THEORY OF SCALES.
MAJOR AND MINOR.
As stated before (Chapter I, page 4), the rate of vibration
is called pitch. Tones vibrating an equal number of times produce
an -unison- which is a perfect concordance and is pleasant to the
ear. Equally as pleasant to the ear is the ratio of two vibrations
against one. A tone vibrating twice as fast as a given tone is called
the given tone's -octave-. Between these two tones many tones may be
found. For example, suppose a note vibrating two hundred times in a
second, its octave would vibrate four hundred times in the second.
Between these two tones there would be (avoiding fractions which would
produce more different pitches) one hundred and ninety-nine tones of
different pitch. The ear is incapable of locating all these tones and
modern custom has divided all octaves into twelve parts, each part
being called a half step or, literally incorrect, a -semi-tone-. These
semi-tones sounded successively upwards or downwards from any tone to
its octave produce the -chromatic scale-.[A]
[Footnote A: All references to scales, intervals and enharmonic changes
treat of the tempered scale.]
A -diatonic scale- is a progression from any tone to its octave in
which certain chromatic steps are omitted. In modern music there are
three forms of diatonic scales, called:--
1. Major.
2. Harmonic minor.
3. Melodic minor.
All three forms have eight tones, the eighth being the octave of the
first and is given the same name.
The tones of the diatonic scale are named in four different ways:--
1. by numerals (Arabic and Roman),
2. by the first seven letters of the alphabet,
3. by the Italian syllables (-do-, -re-, -mi-, -fa-, -sol-,
-la-, -si-,) and
4. by the theory names (-tonic-, -supertonic-, -mediant-,
-subdominant-, -dominant-, -submediant- and -subtonic-).
-The key-tone is the tone from which a diatonic scale is built.-
The numerical system is a movable system which means that 1 is always
the key-tone. The theory name system is a movable system, the tonic
being always the key-tone or 1. The alphabet system is a fixed system
which means that a letter is always the same tone or its octave. The
Italian system is treated as both a fixed system and a movable system.
This book treats of the movable -do-, -do- always being the key-tone, 1
and tonic.
THE MAJOR SCALE.
A major scale is a progression from any tone to its octave in which
chromatic steps are omitted between 1 and 2,--2 and 3,--4 and 5,--5 and
6,--6 and 7; from 3 to 4 and from 7 to 8 half steps are made.
Following is a diagram of a two octave keyboard:--
[Illustration:
C♯ D♯ F♯ G♯ A♯ C♯ D♯ F♯ G♯ A♯
or or or or or or or or or or
D♭ E♭ G♭ A♭ B♭ D♭ E♭ G♭ A♭ B♭
C D E F G A B C D E F G A B C
]
The keyboard shows white and black keys. The black keys are in groups
of two and three. As can be seen in the diagram, the white key next
to the left of the group of two black keys is -c-. The white keys in
order to the right of -c- are respectively -d-, -e-, -f-, -g-, -a- and
-b-. Following -b- is a repetition of -c- at the distance of an octave.
Notice that between -e- and -f- there is no black key as is also the
case between -b- and -c-. In these two cases, where no black key
separates the white keys, the white keys are one semi-tone apart. Two
white keys separated by a black key are one whole step apart. A black
key is at the distance of a semi-tone from an adjoining white key. The
black keys derive their letter names from the white keys. A black key
is named from either of the white keys between which it is situated.
The black key between -c- and -d- is named -c sharp- (♯) or -d flat-
(♭).
Starting at -c- and sounding the white keys in order to the right as
far as the octave produces the ascending major scale of -C-; sounding
in order to the left produces the descending major scale of -C-. Notice
that no black keys are necessary in the case of the -C- major scale,
the whole and half steps being in their proper places; namely, whole
steps between 1 and 2, 2 and 3, 4 and 5, 5 and 6, 6 and 7, and half
steps between 3 and 4 and between 7 and 8. The student must constantly
keep in mind the order of whole and half steps in all scales explained.
In each scale explained the letters will be numbered and a curved line
will connect those figures representing tones one half step apart.
All major keys except -C- major require one or more black keys. The
number of sharps or flats required for a key is placed at the beginning
of the staff and this is called the signature.
