# Music Theory/Fundamentals of Common Practice Music/Notation
## Pitch

Pitch is an indication of a sound's perceived frequency, from low to high. In Western music, we name musical pitches with the first seven letters of the alphabet: A, B, C, D, E, F and G.
From A, if we continue increasing in pitch through all the letters to G, we start over again at A an octave higher.
The collection of all the pitches with the same name, say C and all of its octaves, both higher and lower, is called that pitch's pitch class.
The section below regarding the piano keyboard indicates where each of these seven pitch classes are located on the piano.

## The Keyboard and Basic Intervals

Interestingly, music theory may be taught without reference to any instrument or even to actual sounds and repertoire. Although it is possible to learn in this way, it is uninteresting and doesn't facilitate solid understanding of the concepts of rhythm, harmony, and counterpoint.
Understanding the piano keyboard's layout and design allows one to easily grasp even the most difficult musical concepts. This is as true for those without any instrumental training whatsoever as it is for those with training on wind, string or percussion instruments.
On a keyboard, the white keys represent A through G, and back to A again. However, there are also black keys, which play intermediate notes that are known as sharp or flat notes. It is important to note that the interval between two successive keys is always the same; this distance is known a half-step. Naturally, two half-steps make a whole-step. To illustrate the difference, look at the image of the keyboard and consider the following:
The F key is a whole-step apart from the G key. This is readily apparent as there is another key residing between the two.
Conversely, the B and C keys are only a half-step apart, also apparent as there is no key between the two.
Half-steps and whole-steps may also be referred to as semitones and whole tones. Their meanings are precisely the same.

## The Staff

The staff provides us with a backdrop onto which we can place music and musical symbols.
It is made of five lines, which create four spaces within the outermost two lines.
Music is notated upon the staff in a very logical way. A note increases in pitch as it moves up the staff, and therefore decreases in pitch as it is moved down the staff. A staff of music is read in the same way a line of text is read; from left to right. Therefore, notes on the left are played before notes to the right of it.
This might be compared to a two-dimensional plane in mathematics. Pitch is determined by the Y-Axis, while time is placed on the X-Axis.
As it is, much printed music contains a variety of pitches, many that would go beyond the staff, either above or below. When this happens, the pitch placed beyond the staff is marked with a horizontal line called a ledger line. Ledger lines temporarily extend the vertical length of the staff to accommodate pitches that would go beyond it.

## Clefs

Clefs associate particular pitches with particular lines and spaces on a staff. It is always placed at the beginning of every line of music for this reason.
A note on a certain line in a staff (say, the middle line) will indicate an entirely different pitch if the clef is changed.
Though many exist and were used in the past, today only a few clefs are regularly used. These are:

   ### Treble or G Clef

       This is usually used for those relatively medium to high pitched instruments. Ex. Trumpet, violin, flute, xylophone, upper range of piano, etc. The notes from bottom line to top are E, G, B, D, and F, with the other notes in between.

   ### Bass or F Clef

       This is usually used for those relatively medium to low pitched instruments. Ex. Tuba, Cello, Bassoon, Timpani, lower range of piano, etc. The notes from bottom line to top are G, B, D, F, and A

   ### Alto or C Clef

       This is usually used for those instruments which sound pitches in the middle range and is by far the rarest of the three clefs in use today. It is mostly used by the viola, but also sometimes for the cello and bassoon with an occasional appearance in piano and vocal music. The notes for bottom line to top are F, A, C, E, and G
Another purpose of clefs is to reposition pitches within the staff so that excessive ledger lines don't clutter the music or confuse the reader.
The C Clef is especially versatile in this regard, although the other clefs may also be repositioned on the staff to associate a new line or space with the clef's defining pitch.
Exercise: name the eight notes shown.
^need new images!

