David Loberg Code, Western Michigan University

Harmony parts are made by stringing together triads built on different scale degrees. 

Triadic Harmony: The three most common triads used to harmonize a melody are the tonic, subdominant, and dominant triads: I, IV, and V. 

In a major key, all three of these will be major triads.

For harmonizing in minor keys, use the harmonic minor scale. The tonic (i) and subdominant (iv) will be minor triads; the dominant will be a major triad.

The large-scale form of a musical composition can be projected via any combination of the musical elements (rhythm, dynamics, melody, tone color, texture, form). Traditionally, however, musical form in Western music has been primarily associated with the order of melodic, harmonic, and rhythmic events (or the text) in a piece. Letters (i.e. A, B, C) are used to designate musical divions brought about by the repitition of melodic material or the presentation of new, contrasting material. Some of the most common musical forms are described below:

Strophic form: a design in vocal music, in which the same music is used for several different verses (strophes) of words. [Example: "Deck the Halls" has many verses of words sung to the same music.]

Verse 1.... Verse 2.... Verse 3 (etc.)....

Through-composed: a structure in which there is no repeat of return of any large-scale musical selection.

A    B    C    D    E....

Binary Form: a two-part form in which both main sections are repeated (as indicated in the diagram "repeat marks"). The basic premise of this form is contract:

Ternary Form: A three-part form featuring a return of the initial music after a contrasting section. Symmetry and balance are achieved through this return of material:

The space between any two pitches is called an interval. Whole steps and half steps are two types of intervals. A whole step can also be called a major 2nd, and half steps are sometimes called minor 2nds. Major simply means BIG; minor means little. The number 2 (2nd) comes from counting the number of letters from one note to another. Bigger intervals can also be identified by their interval count (or size) and quality (major, minor, etc.).

When counting, always start on 1 (never zero). For example, the interval count from D to B is a 6th:

D (1) – E (2) – F (3) – G (4) – A (5) – B (6)

Instead of counting letter names, you can also count the number of lines and spaces on the staff (still starting with 1). The answer should be the same. By the way, a count of 1 is called a unison or a prime, and a count of 8 is called an octave (instead of an 8th). Also, when counting, it doesn't matter whether or not there are any sharps or flats. D# to B is also 6th; so is D to Bb, or Db to B#, and so on. The differences between these various kinds of 6ths is called the interval quality. You might think of them as different flavors of 6ths.

As another example, A to C has the same interval count as A to C#: they are both 3rds. However A to C# is a BIGGER 3rd than A to C, so they have different interval qualities. Not surprisingly, the BIG 3rd is called a major third and the little 3rd is called a minor third (just like with major and minor 2nds). Unfortunately, there is more than just major and minor. Other interval qualities include perfect, augmented, and diminished.

Finding the interval count is easy enough, but how do you figure out what the interval quality is supposed to be? The simplest way is to go back to the major scale. Taking the intervals from the starting note (Do) to each successive scale degree we get the following intervals:

From Do to ä

Notice that the second, third, sixth, and seventh are all major intervals. (That is why it is called a major scale.) The unison, fourth, fifth, and octave are all perfect. You can find out why they are these qualities another day, but for now just remember:

In a major scale:

• 1,4, 5, and 8 are always Perfect
• 2, 3, 6, and 7 are always Major

(There is NEVER such a thing as a Major 5th or a Perfect 3rd.)

So, to figure out the interval between two notes:

1.) Pretend that the bottom note is the first note (Do) of a major scale. (Write out the scale if you need to or finger it on your instrument.)

2.) Is the top note already in the scale? If yes, then you already know what the interval is. Just count up the number of notes and add the name of the quality (either major or perfect).

• Let's try the interval from G up to E. The G major scale is: G A B C D E F# G
• E is in the scale. It is the 6th scale degree.
• The 6th scale degree is always major.
  • G to E is a Major 6th.

3.) If the exact note is not in the scale, you will need to adjust the interval quality. If your note is a half step lower than the major interval in the scale, the quality will be minor. For example:

• Let's try the interval from D up to F. The D major scale is: D E F# G A B C# D
• D to F# is a major 3rd. F is a half step lower.
  • D to F is a Minor 3rdFor other qualities, use the following adjustment chart starting from either a perfect or major interval:

• Let's try the interval from F to B. The F major scale is: F G A Bb C D E F
• F to Bb is a perfect 4th. B is a half step higher.
  • F to B is an Augmented 4th.

What if I can't make a major scale using the bottom note? No problem, you can use the same method of adjusting the quality in reverse.

• Let's try the interval from C# to E. I don't like C# major, so I'll spell a C major scale instead.
• The C major scale is: C D E F G A B C. C to E is a major 3rd. C# to E will shrink the size by a half step.
  • C# to E is a minor 3rd.