A sharp (♯) placed before a note raises the tone one half step and a
flat (♭) lowers a tone one half step.
The sharp keys will be considered first and a sharp major scale will be
built from each of the twelve tones.
* * * * *
=Rule 1. The Fifth of a Scale is the Tonic (or 1) of the Scale having
the next Number of Sharps.=
-C- has no sharps, the fifth of -C- is -g- and therefore by following
the rule, we find that -G- has one sharp. The scale of -G- is as
follows:--
G a b c d e f♯ G
1 2 3⌣4 5 6 7⌣8
Notice that the seventh of the scale is a black key.
The fifth of -G- is -d- and has two sharps:--
D e f♯ g a b c♯ D
1 2 3⌣4 5 6 7⌣8
Notice that -f- remains sharped and the added sharp is the seventh of
the scale. This is always the case, the added sharp is the seventh of
the new scale.
The fifth of -D- is -a- and has three sharps:--
A b c♯ d e f♯ g♯ A
1 2 3⌣4 5 6 7⌣8
The fifth of -A- is -e- and has four sharps:--
E f♯ g♯ a b c♯ d♯ E
1 2 3⌣4 5 6 7⌣8
The fifth of -E- is -b- and has five sharps:--
B c♯ d♯ e f♯ g♯ a♯ B
1 2 3⌣4 5 6 7⌣8
The fifth of -B- is -f-♯ and has six sharps:--
F♯ g♯ a♯ b c♯ d♯ e♯ F♯
1 2 3⌣4 5 6 7⌣8
Notice that -e-♯ is not a black key but the white key which has been
previously considered as -f-. It must be called -e-♯ to retain the
alphabetical order.
The fifth of -F-♯ is -c-♯ and has seven sharps:--
C♯ d♯ e♯ f♯ g♯ a♯ b♯ C♯
1 2 3⌣4 5 6 7⌣8
In this scale all the notes are sharped. The -b-♯ as well as the -e-♯
is a white key.
The fifth of -C-♯ is -g-♯ and has eight sharps. This key necessitates
one double sharp and -f- is double sharped. The double sharps are
added in the same order that the single sharps are. The double sharp
(designated thus: =x=) raises a tone one whole step.
G♯ a♯ b♯ c♯ d♯ e♯ f=x= G♯
1 2 3⌣4 5 6 7⌣8
The fifth of -G-♯ is -d-♯ and has nine sharps (two double sharps, -f-
and -c-):--
D♯ e♯ f=x= g♯ a♯ b♯ c=x= D♯
1 2 3⌣4 5 6 7⌣8
The fifth of -D-♯ is -a-♯ and has ten sharps (three double sharps, -f-,
-c- and -g-):--
A♯ b♯ c=x= d♯ e♯ f=x= g=x= A♯
1 2 3⌣4 5 6 7⌣8
The fifth of -A-♯ is -e-♯ and has eleven sharps (four double sharps,
-f-, -c-, -g- and -d-):--
E♯ f=x= g=x= a♯ b♯ c=x= d=x= E♯
1 2 3⌣4 5 6 7⌣8
The fifth of -E-♯ is -b-♯ and has twelve sharps (five double sharps,
-f-, -c-, -g-, -d- and -a-):--
B♯ c=x= d=x= e♯ f=x= g=x= a=x= B♯
1 2 3⌣4 5 6 7⌣8
-B-♯ has taken us back to our starting key called by a different name.
All twelve keys have now been named with their sharp signatures. To
continue counting five would take us over the same keys called by
different names. The student is advised to do a little of this for
mental discipline. If this is done beyond fourteen sharps, it will be
necessary to add triple sharps. Of course, triple sharps are never used
in musical notation and such a research would be entirely arithmetical.
The order of the letters in the sharp signature which follows should be
committed to memory:--
F C G D A E B.
All keys having one double sharp or more would be difficult to read,
and so instead of using the sharp signatures on such keys, the flat
signatures are used. All twelve keys with their flat signatures will
now be given.
* * * * *
=Rule 2. The Fourth of a Scale is the Tonic of the Scale having the
Next Number of Flats.=
-C- has no flats; the fourth of -C- is -f-; therefore, by following the
rule, we find that -F- has one flat:--
F g a b♭ c d e F
1 2 3⌣4 5 6 7⌣8
Notice the fourth of the scale is a black key.