## Accidentals (sharps and flats)

Let us again take a look at the keyboard. As was discussed earlier, the white keys represent A through G and starting again at A, while the black keys represent intermediate pitches. But what name would you give these pitches? How would you notate these pitches on a staff? The answer lies with a notational device called an accidental. An accidental can raise or lower the pitch of any given note. The direction in which a pitch is changed, and by how much a pitch will change (in terms of half or whole-steps) depends on the accidental being used.
When an accidental is being employed, it is always placed immediately before the note whose pitch is intended to be changed.
The flat is an indicator that a pitch is to be lowered one half-step. It looks a bit like a lowercase b. The sharp is an indicator that a pitch is to be raised one half-step. It looks a bit like the "pound sign" #.
Looking again at the keyboard, let's start with the G key. The black key to the right of the G sounds a pitch that is a half-step higher than a G. This pitch can be called a G-sharp. Conversely, the black key to the left of G will sound a pitch a half-step lower than G, which can be called a G-flat.
Following this reasoning to its logical conclusion, you will see that a G-sharp could also be called an A-flat. By which name should you rightfully call that key--G-sharp or A-flat? The answer is, either of them. In fact, all black keys have two note names assigned to them--they are the sharp of the key that precedes it and the flat of the key that follows it. This concept in music theory is called enharmonics. Enharmonic notes are simply two notes which are spelled differently but which have the exact same pitch.
Another way to think of it is to treat enharmonic notes like the American spellings of words versus their British counterparts--for example, American color versus the British colour. While the spelling differs, either spelling is accepted as "correct" and both words mean the exact same thing.

## Key Signature

This shows which notes in the song are to be played sharp (the next higher note) or flat (the next lower note). When the sharp or flat symbol is directly to the left of a note, it only affects that note and all the rest of that pitch in that measure. Key signatures, like time signatures, can change throughout the song.
If a note would usually be sharp or flat, but should be natural in a specific case, a natural sign can be put next to the note.

## Rhythmic Values

Notes on a staff represent several things, among them pitch and the relative temporal position of that note. A musical note will also indicate its duration.
Included here are rests. Rests are the opposite of notes. When a note is notated, it indicates the performance of a certain pitch of a certain length at a certain time. When a rest is notated, it indicates silence of a certain length at a certain time.
There are quite a few symbols to indicate the length of a note. The system is quite simple. Every symbol is two times the length of the symbol that follows it and is one half the duration of the symbol preceding it.
Symbols of Note and Rest Duration :
* Name
* Breve
* Whole
* Half
* Quarter
* Eighth
* Sixteenth
* Thirty-second
The further shortening of durations may be continued to sixty-fourth notes/rests, 128th notes/rests, 256th notes/rests, etc. All that need be done is to add one more flag onto the note or rest for each successive shortening. The practicality of doing so might become a concern as the values become shorter, but it is theoretically possible to continue ad infinitum.
A shorthand exists for long periods of rests. The following picture shows 10 measures of rest.
Also, sometimes a note is followed by one or two dots, meaning that the note is 150% or 175% of its usual length.
The dotted quarter note shown, therefore, would be worth the value of a quarter note plus half that value, or an eighth note.
Or, the note may be a triplet, meaning it takes 2/3 of the normal length. The following picture shows three notes that take up two beats.
Other "tuplets" may occur - duples represent two notes taking the span of three beats, for example. Any number of notes can be forced to take up the space of any number of beats, and if this cannot be written with the standard set of notes, tuplet notation will be used.

## Musical Symbols
### Time Signatures

Music is usually divided into measures, usually containing between 2 and 8 beats. The time signature is written next to the clef, but can change throughout a song.
The upper number shows how many beats are in a measure. The lower number determines what kind of note gets the beat (4 = quarter note, 8 = eighth note). Measures are separated by bar lines. A double bar line represents the end of a section, and an end bar line represents the end of a work of music.

### Dynamics

Dynamics show how loudly or quietly to play the notes.
* ppp - pianississimo (very, very soft)
* pp - pianissimo (very soft)
* p - piano (soft)
* mp - mezzo-piano (moderately soft)
* mf - mezzo-forte (moderately loud)
* f - forte (loud)
* ff - fortissimo (very loud)
* fff - fortississimo (very, very loud)
There is no objective definition of "what is 'loud'". It is up to interpretation by the musician.

### Other Dynamics

* sfz - sforzando (a strong sudden accent)
* crescendo - gradually getting louder
* decrescendo - gradually getting softer

## Final Exercise

Describe, using what you learned so far, the following excerpt from a piano piece.
This piece uses the treble and bass clef, and there are three flats by default, although a number of sharps and naturals are in the piece. There are 9 measures, 6 of which have whole rests on the bass clef. The length of notes ranges from quarter to sixteenth. As some notes extend past the staff, ledger lines are added for some notes.

### More Analysis

Piano pieces nearly always use both the treble and bass clef, which are supposed to be played at the same time. Generally, the left hand plays the bass while the right hand plays the treble. Between the sixth and seventh measure, there is a line connecting two notes of the same pitch. This means that they are actually the same note, connected, creating a tie. When the notes are of different pitch, the notes are played smoothly, and it is called a slur.