Basic Music Notation: Rhythm

Basic Symbols for Notes & Rests

A note’s height signifies its pitch; the type of note signifies its duration. A related symbol called a rest signifies the absence of any note at a given time. The most common notes and rests in modern music notation are:

I’ll be using the American names for notes throughout this document – to be honest, until I began researching it, I didn’t even know the British names differed. Additionally, the above “length” field assumes common time (or some other time signature with a denominator of 4), which I will explain in a moment.

Eighth notes and shorter notes may also be written with beams, e.g., ♫ and ♬. Usually, though not always, the division between beams corresponds to rhythmic divisions within measures.

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Basic Rhythmic Concepts

Measures & Time Signatures: The Basics

It might be a slight oversimplification to say that a measure is to notes what a molecule is to atoms, but it’s not too far off. A single vertical bar 𝄀 marks the end of a measure, and two equally sized double vertical bars 𝄁 mark the end of a section, while a narrow bar before a thick bar 𝄂 indicates the end of an entire piece. A similar symbol with double dots before it 𝄇 indicates that a piece should repeat; a flipped version 𝄆 indicates the start of the section that should repeat.

In brief, a time signature tells you how long each measure is. Its denominator (its lower number, for those of you that don’t remember your fractions) indicates which note type it counts. Thus, the 8 in 𝟔
𝟖 counts eighth notes, while the 4 in 𝟑
𝟒 counts quarter notes. The numerator (upper note) indicates how many of these notes occur per measure. Thus, a measure of 𝟔
𝟖 lasts for six eighth notes, while a measure of 𝟑
𝟒 lasts for three quarter notes. Time signatures are not precisely fractions: there is a difference between these, but we’ll explore it later. For now, note that common time means 𝟒
𝟒.

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Tempo and Beats Per Minute

Tempi (singular: tempo, the Italian word for time) are typically expressed in the manner 𝅘𝅥 = 𝟏𝟐𝟎, meaning that one minute is subdivided into 120 quarter notes of equal duration, and correspondingly that one second is subdivided into two quarter notes of equal length. (Since Italy is the birthplace of opera, Italian musical terms are ubiquitous in classical music throughout the world.) 𝅗𝅥 = 𝟔𝟎 and 𝅘𝅥𝅮 = 𝟐𝟒𝟎 signify the same tempo. Tempi typically use the time signature’s denominator to signify beats per minute (bpm).

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Modifier Dots & Staccato

The above notes can have modifiers. A dot after a note or rest multiplies the duration by one and a half. Thus, a dotted half note 𝅗𝅥𝅭 lasts for three beats in common time, and a dotted quarter note 𝅘𝅥𝅭 for one and a half. Rarely, you’ll see a note or rest with two dots after it, multiplying its duration by one and three quarters. Thus, a doubly dotted half note 𝅗𝅥𝅭𝅭 lasts for three and a half beats.

A dot after a note should not be confused with a dot below or above a note, which signifies to play it staccato, Italian for detached or disconnected. This is one of several articulations, or play styles, that musical scores may specify. Articulations may affect parameters of a note including its attack and decay, its length, its timbre (tone color or tone quality; pronounced tamber), its dynamics (volume), and its pitch.

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Superscripts & Tuplets

Superscripts above notes (or rests) are slightly trickier. A superscript 3 above a note, which is by far the most common such superscript in music, means to multiply a note’s duration by ²⁄₃. These are called triplets, and they’re rarely found on anything longer than eighth notes. Thus, 𝟑𝅘𝅥𝅮 lasts for ¹⁄₃ of a beat in common time, 𝟑𝅘𝅥𝅯 lasts for ¹⁄₆ of a beat, and so on. Quintuplets, written with a superscript 5, are also sometimes seen; they multiply a note’s duration by ²⁄₅. Thus, 𝟓𝅘𝅥𝅮 lasts for ¹⁄₅ of a beat. That said, while higher superscripts are possible, I’ve only ever seen two composers use them, and I’m one of them. (The other is Chris Christodoulou of the Risk of Rain series and Deadbolt; “Arctic Oscillation” uses several tuplets.) Incidentally, superscript multiples of 2 would be entirely pointless: you could just use the next-lowest note value instead.

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Ties & Slurs

A tie between notes with the same pitch 𝅘𝅥(𝅘𝅥𝅮)𝅘𝅥𝅰 represents a single note that lasts the combined length of all tied notes. This example lasts the combined length of a quarter note, an eighth note, and a thirty-second note, or 1⁵⁄₈ beats of common time.

A slur between notes with different pitches 𝅘𝅥𝅘𝅥𝅮)𝅘𝅥𝅰 means to play the passage legato, Italian for connected.