The fourth of -F- is -b-♭ and has two flats:--
B♭ c d e♭ f g a B♭
1 2 3⌣4 5 6 7⌣8
Notice that the -b- remains flat and that the added flat is the fourth
of the scale. This is always the case--the added flat is the fourth of
the new scale.
The fourth of -B-♭ is -e-♭ and has three flats:--
E♭ f g a♭ b♭ c d E♭
1 2 3⌣4 5 6 7⌣8
The fourth of -E-♭ is -a-♭ and has four flats:--
A♭ b♭ c d♭ e♭ f g A♭
1 2 3⌣4 5 6 7⌣8
The fourth of -A-♭ is -d-♭ and has five flats:--
D♭ e♭ f g♭ a♭ b♭ c D♭
1 2 3⌣4 5 6 7⌣8
The fourth of -D-♭ is -g-♭ and has six flats:--
G♭ a♭ b♭ c♭ d♭ e♭ f G♭
1 2 3⌣4 5 6 7⌣8
The fourth of G♭ is -c-♭ and has seven flats:--
C♭ d♭ e♭ f♭ g♭ a♭ b♭ C♭
1 2 3⌣4 5 6 7⌣8
The fourth of -C-♭ is -f-♭ and has eight flats. This key necessitates
one double flat and -b- has the double flat. The double flats are
added in the same order that the single flats are. The double flat
(designated: ♭♭) lowers a tone one whole step.
F♭ g♭ a♭ b♭♭ c♭ d♭ e♭ F♭
1 2 3⌣4 5 6 7⌣8
The fourth of -F-♭ is -b-♭♭ and has nine flats (two double
flats, -b-♭♭and -e-♭♭):--
B♭♭ c♭ d♭ e♭♭ f♭ g♭ a♭ B♭♭
1 2 3⌣4 5 6 7⌣8
The fourth of -B-♭♭ is -e-♭♭ and has ten flats (three double flats,
-b-♭♭, -e-♭♭ and -a-♭♭):--
E♭♭ f♭ g♭ a♭♭ b♭♭ c♭ d♭ E♭♭
1 2 3⌣4 5 6 7⌣8
The fourth of -E-♭♭ is -a-♭♭ and has eleven flats (four double
flats, -b-♭♭, -e-♭♭, -a-♭♭ and -d-♭♭):--
A♭♭ b♭♭ c♭ d♭♭ e♭♭ f♭ g♭ A♭♭
1 2 3⌣4 5 6 7⌣8
The fourth of -A-♭♭ is -d-♭♭ and has twelve flats (five double
flats, -b-♭♭, -e-♭♭, -a-♭♭, -d-♭♭, and -g-♭♭):--
D♭♭ e♭♭ f♭ g♭♭ a♭♭ b♭♭, c♭ D♭♭
1 2 3⌣4 5 6 7⌣8
D♭♭ has taken us back to our starting key called by a different name as
was the case when we had twelve sharps. To continue counting four would
take us over the same keys called by different names. As was advised in
the sharp keys, this research should be continued by the student. If
more than fourteen flats are considered, it will be necessary to add
triple flats.
The order of the letters in the flat signature which follows should be
committed to memory:--
B E A D G C F.
By comparing the order of the letters in the flat signature with that
of the sharp signature, it will be seen that the order of the letters
in the flat signature is that of the sharp signature reversed.
Notice that each key has more than one name; for example, the white key
next to the left of the group of two black keys has been called -C-,
-D-♭♭ and -B-♯.
* * * * *
=Rule 3. An Enharmonic Change is the Change of a Name of a Tone
without Altering its Pitch.=
Two or more scales played from the same pitched tone but called by
different names are called -enharmonic scales-. In practice,[B] fifteen
major scales are used, three of which are enharmonic scales. Following
is a list of the major scales used in practice together with their
signatures:--
C no sharps or flats
G 1 sharp (f)
D 2 sharps (f and c)
A 3 sharps (f, c and g)
E 4 sharps (f, c, g and d)
F 1 flat (b)
B♭ 2 flats (b and e)
E♭ 3 flats (b, e and a)
A♭ 4 flats (b, e, a and d)
D♭ 5 flats (b, e, a, d and g). enharmonical to C♯.