David Loberg Code, Western Michigan University

Keys come from scales. People sometimes make the mistake of thinking that keys come from key signatures. They might say that A major has 3 sharps because of the key signature. This is backwards. It is like saying that deer like to cross the road at particular spot because there is a Deer X-ing sign there. Key signatures are signs. They help remind us of the key and save us the trouble of writing the same sharps or flats over and over again. The easiest and best way to determine a key signature is to think of the scale. When you play a D major scale, you use an F# and a C#, therefore the key signature for D major has 2 sharps (F# and C#). For uniformity, the sharps or flats in a key signature are always written in the same order (regardless of what order they appear in the scale.)

For example, an A major scale is: A B C# D E F# G# A. In the key signature, however, the order of the sharps is rearranged: F#, C#, G#.

The order of sharps is always as follows:

The order of flats is coincidentally the same sequence but backwards:

There are other tricks you can use to determine the name of the key from looking at the key signature. For Major keys, the last sharp in the key signature is always Ti (the seventh scale degree). To find the key, simply go up a minor second (to Do). For example:

• The key signature has 5 sharps (F#-C#-G#-D#-A#).
• The last sharp will be A# (Alleys)
• A minor 2nd (half step) above A# is B.
• The major key is B major.

For Major key signatures with flats, the second to last flat is always Do.

• The key signature has 4 flats (Bb-Eb-Ab-Db).
• The second to last flat is Ab.
• The major key is Ab major.

Obviously, these tricks will not work for C major (no sharps or flats), or F major (1 flat). You will just need to memorize these. Also, these tricks do not work for minor keys.

Meter is the pattern of pulses or beats on which the rhythms of a piece are based. The rhythms of a meledy can go faster or slower, but the beat marches on at a steady pace. It is like drawing a picture on a piece of graph paper. Each square on the graph is like a beat. When you count out the beats, you are counting the meter. Most pieces have either 2, 3, or 4 regular beats per measure. When you play a melody, you usually accent the notes which start on the beat. When you play faster notes, they usually divide the beat into either 2 or 3 parts. Fer examp|e, the song "Yankee Doodle" has two beats per measure and the beat divides into 2 parts:

Hickory Dockery Doc also has two beats per measure, but the rhythms divide the beat into three parts:

A time signature is a sign which helps show you what the meter is. The most common time signatures are 2/4, 3/4, 4/4. For these simple time signatures, the top number tells you
how many beats per measure and the bottom number reminds you that a quarter-note (1/4) gets the beat. "Yankee Doodle" would use a time signature of 2/4. Here is an
example of a piece with 3 quarter—notes per measure (3/4 time):

6/8 is another frequent time signature. Unfortunately, it is not simple; it is rather confusing. Many people think that 6/8 means 6 beats per measure with an eighth-note
getting the beat. Not true. 6/8 is used fer pieces where the beat divides into 3 parts, like Hickory Dickory Dock". The time signature fer "Hockery Dockery" is supposed to show 2
beats per measure with a dotted quarter-note getting the beat, like the examp|e below:

Remember, keys don't come from key signatures and meters don't come from time signatures. When you are listening to actual music, you often can imagine counting it out
in different ways (fast and slow). Follow this basic guideline:
Question: How many beats are in a measure?
Answer: As few as possible.
For examp|e, when you see 6/8, trust the music itself (not the sign post) and count it in
two, not six: 1 la li 2 la li (never 1 23 4 56).

David Loberg Code, Western Michigan University

Minor scales come in three variants: natural, harmonic, and melodic. It is probably easiest to compare them with the major scale.

To form the natural minor scale, we can lower scale degrees 3, 6, and 7. This will change these intervals to a minor 3rd, minor 6th, and minor 7th. (That is why this is called a minor scale.)

The harmonic minor scale uses the same leading tone as the major scale (C#), but a minor 3rd and 6th. The melodic minor scale is more unusual because it is different going up then it is going down. Notice how the 6th and 7th scales degrees change from B and C# to Bb and C natural. Going up, melodic minor is almost the same as major, except for the minor 3rd. Going down it is exactly the same as minor.

Minor key signatures are formed from the natural minor form of the scale. Therefore, the key signature for D minor has only one flat: Bb. If a piece is using the harmonic or melodic forms of the minor scale, the "extra" accidentals are NOT included in the key signature. They are written in separately each time they are needed in the music. It may seem silly, but that is how it is done. As a result, the order of sharps and flats in minor key signatures is the actually the same as for major keys.

To determine the name of a minor key from the key signature, first find the major key using the tricks for sharps or flats described earlier. Once you know the major key, go to the 6th scale degree. This is the starting note for the relative minor, that is the minor key with the same key signature. For example:

• The key signature has 3 sharps (F#-C#-G#).
• The last sharp is G#, a minor 2nd above that is A.
• The major key is A major. The 6th scale degree of
• A major is F#. The minor key is F# minor.

