Table of Contents

Section 3: 

Set theory
Rhythm/ form 
12- tone 
Polyrhythm
Metric modulation
Meter

Section 4: 

Basic Assumptions 
Motive, Phrase and Period
Cadence
Binary form
Ternary form
Rounded binary form
Sonata form
Rondo form
Theme and variation
Dance forms

Section 5: 

Basic assumptions 
and procedures
Harmony
Form and rhythm
Melody
Timbre

Section 6: Bibliography

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Key and Scale

Basic Concepts:

1.  "Key" refers to a specific group of notes that relate to a single note called a tonic.

2.  Keys are either major or minor.  These qualities are referred to as modes.

3.  "Scale" refers to the basic order of the group of notes in a key.  The term is also used to describe a type of musical gesture that features a diatonic stepwise progression.

4.  Each note of the scale is considered a scale degree, and has a name that describes its relationship to the other notes in the scale and the tonic.  Those names are, in ascending order from tonic: tonic, supertonic, mediant, subdominant, dominant, submediant, leading tone.  Please see the definitions of these terms below.

5.  The basic types of scales are major, natural minor, harmonic minor, melodic minor, whole tone, chromatic, and pentatonic.

6.  The key signature, placed at the beginning of every system, indicates the accidentals required to play in the given key.

7.  Each major key has a relative minor, and vice versa.  The relative keys share the same key signature but not the same tonic.  Therefore, C major, which has no accidentals in its key signature, has the relative minor of A, which also has no accidentals in its signature.  The two tonics, C and A are a minor third apart. This property is universal in the diatonic system: the relative minor of a major key is built on the sixth degree of its scale.  The relative major of a minor key is built on the third degree of its scale (G maj. = E min., F min. = A flat maj.).

Definitions of scale degrees:

Tonic-the primary pitch of the key

Dominant-the pitch a perfect fifth above tonic

Mediant-the pitch between the tonic and dominant

Subdominant-the pitch a perfect fifth below the tonic

Submediant-the pitch between the tonic and subdominant

Super tonic-the pitch above the tonic

Leading tone-the pitch a half step below the tonic, leads to tonic

The scales:

MAJOR: Many people know the major scale as the do-re-mi-fa-sol-la-ti-do sequence of notes or as the white keys on the piano starting with C.  Either of these are good starting places for assembling the major scale.

A theoretical definition of the major lists the notes of the scale ascending by whole step (W) and half step (H). The sequence of whole and half steps in the ascending major scale is W-W-H-(W)-W-W-H.  The whole step with parentheses is the link between the lower tetrachord and the upper tetrachord.  A tetrachord is a group of four notes.  In the major scale and all minor scales, there is a whole step between the upper and lower tetrachords. Study the example below and check to make sure the W and H step sequence is correct.

E flat Major Scale

MINOR: There are three types of minor scales: natural minor (the one that matches the key signature), harmonic minor (altered to include the leading tone), and melodic minor. Keep in mind that there are not three types of minor keys.  These three scales represent the function of the pitches contained in the key, not the key itself.  Review the examples of the three types below.

What is important to understand and remember about the differences between the three minor scales is contained in their names.  

Natural minor is exactly as the key signature dictates.  This is the minor scale that is not altered. 

The Harmonic minor scale contains the pitches most commonly used to form the harmony in the minor key.  Therefore, the only altered note is the seventh scale degree which is raised to form a leading tone.  The V chord, the tonicizing chord, requires this leading tone pitch to function properly. 

The Melodic minor scale contains the pitches that are often used in melodies that approach the tonic from below and fall away from the tonic.  In this scale then, the sixth and seventh scale degrees are altered.  In the harmonic minor scale, there is an augmented second between the sixth and seventh scale degree.  This makes no difference in a collection of pitches used to form harmony.  However, intervals like this are avoided in melodic usage, and the melodic minor scale accounts for this by raising the sixth degree as well as the seventh.  This way, a melody can approach the tonic with a leading tone, and the leading tone can be approached by step as well.  Notice that the descending melodic minor scale approaches the dominant the same way the ascending scale approaches the tonic.  Also notice that it is in the natural minor form.

OTHER SCALES: The scales above are considered diatonic scales and comprise the constituents of the diatonic or tonal system. The scales below are not diatonic, but scales used in various styles of music.

Chromatic: this, of course, is simply the collection of all 12 notes.

Chromatic scales have been employed by composers for centuries as passing tone complexes.  However, the use of this scale as basic material for composition is a twentieth century development.

Pentatonic: this scale is best remembered as the black keys on the piano ascending from F sharp. It comprises five notes of the major scale (by scale degree number): 1-2-3-5-6.

Pentatonic scales are used in various styles including blues, rock, and jazz. It has also been used by various composers of serious music.  An example from the standard repertoire is Mahler's "Das Lied von der Erde."

Whole tone: the whole tone scale has no half steps.It has six pitches C-D-E-F sharp-G sharp-A sharp. There is an enharmonic whole step from A sharp to the C above, so the scale is complete.  There are enharmonically only two different whole tone scales. 

Octatonic scale: this is a special scale that has the following sequence of intervals: W-H-W-H-W-H-W-H, producing a scale like: C-D-E flat-F-G flat-A flat-A-B-C.  Notice that there are eight different pitches within the octave, rather than the seven of a diatonic scale, and the the letter name of one pitch will be doubled (A flat-A). (Note: the scale may begin with a half step rather than a whole step: H-W-H-W-H-W-H-W, thus E-F-G-A flat-B flat-C flat-D flat-D-E.)

Stravinsky is well known for his use of this scale.

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