G♭ 6 flats (b, e, a, d, g and c) enharmonical to F♯
C♭ 7 flats (b, e, a, d, g, c and f) enharmonical to B
B 5 sharps (f, c, g, d and a)
F♯ 6 sharps (f, c, g, d, a and e)
C♯ 7 sharps (f, c, g, d, a, e and b)
[Footnote B: Theoretical keys appear in many compositions during
transitions, but they are not obvious (except by analysis) because of
the fact that their signatures do not appear.]
The enharmonic keys used in practice are:--
B (five sharps) enharmonical to C♭ (seven flats)
F♯ (six sharps) enharmonical to G♭ (six flats)
C♯ (seven sharps) enharmonical to D♭ (five flats)
* * * * *
=Rule 4. The Sum of the Enharmonic Flat and Sharp Signatures is
Twelve.= Notice that this is true in the above three keys.
By this rule the theoretical keys (that is, those having more than
seven sharps or flats) are easily found. For example:--to find the key
having eleven flats; the key having eleven flats is enharmonical to the
key having one sharp (11 + 1 = 12). -G- has one sharp and changing its
name to the enharmonic flat key, we obtain -A-♭♭ which, therefore, has
eleven flats. This process should be applied to all keys having eight
to eleven sharps and eight to eleven flats inclusive.
As stated in the first chapter, the pitch of a tone is determined
by the note's position on the staff. The staff of five lines with
its spaces allows of the designation of but one octave and one step,
whereas, in modern music, there is need of the notation of at least six
octaves. This necessitates the use of symbols called -clefs-, and lines
added to the staff called ledger lines. Ledger lines are short lines
parallel to the staff lines added above or below the staff lines.
There are three clefs:--
1. the treble or G clef, 2. the tenor, movable or C clef, 3. the
bass or F clef.
Middle -C- is the tone which all voices can sing. It is in the lower
register of the high female voice and in the upper register of the low
male voice.
The -G clef- (treble clef) is for high voices or instruments. Its
symbol shows the position of the -G- next above middle -C- thus:
[Illustration: [music]]. Middle -C- is found on the first ledger line
below the -G clef-, thus: [Illustration: [music]].
The -tenor- or -C clef- is for the use of medium voices or instruments.
Its symbol shows the position of middle -C-. This clef is movable
and may place middle -C- on any line or space of the staff. Its most
common position is on the third line of the staff, thus: [Illustration:
[music]]. It is not uncommon, however, to find it on the second or
fourth line. For vocal music it is often written in the third space.
The -bass- or -F clef- is for the use of low voices or instruments.
Its symbol shows the position of the -F- next below middle -C-, thus:
[Illustration: [music]]. Middle -C- is found on the first ledger line
above the -F clef-, thus: [Illustration: [music]].
The notation in the treble clef of all the major scales used in
practice follows:
Scale of C [Illustration: [Music: C d e f g a b C]]
Scale of G [Illustration: [Music: G a b c d e f♯ G]]
Scale of D [Illustration: [Music: D e f♯ g a b c♯ D]]
Scale of A [Illustration: [Music: A b c♯ d e f♯ g♯ A]]
Scale of E [Illustration: [Music: E f♯ g♯ a b c♯ d♯ E]]
Scale of B [Illustration: [Music: B c♯ d♯ e f♯ g♯ a♯ B]]
Scale of F♯ [Illustration: [Music: F♯ g♯ a♯ b c♯ d♯
e♯ F♯]]
Scale of C♯ [Illustration:
[Music: C♯ d♯ e♯ f♯ g♯ a♯ b♯ C♯]]
Scale of F [Illustration: [Music: F g a b♭ d e F]]
Scale of B♭ [Illustration: [Music: B♭ c d e♭ f g a B♭]]
Scale of E♭ [Illustration: [Music: E♭ f g a♭ b♭ c d E♭]]
Scale of A♭ [Illustration: [Music: A♭ b♭ c d♭ e♭ f g A♭]]
Scale of D♭ [Illustration: [Music: D♭ e♭ f g♭ a♭ b♭ c
D♭]]
Scale of G♭ [Illustration: [Music: G♭ a♭ b♭ c♭ d♭ e
f G♭]]
Scale of C♭ [Illustration: [Music: C♭ d♭ e♭ f♭ g♭
a♭ b♭ C♭]]
THE MINOR SCALE.
