neirocca sound-first music theory

Note Values and Rests

about 13 min

What this lesson is for

Note values do not encode seconds. They encode ratios between one another. This lesson works through the halving principle, the matching rests, what a dot really adds, and the tuplets that make division by three possible — hearing each ratio rather than just reading it.

  • State the length ratios from a whole note down to a sixteenth note
  • Match each note value to the rest of the same length
  • Explain a dot as "add half the original value" and compute dotted durations in beats
  • Explain why note values are relative, and why tempo is what turns them into seconds
In this lesson
  1. The parts of a note, and division by two
  2. Hear the ratio
  3. Rests are measured silence
  4. A dot adds half
  5. Tuplets divide by three
  6. Values are relative; tempo supplies the seconds

The previous lesson dealt with pitch. This one takes the other half: duration.

The first thing to be clear about is that written notes do not specify seconds. A quarter note is not “half a second.” What a note value expresses is a ratio against the other note values; the actual clock time gets decided later, by the tempo.

The parts of a note, and division by two

A note is built from up to three parts: the notehead, the stem, and the flag. Whether the head is hollow or filled, whether there is a stem, and how many flags hang off it — those three facts determine the length.

wholehalfquartereighthsixteenth
Fig. 1: five note values. Hollow head, then filled head, then one flag, then two.

The relationship between them is as simple as it looks: each step to the right is half the length of the one before.

NoteLength if a quarter note is 1As a fraction of a whole note
Whole note41
Half note21/2
Quarter note11/4
Eighth note0.51/8
Sixteenth note0.251/16

The American names state the arithmetic outright — a quarter note is a quarter of a whole note, an eighth note an eighth of one. British terminology takes a different route entirely (semibreve, minim, crotchet, quaver, semiquaver), which hides the fractions but keeps the same halving chain underneath. Either vocabulary describes the identical system.

The consequential property of that system is that it can only divide by two. Splitting a whole note into 2, 4, 8, or 16 parts is directly writable; splitting it into 3 is not expressible by notehead shape alone. Two separate mechanisms exist to get around that limit, and both appear later in this lesson: the dot and the tuplet.

Check

An eighth note is what fraction of a half note?

Hear the ratio

“Half as long” lands faster through the ears than through a table. Listen to the same pitch played as quarter notes, then eighths, then sixteenths. The tempo never changes.

Same tempo, different note values

Check: The pulse is identical in all three. The only thing changing is how many notes fit inside one beat: one for quarter notes, two for eighths, four for sixteenths. Count along with the first one and keep that count going through the other two.

one per beat

Rests are measured silence

Silence gets written in the same system. A rest has a duration, and the durations map one to one onto the note values.

whole resthalf restquarter resteighth restsixteenth rest
Fig. 2: rests. The whole and half rests look almost the same — position on the staff is what tells them apart.

The pair that actually catches people out is the whole rest and the half rest. Both are small filled rectangles, but:

  • the whole rest hangs below the fourth line
  • the half rest sits on top of the third line

You identify them by position, not by shape.

It helps to think of a rest not as “nothing happening” but as an instruction to stay silent for a stated length. In performance, honoring the length of a rest does as much for the rhythm as playing the notes does.

Check

How many quarter rests does it take to fill one measure of 4/4?

A dot adds half

Halving alone can never produce a length like 1.5. That is what the dot is for. Put one dot to the right of the notehead and it adds half of the original value.

NoteBase lengthThe dot addsTotal
Dotted half213
Dotted quarter10.51.5
Dotted eighth0.50.250.75
dotted half = 3dotted quarter = 1.5dotted eighth = 0.75
Fig. 3: dotted notes. The dot goes immediately right of the notehead; when the head is on a line, the dot moves up into the space above.

A second dot is also possible. A double dot adds half of whatever the first dot added, so a double-dotted half note comes to 2 + 1 + 0.5 = 3.5 beats.

There is a quietly elegant property here. However many dots you add, the total never reaches double the original value — the same structure as 2 + 1 + 0.5 + 0.25 + … converging on 4. That is precisely why dots are safe: a dotted note can never accidentally become the next note value up.

What a dot does to a rhythm

Check: The first is even quarter notes. The second divides the same two beats as 1.5 to 0.5 — a dotted quarter followed by an eighth — so a long-short limp appears. The third applies the identical idea one level finer, as dotted eighth plus sixteenth.

1 : 1 : 1 : 1

Tuplets divide by three

The one thing a dot still cannot do is divide by three. To split a beat into three equal parts you need a tuplet — here, a triplet. Three eighth notes are bracketed with a small “3”, which declares that three of them occupy the space normally taken by two.

Each triplet eighth is therefore 2/3 the length of an ordinary eighth. That framing — “three in the space of two” — is the whole idea, and quintuplets and septuplets are built by the same rule with different numbers.

The split between duple and triple division matters far beyond single beats. The meters in the next lesson are classified by exactly the same question: are we dividing by two, or by three?

Check

Play a triplet across one quarter note. Each note is 2/3 the length of which ordinary note value?

Values are relative; tempo supplies the seconds

Back to where we started. Every number in this lesson has been a ratio. Not one of them was a duration in seconds.

Tempo is what supplies those. At ♩= 60 a quarter note lasts one second; at ♩= 120 it lasts half of one. Double the tempo and every note in the score takes half the time, with no change to a single notehead.

That separation is a genuinely good piece of design. The composer writes only the proportions, and the performer keeps real interpretive room in how fast to take them. It is the reason two recordings of the same piece can feel like different works while agreeing on every note.

Put the pulse in your body with a metronome Feel quarter notes at ♩=80 first, then keep the same tempo and count each beat in two out loud — those are your eighth notes Metronome → Or work backwards and measure a tempo Tap along with a track you know and read off the BPM. Once you know a song's tempo, the real-time length of each note value stops being abstract Tap Tempo →

The next lesson groups these beats into meter. Where note values describe the length of a single sound, meter describes the recurring pattern those lengths get grouped into.

Exercises

Every answer here is cross-checked against the theory engine. Work them out before you grade.

  1. 1

    If a quarter note is one beat, how many beats is a dotted quarter note?

  2. 2

    If a quarter note is one beat, how many beats is a dotted half note?

  3. 3

    If a quarter note is one beat, how many beats is a double-dotted half note?

  4. 4

    If a quarter note is one beat, how many beats is a dotted eighth note?

  5. 5

    Where on the staff is a whole rest written?

0 / 5

Before you move on

Check that you can explain each point above in your own words.

Meter and the Beat