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Time Signatures in Depth

Common Time & Alla breve

The American notes are named after their values in common time, usually written on scores as either 𝟒
𝟒 or 𝄴. It’s called “common time” because it’s Western music’s most widely used time signature by far. (I’m doing my part to change this, but I’m only one person.) Thus, a whole note is so called because it lasts for a whole measure of 𝟒
𝟒; a half note lasts for half a measure of 𝟒
𝟒; a quarter note lasts for a quarter of a measure of 𝟒
𝟒; and so on.

The related symbol 𝄵 represents 𝟐
𝟐, also called alla breve (Italian for on the breve) or cut time.

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³⁄₄ vs. ⁶⁄₈: Simple & Compound Time Signatures

This immediately raises my next point: Time signatures may look like fractions, but there are important differences. You might assume 𝟒
𝟒 can be reduced to 𝟐
𝟐 or even just 𝟏
𝟏. Likewise, you might assume that 𝟔
𝟖 can be reduced to 𝟑
𝟒. “Those mean same thing,” I hear you object.

Well, in theory they should, but they don’t in practice. 𝟔
𝟖 is typically a compound meter, which subdivides its beats into threes: thus, six eighth notes in 𝟔
𝟖 would contain two groupings of three, whereas in 𝟑
𝟒, they’d contain three groupings of two. Put another way, 𝟔
𝟖 typically has two accented beats per measure, whereas 𝟑
𝟒 typically has three (or just one). Thus, over the same duration, you’d count six eighth notes in 𝟑
𝟒 and 𝟔
𝟖 as:

Most music uses either a simple time signature (numerators of 2, 3, or 4) or a compound time signature (if a time signature’s numerator is a multiple of 3, it usually, though not always, qualifies as compound). A piece in 𝟑
𝟒 can easily be rewritten in 𝟑
𝟖 simply by halving the duration of every note in the song. Likewise, a piece in 𝟏𝟐
𝟖 can be rewritten in 𝟒
𝟒 by using triplets. Ultimately, how to notate a piece is very much a matter of discretion.

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Complex Time Signatures

The third most common type of time signature is a complex time signature. These most often have numerators such as 5, 7, 10, 11, 13, and so on. These are commonplace in some non-Western music, and appeared in Greek music such as the Delphic Hymns to Apollo (which were both in 𝟓
𝟖), but they rarely appeared in Western music until the 19th century. Modern classical works, progressive rock, game music, and various subgenres of metal frequently use them. A few well-known examples include:

Famous Works in Complex Time Signatures

• 𝟓
  𝟒 
  • Frédéric Chopin, Piano Sonata No. 1, Movement 3 (written 1828, published 1851)
  • Gustav Holst, “Mars, the Bringer of War” (mostly) and “Neptune, the Mystic” (The Planets, written from 1914 to 1917, premiered 1918-09-29)
  • Dave Brubeck Quartet, “Take Five”, composed by Paul Desmond (recorded 1959-07-01; released on Time Out, 1959-12-14)
  • Lalo Schifrin, “Theme from Mission: Impossible” (1967)
    • Note: The film soundtracks feature lengthy 𝟒
      𝟒 segments, making them abominations unto Nuggan
  • Rush, intro to “YYZ”, composed by Geddy Lee & Neil Peart (recorded 1980; released on Moving Pictures, 1981-02-12). (This may be just as fairly counted as syncopated 𝟏𝟎
    𝟖.)
• 𝟕
  𝟒 
  • Pink Floyd, “Money”, composed by Roger Waters (recorded from 1972-06-06 to 1973-01-09; released on The Dark Side of the Moon, 1973-03-01) – mostly; the solo is partly in 𝟒
    𝟒
• 𝟗
  𝟖 
  • Dave Brubeck Quartet, “Blue Rondo à la Turk” (recorded 1959-07-01; released on Time Out, 1959-12-14) – mostly; one section uses 𝟒
    𝟒
    • Uses an alternating pattern of three bars of (𝟐+𝟐+𝟐+𝟑)
      𝟖 (complex meter) and one bar of (𝟑+𝟑+𝟑)
      𝟖 (compound meter), resulting in a distinctive, an off-kilter rhythm (in full: 𝄆 𝅘𝅥 𝅘𝅥 𝅘𝅥 𝅘𝅥𝅭 | 𝅘𝅥 𝅘𝅥 𝅘𝅥 𝅘𝅥𝅭 | 𝅘𝅥 𝅘𝅥 𝅘𝅥 𝅘𝅥𝅭 | 𝅘𝅥𝅭 𝅘𝅥𝅭 𝅘𝅥𝅭 𝄇). It was inspired by Turkish aksak time signatures; Brubeck heard its distinctive rhythm performed by Turkish musicians on the street and asked them where they got it, and they replied, “This rhythm is to us what the blues is to you,” hence the song title.
• 𝟏𝟏
  𝟖 
  • The Allman Brothers Band, “Whipping Post” opening & reprises thereof, composed by Gregg Allman (studio version recorded 1969-08-07 and released 1969-11-04 on The Allman Brothers Band; definitive live version recorded 1971-03-13 and released 1971-07-06 on At Fillmore East)
    • Gregg Allman thought of it as (𝟑+𝟑+𝟑+𝟐)
      𝟖, which is entirely reasonable