There are two forms of minor scales, -harmonic- and -melodic-, both
differing in construction from the major form.
The minor key having no sharps or flats in the signature is -a-.
Starting at -a- and sounding the seven white keys in order to the right
produces a form of scale with whole steps between 1 and 2, 3 and 4, 4
and 5, 6 and 7, 7 and 8, and half steps between 2 and 3 and between
5 and 6. This scale is unsatisfactory to the ear as its subtonic is
not a -leading tone-. The effect of a leading tone should be urgent,
restless, and demand its tonic in order to obtain a restful effect.
This urgent effect can only be obtained by the subtonic being one
half step below the tonic. This may be obtained by simply raising the
seventh one semi-tone in the above scale formation and thus is produced
the so-called -harmonic minor- scale.
The symbols for raising a note are the -sharp- (♯), the -double sharp-
(=x=), and the -cancel- (♮) (also called -natural-) when placed
before a note that has been previously affected by a flat. The symbols
for lowering a note are the -flat- (♭), the -double flat- (♭♭), and
the -cancel- when placed before a note that has been previously affected
by a sharp. By these statements it can be seen that the cancel (♮) is
both a lowering and a raising symbol. The -cancel- lowers a tone when it
cancels a sharp and raises a tone when it cancels a flat.
-The harmonic minor scale- is formed by whole steps between 1 and 2,--3
and 4,--4 and 5,--half steps between 2 and 3,--5 and 6,--7 and 8,
and an interval of one and one-half steps (called an augmented step)
between 6 and 7. In demonstrating the minor keys, a curved line will be
used to connect those figures representing tones one half step apart
and a bracket to connect those figures representing tones an augmented
step apart.
The key of -a minor- (harmonic form) is as follows:--
a b c d e f g♯ a
1 2 3⌣4 5⌣6⌴7⌣8
The student will notice that this scale has one sharp (-g-).
Nevertheless, the -a minor- is the minor key which has neither sharps
nor flats in its signature. The raised seventh of all minor keys is
-never- present in the signature, but appears as -accidental-.
When a sharp, double sharp, flat, double flat or cancel, which is
not present in the signature, is placed before a note, it is called
an accidental. If the raised seventh were present in the signature,
uniform signatures in the minor would be impossible. It may also be
remarked here that the seventh is not always raised during the course
of a composition and is necessarily raised only when the composer
desires the listener's ear to come at rest on the tonic, in which case
the tonic must be preceded by the raised seventh, if the subtonic
precedes the tonic in the melody or harmony.
The same rules (pages 13 and 15) used in the major for finding the key
having the next number of sharps and the key having the next number of
flats are applicable in the minor. The order of the letters in both the
sharp and flat signatures is the same in the minor as in the major.
-A- minor has no sharps, the fifth of -a- is -e- and has one sharp
(-f-):--
e f♯ g a b c d♯ e
1 2⌣3 4 5⌣6⌴7 ⌣8
The fifth of -e- is -b- and has two sharps (-f- and -c-):--
b c♯ d e f♯ g a♯ b
1 2⌣3 4 5⌣6 ⌴7⌣8
The fifth of -b- is -f-♯ and has three sharps (-f-, -c- and -g-):--
f♯ g♯ a b c♯ d e♯ f♯
1 2⌣ 3 4 5⌣6 ⌴7 ⌣8
The fifth of -f-♯ is -c-♯ and has four sharps (-f-, -c-, -g- and
-d-):--
c♯ d♯ e f♯ g♯ a b♯ c♯
1 2⌣ 3 4 5⌣ 6⌴7 ⌣8
The fifth of -c-♯ is -g-♯ and has five sharps (-f-, -c-, -g-, -d- and
-a-):--
g♯ a♯ b c♯ d♯ e fx g♯
1 2 ⌣3 4 5⌣6 ⌴7 ⌣8
The student will notice that in this key, -f- is double sharped. -F- is
sharped in the signature, but because the subtonic requires raising,
-f- demands a double sharp.
