Essentials of Music Theory: Elementary — Story, Setting & Ideas

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:--

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 ] sextuplet ] group of two notes ]

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.

-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.

-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.

2. Tell the difference between noise and musical tone.

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.

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.

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:--

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:--

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:--

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:--