WARNING: When looking at a piece of music, do not automatically assume that it is in a major key. The key signature could be for either major or minor. You need to look for additional clues to determine which one is correct. What note does the piece start on or end on? Often, but not always, this will be the tonic (Do). Are there any "extra" accidentals? Remember, harmonic and melodic minor will have extra accidentals which are not included in the key signature.

Minuet and Trio form has a special type of compound temary design (in which
each of the sections has its own small form):

• Minuet (an aristocratic dance in 3/4 meter)
  • This section usually has a strong downbeat, and has a binary design
    in which each sub-section is repeated.
• Trio (the texture is usually reduced to three structural lines)
  • The "Trio" is noticeably lighter and sweeter than the Minuet.
    (As in the Minuet, each sub-section is repeated).
• Minuet (returns without repeats)
  • Before 1800, Minuet and Trio was the traditional form used in third movements
    of 4-movement Classic instrumental works.

Scherzo & Trio Form

After 1800, Beethoven and other politically-minded composers replaced the
aristocratic "Minuet" with a heavier "folk-derived" dance in 6/8 meter called a
scherzo (which means "a common joke" in Italian), creating a similar design
called Scherzo and Trio form (the standard 3rd movement form of the late
Classic period).

Rondo Form
This form features an easily recognizable melody ("Theme") that returns two or three times in alternation with contrasting material. (This differs from Baroque ritomello form which features a returning tutti group.

Sonata-Rondo Form
The rondo concept can be combined with the harmonic plan of Sonata Form (tonal exposition, development and recapitulation) to create the hybrid sonata-rondo form:

David Loberg Code, Western Michigan University

The point of music theory is to help you understand how music works, so you can be a better player. Playing the notes without understanding how or why they are put together is like reading a book by sounding out the words without knowing what they actually mean.

Most of what you need to know about how pitches are put together you can learn straight from the scales you play (or are supposed to play) every day. A major scale has seven different notes arranged in order like going up or down a set of stairs. If you repeat the first note when you reach the top there are actually eight notes. The stairs are a little uneven because they are made up of two different sizes of steps.

This is why sometimes you need a bigger space between some adjacent notes and other times they are close together. The big steps are usually called whole steps; and the little ones half steps. All major scales follow the same pattern of whole and half steps:

Sonata Form
Sonata form (also called "sonata-allegro form") is a musical debate vvithin a single
movement based on the conflict and ultimate resolution of tvvo opposing key centers.
Sonata form is the First movement form of virtually every Classic instrumental work,
though It may be used in other movements as vvell.) This unigue Classic form has
three distinct dramatic aspects vvithin a binary harmonic plan:

Expositio (Tonal Opposition)
The two opposing key centers (and associated themes) are introduced:
Thome 1 is in the 'home" key; Thome 2 is in a different key.

Development (Escalation of tension)
The material passes rapidly through many distant keys, and may be fragmented/reworked in a
variety of ways.

Recapitulation (Tonal Resolution)
Thome 1 and Thome 2 both appear in the 'home" key. (In the tradition of Classic debate, Theme
2 realizes its weaker stance, and wholeheartedly throws its support to its opponent's stronger
argument—the "home' key.)

ln this form, a musical theme is stated (the main melody of tne movement),
followed by any number ol varied presentations of that theme. ln subsequent
variations, new countermelodies can be added, and aspects of the theme
(such as key, meter, instrumentation, mood, dynamics, etc.) can be altered.

THEME - VARIATION1 - VARIATION 2 - VARIATION 3 (etc.)

Theme and Variations is found in second movements of many Classic works,
and it is sometimes used in fourth movements.

David Loberg Code, Western Michigan University

Chords are collections of 3 or more pitches sounding at the same time.  They are usually used to accompany a melody.  If the notes of a chord are played separately (one after another) it is called an arpeggio (or broken chord).   A triad is a special type of chord made of three notes: a root, third, and fifth.  You can form a basic triad from three consecutive lines or spaces on a staff (i.e., stacking 3 doughnuts or a triple scoop of ice cream).   Like intervals, triads come in different qualities (flavors).  A major triad is formed by taking the 1st, 3rd, and 5th scale degrees (Do, Mi, and So) of a major scale.  (That is why it is called a major triad.)

• Spell a G major triad.
• The G major scale is: G A B C D E F# G
• G, B, D spells a G major triad.

A minor triad is formed by taking the 1st, 3rd, and 5th scale degrees of a minor scale (Do, May, and So).

• Spell a C minor triad.
• The C minor scale is: C D Eb F G Ab Bb C
• C, Eb, G spells a C minor triad.

An augmented triad is like a major triad but with an augmented 5th.

A diminished triad is like a minor triad but with a diminished 5th.