... in music, is the relative highness or lowness of a tone.

Pitch is the musical term for the scientific concept of Frequency.

Frequency is the number of beats per second something vibrates to produce a tone.

The A below middle C is generally tuned to 440 beats per second.
The A above middle C would then be tuned to 880 beats per second.
Octaves, when in tune, function in a 1:2 or 2:1 ratio

When the frequency of a tone is doubled, the pitch will be one octave higher.

When the frequency of a tone is halved, the pitch will be one octave lower.

Pitches are named by using the first seven letters of the alphabet:

A  B  C  D  E  F  G

Relating pitch to the piano keyboard, the pitches on the left end are the lowest and the ones on the right end are the highest.

Using the pitch C as a reference point, the keyboard can be divided into octaves.

An octave is the distance between a C and the next closest C.

The C closest to the middle of the piano is generally referred to as
"middle C."  It is considered C4.

Starting with the lowest C they are numbered from left to right from C1 to C8.

Example 1-1

All the pitches that lie between one C and the next are said to be in the same octave register.  The register includes the lower C but the upper C begins the next register.  See the diagram below.

C1  D1  E1  F1  G1  A1  B1  C2  D2  E2  F2  G2  A2  B2  C3  etc.

A Staff is used in music to allow us to precisely notate pitches.  It consists of 5 lines and four spaces, but may be extended through the use of ledger lines.
 

Example 1-2

A Clef must appear at the beginning of each staff to indicate which pitches should be associated with the particular lines and spaces.
 

Example 1-3

A Grand Staff is a combination of two staves joined by a brace.  The top clef will be the Treble Clef and the bottom will be the Bass Clef.

Example 1-4

The major scale is a specific pattern of whole steps and half steps encompassing one octave.

A half step is the distance between a key on the piano keyboard and the next adjacent key with no keys in between (white or black).

A whole step is the equivalent of two half steps.  It skips the closest adjacent key and goes to the next one.

Example 1-5

(W = whole step;  H = half step)

The major scale pattern of whole steps and half steps is the same as that found on the white notes of the piano from any C up to the next C.

The whole steps will always fall between scale degrees 1 & 2, 2 & 3, 4 & 5, 5 & 6, and 6 & 7.

The half steps will always fall between scale degrees 3 & 4 and 7 & 8.

When a scale begins on a pitch other than C, accidentals must be used to maintain the pattern of steps.  An accidental will precede the note it alters.  They are as follows:

A sharp raises the note it precedes by one half-step
A double sharp raises the note it precedes by two half steps
A flat lowers the note it precedes by one half step
A double flat lowers the note it precedes by two half steps
A natural returns the pitch it precedes to its natural, unaltered state

The Major Key Signatures

Major scales beginning on different pitches, maintaining the same pattern of whole steps and half steps, will result in sets of accidentals which translate into keys.  The term key is used in music to identify the first degree of a scale.  A key signature is a pattern of sharps or flats that appears at the beginning of a staff and indicates that certain notes are to be consistently raised or lowered.

These key signatures must be learned -- not just the number of accidentals, but their order and placement on the staff as well.

Example 1-6

Some find it easier to learn the key signatures by visualizing what is called a circle of fifths.  Notice, on the diagram below, that as you go clockwise around the circle each consecutive key begins on the fifth scale degree of the previous key.

Example 1-7

Notice the blue letters on the inside of the circle.  These represent the minor keys.  Also notice, that each major key has a corresponding minor key.  The key signatures for each major scale are the same for each of the relative minor scales.  The relative minor scales are built on the sixth scale degree of the major scale and retain the same key signature.

Note:  the major keys are generally indicated by capital letters;  the minor keys, by lower case letters.

Mention should be made at this point about enharmonic notes.  Notice at the bottom of the Circle of Fifths the tonal centers that "overlap."  Enharmonic notes are pitches that share the same piano key but are spelled with different letter names.  Example:  a-sharp is played by the same piano key as b-flat; d-sharp is the same piano key as e-flat; and g-sharp is the same as a-flat.  For theoretical purposes, a-sharp IS NOT the same as b-flat -- they each fit in different musical schemes and have different functions.  When played on the piano, apart from any musical context, the two enharmonic pitches sound identical.

