals are us-
ually reckoned upwards, but occasionally also from the upper tone
downward; then it must be expressly stated. In either case the in-
terval is, of course, the same, but when reckoned downward it is



called an under-interval. Thus the interval



:: is a fifth,



but f is the under-fifth from c.

EXERCISE.— Write out the under-intervals down to the
tenths of the following notes : g, d, a, e, b, f^, cjlf, gj^, d^, f, hk, e!?, at?,
di?, gk, ci2, ft2, as follows :



g^^EJ^Elg



-^^-



1 u2

u = under.



u4



u8



u9



i



ulO



§ 4. MODIFIED INTERVALS.— Intervals may be modified
either by raising or lowering one of their tones. Care must be
taken not to change the name of the interval. Thus, if we wish to'
enlarge the normal fourth C-F by a half-step we must write C-F^,
not C-GI?, otherwise the interval will not be represented as a mod-
ified fourth, but as a modified fifth.

< is the sign for raising the pitch of a note a half step.

> (short decrescendo mark) is the sign for lowering the pitch
of a note a half step,

TABLE.
Showing the meaning of the figures with

1 < raised (augmented) prime,

2 < raised (augmented) second,
2 > lowered (minor) second,
•} < raised (augmented) third,
•) > lowered (minor) third,
4 < raised (augmented) fourth, -

4 > lowered (diminished) fourth, -
< raised (augmented) fifth,

5 > lowered (diminished) fifth,

6 < raised (augmented) sixth

6 > lowered (minor) sixth,

7 < raised (major) seventh,

7 > lowered (diminished) seventh -

8 < raised (augmented) octave,
8 > lowered (diminished) octave) -
9< = 2 = 2>,
10< = 3 = 3 >'.

u 1 > lowered under-prime,
u 2 > lowered under-second, -
u 2 < raised under-second,
u 3 > lowered under-third,
u 3 < raised under-.third, -
11 4 > lowered under-fourth, -
u 4 < raised inider-fourth,
u 5 > lowered under-fifth,
u 5 < raised under-fifth,
u 6 > lowered under sixth, -
u 6 < raised undersixth, -



with '


: and >.




For c.


Forgff.


For f^.


c#


gx


f


c\^


aX


g


dt2


a


giztz


ett


bx


a


et2


b


ai2l2


i^


CX


b^


f!2


c


3l2b


f^


dx


c


g^


d


cl22


ail


eX


d


al2


e


dl22


b


fx


el2


bto


f


3l2e


cfi


gx


f


c^


g


fW


Fore.


For g|.


For e.


Ct2


g


e^


bt2t2


f


di2


b


fx


4


al2l2


ek


Cl2


a


4


■ c lowered under-seventh,

u 7 < raised under-seventh,

u 8 > lowered under-octave,

u 8 < raised under-octave, - -

u 9 > = u 2 >, u 9 < =: u 2< ,

ulO > = u 3 >, u 10 < = u 8


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Online LibraryCarl William GrimmA simple method of modern harmony → online text (page 1 of 12)