The fifth of -g-♯ is -d-♯ and has six sharps (-f-, -c-, -g-, -d-, -a-
and -e-):--
d♯ e♯ f♯ g♯ a♯ b cx d♯
1 2 ⌣3 4 5⌣ 6⌴7 ⌣8
The fifth of -d-♯ is -a-♯ and has seven sharps (-f-, -c-, -g-, -d-,
-a-, -e- and -b-):--
a♯ b♯ c♯ d♯ e♯ f♯ gx a♯
1 2⌣ 3 4 5⌣ 6 ⌴ 7⌣8
The minor keys having more than seven sharps should be found by the
student and submitted to the teacher for correction. For the sake of
brevity, they are not given here, but the student should be thoroughly
capable, by this time, of finding them all.
-A- minor has no flats, the fourth of -a- is -d- and has one flat
(-b-):--
d e f g a b♭ c♯ d
1 2⌣3 4 5⌣6⌴ 7⌣8
The fourth of -d- is -g- and has two flats (-b- and -e-):--
g a b♭ c d e♭ f♯ g
1 2 ⌣3 4 5⌣6 ⌴7⌣8
The fourth of -g- is -c- and has three flats (-b-, -e- and -a-):--
c d e♭ f g a♭ b♮ c
1 2⌣3 4 5⌣6 ⌴7⌣8
The student will notice a contradiction in the above scale; it is
stated that -c- has three flats and in the example, -b- is cancelled.
This cancel, however, appears as -accidental- (the raised seventh) and
must be a flat in the signature.
The fourth of -c- is -f- and has four flats (-b-, -e-, -a- and -d-):--
f g a♭ b♭ c d♭ e♮ f
1 2⌣3 4 5⌣6 ⌴7 ⌣8
The fourth of -f- is -b-♭ and has five flats (-b-, -e-, -a-, -d- and
-g-):--
b♭ c d♭ e♭ f g♭ a♮ b♭
1 2⌣ 3 4 5⌣6 ⌴7⌣8
The fourth of -b-♭ is -e-♭ and has six flats (-b-, -e-, -a-, -d-, -g-
and -c-):--
e♭ f g♭ a♭ b♭ c♭ d♮ e♭
1 2⌣3 4 5⌣ 6⌴ 7 ⌣8
The fourth of -e-♭ is -a-♭ and has seven flats (-b-, -e-, -a-, -d-,
-g-, -c- and -f-):--
a♭ b♭ c♭ d♭ e♭ f♭ g♮ a♭
1 2 ⌣3 4 5⌣ 6⌴ 7 ⌣8
The student should find the minor keys having more than seven flats.
The harmonic minor scale is awkward in formation on account of the
augmented second step between steps six and seven. All augmented
intervals sound harsh and are difficult to sing tunefully. For this
reason, another form of minor scale is sometimes used which eliminates
the augmented second step. This form is called -melodic minor- and
is used, as its name implies, only for melodic purposes. It defies
harmonization for the obvious reason that its ascending form differs
from its descending form.
-The melodic minor scale- has the sixth as well as the seventh raised
by -accidental- in ascending, but in descending, both the sixth and
seventh are restored. The ascending form has whole steps between 1 and
2,--3 and 4,--4 and 5,--5 and 6,--6 and 7, and half steps between 2 and
3 and between 7 and 8. The descending form has its half steps between
6 and 5 and between 3 and 2. Notice that the descending form is as its
signature dictates.
raised raised
Ascending:--1 2⌣3 4 5 6 7⌣8
Descending:--8 7 6⌣5 4 3⌣ 2 1
The ascending form of the melodic minor is nearly the same as the major
scale, and for this reason it is best not to retain the raised sixth
and seventh in descending. The subtonic in a descending scale does not
lead (progress) to the tonic and therefore need not necessarily be
situated one half step below the tonic.
Any minor key is called the relative of the major key having the same
signature; therefore, the relative minor of -C- major is -a-[C] as they
both have neither sharps nor flats.
[Footnote C: Capital letters are used to designate major keys and small
letters to designate minor keys.]