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Decoding Time Signatures

Figuring out time signatures by ear can be tricky, especially because a lot of how to notate time signatures is up to a composer’s discretion. The most important question is “What would you tap your foot to?” Finding the “pulse” of a piece of music is crucial to understanding its time signature.

An important caveat here is that the division of time must be steady – “Theme from Mission: Impossible” has four accents per measure, but they occur at syncopated (irregular) intervals. The division is actually as follows:

It is no coincidence that this spells out –·–– –·–– ––··, the Morse code for “YYZ” (Toronto International Airport’s IATA identification code). This intro has lived rent-free in my head for over 20 years. (Also, since Rush are Canadian, Z is pronounced zed, and while I’m at it, their drummer’s name is pronounced Piert, not Pert.)

Finding the even pulse can be tricky at first, especially in songs with a lot of syncopation, but it gets easier. If you’re having trouble figuring out complex time signatures, I recommend increasing the amount of listening you do to genres known for using them often. Modern classical music, soundtracks, progressive rock, several genres of metal (progressive metal, technical death metal, and black metal in particular), and the aptly named genres of math rock and mathcore tend to love them. It’s also worth increasing your listening to genres known for using a lot of syncopation, such as jazz, funk, and most kinds of dance music.

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Advanced Rhythm

Polyrhythms

A polyrhythm occurs when two simultaneous rhythms suggest different time signatures. Most commonly, you’ll see 3:2 polyrhythms, expressed in forms like 𝟑𝅘𝅥𝅮 against 𝅘𝅥𝅮. This would result in the following rhythm across the duration of a beat of 𝟒
𝟒:

The next most common is 4:3, seen in forms like ³𝅘𝅥𝅮 against 𝅘𝅥𝅯, which would result in the following rhythm:

Because just seeing this printed out may not clarify how these actually sound, I’ve put together a demonstration of several polyrhythms. In order:

In all except the last demonstration, the kick drum and snare represent a particular polyrhythm (e.g., 0:00-0:16 demonstrate a 3:2 polyrhythm), with the hi-hat serving as a metronome of sorts. Math-savvy individuals will note that, until the last demonstration, the hi-hat’s number is always the multiple of snare and the kick drum’s numbers. This is not coincidental. The final demonstration demonstrates a 7:6:5:4:3:2 polyrhythm.

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Irrational Time Signatures

Irrational time signatures have non-power-of-two denominators: thus, 𝟔
𝟔 counts triplet quarter notes (𝟑𝅘𝅥), and 𝟓
𝟓 counts quintuplet half notes (𝟓𝅗𝅥). Don’t worry if this doesn’t make sense; composers tend to avoid them since changing the tempo can accomplish the same thing in a less confusing way, and a lot of DAWs don’t even support them, so you’ll probably never encounter them – especially because time signature modulation generally causes less confusion and renders irrational time signatures unnecessary.

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Time Signature Modulation

If a piece in 𝟑
𝟒 with 90 beats per minute suddenly modulates to 𝟐
𝟒 with 60 beats per minute, you’ve kept the same number of measures per minute but redefined the duration of a note. This is called time signature modulation and is often notated along the lines 𝅘𝅥 = 𝅘𝅥𝅭, in this case indicating that a quarter note has been redefined to last as long as a dotted quarter note had previously lasted. Often times, time signature modulation happens after a polyrhythm became easier to express in a different time signature (maybe the number of parts that used triplets wound up becoming greater than the number of parts that didn’t, or maybe the parts that didn’t use triplets no longer even existed).

I’ve put together a demonstration of this as well. This piece, which I’ve somewhat cheekily entitled “Sympathy for the Time Signature”, contains the following structure:

Observant readers may have noticed that in every row, dividing the tempo by the time signature’s numerator yields 24. This means that despite this piece’s frequently changing tempi, its measures have a constant length of 2.5 seconds. Observant listeners, meanwhile, may have recognized that this piece has a familiar chord progression: I borrowed it outright from the Rolling Stones’ “Sympathy for the Devil”.

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