# Music Theory/Rhythm

Rhythm is, aside from melody, one of the most basic aspects of music, and definitely the fundamental. Many early forms of music consisted only of rhythm; examples being drumming, clapping and shouting to a rhythm.

## Basic durations

There are two systems for naming notes in the English language. Here, the American names are listed first and the European names are listed in parentheses. This book, for consistency's sake, will use the American names throughout.
The whole note is the longest unit we will consider in this book. Earlier music featured the breve, which is twice as long. (This is why the whole note is called the "semibreve" in Europe.) Each unit after that is half the length of the previous.
* Whole note (semibreve)
* Half note (minim)
* Quarter note (crotchet)
* Eighth note (quaver)
* Sixteenth note (semiquaver)
* Thirty-second note (demisemiquaver)
* Sixty-fourth note (hemidemisemiquaver)
There are even shorter notes, such as the 128th note (semihemidemisemiquaver), but they are absurdly short for most music; even 32nd notes are uncommon. However, there are rare situations where they are appropriate. One piece with such notes is the Pathétique Sonata by Ludwig van Beethoven.
Music may also contain rests, in which no note is played or sung.
This image shows notes and rests, in order from longest to shortest.

## More on durations

A staccatoed note is 'separated' from the other notes around it. Space is inserted between the notes by shortening the end of the note being played. Some musicians consider it to be "short and detached", whereas others suggest that a staccatoed note is half its value. This is more a feature of articulation and style, rather than rhythm, but it has rhythmic bearing as playing staccato can often cause musicians to play out of tempo. Staccato is shown by a dot below or above the note.
A very short note is known as appoggiatura or acciaccatura. They are both almost insignificantly short notes also known as "grace notes" for the purpose of expression. The shorter of the two is the acciaccatura. They are shown as shrunken eighth notes, with a score through the shorter and the longer having no such flourish. Common uses include on bagpipes as grace notes or on guitar for slides, string-bends and hammer-on/pull-offs.
A dotted note is 50% longer than the undotted version, i.e. a dotted half note would take 3 beats, lasting as long as three quarter notes tied together. A double-dotted note is 75% longer than the normal note, i.e. a double-dotted half note would take 3½ beats.
Do not confuse dotted notes with staccato notes. Dotted notes have a dot on the right side, while staccato notes have dots on the top or bottom.

## Time signatures

Time signatures are the basic description for the feel of the rhythm; they define how to count the rhythm. They are also known as the meter. This is why one can listen to a piece and know what time signature it is in. It is like hearing Shakespeare and knowing how many syllables are in the lines and what meter it is in. By far the most common time signature is 4/4, the next most possibly being 3/4 (commonly associated with the waltz). A time signature is found at the first measure right after the clef and key signature.
It is made up of two parts. For all meters the top number gives the number of notes per measure and the bottom number gives the note type. The bottom number can be:
* 1 - whole note (very rare)
* 2 - half note (uncommon)
* 4 - quarter note (extremely common)
* 8 - eighth note (common in modern avant-garde music and much other non-western music)
The top number may also be any other power of 2, but they are rare. The bottom number is in most cases a power of two but non-dyadic (irrational) time signatures may be used in special cases, e.g. if a measure contains an incomplete set of triplets.
The time signature 4/4 means there are four quarter notes in a measure; the time signature 3/4 means there are three quarter notes in a measure. The time signature 2/2 is, in a way, the same as 4/4. However, 2/2 has two beats per measure (each a half-note in length), while 4/4 has four beats per measure. Beats are usually accented in some way in a song, especially with percussion in popular music. Usually the thesis is accented, while the arsis is unaccented. Traditionally the thesis is the down-beat and the arsis is the up-beat. The terms down-beat and up-beat come from the movements the director makes while conducting.
NB the Time Signature is not written as a fraction but instead as two numbers one on top of the other, with no line between.
We divide time signatures into three main types:
* simple (each beat is divided into its sub-beats)
* compound (notes are grouped together into beats by the type of sub-beat)
* asymmetric (both duple and triple groupings for its notes)
Time signatures are classified by type (simple or compound) and sub-beat (duple or triple).
In simple meter, the beat is divided into sub-beats or subdivisions:
* 1 - In simple duple meter the beat (this is the type of note specified by the bottom number in the signature) is divided into two sub-beats.
* 2 - In simple triple meter the beat is divided into three sub-beats.
However, for compound meters, the sub-beats are grouped into the beats by duples or triples:
* 1 - In compound duple meter the notes are grouped into twos, these groups make up a whole beat. Example: 6/8, three beats each with two sub-beats.
* 2 - In compound triple meter the notes are grouped into threes, these group make up a whole beat. Example: 6/8, two beats each with three sub-beats.
Asymmetric meters are a type of compound meter where beats are divided into duples and triples. In these the beat actually changes its length because the sub-beat is constant. Examples: 5/8, two beats; either the first with two sub-beats and the second with three, or the first with three sub-beats and the second with two. 7/8, three beats -- either 2, 2, 3; 2, 3, 2; or 3, 2, 2 (in sub-beats).

## Tempo

Beats-per-minute (or BPM) indicate how fast a song is played. Each beat corresponds to one note of the type indicated by the bottom number in the key signature. For example, a song with 60 BPM will have 60 beats in a minute, or one beat per second. A song in 4/4 time at 60 BPM will have 15 bars in a minute, with 4 beats per bar; one each quarter note. A song at 120 BPM will have 30 bars in a minute and 2 beats per second. The number of beats per minute is usually specified at the beginning of a piece using one of two conventions. The first is something like, "M.M.=115". M.M. stands for Mälzel's metronome. (Johann Nepomuk Mälzel) The other common notation is a picture of the note value receiving the beat, an equals sign (=), and the BPM. Most musicians, even professionals, own and regularly use a metronome or drum machine for practicing or recording in order to ensure they play at the desired tempo.