Example 1-8

There are three commonly recognized forms of the minor scale.  They are as follows:

Pure Minor

The scale built on the sixth scale degree of a major scale with no other altered notes besides the ones indicated in the key signature

Example:

The relative minor of "C" major is "a" minor
The pure "a" minor scale would be:  a-b-c-d-e-f-g-a

Harmonic Minor

The same basic scale as the pure minor, with one exception -- it's seventh scale degree is raised by one half step

Example:

The harmonic form of the "a" minor scale would be:
a-b-c-d-e-f-g#-a

Melodic Minor

It has the sixth and seventh scale degrees raised in its ascending form, but is the same as the pure minor in its descending form.

Example:

The melodic form of the "a" minor scale would be:
a-b-c-d-e-f#-g#-a (ascending)
a-g-f-e-d-c-b-a    (descending)

It is advantageous to compare the minor scale forms with the parallel major scale.  This comparison shows the alterations of scale degrees that separate the major and minor modes.

Example 1-9

Click here to see and hear all the MINOR SCALES.

Musicians often refer to scale degrees by a set of traditional names rather than numbers.  Notice that the seventh scale degree has two different names, depending on whether it is raised or lowered.

Example 1-10

The origin of some of these names is not what you would expect.  For example, subdominant does not mean "below the dominant."  The chart illustrates the concept of a dominant a perfect fifth above the tonic, and another a perfect fifth below.  The mediants follow the same concept.

Example 1-11

An interval in music is the distance in pitch between two notes.  When the notes are performed simultaneously they are considered "harmonic" intervals.  When they are performed successively they are considered "melodic" intervals.

"Harmonic" intervals are thought of as vertical sonorities, while "melodic" intervals are thought of as horizontal or linear relationships.

Intervals are generally categorized by two concepts: distance and quality.

Distance refers to the actual space between the two pitches.  The simple "distance" designations are:

Unisons;  2nds; 3rds; 4ths; 5ths; 6ths; 7ths;  and Octaves (8ve)

Intervals, related to the tonic pitch of a major scale, look like this:

Example 1-12

Quality refers to the specific type of relationship between the notes.  The "qualitly" designations are:

perfect (P); major (M); minor (m); augmented (A);  and diminished (d)

The designation "perfect" only refers to unisons, 4ths, 5ths, and 8ves.

Usually, 2nds, 3rds, 6ths, and 7ths are designated "major" or "minor"

Note the quality of the intervals based on the major scale.

Example 1-13
C Major

---
Take note of the M3, M6, and M7 in the major key.

In the minor key, these intervals will be one half-step smaller, making them
m3, m6, and m7.

Example 1-14
c minor

When the distance of a Major or Perfect interval is expanded by one half-step without changing the numerical name, the interval becomes Augmented.

When the distance of a minor or Perfect interval is decreased by one half-step without changing the numerical name, the interval becomes diminished.

The chart below demonstrates the relationships between the interval qualities.

(smaller)<------<-------<------------>------>------>(larger)

diminished<------>minor<------>Major<------>Augmented

diminished<----------------Perfect--------------->Augmented

One other interval that should be mentioned at this point is the A4 / d5.  This interval is also referred to as the Tritone.  It serves a significant purpose in functional, tonal harmony, which will be covered more fully at a later point.

The following chart indicates how the quality of each type of interval is altered by half-step variations.

Decreased by one half-step	Original Interval	Increased by one half-step
diminished o (d)	Perfect P	Augmented + (A)
minor m	Major M	Augmented + (A)
diminished o (d)	minor m	Major M
doubly diminished (rare)	diminished o (d)	Perfect or minor (depending on the interval)
Perfect or Major (depending on the interval)	Augmented + (A)	doubly Augmented (rare)

Any interval can be inverted by placing the upper pitch underneath the lower pitch.  For example, when the interval C--G is inverted it becomes G--C.

When intervals are inverted the distance relationships are as follows:

2nd inverts to 7th (7th inverts to 2nd)
3rd inverts to 6th (6th inverts to 3rd)
4th inverts to 5th (5th inverts to 4th)

When intervals are inverted the quality relationships are as follows:

m inverts to M (M inverts to m)
A inverts to d (d inverts to A)
P inverts to P

Examples

m2 inverts to M7
M3 inverts to m6
P4 inverts to P5

Click here to see and hear Intervals on the Staff.