* * * * *
=Rule 5. The Relative Minor is found on the Sixth of the Major
Scale.=
* * * * *
=Rule 6. The Relative Major is found on the Third of the Minor
Scale.=
Some writers have called the -relative- minor -parallel- minor, using
-relative- and -parallel- synonymously. This is a usage to be regretted
as it causes considerable confusion. By most writers, the parallel
minor is treated as the scale commencing on the same key-note as the
major and will thus be treated in this book, therefore:--
the relative minor of C is -a-;
the parallel minor of C is -c-.
The parallel minor scale has three more flats or three less sharps in
its signature than the major scale. In other words, by lowering steps
3, 6 and 7 of the major scale one semi-tone, the signature of the
parallel minor is obtained.
The notation in the treble clef of all the minor scales (harmonic and
melodic) follows:--
Scale of a [Illustration: [music]]
Harmonic
Scale of a [Illustration: [music]]
Melodic
Scale of e [Illustration: [music]]
Harmonic
Scale of e [Illustration: [music]]
Melodic
Scale of b [Illustration: [music]]
Harmonic
Scale of b [Illustration: [music]]
Melodic
Scale of f♯ [Illustration: [music]]
Harmonic
Scale of f♯ [Illustration: [music]]
Melodic
Scale of c♯ [Illustration: [music]]
Harmonic
Scale of c♯ [Illustration: [music]]
Melodic
Scale of g♯ [Illustration: [music]]
Harmonic
Scale of g♯ [Illustration: [music]]
Melodic
Scale of d♯ [Illustration: [music]]
Harmonic
Scale of d♯ [Illustration: [music]]
Melodic
Scale of a♯ [Illustration: [music]]
Harmonic
Scale of a♯ [Illustration: [music]]
Melodic
Scale of d [Illustration: [music]]
Harmonic
Scale of d [Illustration: [music]]
Melodic
Scale of g [Illustration: [music]]
Harmonic
Scale of g [Illustration: [music]]
Melodic
Scale of c [Illustration: [music]]
Harmonic
Scale of c [Illustration: [music]]
Melodic
Scale of f [Illustration: [music]]
Harmonic
Scale of f [Illustration: [music]]
Melodic
Scale of b♭ [Illustration: [music]]
Harmonic
Scale of b♭ [Illustration: [music]]
Melodic
Scale of e♭ [Illustration: [music]]
Harmonic
Scale of e♭ [Illustration: [music]]
Melodic
Scale of a♭ [Illustration: [music]]
Harmonic
Scale of a♭ [Illustration: [music]]
Melodic
EXERCISES
ORAL AND WRITTEN
1. Into how many parts does modern custom divide an octave?
2. What is each part called?
3. What is the difference between a chromatic scale and a diatonic
scale?
4. How many forms of diatonic scales are there and what are their names?
5. Name and define the four ways in which the tones of the diatonic
scales are named.
6. What is the key-tone?
7. Describe the movable and fixed systems.
8. Describe the major scale.
9. Describe the effect of a sharp; of a double sharp; of a flat; of a
double flat; of a cancel.
10. State the rule for finding the key having the next number of sharps
and the rule for finding the key having the next number of flats.
11. Write on the staff, using the treble clef, all the major keys to
eleven sharps and eleven flats. Write several scales (the teacher
deciding the number) using the bass and tenor clefs. (Show by curved
line those notes situated one semi-tone apart.)
12. What is the order of the letters in the sharp signature? In the
flat signature?
13. What is meant by -enharmonic?-
14. What are the -enharmonic- scales used in practice?
15. Give -enharmonic- letter names for each of the twelve keys.
16. What is the sum of sharp and flat signatures of enharmonic keys?
17. By the use of this enharmonic sum, find all the theoretical
keys.
18. What is the construction of the harmonic minor scale? Of the
melodic minor?
19. Write on the staff all the minor scales (both harmonic and
melodic) to eleven sharps and eleven flats, letting the teacher
determine which clef or clefs to use.
20. What is the reason for raising the seventh in harmonic minor?
21. What is the reason for raising the sixth in melodic minor?
22. Why does the descending form of melodic minor differ from the
ascending form?
23. Why does not the raised sixth or seventh appear in the
signature?
24. What is an accidental?
25. What is the -relative- minor and how is it found?
26. What is the -parallel- minor and how does its signature differ
from its parallel major?
N. B. Before proceeding to the next chapter all these exercises should
be properly answered and corrected by the teacher.